Modulated (Ga,TM)N Structures: Optics & Magnetism

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JOHANNES KEPLER UNIVERSITÄT LINZ JKU

Technisch-Naturwissenschaftliche Fakultät

Modulated (Ga,TM)N structures: optics & magnetism

DISSERTATION

zur Erlangung des akademischen Grades

Doktor der Technischen Wissenschaften

im Doktoratsstudium der

Technischen Wissenschaften

Eingereicht von: Andreas Grois

Angefertigt am: Institut für Halbleiter- und Festkörperphysik

Beurteilung: Assoz. Prof. Dr. Alberta Bonanni (Betreuung) Prof. Dr. Norbert Esser

Linz, März, 2015

Ich erkläre an Eides statt, dass ich die vorliegende Dissertation selbstständig und ohne fremde Hilfe verfasst, andere als die angegebenen Quellen und Hilfsmittel nicht benutzt bzw. die wörtlich oder sinngemäß entnommenen Stellen als solche kenntlich gemacht habe. Die vorliegende Dissertation ist mit dem elektronisch übermittelten Textdokument identisch.

Dipl. Ing. Andreas Grois

Abstract

Gallium nitride and related compounds are not only the building blocks of many state of the art devices (e.g. blue and white LEDs, high electron mobility transistors), but once combined with magnetic dopants (i.e. transition metals and rare earths), further functionalities (e.g. spintronics - the simultaneous utilisation of the electrons electric charge and magnetic moment) are enabled. The incorporation of the magnetic dopants depends on the growth conditions and the type of dopant. As a function of these parameters various phases with quite different properties can be produced. In this work the optical and magnetic properties of three of these phases which are interesting from a technological and fundamental point of view and can be produced by metalorganic vapour phase epitaxy are studied by advanced structural, chemical, spectroscopic and magnetomet- ric techniques as a function of the transition metal concentration, growth temperature and codopant concentration. These phases are dilute (Ga,Mn)N and (Ga,Fe)N, iron nitride and galfenol nanocrystals embedded in (Ga,Fe)N, and Mn-Mgx complexes in (Ga,Mn)N:Mg. Dilute (Ga,Mn)N is found to be a superexchange ferromagnet with Mn3+ concentration dependent Curie temperature, which is of the order of 1 K for the highest studied Mn concentration of 3%. The lack of carrier mediated ferromagnetism is explained by ≈ confirming the presence of strong coupling between the Mn 3d electrons and valence band holes via giant Zeeman effect measurements. Upon Si donor codoping the charge state of Mn is reduced to 2+, and hints towards superexchange antiferromagnetism between the Mn2+ ions are observed. 0 The magnetic properties of a single planar array of γ -GaxFe4−xN nanocrystals embedded in GaN are analysed and a clear uniaxial shape anisotropy is revealed. The puzzling finding of a six-fold in-plane anisotropy is discussed and various possible explanations are presented. The interplay of Fe and Mg in codoped samples, and its influence on the formation of secondary phases is investigated, and in combination with values from first principles calculations the incorporation of both dopants is found to be a surface dominated process, where both dopants compete for incorporation, so their individual concentration

i is reduced compared to non-codoped samples. For digitally Mg doped samples an enhanced incorporation of dopants is observed, leading to the conclusion that in this case the incorporation of the dopants is bulk dominated. When codoping (Ga,Mn)N with Mg acceptors complexes are formed, where up to three Ga positions next to Mn are occupied by Mg. These complexes allow ﬁne tuning of the Mn charge and spin state from 3d5 to 3d2 by varying the number of Mg neighbours.

The intra-d-shell luminescence of Mn can be greatly enhanced by forming such Mn-Mg3 complexes, making them an interesting candidate for near infrared optical applications. The obtained understanding, and with it the control of magnetic and optical properties of transition metal doped gallium nitride enables the utilisation of the material as a building block of further electronic, magnetic, spintronic and optical devices.

ii Kurzfassung

Galliumnitrid und verwandte Gemische sind nicht nur, nach derzeitigem Stand der Tech- nik, die Grundlage vieler elektronischer Geräte (zum Beispiel blaue und weiße Leucht- dioden, Transistoren hoher Elektronenmobilität), sondern können auch durch Dotierung mit magnetischen Elementen, das heißt Übergangsmetallen oder seltenen Erden, weitere Funktionalitäten, unter anderem in der Spintronik - der gemeinsamen Nutzung der elek- trischen Ladung und des magnetischen Moments von Elektronen, bieten. Die Art, wie diese magnetischen Elemente in Galliumnitrid eingebettet werden, hängt sowohl vom jeweiligen Element, als auch von den Wachstumsbedingungen des Kristalls ab. Als Funktion dieser Parameter können diverse Phasen mit teils sehr unterschiedlichen Eigenschaften hergestellt werden. Diese Arbeit beschäftigt sich mit den optischen und magnetischen Eigenschaften dreier dieser Phasen, welche sowohl aus akademischem Interesse, als auch im Hinblick auf technologische Anwendungen beachtenswert sind, und mit metallorgani- scher Dampfphasenabscheidung hergestellt werden können. Diese Materialien werden mit fortschrittlichen kristallographischen, chemischen, spektroskopischen und magnetometri- schen Verfahren charakterisiert, und die Verbindung zwischen den Materialeigenschaften und den Wachstumsbedingungen wird untersucht. Es handelt sich dabei um die verdünnt magnetischen Halbleiter (Ga,Mn)N und (Ga,Fe)N, um Nanokristalle aus Eisennitriden und Galfenol welche in hoch mit Eisen dotiertem GaN ausﬂocken, und um Komplexe aus Mn- und Mg-Ionen, welche bei der Koditierung von GaN mit diesen Elementen entstehen. Im Fall von in GaN gelöstem Mn weisen die Proben über Superaustausch vermittelten Ferromagnetismus auf, dessen Curietemperatur von der Mn3+-Konzentration abhängt. Für die höchste untersuchte Konzentration von 3% werden Curietemperaturen der ≈ Größenordnung von 1 K gemessen. Das Fehlen von ladungsträgervermittelter magnetischer Wechselwirkung wird erklärt, indem durch Messung der Riesen-Zeemanaufspaltung gezeigt wird, dass eine starke Kopplung zwischen den Elektronen der 3d-Schale von Mn und den Defektelektronen in GaN besteht. Kodotiert man GaN mit Si Donatoren und Mn, wird der formelle Oxidationszustand von Mn auf 2+ reduziert, und man ﬁndet Hinweise darauf, dass zwischen Mn2+ Ionen eine über Superaustausch vermittelte anti- ferromagnetische Wechselwirkung auftritt.

iii Die magnetischen Eigenschaften einer ebenen Anordnung von in GaN eingebetteten 0 γ -GaxFe4−xN Nanokristallen werden in dieser Arbeit analysiert. Die Kristalle zeigen eine eindeutige uniaxiale Formanisotropie. Zusätzlich weisen sie eine sechsfache Aniso- tropie senkrecht dazu auf, deren Ursprung nicht auf Anhieb klar ist. Mehrere mögliche Erklärungen für deren Ursache werden diskutiert. Weiters wird in dieser Arbeit der Einﬂuss der Wechselwirkung zwischen Fe und Mg auf die Entstehung von Prezipitaten in kodotierten Proben untersucht. Der Vergleich mit ab initio-Rechnungen führt zu dem Schluss, dass die Einbettung beider Fremdatome ein Oberﬂächenprozess ist, bei dem beide Elemente um Gitterplätze wetteifern, sodass im Vergleich zu nicht kodotierten Proben die Konzentration der jeweiligen Elemente geringer ausfällt. Im Fall digitaler Mg-Dotierung wird eine höhere Konzentration als im nicht kodotierten Fall beobachtet, was den Schluss eines volumendominierten Prozesses nahe legt. Bei der Kodotierung von GaN mit Mg Akzeptoren und Mn bilden sich Komplexe, bei denen bis zu drei der einem Mn Ion benachbarten Ga Gitterpositionen durch Mg Ionen besetzt werden. Durch Anpassung der Zahl der Mg-Nachbarn lässt sich der formale Oxi- dationszustand und damit das magnetische Moment der Mn Ionen zwischen 3+ und 5+ einstellen. Die Intra-Schalen-Lumineszenz der Mn 3d-Schale ist in Mn-Mg3-Komplexen deutlich stärker als bei isoliertem Mn, was diese Komplexe zu interessanten Kandidaten für optische Anwendungen im nahen Infrarot macht. Das gewonnene Verständnis und die dadurch ermöglichte Kontrolle der magnetischen und optischen Eigenschaften von mit Übergangsmetallen dotiertem Galliumnitrid erlaubt es nun, dieses Material als Grundlage zusätzlicher elektronischer, magnetischer, spintro- nischer und optischer Geräte zu nutzen.

iv The best that most of us can hope to achieve in physics is simply to misunderstand at a deeper level.

WOLFGANG PAULI

Contents

1 Introduction 1 1.1 Gallium nitride ...... 3

2 Methods, theory and modelling 7 2.1 Growth ...... 7 2.2 Magnetic techniques ...... 8 2.2.1 Magnetic resonance ...... 8 2.2.2 Spin Hamiltonian model of transition metals in GaN ...... 23 2.3 Optical characterisation ...... 27 2.3.1 Giant Zeeman splitting of excitons in GaN ...... 27 2.3.2 Modelling of optical reﬂectivity in multilayer structures ...... 30

3 Incorporation of transition metals into GaN 33 3.1 Manganese ...... 33 3.2 Iron ...... 45

4 Donor and acceptor codoping of transition metal doped GaN 55 4.1 Control of the transition metal charge state ...... 55 4.1.1 Eﬀect of codoping on iron incorporation ...... 55 4.1.2 Eﬀect of Si codoping on the incorporation of manganese ...... 62 4.2 Formation of complexes in (Ga,Mn)N:Mg ...... 66

5 Synopsis and outlook 73

Acknowledgements 75

Bibliography 77

Acronyms 93

Curriculum Vitae 95

vii

1 Introduction

Since the advent of electronics the manipulation and detection of electric charge has been the basic building block for data processing, while ferromagnetism has been exploited mainly in order to store data. Initially magnetism and electric charge were treated as if they were completely separated phenomena, connected through Maxwell’s equations. De- spite already in the 1920s a further connection between them, the spin quantum number, and with it the intrinsic magnetic moment of electric charge carriers was discovered, the path for widespread technological applications of the spin phenomenon was not opened until 1988, when Fert [1] and Grünberg [2] revolutionised the field with the discovery of giant magnetoresistance. This phenomenon, caused by the dependence of the scattering probability of a spin-carrying particle on the spin polarisation of the surroundings, allows to readout the relative magnetisation of ferromagnetic multilayers, and consequently the development of highly-sensitive magnetic field sensors [3]. Yet, this development also opened up a brand new field of research, spintronics (a sub-field of magneto-electronics), which focuses on the study and application of this combination of charge- and spin- transport for information storage and transfer. One of the many goals of the material research side of spintronics is the development of materials, that allow to use electric fields to control the magnetic properties, or which allow to control both, magnetic and electric properties independently of each other. For both prospects, dilute magnetic semiconductors (DMS) are exciting candidates, combining the excellent control over the electric charge carrier concentration of semiconductors with ferro-/paramagnetism introduced by magnetic ion doping. While DMS materials were no new discovery of the spintronics age - work on these systems started already as early as the 1970s and continued during the 1980s [4, 5, 6] - the emerging field of spintronics brought them back into focus, and the pioneer theoretical work by Dietl et al. [7], which suggested that room temperature (RT) ferromagnetism in certain III-V semiconductors in the presence of free carriers might be possible, caused a boom in the field. Good agreement between theory and experimental findings has been found in (Ga,Mn)As [8], and successive work revealed a Curie temperature for this material close to 200 K [9, 10, 8]. Nevertheless, the materials that seemed most promising at that point, GaN and ZnO, pose challenges that are not easy

1 1 Introduction to overcome. Previously transition metal (TM) doping has already been studied in order to compensate residual donors to obtain high resistivity material [11], concentrations of magnetic dopants required for RT ferromagnetism ( 1020 cm−3) and as a sufficiently ≈ high charge carrier concentration are challenging to obtain due to the low solubility of TMs in semiconductors. In order to overcome these limitations, non-equilibrium pro- duction techniques have been considered, including epitaxy [12, 13, 14, 15, 16], diffusion [17], and ion implantation [18]. For these samples a plethora of magnetic properties has been reported, ranging from the observation of Curie temperatures at or above RT [17, 19, 15, 20, 13] to antiferromagnetic coupling between the TM ions [21, 22]. In many cases Curie temperatures exceeding the predictions of the Zener model could be traced back to the presence of physical or chemical phase separation [23]. The first meaning the presence of crystallographically different inclusions in the semiconductor matrix, the second denoting a non-uniform distribution of the magnetic ions without the emergence of a crystallographically different phase. On the other hand, for samples which are known not to show any phase separation, if they are ferromagnetic the Curie temperature usually lies below the value predicted by the Zener model [24, 25, 16]. A possible explanation for this is that the holes in wide gap semiconductors can bind to TM impurities [26]. With these contradicting results and the respective models, it has become increasingly clear, that in order to be properly interpreted, magnetic measurements have to be complemented by a thorough structural and (electro-)chemical analysis. In this thesis the contribution of magnetic resonance, photoluminescence (PL), optical absorption, and x-ray absorption spectroscopy (XAS) to the understanding of Fe and Mn- doped GaN in the broader context of various complementary characterisation techniques and the interpretation of the combined results is detailed. The content of this thesis has been published in scientific journals [27, 28, 29, 30, 31, 32] and some parts were patented [33]. While this thesis will summarise the results and present the data contributed by the author in full detail, complementary data has been condensed. In the remainder of this chapter some insight into the material properties of GaN is given. In Chap. 2 the structure of the studied samples, and the growth procedure will be outlined, followed by a theoretical introduction to magnetic resonance techniques, including a brief presentation of the standard modelling approaches used for these techniques. Chapter 2 is completed with a description of the models used to describe the optical measurements. The experimental results are presented in chapters3 and 4. Chap. 3 will focus on samples doped solely with TM ions, Mn or Fe. In Chap. 4, the effect of donor and acceptor codoping on the incorporation of TMs in GaN is explored. While in Sec. 4.1, which focusses on Si codoping of (Ga,Mn)N and (Ga,Fe)N and Mg codoping of

2 1.1 Gallium nitride

(Ga,Fe)N, the codoped atoms are incorporated randomly, the case of (Ga,Mn)N:Mg is fundamentally diﬀerent, and presented in Sec. 4.2.

1.1 Gallium nitride

Gallium nitride (GaN) is a transparent polar covalently bound crystal of wurtzite equilibrium structure. It has a direct band gap of approximately 3.5 eV at RT [34], putting it at the border between semicondutor and insulator. In spite of the wide band gap, well controlled electrial doping of both n- and p-type is possible. While doping with donors like Si, Ge, Se or O can yield electron concentrations up to 1020 cm−3, achieving hole concentrations above 1018 cm−3 still poses a challenge, yet can be realized with Mg or Be doping followed by annealing or electron beam irradiation. The band gap can be taylored by alloying with the elements aluminum (increase of band gap), or indium (decrease of band gap) [35]. This tunability of the electrical properties makes GaN a highly interesting material for optical devices, and indeed the 2014 Nobel Prize in physics was awarded to I. Akasaki [36], H. Amano [37] and S. Nakamura [38] for the development of high-efficiency GaN based blue light emitting diodes and lasers. On the other hand, the relatively high RT electron mobility of up to 1400 cm2V−1s−1 makes it suitable for high mobility transistors [35]. Thin films of GaN can be prepared by standard semiconductor processing techniques. Electronic device quality films are routinely obtained by using metalorganic vapour phase epitaxy (MOVPE), which is the epitaxial form of metalorganic chemical vapour deposition (MOCVD), or molecular beam epitaxy (MBE). The structures are usually grown heteroepitaxial on various substrate materials, most commonly SiC and sapphire [35]. Free standing GaN can be obtained either by growing thick layers heteroepitaxially, for instance by hydride vapour phase epitaxy (HVPE) on sapphire substrates, and separat- ing them from the substrate [39, 40, 35], by high pressure solution growth [41, 35], or by an analogue to the hydrothermal growth, the ammonothermal method [42]. The ideal wurtzite crystal structure can be described by a unit cell with two basis vectors of the same length in the basal plane having an angle of 2π (indicated as ~a and q 3 ~ 8 b), and a vector normal to them, which is longer by a factor of 3 (called ~c). Four atoms are contained in the unit cell, two of each constituting element. The atoms of one of the 2 1~ 1 constituents are located at the origin and at 3~a + 3 b + 2~c. The other constituents atoms 3 2 1~ 7 are located at 8~c and 3~a + 3 b + 8~c. Each atom is therefore surrounded by four atoms of the other element, which form the edges of a tetrahedron. Along the ~c direction each of the tetrahedrons is standing on the tips of three other tetrahedrons, which are rotated by

3 1 Introduction

Figure 1.1: Graphical representation of the wurtzite crystal structure unit cell. The left image displays the positions of the atoms within the cell, the picture on the right also shows atoms on the cells edge that belong to neighbouring cells.

π 3 . A graphical representation is provided in Fig. 1.1. Wurtzite symmetry is described by 4 the P63mc space group (or C6v in Schönﬂies notation). The lack of inversion symmetry makes this crystal structure polar, allowing for pyro- and piezoelectric eﬀects, while its uniaxiality gives rise to birefringance. In GaN the structure is compressed along the ~c direction and has lattice constants of a = b = 3.19 and c = 5.18 [43], the actual values vary depending on growth conditions.

At the Γ point the conduction band of GaN is s-like (Γ7 symmetry), nearly isotropic and can be described by a bare effective mass of 0.2m0 [35]. The valence bands of GaN are nondegenerate at the Γ point, with direction dependent effective masses. Experimental and theoretical values, taken from Ref. [35] are shown in Tab. 1.1. The valence band lying highest in energy has Γ9 symmetry, the two lower lying bands are of Γ7 symmetry. Since both major contributions to valence band splitting, namely the trigonal crystal field and spin orbit coupling, are comparable in energy (10.2 0.1 and 18.1 0.2 meV ± ± respectively), they cannot be treated independently [44]. By selecting appropriate growth conditions and substrates, GaN can also be grown in a zinc-blende crystal structure[49]. This crystals have a lower band gap than the wurtzite phase, yet measurement results are scattered, with the most reliable values between 3.29 eV and 3.35 eV [34] at RT.

4 1.1 Gallium nitride

Table 1.1: Eﬀective hole masses in wurtzite type GaN, taken from Ref. [35] in units of the free electron mass.

Heavy Holes Light Holes Split Oﬀ Holes m∗ ~c m∗ ~c m∗ ~c m∗ ~c m∗ ~c m∗ ~c ⊥ k ⊥ k ⊥ k Calc 1.4 0.3 0.15 Meas [45, 46, 47] 1.6 1.1 0.15 1.1 1.1 0.15 Meas [48] 1.61-2.255 1.1-2.007 0.14-0.261 1.1-2.007 0.252-1.96 0.12-0.16

2 Methods, theory and modelling

2.1 Growth

The samples studied in this work are grown by MOVPE heteroepitaxy on saphhire (0001) substrates in an Aixtron 200 RF reactor [50, 51].

The lattice mismatch between sapphire and GaN is approximately 13%. Due to this, the first growth step after desorbing the contaminants from the sapphire is the low temperature (540 ◦C) growth of a GaN nucleation layer, which is afterwards annealed at 1030 ◦C. At this temperature an about 1 µm thick GaN buffer layer is grown to allow most of the stress caused by the lattice mismatch to relax. The layers to be studied are then grown on top of this buffer layer.

The precursors used for the GaN growth are NH3 (ammonia) and Ga(CH3)3 (trimethyl- gallium - TMGa). Dopant sources are (CH3C5H4)2Mn (bismethylcyclopentadienylman- ganese - Cp2Mn), (C5H5)2Fe (ferrocene - Cp2Fe), (C5H5)2Mg (biscyclopentadienylmag- nesium - Cp2Mg) and SiH4 (silane). Where not stated otherwise, the doped layers are grown at 850 ◦C with an ammonia flow of 1500 standard cubic centimetres per minute (sccm) and a TMGa flow of 5 sccm. The flow rate of the TM precursors is varied between 0 and 490 sccm, depending on the desired dopant concentration. To achieve TM dopant cation concentrations above 1 % , the TMGa flow can be reduced down to 1 sccm, for all samples where this was done it is explicitly noted.

To establish the relation between growth conditions and the structural, electrical, chemical and magnetic properties, the samples have been carefully analysed using an extensive characterisation protocol, including but not limited to in-situ ellipsometry, atomic force microscopy (AFM), x-ray diﬀraction (XRD), secondary ion mass spectroscopy (SIMS), transmission electron microscopy (TEM), superconducting quantum interference device (SQUID) magnetometry, PL, optical absorption measurements, magnetic resonance, and synchrotron based XAS and synchrotron x-ray diﬀraction (SXRD).

7 2 Methods, theory and modelling

Doped layer (850 ◦)

GaN buﬀer layer (1030 ◦)

◦ GaN nucleationX layer (540 ) XXXz

Sapphire waver

X ¨ ¨¨ XX ¨ Q a ¨ XXX¨¨ Q aa QQ

Figure 2.1: Sketch of the sample structure. The few monolayers thick GaN nucleation layer is deposited at low temperature on the sapphire and then annealed. A one micrometer thick GaN buﬀer layer is grown to reduce strain, on which the doped layer to be studied is deposited.

2.2 Magnetic techniques

In the studied material systems the magnetic response is in general relatively weak, since it is either caused by a dilute dopant within a thin layer, or by a secondary phase that just makes up a tiny fraction of the volume. The tool of choice to analyse the magnetic response of the samples is SQUID magnetometry due to its high sensitivity. While the magnetic suszeptibility signal measured by SQUID can be disentangled into its various contributions by ﬁtting it with appropriate models, magnetic resonance directly allows to distinguish them and to analyse them individually, since the precession frequency of the magnetisation or single magnetic moments is sensitive to the local environment of the magnetic atoms. Subsect. 2.2.1 introduces the physical principles behind this technique. In Subsec. 2.2.2 the spin Hamiltonian model suitable for the description of TM-doped GaN, underlying the data analysis of both, SQUID magnetometry and paramagnetic resonance, is detailed.

2.2.1 Magnetic resonance

Magnetic resonance spectroscopy techniques study the absorption of a driving ﬁeld by the precession of magnetic moments around their equilibrium direction as a function of

8 2.2 Magnetic techniques

6H~ driving H~ -ext

Figure 2.2: Geometry of a magnetic resonance experiment. An oscillating driving field is applied orthogonal to the external field. frequency or as a function of applied magnetic field. The physics that governs it depends on the magnetic ordering of the probed magnetic moments. For measurements of electron magnetic moments, one distinguishes ferromagnetic resonance (FMR), antiferromagnetic resonance (AFMR), and electron paramagnetic resonance (EPR), which is also known as electron spin resonance (ESR). Nuclear magnetic moments are studied by nuclear magnetic resonance (NMR), which is goverend by the same dynamics as EPR. The measurement geometry is the same for all types of magnetic resonance measurements. A static magnetic field is applied to define an equilibrium direction of magnetisation (which is, as discussed individually for EPR and FMR, given by the sum of this external field and internal fields of the sample). Perpendicular to the external field an oscillating magnetic field is applied, which drives the precession of the magnetisation. At laboratry magnetic fields (of the order of 1 T) the resonance frequencies of nuclear magnetic moments lie in the radio frequency range, the driving fields are therefore simply applied via magnetic coils. For electron magnetic moments the resonance frequency is larger, and lies in the microwave regime. In the latter case, the sample is usually placed within a microwave resonant cavity, which defines the applied microwave frequency by its geometry. In this case the resonance frequency of the sample is changed by varying the strength of the applied static field. Although, according to the Bohr-van Leeuwen theorem [52] magnetisation of (non- rotating) matter cannot be described classically, a classical picture will now be employed to illustrate the correspondence of angular momentum and magnetic moment, which is the basis of the equations of motion used later. This is just an illustration and only gives correct results for orbital angular momenta, yet fails as soon as spin momenta play a role. Classically a magnetic moment can be described by a charge moving on an infinitesimal circular path. By reformulating one can show, that then the magnetic moment is proportional to the angular momentum.

q ω L L~ q ~µ = IA~ = ~n A = ~nq A = ~nq A = q r2π = L~ =: γL~ (2.1) T 2π 2πJ 2πmr2 2m

9 2 Methods, theory and modelling

In Eq. 2.1 the gyromagnetic ratio γ is deﬁned. For a purely orbital angular momentum, it is given as in Eq. 2.1. For all other types of angular momenta, an additional prefactor, the Landé-factor, or g-factor, has to be included, giving:

gq γ := (2.2) 2m

The exact value of g depends on the type of angular momentum. As already said, for a purely orbital moment it is gL = 1. For electron spin it is gS = 2.002319. In the case of coupled spin and orbital momenta, the g factor lies between these values and (in ﬁrst order perturbation theory, therefore valid for weak ﬁelds) is given by the Landé formula:

1 gL (J (J + 1) + L (L + 1) S (S + 1)) + gS (J (J + 1) + S (S + 1) L (L + 1)) gJ = − − 2 J (J + 1) (2.3) In the case of coupled spin- and orbital angular momenta, the total angular momentum and the total magnetic moment are generally not parallel due to the different g-factors. Nevertheless, as a consequence of the Wigner-Eckhart theorem [53], their expectation values are parallel. In NMR, both, protons and neutrons contribute to the magnetic moment. By convention, the proton mass and charge are used for the neutron as well, the difference between these particles is expressed solely by their different g-factor. For the proton spin it is given by gIP = 5.585695, and for the neutron spin by gIN = 3.826085. − Due to the negative charge of electrons, their magnetic moment has the opposite sign of the angular momentum.

In a quantum mechanical formulation using the common eigenstates of the square and the z-component of the angular momentum operator as basis, these two operators have eigenvalues which are given in units of h¯, and also the prefactors obtained when applying

Jx and Jy have h¯ as natural unit:

J~2 j, m =h ¯2j (j + 1) j, m (2.4) | i | i Jz j, m =hm ¯ j, m (2.5) | i | i 1 p p Jx j, m =h ¯ (j m)(j + m + 1) j, m + 1 + (j + m)(j m + 1) j, m 1 | i 2 − | i − | − i (2.6) ı p p Jy j, m =h ¯ (j + m)(j m + 1) j, m 1 (j m)(j + m + 1) j, m + 1 | i 2 − | − i − − | i (2.7)

Since the angular momentum quantum numbers are half integer or integer, it is convenient

10 2.2 Magnetic techniques and has become convention to group together the h¯ prefactor of the angular momentum and the gyromagnetic ratio. For the electron, this value is the Bohr magneton, with the symbol µB. Since for nuclear spins the proton mass and charge are used in the gyromagnetic ratio, the value of the nuclear magneton is diﬀerent.

eh¯ −5 µB = = 5.78838110 eV/T (2.8) 2me eh¯ −8 µN = = 3.15245110 eV/T (2.9) 2mp

This is especially useful when calculating the energy contribution from the interaction of the magnetic moment and a magnetic ﬁeld (Zeeman energy), which is given by the scalar product of these two quantities.

J~ EZeeman = gµB,N B~ (2.10) · h¯ As long as no additional magnetic fields or field-like contributions are present, this field defines the quantisation axis of the angular momentum and for a system in an eigenstate of the Jz operator with magnetic quantum number m, the energy is given by gµB,N Bm.

For an eigentstate of Jz, as it can be seen from Eq. 2.10, the change in energy is proportional to the magnetic field and the magnetic quantum number. For a spin 1/2 particle, the energy difference between the two possible z-components of spin, which is (neglecting the effect of the to be absorbed field itself) also the resonance frequency of absorption, is given by:

∆EZeeman = gµB,N B (2.11)

While this tells the energy diﬀerence between possible states, the dynamics of the absorption process has yet to be discussed. Due to the diﬀerent theories used, they will now be treated separately for ordered magnetic phases and individual atoms.

Ferromagnetic resonance

Of all magnetic resonance techniques, only those that deal with ordered magnetic phases can be described suﬃciently well by a classical equation of motion. The dynamics of these phases is described by the Landau-Lifschitz-Gilbert equation. ! dM~ dM~ = γ M~ H~ eﬀ ηM~ (2.12) dt − × − × dt

11 2 Methods, theory and modelling

Heﬀ MxH MxdM/dt

Figure 2.3: Sketch illustrating the precessional movement of the magnetisation after it has been brought out of equilibrium. While M~ H~ eﬀ leads to a precession ~ dM~ × around it, M dt is a damping term, that brings the magnetisation back to equilibrium.×

The first term on the right hand side of this equation is the torque caused by the effective magnetic field acting on the magnetisation. It is responsible for a precessional movement of the magnetisation around its equilibrium direction. The second term is related to damping, which directs the magnetisation towards equilibrium. Both these torques are acting orthogonal to the orientation of the magnetisation, keeping its magnitude constant. The effective field written in the first term is the sum of all magnetic fields and magnetic field-like contributions acting on the magnetisation. This explicitly includes the exchange coupling between neighbouring atoms, the demagnetizing field and in a resonance measurement also the driving field. The constants γ and η are the electrons gyromagnetic ratio and a phenomenologic damping constant. The Landau-Lifshitz-Gilbert equation is a more convenient equivalent formulation of the original Landau-Lifschitz equation, in which the damping term is written as M~ M~ H~ . × × Although the Landau-Lifschitz-Gilbert equation can be used to directly calculate the FMR frequency by linearising it around the equilibrium magnetisation, usually a different, but equivalent approach is used, which exploits the curvature of the free energy density at the equilibrium magnetisation. The free energy density can be written as a sum of terms stemming from the different contibutions to H~ eff . The contributions are generally:

Zeeman energy: Interaction between the magnetisation and the external ﬁeld.

12 2.2 Magnetic techniques

Shape anisotropy energy: Interaction between the magnetisation and its own demagnetising ﬁeld.

Crystal anisotropy energy: Contribution of interactions within the sample. Usually this is a phenomenologic description of the exchange interactions in a crystal.

Strain anisotropy energy: Similar to crystal anisotropy, but takes into account (possibly symmetry breaking) displacement of atoms by strain.

Surface anisotropy energy: Energy caused by the diﬀerent environment of atoms at a surface or interface.

Step anisotropy energy: Energy contribution of steps on epitaxial surfaces.

The equation that relates the free energy density and the resonance frequency is obtained by linearising the Landau-Lifschitz-Gilbert equation around the equilibrium and using an oscillatory ansatz for the motion of the individual components of the magnetisation. The effective field is given by the gradient of the free energy with respect to the magnetisation. A comparison of coefficients gives the final formula, which in its most prominent form was first published by Smit and Beljers [54].

2! ω 2 1 + Mγη ∂2F ∂2F ∂2F = (2.13) γ M 2 sin (θ)2 ∂θ2 ∂φ2 − ∂φ∂θ

Baselgia et al. suggested alternative formulations of this equation. One of them does not mix terms of diﬀerent symmetry when taking derivatives, and the other is using a rectangular coordinate system to avoid the numeric instabilities at the poles [55]. As said above, the free energy density is usually written as the sum of several terms.

F = FZeeman + FShape + FCrystal + FStrain + FSurface + FSteps (2.14)

The ﬁrst term, the Zeeman energy density FZeeman, is given by the scalar product of the magnetisation and the external ﬁeld:

FZeeman = µ0M~ H~ (2.15) − · The shape anisotropy energy density is the scalar product of the demagnetising field, which is the magnetic field caused by the magnetisation, and the magnetisation itself. In order to obtain the demagnetising field at a certain position, one has to integrate over the field element contributions in the sample volume. For a homogeneously magnetised

13 2 Methods, theory and modelling sample, this integration reduces to the product of a shape dependent tensor and the magnetisation [56]. In this case, the shape anisotropy energy can be written as:

µ0 > FShape = M~ N M~ (2.16) 2 · · Crystal anisotropy is more arcane. This term has microscopic origins, which are usually completely ignored and instead an expansion in the direction cosines1 is used instead. The prefactors of the terms are the anisotropy constants. Crystal symmetry deﬁnes, which terms have nonvanishing anisotropy constants. Experience shows, that terms of orders higher than eight do not signiﬁcantly contribute. For cubic and uniaxial crystal symmetries, the anisotropy can be written the following way:

2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 FCrCubic = K1 a1a2 + a1a3 + a2a3 + K2 a1a2a3 + K3 a1a2 + a1a3 + a2a3 (2.17) 2 2 2 22 FCrHex = K1 a1 + a2 + K2 a1 + a2 + 6 a1 4 2 2 2 2 22 + K3 32 2 2 48a1 + 18a1 a1 + a2 a1 + a2 (2.18) a1 + a2 − − 2 2 2 22 3 3 FCrTetra = K1 a1 + a2 + K2 a1 + a2 + 2K3 a1a2 + a1a2 (2.19) 2 2 2 22 2 2 FCr = K1 a + a + K2 a + a + K3a2a3 a 3a (2.20) Rhombo 1 2 1 2 2 − 1 ai are the direction cosines, Ki the anisotropy constants. Non hydrostatic strain causes a uniaxial anisotropy. It is often suﬃcient to take only a second order term into account.

2 FStrain = KUStrain sin (θStrain) (2.21)

The angle θStrain is the angle between the easy/hard axis caused by strain and the magnetisation. Since surface anisotropy energy is a surface energy, its contribution to the average energy density has to be scaled by the ratio of the surface in question and the sample volume. For a ﬁlm this means that one has to divide the surface anisotropy constant by the ﬁlm thickness. For a plane surface, it is given by:

2 FSurface = KS cos (θSurface) (2.22) Plain −

1Direction cosines are the cosines of the angles between a vector and the coordinate axes.

14 2.2 Magnetic techniques

Where KS is the surface anisotropy constant, already scaled by the surface/volume ratio, and θSurface is the angle between the surface normal and the magnetisation. The step anisotropy is caused by steps on highly ordered epitaxial surfaces and completely irrelevant on any other types of samples. Formally it is equivalent to the surface anisotropy, yet it acts along a direction in the surface, not normal to it.

2 2 FStep = KU sin (θSurface) cos (δ) (2.23) − Step

In this formulation, θSurface and δ are the angles of the magnetisation with respect to the surface normal and the easy axis of the step anisotropy, respectively. Again, since this is a surface term, KUStep has to be scaled by the surface/volume ratio. In a typical ferromangetic resonance measurement, the orientation of the sample with respect to the external field is varied. Based on the measured angle dependence of the resonance frequency or the resonance field and previous knowledge on the sample properties, a suitable free energy ansatz is composed from the Eq. 2.15 to 2.23. To obtain the unknown anisotropy constants, the resonance condition in Eq. 2.13 has to be fitted to the measured angular depencence. The determination of the anisotropy constants consists of two steps: For each orientation of the external field the equilibrium magnetisation direction, which is a function of the to anisotropy constants that have to be fitted, has to be found by minimising the free energy. The Eq. 2.13, evaluated at the equilibrium angles then gives the resonance frequency or resonance field. For resonance magnetic fields of the order of 0.1 T, as often observed if microwaves are used as the driving field, the magnetisation is nearly parallel to the external field2, so that the search for the free energy minimum can be omitted [57].

Electron paramagnetic resonance

If the magnetic moments in the sample are precessing individually, one speaks of EPR. The case of NMR is formally, and in nearly all aspects physically equivalent and will not be treated in detail in this work. As stated above, the gyromagnetic ratio γ (Eq. 2.2) links a magnetic moment to each angular momentum involving charges (also the neutron, due to its internal structure of charged particles) and the interaction of this dipole moment with the external field has a Zeeman energy given by Eq. 2.10. To directly use Eq. 2.10, one needs to know the magnetic field at the position of the magnetic moment. For isolated spins this is given by the external field only, but in liquids, solids and even

2This is the case, if all internal fields and the demagnetising field of the sample under study are much weaker than the external field. This condition can be checked for consistency once the anisotropy constants are known.

15 2 Methods, theory and modelling isolated atoms exist local fields that contribute as well. In many cases, terms of higher order in the various angular momenta (e.g. quadrupole effects) cannot be neglected. Furthermore, the quantisation axis is given by the direction of this total magnetic field. Therefore, a Hamiltonian including the various possible field contributions has to be diagonalised in order to determine the energy levels, or resonance frequencies, of the system. The most straightforward phenomenologic ansatz is the spin Hamlitonian or Heisen- berg Hamiltonian approach [53], where one writes the Hamiltonian as a sum of terms which describe the coupling between the magnetic moment under study, the external field and nearby magnetic moments it couples to as products of the angular momenta, each term with an appropriate tensor prefactor. Since the spatial dependence of the wave functions is regarded only in form of the prefactors, this is a crude, yet surprisingly useful approximation. A further approximation, that greatly simplifies this approach in the presence of strong ligand fields, i.e. ligand fields comparable in strength to spin orbit interaction, intra-atomic angular momentum coupling or the external field, or in the case of covalent bonds, is the usage of an effective spin instead of the true angular momentum. In these cases, groups of states with relatively small energy separation, well separated from the other groups exist. The effective spin is used to address the closely lying states in the group that contains also the ground state, a reasonable procedure considering the small changes in energy caused by an external field. This effective spin is therefore chosen in such a way, that the (nearly) degeneracy of the ground state is given by 2S + 1, e.g. a doublet would have effective spin 1/2. In its strictest form, the effective spin approach is only valid in cases where the various states it describes transform into each other under allowed symmetry transformations of the sample, similarly to the transformation of true angular momentum eigenstates in a free atom under rotation. This implies that the states have to be degenerate at zero external field, yet in reality the Spin Hamiltonian can also be used in non-degenerate cases. To take into account the lifting of the zero field degeneracy due to crystal fields, additional terms are added to the Zeeman Hamiltonian, e.g. a term D S2 1/3S~2 in a uniaxial field. z −

Spins  Spins  X † 1 X † † H = δαµαJ~ gB~ + J~ K J~ + J~ K J~α + higher orders  α external 2 α α,β β β α,β  α=1 β=α (2.24) Here the involved angular momenta, both eﬀective electron and nuclear, are indicated as

J~α and are accompanied by the corresponding magneton µα. If J~α is an electron angular momentum, the prefactor δα is +1, and δα is 1 if J~α is a nuclear momentum. The −

16 2.2 Magnetic techniques g-factor is, in the presence of local fields, in general direction-dependent and therefore written as a tensor. Since an effective angular momentum is used, it is not equal to the g-factor encountered in the gyromagnetic ratio if the states in question are nondegenerate at zero field and therefore better labelled spectroscopic splitting factor. The tensors Kα,β describe the direction dependent coupling between the momenta J~α and J~β, or if α = β the strength of the quadrupole self interaction. The not explicitly written higher order terms will be discussed later, when constraints arising from the symmetry of the crystal field will be imposed.

A commonly encountered formulation of Eq. 2.24, taylored to the use in EPR where only one electron shell is taken into account is given in equation 2.25.

† † H = µBS~ gB~ + S~ DS~

Spins  Spins  X ~† ~ ~† ~ ~† ~ 1 X ~† ~ ~† ~ + S AαIα µN IαgαB + IαPαIα + IαJα,βIβ + I Jα,βIα  − 2 β α=2 β=α+1 + higher orders (2.25)

In this formulation, S~ is the effective electrons angular momentum, while I~ are nuclear angular momeenta that interact with the electron shell and with each other. The matrix D is called fine structure parameter, since its usually the strongest contribution to zero field splitting. The A-Matrix gives the hyperfine structure, which originates from coupling of the effective electron spins magnetic moment with nuclear magnetic moments. These nuclear magnetic moments are subjected to the same types of interaction that act on the electrons, and are described by ga, Pa and Jα,β.

In a crystalline environment, the terms of second and higher order can be utilised to describe the crystal field. This is done by projecting the crystal field potential on functions that have the same symmetry properties as spherical harmonics. A time honoured, yet suboptimal choice due to a lack of normalisation are the Steven’s equivalent operators, which are commonly encountered in literature, especially in experimental works. The relation to the crystal field model is not trivial and, in all details, rather lengthy [53], and only a brief overview will be given here.

The crystal field by definition is the contribution to the potential experienced by an ion in a host, that is not experienced by the free ion. The full Hamiltonian is the sum of H0, the Hamiltonian for the free ion, and V , the crystal field: H = H0 + V . By definition, the crystal potential is source-free within the volume passed by the unpaired

17 2 Methods, theory and modelling electrons of the magnetic ion, and the following expansion is possible:

∞ k X X q k q V = Bkr Yk (θ, φ) (2.26) k=0 q=−k

Not only does this expansion simplify the calculation of matrix elements in the basis

L, ML, S, MS (exploiting the transformation properties of the spherical harmonics), it | i q also allows to use symmetry arguments in order to deduce which of the Bk are possibly non-zero. Most important to mention is, that the k = 0 prefactor, while not excluded by symmetry elements, only yields an overall shift of energy levels. Therefore it can be neglected for magnetic resonance. An extensive list of allowed prefactors for various crystal symmetries is given in Ref. [58]. To calculate the matrix elements, one would need the many-electron wave function of the transition ion. Often one can take either L and S (3d-shell) or J and S (4f-shell) as good quantum numbers, and in these cases it is safe to completely ignore the core levels, and build the many-body wave function as a Slater determinant of states of the non-ﬁlled shell only (since V is a single particle potential). This also allows to rewrite the matrix element of the crystal ﬁeld and the many-particle wave function as a sum over matrix elements of single particle wave functions, with the potential evaluated at the coordinates of the contributing single particles (ϕ is a single particle wave function of the shell under consideration).

X Ψ V Ψ = ϕa V ϕb (2.27) h | | i h | | i These single electron wave function matrix elements can be calculated from Eq. 2.26, and yield:

X q 0 0 X D kE X q q 0 0 l, ml, ms V l, m , m = r B l, ml Y l, m δ ms, m (2.28) h | k l s k h | k l s k,q k q

k k The averaged r has to be weighted by the radial part of the wave function fl: r = ∞ R 2 k 2 fl (r) r r dr. 0 | |

Despite the convenience of using spherical harmonics, in literature, especially in experimental works, usually a diﬀerent expansion of the potential is employed, using non- normalised homogeneous polynomials. A common set of polynomials is listed in Tab. 15 of Ref. [53], where also conversion factors for the prefactors are given. For easier calculation of the matrix elements, equivalent operators are deﬁned, that transform like

18 2.2 Magnetic techniques these polynomials.

X q 0 D kE q 0 L, ML P (~ri) L, M =: ak r L, ML O L~ L, M (2.29) h | k L h | k L i

q These operators have to be carefully constructed from the polynomials Pk , taking into account the non-commutativity of the angular momentum operator. The most commonly encountered set of operators, the Stevens’ equivalent operators, is listed in Tab. 16 of Ref. [53], and the matrix elements are given in Tab. 17 of the same reference. The prefactors ak have to be calculated individually, by comparing the expectation values q q of Pk and Ok using single electron wave functions. In order to switch between single electron and many-electron wave functions, one has to compare their matrix elements, according to X q q l ak l O ~li = L ak L O L~ (2.30) h | | i k h | | i k i where the state L is a Slater determinant of all states l . Again, the results of this | i | i calculation have been tabulated, and are available in Tab. 19 of Ref. [53]. The main issue with this whole crystal field theory is, that the crystal field potential V usually is not known exactly. While for iron group elements, one might argue that a point charge model, where the whole charge of each surrounding atom is simply placed as a point potential, is a more or less acceptable approximation, for heavier elements it does not match experimental observations, and even more realistically smeared out charge distributions do not generally yield acceptable reasults. Therefore, it has become common practice to fit those prefactors of the Stevens’ equivalent operators, that are not required to be zero by crystal symmetry [58] to the observed magnetic resonance data and to publish them without directly linking their numeric values to a crystal field model. While the spin Hamiltonian can be used to describe the energy of an absorption line, the line intensity is determined by absorption dynamics. For an individual absorber the absorption process can be calculated using perturbation theory with the Zeeman energy of the oscillating field as perturbation. This is reasonable, because the oscillating field is generally much weaker than the static external field. Conventional first order time dependent perturbation theory can be used to describe pulsed measurements as long as the pulse durations are short enough so that transition probabilities are much smaller 3 than 1 (t h/¯ Wfi , where Wfi is the matrix element ). As a reminder, the result | |

3The spatial dependence of the perturbation can be safely neglected in the case of magnetic resonance, since the wavelength is by orders of magnitude larger than the spatial extension of the wave

19 2 Methods, theory and modelling of first order perturbation theory is that the probability to find the system starting from state i in state f after a time t is proportional to the Fourier transform of the perturbation evaluated at the Bohr frequency (∆E/h¯) [59]. For the special case of a sinusodial perturbation, as in magnetic resonance, the probability to find the system in the state f is given by a sinc-like function.

2 2 Wfi ıφ sin ((ωfi ω) t/2) −ıφ sin ((ωfi + ω) t/2) Pif (t, ω) = | 2| e − e (2.31) 4¯h (ωfi ω) /2 − (ωfi + ω) /2 −

Here, ωf,i is the Bohr frequency, t is the duration of the perturbation and ω is its frequency. The second term is only relevant when dealing with extremely short pulses, where the pulse duration is comparable to 1/ω. In such a case, where there are only few or no complete osciallations, also the phase φ of the oscillating field becomes important. In Eq. 2.31 it is chosen in such a way, that if time is counted from the onset of the perturbation, the time dependence of the perturbation is written as sin (ωt + φ). For continuous wave EPR the condition of small transition probabilities is not fulfilled by definition and first order perturbation theory cannot be used. However, exploiting the resonant nature of the process, one can use the secular approximation, where only the coefficients of the two levels coupled by the applied oscillating field are considered to be time dependent and only the slowly varying resonant and antiresonant terms, which couple the states are kept in the differential equations (complement C-13 in [59]) with the argument, that the fast varying terms, which do not couple states will average out at integration. This gives the Rabi formula:

 s 2 2 2 Wif Wif 2 t Pif = 2 | 2 | 2 sin  | 2 | + (ω ωfi)  (2.32) Wif + ¯h (ω ωfi) h¯ − 2 | | −

The system oscillates between the coupled states, only temporarily absorbing energy and releasing it soon after. In order to get net absorption, additional processes must be taken into account. Since these relaxation processes are statistical in nature, they are usually treated in a (classical) ensemble framework with phenomenologic time constants. If such an ensemble is in thermal equilibrium, the average ratio between the populations in the states coupled by the microwave is given by Boltzmann statistics. Here for simplicity a two level system will be considered, but the principles can be extended to

function of the absorbing electron. Under this assumption the matrix element is simply given by ~† ~ † ~ hΦf | µB S gBmw |Φii, where Bmw is the amplitude and direction of the microwave ﬁeld.

20 2.2 Magnetic techniques multilevel systems. N↑ E↓ E↑ = exp − (2.33) N↓ kBT As a rule of thumb, in order to observe magnetic resonance, the population diﬀerence 10 ∆N = N↑ N↓ in the sample has to be on the order of 10 spins. From Eq. 2.32 it can − 2 2 be seen, since Wif = Wfi , that the rate of transitions from state i to f is the same | | | | as for transitions from f to i. If no additional processes are allowed, the rate equations for the populations read:

dN↑ = R (N↓ N↑) (2.34) dt − dN↓ = R (N↑ N↓) (2.35) dt −

Here, the transition rate is indicated as R. The quantities used here are time averaged values, with the averaging process carried out over several oscillations of the driving field [60]. As it can be seen by subtracting these two equations, the solution is an exponential decay of the population difference (cf. Eq. 2.33 - the temperature of the spin system will increase towards infinity).

∆N (t) = ∆N0 exp ( 2Rt) (2.36) − The consequence is, that no matter how big the initial population diﬀerence is, it will decrease over time. The same applies for the rate of energy absorption, since it is proportional to the diﬀerence between absorbed and emitted energy.

dE (t) = ¯hω R∆N (t) (2.37) dt ↓↑ To obtain reasonable results, one needs to couple the spin system to a thermal reservoir that is able to absorb heat, i.e. the crystal lattice. This will now be treated on a purely phenomenologic basis. The consequence of such a coupling will be, that the transition rates will not be equal for emission and absorption. The coupling is treated by imposing a certain steady state temperature on the spin system. Rewriting the rate equations using the transition rates Q, one gets:

dN↑ = Q↓↑N↓ Q↑↓N↑ (2.38) dt − dN↓ = Q↑↓N↑ Q↓↑N↓ (2.39) dt − The requirement of a ﬁnite steady state temperature ﬁxes the ratio between the two

21 2 Methods, theory and modelling transition rates, since Boltzmann statistics has to be obeyed. Q↑↓ E↑ E↓ = exp − (2.40) Q↓↑ kBT

Again introducing the population diﬀerence ∆N and the constant total population N, the rate equations give:

d∆N = N (Q↓↑ Q↑↓) ∆N (Q↓↑ + Q↑↓) (2.41) dt − −

One can now deﬁne the spin lattice relaxation time T1 and put in the thermal equilibrium population ∆N0 to arrive at the commonly encountered form of Eq. 2.41.

1 T1 := (2.42) Q↓↑ + Q↑↓ Q↓↑ Q↑↓ ∆N0 := ∆N (t = 0) = N − (2.43) Q↓↑ + Q↑↓ d∆N ∆N0 ∆N = − (2.44) dt T1

If now both, the coupling to the reservoir and the oscillating driving ﬁeld are put in one equation, one gets the following rate equation and steady state population diﬀerence:

d∆N ∆N0 ∆N = 2R∆N + − (2.45) dt − T1 ∆N0 ∆Nsteady = (2.46) 1 + 2RT1

As long as 2RT1 is much smaller than one, the population stays close to the thermal equilibrium ∆N0. The rate of energy absorption is still given by Eq. 2.37, so in the steady state the absorption rate reads: dE ∆N0 =hωR ¯ (2.47) dt steady 1 + 2RT1

For weak excitations, where RT1 1, the absorption rate increases linearly with R. Nevertheless, as soon as RT1 1, the absorption levels off (saturation), a condition that ≈ is very important in experiments. Since the transition rate R is proportional to the square of the matrix element, which in turn is proportional to the amplitude of the oscillating field, R is directly proportional to the applied power of the driving field. The absorption signal will therefore also scale linearly with the driving field power until saturation sets in, when it will no longer be

22 2.2 Magnetic techniques possible to increase the absorption signal by increasing the driving ﬁeld power. A way to work around this is to increase the temperature, increasing in this way the number of phonons present and therefore also augmenting the spin-lattice coupling T1. In addition to the thermal coupling to the lattice, a second relaxation time T2 can be observed, which is realted to the dephasing of the spin precession, generally caused by the diﬀerent local surroundings.

2.2.2 Spin Hamiltonian model of transition metals in GaN

In order to describe the magnetic susceptibility of a material and its dependence on temperature, the previously discussed spin Hamiltonian approach has to be combined with Boltzmann statistics. For this work, the 3d4 and 3d5 electron configurations are of interest, both in a trigonal crystal field of intermediate strength4. While the 3d3 configuration has been investigated as a possible candidate for (Ga,Mn)N:Mg, experimental evidence leads to a different explanation, so it is not treated here. For the 3d5 configuration with vanishing orbital angular momentum, naively a degenerate set of levels would be expected, that only experiences Zeeman and hyperfine splitting. Nevertheless, in reality a more complex structure is observed, which can be described by the following Hamiltonian [53]:

H3d5 = HZeeman + HCubic + HTrigonal + HHyperﬁne (2.48)

The summands are the Zeeman energy, the contribution of a cubic crystal field (or, more precisely, a tetrahedral field, which is formally equivalent to the cubic case), a trigonal distortion of this cubic field, and the hyperfine interaction. In the case of 3d5, all these summands are functions of the spin operator and read:

† HCubic = µBS~ gB~ (2.49)

2 0 3 HCubic = B4 O + 20√2O (2.50) −3 4 4 0 0 0 0 HTrigonal = B2 O2 + B4 O4 (2.51) † HHyperﬁne = S~ AI~ (2.52)

4Intermediate strength in this case means that the Coulomb interaction is the dominant energy contribution, leading to the choice of L,S eigenstates as the basis system. The crystal ﬁeld consists of a cubic/tetrahedral contribution, which is slightly modiﬁed by a tetragonal or trigonal distortion, so that the cubic/tetrahedral part can be diagonalized, and the distortion can be treated by perturbation theory.

23 2 Methods, theory and modelling

~ m 5 In these formulas S is the spin operator, Ol are Stevens equivalent operators . The nuclear spin of the TM is labelled I~. While for electron configurations with non-vanishing orbital angular momentum a link between a model crystal field potential and the spin Hamiltonian can in principle be given (Chap. 2.2.1 for an overview, and Chap. 16 of Ref. [53] for details), in this case the orbital angular momentum vanishes and the spin-orbit interaction cannot be treated as dominant over the crystal field (as it would be in the 4f m case). This has the consequence, that one cannot directly derive the prefactors Bl from the crystal field potential and vice versa, but one would have to solve the full Hamiltonian, including the realspace dependence. This is an additional argument, adding to the fact that the typical point charge crystal field model is a very crude approximation, why in this case in the literature mainly the splitting parameters due to the crystal field, but no details about the field itself are found. A comparison between the angular dependence of EPR transitions in (Ga,Fe)N as calculated6 with Eq. 2.48 and Eq. 2.49 with parameters from literature [61] and actual measurement data is given in Fig. 2.4. In the case of Mn3+ the crystal field contributions to the Hamiltonian are formally the same, yet in this case they are functions of the orbital angular momentum, since wave functions with different magnetic quantum number of the orbital angular momentum have a different spatial distribution, which is very likely dominant over all spin-dependent interactions. Since the 3d4 configuration is not symmetric and has nonzero orbital angular momentum, in this case also the Jahn-Teller distortion [62] needs to be considered, along with the spin-orbit coupling [4, 63]. The full Hamiltonian used to calculate the magnetization of independent Mn3+ ions is

H3d4 = HZeeman + HCubic + HTrigonal + HHyperﬁne + HJ−T + HLS (2.53)

While the crystal ﬁeld predominantly acts on the orbital angular momentum, the Zeeman interaction applies to both angular momenta (with their respective g-factor). The two additional terms can be written as

HLS = λL~ S~ (2.54) · ˜0 0 ˜0 2 HJ−T = B2 Θ4 + B4 Θ4 (2.55)

5Polynomials in the angular momentum operator components and tabulated in Ref. [53], Tab. 16. Which Stevens operators have nonvanishing prefactors depends on the crystal symmetry, a list can be found in Ref. [58]. 6The EPR spectra were calculated using the EPRNMR program developed by F. Clark, R.S. Dickson, D.B. Fulton, J. Isoya, A. Lent. D.G. McGavin, M.J. Mombourquette, R.H.D. Nuttall, P.S. Rao, H. Rinneberg, W.C. Tennant, J.A. Weil, University of Saskatchewan, Saskatoon, Canada, 1996.

24 2.2 Magnetic techniques

7000 7000

6000 6000

5000 5000

4000 4000

3000 3000 Magnetic ﬁeld [G] Magnetic ﬁeld [G]

2000 2000

1000 1000

0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Angle [rad] Angle [rad]

Figure 2.4: Comparison between a spin Hamiltonian calculation using literature parameters [61] (left panel) and experimental data (right panel) for the angle dependence of EPR transitions in dilute (Ga,Fe)N. The electron conﬁguration of Fe is 3d5 in this material.

m The operators Θl are also Stevens operators, yet they are rotated with respect to the coordinate system defined by the crystal main symmetry axis by Euler angles α = π/4, p β = arcsin 2/3 , γ = 0. The Hilbert space where these Hamiltonians are defined is spanned by the possible orientation of spin and orbital angular momenta in the ground state. For 3d5 the orbital angular momentum in the ground state is zero, while the spin is S = 5/2, giving a set of 6 basis functions (MS = 5/2 to MS = 5/2 - MS denoting the magnetic quantum − 6 number in this case). Without external magnetic field the S 5 ground state splits in three 2 Kramers doublets (Chap. 7 and 15 in Ref. [53]), an external field lifts this degeneracy (since the Zeeman interaction is not invariant under time reversal). The spin and orbital 4 momentum of the 3d configuration is 2, yielding a basis set of 25 states (ML = 2 to − ML = 2, and for each ML value MS = 2 to MS = 2). The action of the cubic crystal 5 − 5 5 field Hamiltonian on the D ground state first splits it into E and T2, the latter of lower energy, wich is further split into a singlet 5B (ground state) and a doublet 5E by the Jahn-Teller distortion. The trigonal field then splits the 5E terms, while the spin-orbit interaction removes the spin degeneracy. It has to be emphasized, that, while these splittings are given in a perturbation-like description in this paragraph, for the calculations the full Hamiltonian has been diagonalized on the basis set ML,MS . The | i

25 2 Methods, theory and modelling order in which the different contributions have been given is based on the values for the appropriate prefactors as reported in [64]. As it turns out, these numbers describe our findings as well, with a slight deviation ( 10% on B0 and λ). ≈ 2 The ions can be subjected to three possible orthogonal directions of the Jahn-Teller distortion, leading to three allowed configurations with different directions (A, B, C) for the magnetic anisotropy, which is caused by both, Jahn-Teller distortion and trigonal crystal field. The average magnetic moment per Mn3+ ion is then given by:

−1 A B C ~m = Z ZA ~m + ZB ~m + ZC ~m (2.56) h i h i h i h i

In this formula, the Zi are the partition functions for the respective centers (i stands for A, B, or C), and Z is their sum. The average magnetization of each center is determined by Boltzman statistics:

N Ei P j φj L~ + 2S~ φj exp kbT i j=1 h | | i ~m = µB (2.57) h i N Ei P exp j kbT j=1

For Mn concentrations above 0.9 % the noninteracting ion model is no longer sufficient, because a significant fraction of the dopant atoms will be in the close proximity of another dopant atom, making short range magnetic interactions possible. The second most probable configuration for randomly incorporated dopant ions are nearest neighbour pairs. In order to describe them, the basis set ML ,MS ,ML ,MS can be employed. | 1 1 2 2 i The individual atoms are still experiencing the interactions previously described, but in addition a coupling term has to be added:

H12 = JnnS~1S~2 (2.58) −

The value Jnn is the nearest neighbour coupling constant, which is positive for ferromagnetic, and negative for antiferromagnetic nearest neighbour interaction. The average magnetic moment per pair can then be calculated the same way as in the single ion case, and the total magnetisation of a sample containing both, pairs and individual ions, is then given by:

M~ = µBxN0 ( ~mindividual Pindividual + ~mpair (1 Pindividual)) (2.59) h i h i −

In this equation Pindividual denotes the probability that a TM ion does not have any TM

26 2.3 Optical characterisation ions at nearest neighbour positions.

2.3 Optical characterisation

2.3.1 Giant Zeeman splitting of excitons in GaN

The near band gap optical properties of GaN are dominated by excitonic, or more precisely exciton-polariton mechanisms. A detailed review on excitons in GaN can be found in Ref. [65]. The valence band splitting of GaN already leads to three excitons, which are further split by the crystal field and exchange interaction. Nevertheless, due to the optical selection rules, only states with Γ1 symmetry give a significant signal. This leaves three free exciton lines observable for the ~k ~c direction, and five lines for ~k ~c. In this work k ⊥ the optical measurements have been performed along the c-direction of GaN, and the three free exciton lines are, as usual in literature, labelled FXA to FXC with increasing wavelength. In addition to the free excitons, excitons bound to impurities can in general be observed. The most prominent contribution comes from donor bound excitons (DBE) (in general consisting of several transitions involving different donor elements). The residual donor concentration in MOVPE grown GaN is usually on the order of 1016 cm−3. While this concentration is far below the density of free exciton states ( 1919 cm−3 [66]), the ≈ DBE still dominate the luminescence of GaN, due to the conservation of crystal momentum, which is close to zero for all bound excitons, yet can have any value in the Brillouin zone for free excitons. On the other hand, in absorption measurements the free excitons dominate over the DBE due to the easily fulfillable crystal momentum conservation. By measuring both, emission and absorption, the exciton lines can be identified. While this is just a rule of thumb number depending on the type of donor atom, the DBEs usually have an energy that is about 6 meV below the free excitons. At even lower energies excitons bound to acceptors can be found. A PL spectrum of nominally undoped GaN is displayed in Fig. 2.5 For all these excitons phonon replicas can be observed. The optical phonons have energies of 70 meV (TO) and 91 meV (LO), as established by Raman spectroscopy. The coupling to phonons is different for free and bound excitons, giving a further option to distinguish them. Alternatively the temperature behaviour can be utilised, since an activation energy for thermally freeing bound excitons can be observed7 [67].

7Also free excitons show an activation energy apart from their dissociation energy, which is probably coming from polariton eﬀects [65].

27 2 Methods, theory and modelling

100000 DBE

10000

FXA

1000 ABE

100 FXB PL Signal [arb. units]

FXC

1 3.45 3.46 3.47 3.48 3.49 3.5 3.51 3.52 3.53 3.54 Energy [eV]

Figure 2.5: PL spectrum of nominally undoped GaN recorded along the c-direction. The peaks originating from DBE, FXA and FXB are indicated. The approximate energy of FXC, which is below the noise level of this measurement, is labelled as well.

Due to the interaction between band carriers and localised d electrons of transistion metal dopants, the excitons show a surprisingly strong magnetic ﬁeld dependence in TM- doped GaN, the giant Zeeman Splitting. The sign of the apparrent exchange constants describing this giant Zeeman splitting can serve as a measure for the presence of strong coupling [26]. Following Ref. [68, 69, 70, 71, 72, 73], the Hamiltonian describing the giant Zeeman splitting has the following form:

H = E0 + Hvb + He-h + Hdiam + HZ + Hs,p−d (2.60)

Here E0 is the energy of the band gap, Hvb gives the crystal field and spin-orbit splitting of the valence band near the Γ-point, He-h is the electron-hole exchange interaction, Hdiam the diamagnetic shift, HZ the conventional Zeeman splitting, and Hs,p−d an effective Heisenberg-like exchange interaction between band carriers and localised d electrons (as used in the virtual crystal and molecular field approximation, which are known not to apply in the case of strong coupling [26] - therefore the exchange constants used here are only apparent values). The basis system can be restricted to the optically active states, in Faraday configuration these are s , p+ , s , p+ and s , pz , which are visible + − | ↓ ↑i | ↑ ↓i | ↑ ↑i in σ polarisation, while in σ polarisation the basis set used is s , p− , s , p− | ↑ ↓i | ↓ ↑i

28 2.3 Optical characterisation

and s , pz . In this notation, the arrow is the spin value, so s means a conduction | ↓ ↓i ↓ band electron of spin S = 1/2. For valence band states, the index +, , z denotes the − − orbital angular momentum of 1, 1, 0 respectively. The contributions to the Hamiltonian − in this basis are:   ∆2 0 0 − Hvb =  0 ∆2 √2∆3  (2.61)  −  0 √2∆3 ∆˜ 1 −  1 2 0  γ − He-h =  2 1 0  (2.62) 2  −  0 0 1   B2 0 0  2  Hdiam = d  0 B 0  (2.63) 0 0 B2  1  ge 3˜κ 0 0 − 2 − σ± =  0 1 2 3˜ 0  (2.64) HZ µBB  2 ge κ  ± − − 1 0 0 2 ge + 1   βapp αapp 0 0 σ± − app app H = N0x Sz  0 α β 0  (2.65) s,p−d ± h− i  −  0 0 αapp + βapp

The values appearing in these formulas are: ∆˜ 1: crystal ﬁeld splitting of the valence band;

∆2: parallel spin orbit interaction; ∆3: perpendicular spin orbit interaction; γ: measure of the electron-hole exchange interaction strength, according to Ref. [71] γ = 0.6 meV; d 2 is a measure for the diamagnetic shift, given by 1.8µeV/T ; ge is the electron g-factor, set to 1.95; κ˜ is the Luttinger parameter [74] describing the band splitting, set to 0.36. σ± The values for d, ge and κ are taken from Ref. [72]. In the Hs,p−d eﬀective exchange Hamiltonian the parameter N0 is the number of total cation lattice sites, x the fraction of lattice sites occupied by TM ions, Sz the expectation value of the TM ion spin (the h− i spin Hamiltonian parameters used to calculate it are gk = 1.91 and D = 0.27 meV [68]). The values αapp and βapp are the apparent exchange energies between d-level electrons and conduction band electrons or valence band holes, respectively.

29 2 Methods, theory and modelling

2.3.2 Modelling of optical reﬂectivity in multilayer structures

In order to extract the exciton energies from the measured spectra, nonlinear fitting can be applied. In the case of PL, simply fitting a Lorentzian peak function to each transition describes the spectra reasonably well [75]. In the case of reflectivity and transmission spectra, the situation is not as simple, because of the possibility to reach excited states of the excitons and the fact, that the samples are composed of a multilayer structure. The discrete states of the free excitons have been modelled following the formulas from [76] as a sum of Lorentzians8, where the binding energy of the excited state n goes with 1/n2, and the intensity of the excited states is reduced by 1/n3. For the continuum states the description of Tanguy [78] has been employed.

∞ 2 ! X X 4πα0j ωn,j (ω) = 0 + 3 2 2 + j,ub (ω) (2.66) n ω ω ıωΓn,j j=A,B,C n=1 n,j − −

Here, 0 is the background dielectric function, which, in the excitonic region of GaN can be set to 5.2 [79], α0j is the polarisability of exciton j, and ωn,j is the frequency of the n-th state of exciton j: −1 ∗ ∗ 2 ωn,j =h ¯ Ej + R R /n (2.67) j − j

In this formula, Ej is the ground state energy of exciton j, while Rj is the binding energy.

The variable Γn,j gives the damping. Following Ref. [79] a phenomenological relation between the damping of the ground state and the excited states is assumed.

Γ∞ Γj Γn,j = Γ∞ − (2.68) − n2 The following formulas are taken from Ref. [78], and they describe the optical contribution of the continuum (unbound) states of the excitons:

3 4πα0 (¯hωj) (ω) = j j,ub ∗ 2 8Rj (¯hω + ıh¯Γub) ∗ (gub (ξj (ıh¯Γub + ¯hω)) + gub (ξj (ıh¯Γub hω¯ )) 2gub (ξj (0))) (2.69) ∗ − − gub(z) = 2Ψ(z) + 2 log(z) + 1/z (2.70) s ∗ Rj ξj (z) = (2.71) Eg z −

8This is just a phenomenologic approximation, since it does not take into account polariton eﬀects. A description of the procedures to model exciton polaritons can be found in Ref. [69, 77]

30 2.3 Optical characterisation

The damping of the unbound continuum states has, for this work, been ﬁxed at Γub =

Γ∞/2. The complex function Ψ denotes the digamma function.

d Ψ(z) = log (Γ (z)) (2.72) dz

Through Eq. 2.66 the absorption of a single layer of GaN in the near edge region can be described. Since in the samples considered in this work an undoped GaN buﬀer below the doped layer of interest is present, which in turn is placed on top of a sapphire substrate, the whole multilayer stack has to be taken into account when treating the optical data.

The method of choice to describe time independent steady state solutions for multilayer structures is the transfer matrix method, in this case in the standard fully polarised linear materials 2x2 form9. This formalism makes use of the standard Fresnel formulas [82] for reflection and transmission of electromagnetic waves at interfaces, and takes into account the phase shift light experiences while travelling through layers of various thickness. For an arbitrary direction of incoming light, the basis used to describe the polarisation is given by the senkrecht (s) and parallel (p) components, the first having its E~ vector perpendicular to the plane defined by the lights ~k vector and the surface normal, the second with E~ in this plane. In linear materials these two components can be treated independently, and for non-normal incidence the resulting formulas are slightly different for them. The natural choice for the field component to be considered is the component of the electric field that is parallel to the interfaces between the layers since its sum for all incoming and outgoing waves has to be zero. At a single interface, the relation between incoming and reflected wave electric field amplitude parallel component is given by:

Ek,f,i neff,i (ω, θ) neff,i+1 (ω, θ) ri,i+1 (ω, θ) = = − (2.73) Ek,b,i neff,i (ω, θ) + neff,i+1 (ω, θ)

For the ratio between the E~ -ﬁeld components of the transmitted and incoming wave, the following relation applies:

Ek,f,i+1 2neff,i (ω, θ) ti,i+1 (ω, θ) = = (2.74) Ek,f,i neff,i (ω, θ) + neff,i+1 (ω, θ)

9For arbitrary polarisation states the more advanced 4x4 Müller matrix formalism would be required [80]. Within 2x2 matrices depolarisation due to rough interfaces can nevertheless be treated, if one only considers intensities, not ﬁeld amplitudes [81]

31 2 Methods, theory and modelling

The eﬀective refractive index neﬀ in these formulas is, for s-polarisation, given by:

s neﬀ,i (ω, θ) = ni (ω) cos (θ) (2.75)

For p-polarisation, it reads: ni (ω) np (ω, θ) = (2.76) eff,i cos (θ) At each point in the multilayer the current state of the electromagnetic wave can therefore be given by a vector containing the parallel E~ -field component of the forward running (in the picture used here: from left to right) and of the backwards running (reflected, from right to left) wave. For each layer, the light gains a phase factor depending on light frequency and the layers refractive index and thickness: ! ! ! ! E exp (ıkn cos (θ) d) 0 E E k,f,i = k,f,i,right =: P k,f,i,right E 0 exp ( ıkn cos (θ) d) E E k,b,i − k,b,i,right k,b,i,right (2.77) This equation relates the field amplitudes at the left end of a layer to the field amplitudes at the right end. The value k that appears here is the magnitude of the wave vector, given by k = 2π = cω (λ is the vacuum wavelength). Using Eq. 2.73 and 2.74 combined λ0 0 with the requirement that the sum of all parallel field components has to vanish, the relation between field amplitudes on the sides of an interface can be given: ! ! ! ! E 1 1 ri,i+1 E E k,f,i,right = k,f,i+1 =: D k,f,i+1 (2.78) Ek,b,i,right ti,i+1 ri,i+1 1 Ek,b,i+1 Ek,b,i+1

For multiple layers, a series of these matrices D and P can be multiplied, in order to yield the ratio between field amplitudes on the left of the first interface, and on the right of the last interface. One of the equation components simplifies, if one imposes the requirement, that on one side light is only coming out of the layer stack, but no light is sent into it. With this, the ratio of the incoming and reflected light on the other side can be directly calculated.

32 3 Incorporation of transition metals into GaN

3.1 Manganese

As stated in the introductory chapter, many contradicting reports on the magnetic properties of GaN doped with TMs can be found in literature, and Mn doping is no exception. While many works show Curie temperatures below those predicted by the mean-ﬁeld Zener model [16, 24, 25], what can be explained by hole localisation at the Mn ions

[83, 26], others claim antiferromagnetism [21, 22] or high TC ferromagnetism [17, 19, 15]. In order to shed light on the issue, a series of (Ga,Mn)N samples with Mn cation concentrations up to xMn = 3% has been grown by MOVPE and studied by advanced chemical, structural, magnetic and electrical analysis techniques.

The growth procedure used is outlined in Sec. 2.1. For samples with xMn > 1% the Ga precursor flow is reduced to 1 sccm. Some of the samples have been grown using digital doping, meaning that the Mn and Ga precursors are switched on alternatingly, so that the average Mn cation concentration xMnav can be tuned by varying the ratio of the time the sources are open. A complete list of the studied samples, not including the codoped samples to be discussed in Chap. 4, is given in Tab. 3.1. The crystallinity of the samples and the absence of precipitates are confirmed by high resolution TEM, high resolution (HR)-scanning transmission electron microscopy (STEM), HR-XRD, SXRD and extended x-ray absorption fine structure (EXAFS) spectroscopy. The cross sectional sample pieces studied by HR-TEM show a high crystal quality, and do not reveal any crystallographic phase separation for all studied Mn concentrations in both, imaging and diffraction mode. This local information is complemented by HR- XRD and SXRD measurements. None of the radial XRD ω-2θ scans between GaN (002) and GaN (004) show any traces of secondary phases, while the GaN peaks are narrow (240-290 arcsec), confirming the good crystalline quality, which is comparable to undoped GaN reference samples. With increasing Mn concentration the (002) peak of GaN shifts

33 3 Incorporation of transition metals into GaN

Table 3.1: List of all (Ga,Mn)N samples discussed in this section. The codoped samples that were part of the same growth series will be listed in Chap. 4. Concen- trations are determined by ﬁtting the spin Hamiltonian model as described in Chap. 2.2.2 to SQUID data. For samples grown in a digital fashion (δ- doped), the given Mn content is an average, since STEM reveals (expected) concentration modulations.

xMn [%] Ga [sccm] Mn [sccm] Thickness [nm] < 0.01 5 0 470 0.06 5 25 450 0.18 5 50 400 0.18 5 100 400 0.06 5 100 520 0.14 5 125 400 0.23 5 150 400 0.5 5 175 400 0.21 5 200 50 0.36 5 225 370 0.32 5 250 370 0.36 5 275 400 0.32 5 300 400 0.32 5 300 520 0.5 5 325 400 0.5 5 350 370 0.57 5 375 400 0.59 5 400 370 0.46 5 400 500 0.62 5 475 700 0.87 5 490 700 0.62 5 490 470 0.5 5 490 470 1.8 5 δ-490 140 2.6 5 δ-490 135 1.1 5 490 740 1.8 1 490 750 1.8 1 490 200 3.1 1 490 230 1.5 1 δ-490 140 0.53 5 490 780

34 3.1 Manganese slightly to lower angles, hinting towards an increased c-lattice parameter. It has turned out by annealing experiments performed for a sample with 0.5 % Mn concentration at the BM20 of the ESRF, that the dilute phase of the material is stable up to 900 ◦C (while keeping the sample in a pure N atmosphere at 200 mbar), in contrast to the case of Mn doped GaAs [84].

For selected samples (x=0.18 %, x=0.5 %, xav=2.6 %, x=3.1 %) the EXAFS and the x-ray absorption near edge structure (XANES) at the Mn K-edge have been measured at the italian collaboration ESRF beamline BM08. Qualitatively there is no difference in the EXAFS of the studied samples, and also quantiative asessment by fitting the data with a model does not show differences that would exceed the error bars. The model used to describe the data contains a contribution from isolated Mn within a GaN host and a Mn-N-Mn contribution based on MnN. The fitted Mn-N-Mn coordination number lies below 0.4 for all samples, what is, considering the large coordination numbers of possible metallic nanocrystals (NC)s (as in the case of Fe doped GaN), a strong hint that there are no such precipitates present in the samples studied. The possibility of having interstitial Mn has been taken into account as well, yet the fit quality does not improve by allowing their presence. For the samples below 1 % the fitted Mn-N distance increases to 1.99(1) Å, while for the sample with the highest concentration it is given by 1.94(3) Å, and for the δ-doped sample by 1.95(3) Å. The long range extension of the lattice has 2 been fitted as 0.1(2) % for all samples, and the amplitude reduction factor S0 confirms the assumed coordination numbers for substitutional Mn with values of 0.95(5) % for samples below 1 % of Mn cations, 0.94(5) % for the sample with 3.1 %, and 0.90(5) % for the δ doped sample. With these numbers, the Fourier transformed, k2-weighted EXAFS spectra agree well with the model up to 8 Å, and the agreement for the non-transformed k-dependent k2-weighted signal is excellent up to more than 13 Å−1. The distribution of the Mn ions within the GaN layers has been assessed by SIMS. For the studied samples the concentration of Mn does not vary significantly as a function of the depth, with an abrupt interface to the undoped buffer layer. If all other growth conditions are kept constant, in the considered concentration range the Mn concentration scales nearly linearly with the Mn precursor flow rate. This is confirmed by energy- dispersive x-ray spectroscopy (EDX), which has a sensitivity of 0.1 atomic percent and allows much higher depth resolution than SIMS. Employing high angle annular dark field (HAADF) imaging using STEM, and recording electron energy loss spectroscopy (EELS), these results have been reproduced for homogeneously doped samples up to the highest studied concentrations, yet for δ-doped samples a variation of the Mn concentration can be seen in HAADF-STEM and EELS, with a periodicity imposed by the growth

35 3 Incorporation of transition metals into GaN conditions. Due to the wide band gap of GaN, substitutional Mn can assume several electronic configurations. Since three of the Mn electons are part of the bonds to the neighbouring N atoms, the electrically neutral state has a formal valence of 3+. Two possible models for a formal 3+ valence state have been suggested, which cannot be distinguished by only taking into account symmetry considerations. The straightforward model considers four tightly bound electrons in the 3d shell, the other possible explanation are five tightly bound electrons in the Mn 3d shell together with a weakly bound hole, which is localized in a volume including the neighbouring N anions. The other possible formal valence state is 2+, with a 3d5 configuration of Mn. Which of the charge states is present in a particular sample depends on the position of the chemical potential in the band gap and can therefore be altered by codoping [85, 86], as described in Chap. 4.1.2. Codoping with acceptors has been reported to lead to the formation of Mn4+ [87], yet our findings point towards a different interpretation of comparable data, and will be covered in Chap. 4.2. For samples that were not intentionally codoped, both states, 2+ [88, 89] and 3+ [16, 90] were reported in literature, indicating that the valence state depends on the number of residual donors. We employ various techniques to verify the charge state of Mn in the studied samples, namely XANES [91], optical absorption measurements in reflection geometry, EPR and magnetic anisotropy measurements employing SQUID. All these techniques rely on the splitting of the Mn 3d energy levels in the GaN crystal field, which can be described using the formalism outlined in Chap. 2.2.1, and described in detail in Ref. [53]. The main difference between the measurement methods are the states that are employed to probe the 3d states1. While XANES uses electronic transitions originating from tightly bound and therefore nearly dispersionless orbitals, the magnetic methods rely on transitions within the 3d shell. Optics on the other hand is sensitive to these intra-shell transitions, but also other allowed transitions to states with comparable energies. The XAFS spectra of all studied non-codoped samples are equivalent, indicating that the charge state is independent of the Mn concentration2. The main features of the Mn K-edge XANES spectrum include the main absorption edge, two well separated pre-edge peaks and two peaks close to the edge energy. The valence state of an atom induces a chemical shift on the absorption edge (Haldane-Anderson rule), so the absorption edge

1For optics, the perturbation Hamiltonian contains the electric dipole operator, which, in order to be used with the theory presented in Chap. 2.2.1, has to be projected onto the basis functions employed there, namely the angular momentum eigenstates. 2This may not be valid for very low Mn content, comparable to the residual donor concentration. Further details are provided in Chap. 4.1.2

36 3.1 Manganese

(Ga,Mn)N (Ga,Mn)N:Si 1.2 (E) [a.u.]

µ 1

0.8 0.8 0.6 6540 6550 6560 0.6 0.4 0.4 A2 A3 A1 0.2 A34 0.2 0 Norm. partial fluorescence yield 6537 6540 6543 6546 6549

Normalised Absorption Coeﬃcient 0 6536 6538 6540 6542 6544 6546 6548 6550 6552 6554 6525 6540 6555 6570 6585 6600 6615 6630 6645 Energy [eV] Energy (eV)

Figure 3.1: Left panel: transmission XANES spectrum of the Ga1−xMnxN sample with x=0.87, with an inset comparing the edge energy to reference oxides MnO, Mn2O3 and MnO2, their positions marked by grey lines, while the position of the Mn edge is marked in black. The pre-edge peaks are labelled A1, A2, A3 and A34. Right panel: comparison of the ﬂourescence XANES spectra of a non-codoped and a Si-codoped sample to illustrate the shift of the edge with the changing charge state. (from Ref. [27])

energy can serve as a measure. Nevertheless, this requires comparion with a reference compound, and for nitrides no reference data is available. A comparison with reference oxides, MnO, Mn2O3 and MnO2, is provided in Fig. 3.1. The edge energy in Ga1−xMnxN is nearly the same as in Mn2O3, hinting towards a 3+ valence. Nevertheless to obtain this result, the energy at half the edge height has been taken, since the conventional procedure of using the inflection point fails due to the additional absorption peaks close to the edge in the reference oxides. If one would simply take the inflection point energy, the result would point to Mn2+. The presence of two clearly resolved pre-edge peaks, A1 and A2, also hints towards a 3+ charge state. Their energies, as obtained by fitting Gaussians, is given as A1=6538.9 0.2 eV and A2=6540.8 0.2 eV. These peaks are interpreted as ± ± transitions from the Mn 1s level to unoccupied Mn 3d levels. The final state of the 3d 5 6 shell for peak A1 can be attributed to a 3d configuration with an A1 symmetry, or 2↑ 3↑ e t2 written in single electron states. For the A2 peak, an assignment to a crystal field 4 2↑ 2↑ ↓ split off multiplet of the G state (e t2 t2) is possible, which lies, in theory, 2.5 eV above 6A. These transitions can be observed since, according to first principle calculations

[92, 90], the t2 states of the Mn ions hybridise with p-like conduction band states. In contrast, the contribution of the p-like states to the e states is much weaker, preventing their observation. The p-like conduction band states also serve as an explanation for the observed peaks A3 and A34, considering the absorption edge value obtained by ﬁtting the EXAFS, which lies at 6543 1 eV, between A2 and A3. The presence of a ﬁnal state ±

37 3 Incorporation of transition metals into GaN of 3d5 is only possible, if the initial electron configuration is 3d4, again hinting towards a nominal 3+ valence state of Mn in the studied samples. Furthermore, in Mn doped GaAs only one pre-edge peak is observed [92], what can be explained, considering that the initial state has a 3d5 configuration in the Mn2+ present there, so the transition is only possible for one spin orientation. A comparison to first principle calculations can be found in Ref. [84, 92]. Another indication of the presence of a significant amount of Mn3+ is provided by optical absorption in the near infrared [93]. The aforementioned crystal field splitting of the 3d levels in Mn3+ has been reported in literature to be 1.4 eV [89, 64, 94, 95].

As stated above, the t2 states have a significant admixture of p-like conduction band states, making the transition from e to t2 optically allowed. Indeed, reflectivity and transmission measurements at temperatures below 100 K clearly show an absorption ≈ feature at 1.41 eV. In Si codoped samples, where the electrons added by the additional donors are transferred to Mn as detailed in Chap. 4.1.2, the intensity of these absorption features is reduced, supporting the assignment of this peak to Mn3+. While EPR in principle allows to detect Mn2+, the 3d4 configuration of Mn3+ is expected to be EPR silent [93]. Indeed no EPR signals (apart from Mo and occasionally Cr contamination in the substrate) could be found in non-codoped samples, in contrast to samples codoped with Si. Nevertheless EPR is no rigorous proof that only a 3d4 configuration is present, since in codoped samples with high Mn concentration the signal of Mn2+ could not be observed, although other measurement methods clearly reveal its presence. The magnetometry data obtained by SQUID clearly confirms that in non-codoped samples the vast majority of Mn is in the 3d4 configuration. Not only is a clear magnetic anisotropy present, the magnetisation can also be described very well using the model for noninteracting Mn3+ centers as described in Chap. 2.2.2 for samples with Mn concentrations below 0.9 %, yet for concentrations between 1 and 3 % the magnetisation is found to saturate faster than expected in the noninteracting case. Nevertheless, standard laboratory SQUID (T > 1.85 K) does not show any ferromagnetic features, indicating that no ferromagnetic secondary phases (or chemical phase separation) are present in the samples. The question arises whether this faster saturation is a consequence of the onset of ferromagnetic interactions between the dopant ions. Indeed a change in charge state is unlikely, because the magnetic anisotropy is preserved. The susceptibility (M/H) of the film follows a Curie law at temperatures between 150 and 300 K, that can be interpreted 2 as either a completely uncorrelated system ( Jnn S kBT ), or a rigidly coupled one | |

38 3.1 Manganese

2 ( Jnn S kBT ). The magnetic model of a single ion has been extended to include | | nearest neighbour interactions ( JnnS~1S~2), and indeed applying this and assuming a − random distribution, the C/T dependence of the susceptibility can be reproduced for nearest neighbour coupling constants Jnn > 10 eV, yet the constant C is found to be greater than the Curie constant for noninteracting Mn ions. This increase of the pro- portionality constant can also be observed experimentally, yet the exact magnetic ion concentration needs to be known. To ensure consistency within the dataset, for each sample this number has been calculated from the saturation magnetisation. The agreement between theory and experiment is excellent in the case of homogeneously doped samples. In the case of digitally Mn doped ones the observed values of C are much higher than the theoretical values for a completely random incorporation, not surprisingly considering the nonhomogeneity of the dopant concentration as observed by EELS. As mentioned, the Curie like behaviour is followed above 150 K, yet at lower temperatures the magnetisation is even stronger than expected by the nearest neighbour interaction model, pointing to the existence of additional ferromagnetic interactions. This data is sufficient to ensure the presence of a short range ferromagnetic interaction, which can be attributed to superexchange, since Mott-Hubbard localisation hinders carrier hopping, the conductivity of the samples is minimal and the charge state of Mn is nearly solely 3+ without codoping. Two questions still remain unanswered: the value of the Curie temperature, and the lack of carrier mediated Mn-Mn interaction. Previous optical measurements of the band gap of GaN as a function of the Mn concentration already showed an increase of the gap with increasing Mn content [96], in agreement with the expectations for strong coupling between 3d states and valence band holes [26]. To strengthen the claim that indeed strong coupling is present - and with it localisation of valence band carriers at the Mn dopant atoms - the magnetic field and temperature dependence of all three free exciton absorption lines has been measured in reflectivity geometry for the samples up to 1% of Mn in magnetic fields up to 7 T. While previous work [70] allowed already to determine the sum of the apparent exchange app constants N0α (characterising the coupling between Mn 3d states and the s-like con- app duction band electrons) and N0β (giving the interaction between Mn 3d and p-like valence band states), the difference was previously unknown, since in order to obtain its value, all three free excitons need to be analysed, and in order to observe FXC a relatively good crystal quality is required. The reflectivity measurements have been performed in a pumped helium cryostat, so temperatures slightly below 2 K could be reached. As light source, a high pressure Xenon lamp has been employed, and focused onto the sample surface at nearly normal incidence.

39 3 Incorporation of transition metals into GaN

The same lens used for focusing has been employed to gather the reflected light, which has then been analysed in a 2400 cuts/mm grating spectrometer. To extract the exciton energies from the spectra, the model described in Chap. 2.3.2 is employed. The magnetic field dependence is then described with the model presented in Chap. 2.3.1. In order to reduce fitting parameters, several parameters are fixed. When extracting the exciton energies these are the refractive index of sapphire, which is set to 1.8, the background dielectric function of GaN 0 = 5.2, the exciton binding energies ∗ ∗ ∗ RA = 27.2 meV, RB = 23.9 meV and RC = 26.5 meV. The damping in the Mn doped layer is set to Γ∞ = 15 meV, while in the undoped layer, due to its (expected) better crystalline quality, it is fixed at Γ∞ = 8 meV. Free parameters are the exciton energies, the polarisabilities, and the different damping parameters for the individual excitons

Γj. This description allows to sucessfully fit the exciton lines, and also reproduces the Fabry Perot interferences in the energy region below, which are not purely caused by the interface between GaN and sapphire, but also influenced by the different exciton energies in GaN and (Ga,Mn)N, therefore depending on the exciton energies to be fitted. An interesting result of the direct comparison of reflectivity and PL, as displayed in Fig. 3.2, is that no excitons bound to neutral donors can be observed in PL for the Mn doped layer. An explanation, that fits to the results obtained with Si codoping (Chap. 4.1.2) and with the fact, that TM doping can be employed to get highly resistive samples [11], is that the carriers supplied by Si are effectively gathered by the Mn ions, causing the donors to remain charged even when cooling the sample. Generally, no emission from excitons bound to charged donors is observed in GaN [65]. A more careful analysis of the raw input data from all measurement methods allows to refine the previously reported [96] dependence of the band gap (or, more precisely, of the difference of the FXA energy between undoped buffer and Mn doped GaN) on the Mn concentration. The linear fit yields a slope of 27.4 2.6 meV/%. The fact that it does ± not pass through the zero point ( 0.89 1.13 meV), and that for the nominally undoped − ± sample a clear offset between the buffer excitons and the top layer excitons is observed, indicates that the top layer is somehow different from the buffer due to the different growth conditions. In view of this, the question arises, whether strain plays a role in the observed band gap change. While it cannot be completely ruled out that the top layer experiences strain, using the literature values for the deformation potentials [34, 97] and lattice parameters determined from EXAFS, one would actually expect a decrease of the gap. At the interface to the buffer nevertheless strain might be present. The lattice parameters, as obtained from XRD reciprocal space maps, are - within the experimental error - the same in buffer and top layer. Furthermore, while the exciton energy in the top

40 3.1 Manganese layer shows a clear trend with increasing Mn concentration, the excitons from the buffer layer do not show a clear dependence. The phonon dispersion has been probed by Raman high spectroscopy, since in-plane strain would cause a shift of the E2 phonon line. While the phonon energy is scattered within 0.6 cm−1 between different samples, no dependence on the Mn content can be observed. An approximation of the strain caused by the Mn doping using Vegard’s law indeed yields an increase, but an order of magnitude lower than the observed value, so strain is most probably not the sole cause of the observed increase of the gap, pointing to a case of strong coupling between valence band p-states and Mn d-states. According to the generalised alloy theory [26, 98], in which the effects of the p d hybridisation are calculated in a non-perturbative way, in the case of strong − coupling, when bound hole states can form at the Mn ions, the valence band states are renormalised and the observed band gap increases. Further insight into the coupling between band carriers and localised d states is obtained by analysing the magnetic field dependence of the exciton lines. For all samples measured in reflectivity, all three free exciton lines are observed, yet for very low Mn concentrations they cannot be clearly separated from the buffer layer excitions. The description outlined in 2.3.1 fits well to the observed exciton energies, as can be seen in Fig. 3.3, displaying the energy of both circular polarisations as function of positive magnetic field. This field splitting can be traced up to 100 K. The magnitude of the splitting depends on the Mn concentration, and anticrossing between the lines leads to a nonlinear magnetic field dependence at higher fields in samples with higher concentration. The main contribution to the anticrossing between FXA and FXB stems from the electron-hole exchange term, while the FXB/FXC anticrossing is dominated by spin-orbit coupling [70]. app The free parameters in these fits are the apparent exchange constants N0α and app N0β , the band gap energy and the spin-orbit splitting parameters of the valence band. Comparing the different samples, the values for the apparent exchange constants have app app been found to be N0α = 0.0 0.1 eV, and N0β = 0.8 0.2 eV. The sign, and mag- ± ± nitude of these values is unexpected, compared to TM doped CdS [99, 100, 101], where app positive values for N0α have been found, in agreement with molecular field theory. app On the other hand, in (Ga,Mn)As the value for N0α has been reported to be negative, and the explanation given is a possible electron configuration of Mn in (Ga,Mn)As to be 3d5 +h, so a half full 3d shell, where one electron is compensated by a weakly bound hole [102]. This configuration would lead to a near cancellation of the s d and s p exchange − − app terms [103]. In this perspective, our very small and possibly negative value of N0α can be a sign that here a similar situation is reproduced, so that the formal valence of

41 3 Incorporation of transition metals into GaN

30 1

25 0.8 ] 3 20 − cm

0.6 20 15 10

10 0.4 FXA shift [meV] concentration [

5 0.2 3+ Mn

0 PL ← Reﬂectivity ← 0 Linear Fit of PL ← Concentration (SQUID) → -5 0 50 100 150 200 250 300 350 400 450 500 Mn source ﬂow [sccm]

Figure 3.2: Left panel: comparison of PL at 10 K, and reflectivity at 2 K for three selected samples, confirming the excellent agreement between PL and reflectivity. In PL no DBE lines of the doped layer are observed. The dashed line gives the FXA energy. The PL lines at 3447 meV and 3537 meV are originating from Raman scattered light from the excitation laser. Right panel: energy difference between the FXA line of the Mn doped layer, and the FXA position of the underlying buffer layer, interpreted as a shift of the band gap. For samples,where the FXA line of the buffer cannot be resolved, the DBE line is used, and the average measured energy difference between DBE and FXA lines (8.35 0.25 meV) is subtracted. [29]. ±

42 3.1 Manganese

Figure 3.3: Left panel: fitting of the giant Zeeman splitting measured at 1.8 K for samples with 0.32% and 0.62% of Mn. Both polarisations are measured simultane- ously, so the magnetic field is positive for all points. The anticrossing between the lines is visible at the edge of the measurement range. Right panel: values for the apparent exchange constants extracted by these fits. [29].

43 3 Incorporation of transition metals into GaN

3+ might be composed of 3d5 + h. First principle calculations also hint towards such an app electron configuration (Chap. 4.2 and Ref. [31]). While our value for N0β seems to contradict values reported from photoelectron emission spectroscopy, where a negative value was measured [104], one has to keep in mind, that optical measurements in the case of strong coupling only yield apparent exchange constants, which, above a critical exchange interaction energy, are expected to have the opposite signs compared to the bare values [26]. This again hints towards a case of strong coupling. These findings lead to the conclusion, that most likely strong p d coupling leads to − the formation of bound hole states at Mn ions, hampering the contribution of these holes to the mediation of magnetic interaction between Mn, and that, in order to enable carrier mediated ferromagnetism in GaN, a much higher hole concentration is required, possibly exceeding the concentration of magnetic ions. In order to determine the Curie temperature caused by the observed short-range ferromagnetic superexchange interaction, for samples with x=1.1%, x=1.8% and x=3.1% magnetometry at temperatures below the previously mentioned 1.85 K has been measured in a custom built 3He-4He dilution fridge at the Institute of Physics of the Polish Academy of Sciences in Warsaw. This custom made setup allows fields up to 800 Oe and can cool down to 20 mK. Indeed an opening of the hysteresis is found for temperatures of approximately 0.15 K, 0.83 K, and 1.08 K. The coercive field as function of temperature is depicted in Fig. 3.4. These values are much lower than those predicted by ab initio calculations [25], and this can be attributed to the not precise description of correlations by the approximations used in density functional theory (DFT), and to the fact that defects and of structural disorder are neglected. A much better agreement between experiment and theory is obtained by using perturbation theory, treating the TM ions with Parmenter’s gerneralization of the Anderson Hamiltonian, taking into account Jahn-Teller distortion and modelling the GaN band structure using the tight binding approach. When using experimental values for the free parameters of this model (position of the Mn levels in the band gap, correlation energy of the states at the ion, crystal field splitting, p d-hybridisation), combined with a − monte carlo simulation for ion positions in the host, the theoretical Curie temperature is already close to the experimental value (Fig. 3.4). Changing the parameters slightly, within the error bars, would allow a perfect match. Details on the parameters used and the numeric values for the exchange energy as a function of the Mn-Mn distance can be found in Ref. [30]. Important is the result, that the nearest neighbour exchange energy obtained is approximately 9 K. The combination of millikelvin magnetometry and theory allows to identify the pri-

44 3.2 Iron

Figure 3.4: Coercive field as function of temperature for three different (Ga,Mn)N samples. Inset: our data (full squares), an experimental point from Ref. [16] (full circle) and theoretical points obtained by tight binding (open squares) and first principles (diamonds) calculations. [30]. mary magnetic interaction in non-codoped (Ga,Mn)N to be a ferromagnetic superexchange. Furthermore, the comparison with predictions based on local density approximation shows, that this technique overestimates the nearest neighbour exchange energy.

3.2 Iron

For Fe the situation is drastically different. A significant contribution of the 3d states to bonding leads to an attractive interaction between Fe ions [105]. This causes Fe to precipitate into secondary phases (NC) already at moderate concentrations of magnetic doping (0.4 % at 850 ◦C growth temperature, yet at lower temperature higher concentrations can be incorporated dilute). While first principles calculations give comparable pairing energies for Fe-Fe in the bulk and on the surface, our observations, showing a relatively narrow size distribution and the tendency of the secondary phases to be incorporated in thin layers parallel to the sample surface, hint that the secondary phase formation is primarily taking place at the growth surface. Our interpretation is that the NCs follow the growth surface while their size increases, until at a critical size they get incorporated. Depending on the growth conditions, temperature and Fe source flow rate [106, 28] as well as codoping (Chap. 4.1.1), various iron nitride and galfenol phases

GaxFey−xN can be realised by MOVPE, with 0 x 1 and 2 y 4. The most stable 0 ≤ ≤ ≤ ≤ ones are hexagonal -GaxFe3−xN and cubic γ -GaxFe4−xN. While these two phases are ◦ ferromagnets with (bulk) Curie temperature above RT (767 C for Fe4N [107] and 575

45 3 Incorporation of transition metals into GaN

◦ for Fe3N [108]), Fe2N and galfenol (GaFe3N) are expected to be antiferromagnetic [106], opening a wide range of accessible magnetic susceptibilities. A recent breakthrough was the achieved controlled fabrication of single planar arrays of NCs at a well defined depth from the sample surface and of a single GaxFe4−xN phase [107] by δ-doping with Fe. Again, by changing growth conditions, control over phase, size, coverage and shape of the NCs can be obtained. The single plane is obtained by switching the Ga flow on for 10 seconds, then off for 50 seconds, while leaving the Fe precursor open all time, for 15 periods. The most important parameters adjusted in order to control the NC growth are the TMGa and ferrocene flow rates, where ferrocene primarily influences the coverage, while TMGa allows to tune the Ga content of the NCs. Many electronic and magnetic applications of such NC layers can be envisioned, since

Fe4N is interesting for magnetic data storage [109, 110, 111, 112], and its high spin polarisation of conduction electrons [113, 114, 115, 116] makes this material well suited for magnetic write heads and as spin injector in semiconductors [117, 118]. Nevertheless, in order to technically exploit the magnetism of single NC layers, the magnetic properties have to be known. As part of this work, the magnetic anisotropy of a planar array of

GaxFe4−xN NCs in GaN at RT has been determined by measuring FMR [32]. For this particular sample 30 periods of δ-Fe doping, with a TMGa flow of 5 sccm, ferrocene flow of 490 sccm and ammonia flow of 800 sccm have been used, otherwise the growth procedure is the same as detailed in Ref. [107]. The sample has been cut into 4 mm2 square pieces, for measurements in the EPR spectrometer used for the FMR experiments. Cross-sectional TEM images show clearly that the NCs distribute in a plane perpendicular to the c-direction of the GaN crystal, and are confined within a thickness of 40 nm. ∼ From plan-view TEM data the average NC diameter in this plane has been found to be (24.7 5.2) nm, while normal to the plane they have an average height of (16.9 2.2) nm. ± ± Their coverage can also be estimated as (4.8 0.2)% of the basal plane. ± 0 For the identification of the crystal structure as γ -GaxFe4−xN XRD measurements along the c-direction have been carried out. The position of the (111) asymmetric peak shows that a majority of the crystals has an epitaxial relationship with the GaN host given by [001] [001] and (001) [110] (0001) 1120 , yielding 12 equivalent NC k GaN NC k GaN in-plane rotations, while the NC basal plane is parallel to the c-plane of GaN. A minority of the NCs is likely to be oriented differently, the epitaxial relation being [111] NC k [0001]GaN. This second orientation is indicated by a shoulder on the (006) diffraction peak of the substrate, and this overlapping between the peaks makes quantification based solely on XRD impossible. For this particular sample, reciprocal space maps of the

46 3.2 Iron

107 (a) 106

GaN(002) (006) 5 3 10 O 2 Al GaN(004) 104

103 (009) 3 2 N(002) O

Intensity10 [cps] 4 2 Fe Al 101

30 40 50 60 70 2θ [deg]

1.9 1.9

¥ ¥ ¤ ¤ = 0 (b) = 30 (c) 1.4 1.4

1.8 1.2 1.8 1.2 ]

A 1.0 1.0 [ 1.7 1.7 z

Q 0.8 0.8

1.6 1.6 0.6 0.6

2.2 2.3 2.4 2.5 2.2 2.3 2.4 2.5

¡ ¡ ¢ ¢ 1 1 Qx [A ] Qx [A ]

Figure 3.5: (a) GaxFe4−xN θ 2θ XRD spectra,: alignment of the (002) direction of the NCs with the− (002) of GaN. (b,c) reciprocal space maps of the (111) diffraction peak of GaxFe4−xN in the (x0z) and (xxz) planes of the GaN reciprocal space (φ = 0◦ and φ = 30◦). [32]. majority NCs (111) asymmetric peak have been collected at different azimuths, to proof whether strain is present, that would lift the 12-fold symmetry. As evidenced in Fig. 3.5, there is no noticable difference between two (111) peaks offset by 30◦, ruling out the presence of significant in-plane strain. Out-of-plane strain is not indicated, yet cannot be ruled out completely. The FMR measurements have been performed at a Bruker Elexsys E580 EPR setup, operated in continuous wave mode at microwave frequencies around 9.4 GHz. Due to the small sample size and the relatively small fraction of the sample volume occupied by ferromagnetic NCs, the signal to noise ratio is for some orientations of the sample as low as 3. This is the reason why the measurements are limited to RT, since the signal broadens ≈ with lowering temperature and completely vanishes at around 40 K. A typical in-plane signal and the temperature dependence obtained from an out-of plane measurement is displayed in Fig. 3.6. Bardeleben et al. reported a similar temperature dependence for Co secondary phases in ZnO, ascribing this observation to the nanocrystalline structure of the sample [119]. Furthermore, thermal broadening of resonance lines may play a role

47 3 Incorporation of transition metals into GaN

55000 3.5 400 Peak area Peak FWHM 50000 3 350 45000 2.5 300 40000 2 250 35000 1.5 200 FMR [arb. units]

30000 Peak FWML [mT] Peak area [arb. units] 1 150 25000 FMR Signal Fit 20000 0.5 100 0.2 0.25 0.3 0.35 0.4 100 150 200 250 300 Magnetic Field [T] Temperature [K]

Figure 3.6: Left panel: Typical in-plane FMR spectrum. The in-plane measurements give the best signal to noise ratio. Right panel: Broadening of an out-of- plane FMR peak with decreasing temperature. Due to the low signal to noise ratio of the spectra the angle dependent measurements are limited to RT. when it comes to the diminishing of the signal [120]. Although the expectation from XRD would be to observe three FMR peaks caused by the 30◦offset between cubic crystals, only one line has been observed, which shows predominantly uniaxial behaviour out-of-plane (θ: out-of-plane angle), while in-plane (φ: in-plane angle) a six-fold symmetry is observed. Indeed, a simple sin (6φ) describes the in-plane dependence excellently, as does a cos2 (θ) for the out-of-plane dependence. In Fig. 3.7 the angular dependence of the FMR resonance field is plotted. The most probable origin of the out-of-plane uniaxial dependence is the demagnetising field caused by the shape of the NCs. Using the dimensions obtained from TEM and approximating the crystals as oblate spheroids [121], the demagnetising field tensor in diagonal form reads Nxx = Nyy = 0.31 0.03 and Nzz = 0.38 0.06. It should be ± ± noted that the error bars are still not small enough to completely rule out that on average the shape anisotropy might vanish, and that an alternative explanation for the uniaxial behaviour would be necessary, for instance strain induced by the host crystal. Furthermore, the coverage of this sample is at the limit at which even at RT a random array of NCs should show magnetic ordering due to dipole-dipole interactions (This can be seen by scaling the energy values published in Ref. [122] for Fe by the square ratio of the 6 6 saturation magnetisation of Fe (1.76 10 A/m (Ref. [123])) and Fe4−xN(1.51 10 A/m × × [124, 125, 111] in powder samples, 1.42 106 A/m in thin films [126])). If present, such × a coupling will also contribute to the uniaxial anisotropy [119]. The in-plane anisotropy is not as easy to explain. For single domain particles shape

48 3.2 Iron

0.39 0.31

0.38 (a) (b) 0.308 0.37

0.36 0.306 0.35

0.34 0.304

0.33

Resonance field [T] Resonance field [T] 0.302 0.32

0.31 0.3 Measured Models (iii), (v) 0.3 Models (ii), (iv) Model (i) 0.29 0.298 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 Out-of-plane angle θ [rad] In-plane angle ϕ [rad]

Figure 3.7: Angular dependence of the FMR signal (points) and fitting results of the models (i)-(v) described in the text. Solid line: phenomenological crystal field anisotropy; dashed line: fits with cubic NCs with their [111] axis along the [001] axis of GaN, having the uniaxial out-of-plane anisotropy induced by shape anisotropy or coupling, both yielding the same fit quality and lineshape; point-dashed line: fits accounting for the phenomenological hexagonal in-plane anisotropy and having the out-of-plane uniaxial anisotropy induced by shape or coupling, both giving commensurate fit quality and line-shape. (a) out-of-plane FMR measurement: the in-plane angle is fixed at φ = 0, and the out-of-plane angle θ has been varied between 0 and 2π; (b) in-plane data-points; here the out-of-plane angle is kept at θ = π/2 and the in-plane angle φ is varied between 0 and π. [32].

49 3 Incorporation of transition metals into GaN can be ruled out, since it only can give uniaxial contributions. Also strain can be excluded by microscopic arguments, since every isotropic in-plane strain will preserve the four-fold symmetry, and non-isotropic strain can be ruled out based on the XRD data. Furthermore, the three equivalent orientations of the NCs cannot be the reason, because not only would they lead to three distinct FMR lines, but also the sum of these FMR lines, if mistakenly interpreted as a single peak, would show nearly no angle dependence, with a weak, seemingly 12-fold residual anisotropy. The aforementioned possibility of dipolar coupling between the crystals up to RT could serve as a possible explanation, yet, in addition uniaxial strain along three different dirctions for different NCs, not observed in XRD, would be required. Also the presence of non-interacting, dilute Fe ions in the GaN host matrix can not account for the observed anisotropy, because, although they are placed in a hexagonal environment, their in-plane magnetic response is expected to be isotropic for symmetry reasons [53]. Yet, although the NCs show a well defined crystallographic interface with the surrounding hexagonal crystal, our TEM data does not rule out that the chemical interface might be less sharply defined, so that in a volume around the NCs, which has hexagonal structure, a significantly higher amount of Fe than in the dilute matrix might be present. Given the small size of the crystals, yielding a surface/volume ratio of the order of 10, such a surrounding hexagonal high Fe content volume, even if it is very thin, could have a noticable effect, especially since the phase GaFe3N is expected to be antiferromagnetic and therefore relatively robust against external fields. Nevertheless, the minority of NCs with their [111] direction along the [001] direction of the GaN host is expected to give exactly such an in-plane angular dependence. When measuring the anisotropy exactly in a plane normal to [111], the observed cut through the free energy surface would show sixfold symmetry. Indeed, a model combining both shape anisotropy, and the crystal anisotropy of this minority of NCs gives a reasonable agreement with the measured data.

The measured data has been fitted with five models, both purely phenomenologic, and based on the just mentioned possible explanations. Model (i) is a fit of a phenomenologic hexagonal crystal anisotropy, completely ignoring NC shape anisotropy. This only gives apparent anisotropy constants. Fit (ii) is the same model, yet it includes the shape information from TEM. The model that takes into account the minority of NCs with [111] along [001] of GaN is presented in fit (iii), which also takes into account the shape information. Models (iv) and (v) use the shape anisotropy of a rigidly coupled thin layer, where in (iv) a phenomenologic hexagonal crystal anisotropy term is used for the in-plane anisotropy, as would be induced by strain. Model (v) on the other hand consists of rigidly coupled minority NCs. The fitted curves are plotted in Fig. 3.7, and the obtained fitting

50 3.2 Iron

Table 3.2: Fitting/material parameters. In the models (i), (ii) and (iii) the NCs are treated as isolated magnetic moments. In the purely phenomenologic model (i), which simply fits a hexagonal crystal anisotropy and neglects shape, K1 and K2 are the prefactors of the second and fourth order uniaxial term, and K3 is the prefactor of the sixth order hexagonal term. The uniaxial crystal anisotropy is set to zero in model (ii), all uniaxial contributions are taken to be coming from the NC shape as determined by TEM. In model (iii), a cubic crystal anisotropy with its [111] direction parallel to the [001] direction of the GaN host is assumed and combined with shape information from TEM. K1 and K2 are in this case the cubic anisotropy term prefactors of second and fourth order. Model (iv) is the same as (ii) and (v) the same as (iii), but with the shape anisotropy of an infinitely extended layer (Nxx = Nyy = 0, Nzz = 1). The error values given in this table are only a measure for the convergence of the fit, and do not include the error propagated from the input values, what is especially important for models (ii) and (iii), where the error of the shape information from TEM is not considered here. This is the same data, that has been published in Ref. [32]

Individual Coupled Crystal/Strain Shape + Hex Shape + Cube Hexagonal Cubic (i) (ii) (iii) (iv) (v) g 2.069 2.069 2.065 2.069 2.065 kA msat [ m ] 1443 12 695 5 589 8 49 0.4 41.7 0.6 J ± ± ± ± ± K1 [ m3 ] -40492 495 set 0 729 170 set 0 51 12 J ± ± ± K2 [ m3 ] -3408 251 set 0 -7768 1000 set 0 -551 71 J ± ± ± K3 [ m3 ] -74 11 -24 8 -1.7 0.6 Fit Error 57.46± 91± 165 91± 165

parameters are displayed in Tab. 3.2. The fitting is performed using the formalism presented in Sec. 2.2.1, where in Eq. 2.14 only the first three terms (Zeeman, crystal anisotropy, and shape anisotropy) are used. For models (i), (ii) and (iv) the crystal anisotropy was given by Eq. 2.18, while for the other models Eq. 2.17 is employed. Damping has been neglected, and fitting parameters are the anisotropy constants, g- factor and saturation magnetisation. Since the first order uniaxial crystal anisotropy (as encountered in hexagonal crystals) and shape anisotropy are formally equivalent, models (ii) and (iv) give exactly the same fit quality. Similarly, the residual error of model (iii) is equal to the residual error of model (v). Surprisingly the saturation magnetisation obtained by fitting the phenomenlogic model 6 (i) is in the range of literature values for Fe4N, which are between 1.42 10 A/m [126] and ×

51 3 Incorporation of transition metals into GaN

1.51 106 A/m [111, 124, 125]. Nevertheless the fitted g-factor differs from the literature × value [127]. Due to the large error bars of the shape information from TEM, a broad range of possible values for the saturation magnetisation can be fitted by models (ii) and (iii). The literature value of the saturation magnetisation could be obtained by setting the aspect ratio to 1.08, lying within the error bar of the TEM data. One has to keep in mind nevertheless, that due to the similar lattice parameter the incorporation of Ga in the NCs, which would reduce the saturation magnetisation, can neither be ruled out or confirmed by our XRD data. On the other hand, the saturation magnetisation values for the models of coupled NCs (iv) and (v) are giving values of the saturation magnetisation, which would correspond well with the measured coverage from TEM. The ratio between the fitted and the literature Fe4N saturation magnetisation hints towards a coverage of about 3%.

Since the purely phenomenologic model (i) yields a saturation magnetisation close to the literature value, it is worth considering which physical eﬀect can account for the uniaxial out-of-plane anisotropy. A natural candidate is strain, which can be related to the anisotropy constant by [123]:

3 K = λ E (3.1) 1 2 S

For the Young modulus E of Fe4N a broad range of values has been reported, between 159 GPa and 205 GPa [128, 97, 129, 130, 131, 132]. The knowledge of the saturation magnetostriction λS is even less clear, due to misinterpretation of many experimental works, which attributed data of N contaminated α-Fe to Fe4N. From DFT simulations −6 a relatively trustworthy value of λS = 10 10 has been obtained [111]. With these − × values, the strain needed to induce a uniaxial anisotropy in a completely spherical particle would be between 1.3% and 1.7%, what is unlikely, but cannot be fully excluded based on XRD data. Due to the complete ignorance of the NC shape in model (i), model (iii), with the minority of NCs with their [111] along [001] of GaN, is a more reasonable explanation.

The measurement of the magnetic anisotropy of GaxFe4−xN NCs, which was found to be uniaxial along the host [001] direction and three easy axes in the (001) plane, and can be explained by both shape of the NCs and the presence of a minority of NCs which are aligned with their [111] direction along the [001] direction of the host, is the ﬁrst step towards novel applications of these crystals. An interesting prospect for these crystals is to exploit them as spin injectors [116], maybe by pumping them by FMR [117, 118]. Inverse spin Hall eﬀect would permit the usage as spin current detectors [133], and,

52 3.2 Iron given the possibilty to induce stronger in-plane anisotropy - as preliminary data on other samples hint - magnetic storage applications could be envisioned. Also, since the NCs are embedded in a semi-insulating matrix, ﬂash-memory like electric charge storage might be possible [134, 135]. Since, from a basic physics point, frustrated magnetic systems and spin-glasses are of very high interest, the possibility to observe coupling in these NC layers can make them a workbench to study these phenomena [122].

4 Donor and acceptor codoping of transition metal doped GaN

4.1 Control of the transition metal charge state

4.1.1 Eﬀect of codoping on iron incorporation

Based on the theoretical predictions that codoping with electrically active impurities can influence the incorporation of TMs [136], samples codoped with Fe and Mg (acceptor) and samples codoped with Fe and Si (donor) have been studied. It has been shown previously by the combination of SXRD data with SQUID magnetometry, EPR and TEM that in (Ga,Fe)N samples codoped with Si the formation of secondary phases during MOVPE growth is hampered leading to either paramagnetic dilute samples, or spinodal decomposition in regions rich in Fe, but crystallographically coherent with the host, which gives a ferromagnetic SQUID signal up to RT [108]. Syn- chrotron XAS combined with DFT simulations has been used to investigate the reasons for this phenomenon. The XANES analysis reveals that upon Si codoping the pre-edge peak, attributed to the transition from 1s to 3d states, which consists of a single peak at 7113.9 0.1 eV in non-codoped samples is showing a second component at 7112.8 0.1 eV. ± ± This second component is assigned to the chemical reduction of a part of the dilute Fe ions from Fe3+ to Fe2+ [137]. It has been suggested, that this change in the formal charge state leads to a lowering of the binding energy of Fe ion pairs and therefore shifts the onset of phase separation to higher Fe concentrations. For Fe/Mg codoped samples a similar effect, the hampering of phase separation at the same Fe precursor flow rate, was observed [108]. Yet, some questions remained unanswered.

1. For Si codoping a change in the Fe charge state had been clearly found. Does Mg codoping also aﬀect the charge state, and if yes, does it lead to oxidation, or is a hole weakly bound at the ions [69, 95]?

2. Is Mg codoping hampering Fe aggregation, or is another mechanism responsible for

55 4 Donor and acceptor codoping of transition metal doped GaN

the lack of secondary phases?

3. What about the magnetic properties? If the charge state is modiﬁed or a hole bound, a change in magnetic moment and anisotropy would be expected.

4. Is the formation of secondary phases happening in the bulk, or is it a surface eﬀect, as suggested by the eﬀect of the growth rate on Fe aggregation in the non codoped case [108]?

To answer these questions, a series of samples grown with different Fe and Mg precursor flow rates has been studied by XRD, SXRD, SIMS, TEM, SQUID magnetometry and EPR. The Mg doping has been carried out in two different modes: homogeneous and digital (δ-doping). Digital doping is achieved by periodically switching off the Fe and Ga precursors, and while these are disabled flowing the Mg precursor. The NH3 flow is kept constant to guarantee an ample supply of N at the growth surface. The samples considered here are grown using 60 such δ-doping periods. The list of samples is given in Tab. 4.1, including the flow rates of the dopant sources and the mean cation concentrations as determined by SIMS. From the SIMS results (Tab. 4.1 and Fig. 4.1), the Fe concentration increases with Fe precursor flow rate. At the same Fe precursor flow rate, nevertheless it changes upon Mg codoping. In δ-doped samples the total Fe concentration is higher than in the reference, while the opposite is observed in the homogeneously codoped case. Also, the incorporation of Mg is affected by the presence of Fe. At constant Mg precursor flow rate the Mg concentration is decreased with increasing Fe concentration (see Fig. 4.1). From XRD and also TEM it can be seen, that in the (Ga,Fe)N films phase separation is present for precursor flow rates at and above 300 sccm at the growth conditions detailed in Chap. 2.1. In the samples under study the -Fe3N phase is dominant, and the crystallographically similar -Fe2N and -Fe4N can also be detected. In contrast to this, when the samples are homogeneously codoped, no crystallographic phase separation can be detected for all studied Fe precursor flow rates. Again, the situation is dramatically different in the digitally doped samples. Here already at the lowest Fe precursor flow rate crystallographic phase separation is observed, and the variety of phases is greater than in the non codoped case. Synchrotron XRD reveals 8 peaks related to secondary 0 phases, which are attributed to -Fe3N, -Fe2N, Fe3Ga, α-Fe, Fe0.7Ga0.3, γ -Fe4N and -

Fe4N. There is no sign of the galfenol Fe1−xGax phases in non codoped samples. Another important ﬁnding of the SIMS measurement is that in the digitally codoped samples the secondary phases are not homogeneously distributed in the layer, but form planar arrays at a well deﬁned height below the surface and in the sample with the highest Fe precursor

56 4.1 Control of the transition metal charge state

Table 4.1: Samples analysed to study Fe-Mg codoping. The (mean) concentrations are determined by SIMS

sample type Cp2Fe Cp2Mg xFe xMg [sccm] [sccm] [%] [%] S907 ref. 100 0 0.06 0 S911 ref. 200 0 0.11 0 S910 ref. 300 0 0.21 0 S994 δ 100 350 0.15 0.02 S995 δ 200 350 0.20 0.016 S993 δ 300 350 0.38 0.016 S1193 δ 50 350 0.08 0.03 S1192 ref. 50 0 0.08 0 S1406 ref. 300 0 0.20 0 S1407 h 0 350 0.00 0.15 S1402 h 50 350 0.03 0.23 S1405 h 100 350 0.04 0.22 S1404 h 200 350 0.07 0.20 S1403 h 300 350 0.11 0.19 S1415 h 400 350 0.12 0.17 S1416 h 450 350 0.15 0.17 S1427 h 300 250 0.12 0.07 S1428 h 300 150 0.10 0.01

flow rate also close to the interface with the buffer layer. Meanwhile this phenomenon has been investigated further and a protocol to control the formation of these layers has been established [107]. See also chap. 3.2. Magnetic methods are employed to distinguish between the Fe that is dilute in the GaN matrix and the Fe forming precipitates, and to get information on the formal valence state of the dilute Fe. While magnetometry measures the sum of all magnetic moments in the sample and requires fitting of a model in order to separate the different contributions (Sec. II.E of Ref. [28]), magnetic resonance allows to distinguish between ions in different environments directly due to their different resonance frequency. Both methods, EPR and SQUID, show a clear presence of Fe in a 3d5 electron configuration. Further, the anisotropy of the paramagnetic contribution to the overall magnetisation shows little (less than 3 % ) anisotropy in SQUID, indicating that the vast majority of Fe ions in solution is in this state. As reported in Fig. 4.2, the ferromagnetic component in non codoped samples is observed at precursor flow rates of 100 sccm and above, while

57 4 Donor and acceptor codoping of transition metal doped GaN

0.25 (%)

(Ga,Fe)N: Mg x

0.20 0.3 (%)

(Ga,Fe)N:Mg Mg x

0.15

(Ga,Fe)N GaN:Mg

0.2

GaN: Mg

0.10

0.1

(Ga,Fe)N: Mg (Ga,Fe)N:Mg 0.05

crystallographic phase separation

0.0 0.00 Mg concentration concentration Mg Total Fe concentration concentration Fe Total

0 100 200 300 400 0 100 200 300 400

Cp Fe flow rate (sccm) Cp Fe flow rate (sccm)

2 2

Figure 4.1: Fe (left panel) and Mg (right panel) cation concentration as a function of Fe precursor flow rate with constant Mg precursor flow for (Ga,Fe)N, (Ga,Fe)N:Mg and (Ga,Fe)N:δ-Mg, as determined by SIMS. For all δ-doped samples crystallographic phase separation is found by XRD, while homogeneously codoped samples do not show it. [28]. supplying Fe and Mg together shifts this onset to 300 sccm. In digitally Mg doped samples, the ferromagnetic component is already seen at 50 sccm. At the same Fe precursor flow rate, the ferromagnetic component is much stronger in digitally codoped samples than in homogeneusly or non codoped samples. On the other hand, in homogeneously codoped samples a weaker ferromagnetic contribution is observed. The paramagnetic component of magnetisation has been studied by EPR in addition to SQUID. In both measurements, the digitally codoped and the non codoped samples are comparable, while the homogeneously codoped sample shows a weaker signal below a Fe precursor flow rate of 200 sccm. This finding of a lower total Fe concentration in homogeneusly codoped samples agrees with SIMS data, yet at high Fe content a discrepancy exists between these methods, suggesting that some Fe is neither para- nor ferromagnetic. A possible explanantion for this is the presence of antiferromagnetic phases. The concentration of paramagnetic Fe is given in Fig. 4.3. The concentration as determined from SQUID has served as a calibration standard for the count rate in EPR in such a way, that the total difference between SQUID and EPR concentration is minimized over all samples considered:  Samples  P IEPRjxSQUIDj  j=0  x =   I (4.1) EPRi  Samples  EPRi  P I2  EPRj j=0 I is the integrated intensity of EPR (normalised by the sample volume), x is the cation

58 4.1 Control of the transition metal charge state

(Ga,Fe)N: Mg

0.10

0.05

(Ga,Fe)N

(Ga,Fe)N:Mg

0.00 Concentration of FM Fe (%) Fe FM of Concentration

0 100 200 300 400

Cp Fe flow rate (sccm)

Figure 4.2: Cation concentration of ferromagnetic Fe, as extracted from SQUID, as function of the Fe precursor ﬂow rate. The δ-Mg-doped samples (triangles) show a much stronger ferromagnetic signal than the non codoped samples (circles) grown at the same Fe precursor ﬂow rate. In homogeneously codoped (squares) samples the ferromagnetic component is weaker than in the other cases. [28]

concentration. To obtain comparable results all EPR data are acquired under the same conditions, namely a sample temperature of 2 K, a microwave frequency of 9.8 GHz and power of 2 mW and a magnetic field modulation amplitude of 5 Gauss. Due to an overlap between the strongest Fe EPR peak and a peak originating from contamination in the substrate (likely molybdenum [138, 139]) the strongest Fe peak cannot be used to determine the Fe concentration from EPR. The concentration determined from the four weaker fine structure components has been averaged for each sample. In order to get insight into these findings, and in the fundamental difference to the

Si codoping case, the FenMgm and FenSim (n,m 2) complex formation energies at ≤ the surface and in bulk are determined via first principle simulations using DFT. The GGA+U approximation has been employed, with the U-parameter set to 4.3 eV. Due to the use of ultrasoft pseudopotentials and the Perdew-Burke-Enzerhof exchange, a reasonalby low energy cutoff of 30 Ry for the kinetic energy and 180 Ry for the charge density is sufficient. For bulk, a zinc-blende type GaN supercell consisting of 64 atoms is used, while for the Ga terminated surface a wurtzite type supercell with two times 48 atoms is employed, which is passivated with hydrogen on the N terminated back side, and has a 1 nm high empty space on top of the supercell to simulate the surface. The most stable configuration for a Fe-Mg or Fe-Si pair in the bulk is on nearest neighbour positions. If an additional Mg or Si is added, the three dopants align along a line, while if

59 4 Donor and acceptor codoping of transition metal doped GaN

(Ga,Fe)N (Ga,Fe)N (Ga,Fe)N:Mg (Ga,Fe)N:δMg

ESR (arb. units) 4.2 4.4 4.6 4.8 5 ESR (arb. units) 4.3 4.5 4.7 4.9 5.1 Field (kOe) Field (kOe)

(%) 0.13 (Ga,Fe)N (%) (Ga,Fe)N 3+ 3+ 0.11 (Ga,Fe)N:Mg (Ga,Fe)N:δMg Fe 0.11 Fe x x 0.09 0.09 0.07 0.05 0.07 0.03

concentration concentration 0.05

3+ 0.01 3+

Fe 50 100 150 200 250 300 350 Fe 50 100 150 200 250 300 350 Cp2Fe flow rate (sccm) Cp2Fe flow rate (sccm)

Figure 4.3: Top: Fine structure split off EPR peak of Fe3+. The lines are the double integral of the peak, a measure for the concentration. Bottom: Concentration of the Fe3+ ions in solution, as determined from SQUID (open symbols) and EPR (full symbols). The EPR concentrations are calibrated using the SQUID data. Left panel: Comparison of a homogeneously codoped (squares) and a non codoped (circles) reference sample grown with 200 sccm Fe precursor flow rate recorded at a temperature of 2 K. At the same precursor flow rate, the amount of Fe in solution is weaker in the homogeneously codoped sample, until saturation is reached. Right panel: Comparison of a δ-Mg codoped (triangles) and a non codoped (circles) reference sample grown with 300 sccm Fe precursor flow rate recorded at a temperature of 2 K. At the same precursor flow rate, the concentration is comparable for δ-codoped and non-codoped samples. [28]

60 4.1 Control of the transition metal charge state two Fe and one Si or Mg atoms are present, they form an isosceles triangle. In equilibrium the complex of two Fe and two Mg/Si atoms has a rhombic arrangement, with the atoms of the same type on the opposite edges. For Si, the shape of the complexes is the same on the surface. In the case of Mg, the formation energy of a Fe-Mg pair is only negative in the bulk (-0.178 eV). On the surface the ions repulse each other (0.187 eV), what is opposed to the Fe-Si case (-0.309 eV). Pairs of Fe atoms tend to form on the surface with a pairing energy of -0.125 eV. Also of interest is the formation energy of Fe pairs in the vincinity of Si or Mg. If one of these atoms is placed at a distance of 0.6 nm from a Fe atom, a second Fe atom needs the energy of 0.155 eV for Si and 0.267 eV for Mg to occupy a nearest neighbour position to the already present Fe. Further complex formation energies are displayed in Figs. 13 and 14 of Ref. [28]. An important finding displayed there is that the energy needed to add another Fe or Mg ion is always negative in the bulk, while at the surface it is always positive, except for the formation of Fe-Fe pairs. In the case of Si codoping the formation of FeSi has a negative energy at the surface as well. Previous studies on non-codoped samples revealed a strong dependence of the Fe incorporation on the growth rate and no precipitation during post growth annealing, hints that the formation of NCs already occurs at the growth surface (see Sec. 3.2 and Ref. [108, 106]). This agrees with the negative formation energy of Fe pairs at the surface, and another indication is that in the case of Mn doping, where there is no attractive force between Mn ions on the surface, the solubility is much higher [140]. The repulsion between Fe atoms induced by Si or Mg in their surroundings can serve as an explanation of why in the case of codoping the limit for the formation of NCs is shifted towards a higher Fe precursor flow rate. It can be speculated that the significant reduction of Fe incorporation in the case of homogeneous Mg codoping, as well as the increased Mg incorporation when Fe is present (as opposed to samples without Fe, Fig. 4.1) could be caused by a weakening of the repulsive force between Mg ions. If this really is the case, the Mg incorporation would be promoted. Since in the (Ga,Fe)N:δ-Mg samples the opposite behaviour is observed, namely an increase in the formation of secondary phases, both in magnitude and variety, while the overall Mg concentration is lower than in GaN:δ-Mg samples, it seems reasonable to consider that in this case, for reasons yet unknown, possibly interdiffusion of Mg and Fe, the bulk pairing energies apply for the NC formation, which are negative for all complexes FenMgm studied (n, m 2), while the overall Mg concentration is reduced ≤ due to repulsive forces between Fe-Mg pairs on the surface. The observation that the NCs arrange in planar arrays at a given distance from the

61 4 Donor and acceptor codoping of transition metal doped GaN substrate and surface can be linked to the observation, that the average size of the crystals does not depend on the Fe precursor flow rate. These considerations suggest, that the NCs get incorporated after a certain critical size has been reached. Until that point they follow the growth front. If all NCs have approximately the same growth rate, they will end up in a narrow layer with a well defined distance from the interface, as observed by TEM. To summarise, this study of the interplay between Fe and Mg dopants during growth of codoped GaN shows that in the case of homogeneous doping the presence of Mg reduces the Fe incorporation due to a competition between these dopants for the Ga substitutional positions, while with δ-Mg doping the incorporation and with it the formation of secondary phases is enhanced and the types of secondary phases are more varied. The comparison with DFT results points to the fact that in the homogeneous doping case the Fe incorporation is a surface process, while for digital doping interdiffusion might play a role, so that in this case the incorporation of Fe is effectively a bulk process.

4.1.2 Eﬀect of Si codoping on the incorporation of manganese

While for Fe doped GaN the most prominent consequence of codoping with Si or Mg is its effect on the formation of NCs, for Mn, which has not been observed to form secondary phases in any samples studied for this work, i.e. at concentrations up to 3%, codoping is expected to mainly alter the electronic configuration of Mn due to its effect on the chemical potential, and by this also to affect the magnetic properties of the material. To probe to which extent these changes of the magnetic properties caused by codoping can serve as an explanation for the contradicting statements about the magnetism of (Ga,Mn)N reported in literature, a series of samples with Mn cation concentrations up to 3% and codoped with Si or Mg have been studied. Since the effects of Mg and Si are quite different, they will be discussed individually. As already discussed in Sec. 3.1, the formal valence of the majority of Mn in MOVPE grown (Ga,Mn)N without intentional codoping is 3d4. Since GaN has a relatively large band gap, sufficient donor codoping can alter the valence of Mn towards 3d5, as observed experimentally [93, 89, 64, 94, 95]. To reproduce this observation and to study the effect on the magnetic properties, (Ga,Mn)N:Si samples were grown as part of the sample series used to study the magnetic interaction between Mn ions as described in Sec. 3.1. The growth procedure has already been outlined in Sec. 2.1. The Si codoped samples and their non-codoped counterparts are listed in Tab. 4.2. As already mentioned, the digitally-, or δ-doped samples are grown with Mn- and Ga-precursors switched on alternatingly, control about the average Mn concentration is in this case obtained by varying the time

62 4.1 Control of the transition metal charge state

Table 4.2: List of (Ga,Mn)N:Si samples and their corresponding references, together with their nominal (average) Mn cation concentration and precursor ﬂow rates. Samples #1159 and #1160 are grown in a δ (digital) fashion.

Sample # xMn [%] Ga [sccm] Mn [sccm] Si [sccm] 1106 1.8 1 490 0 1130 1.8 1 490 0 1134 1.8 1 490 2 1142 3.1 1 490 0 1152 3.3 1 490 2 1159 1.5 1 δ-490 0 1160 2.4 1 δ-490 2 1161 2.9 1 490 1 1268 2.0 1 400 2 1269 1.9 1 300 2 1273 0.49 5 490 2 1274 0.53 5 490 0

at which each precursor is present. The codoped specimens have been analyzed by means of HR-TEM, HR-STEM, XRD, SXRD and EXAFS to probe the presence of secondary phases. The TEM data shows well ordered crystals without any secondary phases, and also (synchrotron) XRD does not give any hints towards segregation or phase separation. The high crystallinity, investigated locally by TEM, is confirmed on larger scales by the narrow GaN XRD peaks (below 240 arcsec). No indications of an increased concentration of structural defects in the codoped samples have been found. The local environment of the Mn ions has been probed by XAS for three samples, one Mn doped with x = 3.1 % (#1142), one digitally Mn doped with xav = 2.6 % (#1071), and a (Ga,Mn)N:Si sample with x = 3.3 % (#1152). The observed spectra are equivalent for all three samples, and the results obtained by fitting a structural model are within the error bar. The coordination number of Mn (i.e.: the number of neighbouring Mn ions of each Mn ion) has been assessed by fitting a linear combination of a model for a single Mn impurity in GaN and a Mn-Mn contribution based on MnN. Considering the high coordination number expected for secondary phases, their presence can be ruled out by EXAFS with an uncertainty of 5 %. The Mn-N distance has been ≈ found to be 1.95(3) Å for the δ- and the codoped sample, for the (Ga,Mn)N sample it is 1.94(3) Å. The Mn-Ga distance is 3.20(2) Å in the δ-doped sample, while for the (Ga,Mn)N and the (Ga,Mn)N:Si samples it is 3.19(2) Å. Coordination numbers are 0.4(4)

63 4 Donor and acceptor codoping of transition metal doped GaN for the δ-, 0.0(4) for the co- and 0.2(4) for the non-codoped sample. The distribution of dopants as a function of the depth within the codoped samples has been investigated by SIMS. Both dopants are found to be homogeneously distributed within the doped layer, with approximate concentrations of Mn as in Tab. 4.2, and a Si concentration of the order of 1020 at/cm3 (with the exception of the codoped sample with the highest Ga precursor flow rate). At the interface these concentrations drop by approximately 3 orders of magnitude within 100 nm (it must be considered, that SIMS has limited z-resolution, and that HAADF-STEM with EELS which has been measured for the non-codoped case shows atomically sharp interfaces). In order to distinguish between the charge states of Mn, the optical intra-ion transition of Mn3+ in GaN at approximately 1.41 eV [93] has been assessed by reflectivity and transmission measurements at a temperature of 2 K for codoped samples with a Mn concentration of x = 1.8% and x = 0.5% together with their corresponding non-codoped references. Transmission has been measured on the x = 0.5 samples. The spectra have been fitted using a transfer matrix model (Chap. 2.3.2), taking into account the doped layer, the buffer, and the sapphire substrate. The GaN dielectric function is modelled with the Sellmeier equation [141], the sapphire refractive index is fixed at 1.8. The absorber is modelled by a single damped Lorentzian oscillator, giving the following relation for the dielectric function of the doped layer:

fNMn3+ (ω) = GaN (ω) + (4.2) E2 (¯hω)2 ıhω¯ Γ 0 − − The thickness of the layers is ﬁtted as well, yet the ratio of the thicknesses of the doped and undoped layers is ﬁxed following the results of in-situ ellipsometry. This is necessary, since the absolute thickness values from ellipsometry do not reproduce the observed

Fabry-Perot intereferences. The difference of the peak area fNMn3+ between codoped and non-codoped samples allows to estimate the concentration of Mn2+ ions. For the 2+ 20 −3 x = 1.8% samples, this yields a Mn concentration of xMn2+ = 4 10 atoms cm , 2+ 19 × −3 while for the x = 0.5% a Mn concentration of x 2+ = 6 10 atoms cm is obtained. Mn × The fitting results are displayed in Tab. 4.3. The presence of Mn2+ has been confirmed 2+ by EPR. For the sample with xMn 0.5% a clear Mn signal, resolving both fine- and ≈ hyperfine structure can be observed at a temperature of 2K, yet for samples with higher Mn concentration the signal starts to broaden until it cannot be resolved any more. This broadening is attributed to Mn-Mn interaction, which can no longer be neglected at higher concentrations. Since the 3d4 configuration of Mn3+ is EPR silent[53], its direct observation is not possible with standard laboratory X-Band EPR spectrometers.

64 4.1 Control of the transition metal charge state

Table 4.3: Parameters of the damped Lorentzian model used to describe the intra-ion absorption of Mn3+ in GaN. The concentrations of Mn2+ are calculated using codoped reference codoped reference x x fN 3+ / fN 3+ . − Mn Mn

2 2+ 20 3 Label xMn (%) E0 (meV) fNMn3+ (meV ) Γ (meV) Mn (10 /cm ) (Ga,Mn)N 1.8 1415 13000 6.4 (Ga,Mn)N:Si 1.8 1414 5300 3.6 4 1 ± (Ga,Mn)N 0.53 1413 950 2.57 (Ga,Mn)N:Si 0.49 1415 490 3.0 0.6 0.1 ±

Wavelength (nm) Wavelength (nm) 950 925 900 875 850 950 925 900 875 850

0.8 0.2

0.6 0.15

0.1 0.4 Model Model (Ga,Mn)N (Ga,Mn)N

0.8 0.2

0.6 0.15 Reflectivity (relative units) Transmission (relative units) 0.1 0.4 Model Model (Ga,Mn)N:Si (Ga,Mn)N:Si 1.3 1.35 1.4 1.45 1.5 1.3 1.35 1.4 1.45 1.5 Energy (eV) Energy (eV)

Figure 4.4: Comparison of the optical absorption by the 3d internal transition of Mn3+ at 1.41 eV of (Ga,Mn)N (top panels) with (Ga,Mn)N:Si (bottom panels). Left panels: Transmission spectra for samples with xMn = 0.5%. Right panels: Reﬂectivity spectra for samples with xMn = 1.8%. Dashed line: Fitting result. The phonon replicas at higher energy than the main peak are neglected in the model. [27]

65 4 Donor and acceptor codoping of transition metal doped GaN

The near edge part of the x-ray absorption spectra indicates a change of the Mn charge state upon codoping as well, since in the codoped samples the energy of the Mn absorption edge is slightly shifted to lower values, while the energy of the pre-edge (localized Mn3+ states) peaks remains constant (cf 3.1). The only available model compounds are oxides, so quantification is not possible. It can nevertheless be deduced from the EXAFS part of the spectra, that only a minority of the Mn ions is in the 2+ state, since the measured Mn-N distance does not change significantly, although the ionic radius of Mn2+ is by 12% larger than for Mn3+. The change in charge state directly affects the magnetic properties of the samples. The measured magnetic anisotropy is lower than for non-codoped samples, due to the contribution of 3d5 Mn2+, and, surprisingly, in contrast to the observations for non- codoped samples, the magnetisation saturates slower than what would be expected for noninteracting Mn. This leads to the conclusion, that an antiferromagnetic coupling is established between Mn2+ ions.

4.2 Formation of complexes in (Ga,Mn)N:Mg

Since it has been shown that codoping with donors can reduce the charge state of Mn, and the band gap of GaN might be large enough to allow a stable Mn4+ configuration, the question has to be asked, whether acceptor codoping can realise this state. Indeed, by codoping GaN with Mn and Mg, control over the Mn charge state can be obtained, yet in a way that is fundamentally different from the case of codoping with donors. A series of samples with a different ratio between the Mn and Mg dopant concentrations has been grown at the growth conditions detailed in Chap. 2.1, and with Mn and Mg precursor flow rates varied between 150 and 450 sccm for Mn, and 75 to 490 sccm for Mg, yielding concentrations up to 1% for both ions. The dopant concentration has been measured by SIMS, which, as for all previous Mn doped films, shows a homogeneous distribution of both elements in the doped layser, with a narrow interface to the buffer layer, at which the concentrations drop by orders of magnitude. Another important result from SIMS is, that the presence of Mn hampers the incorporation of hydrogen1, which without Mn would be abundant in GaN:Mg. This lowering of the H concentration by 1-2 orders of magnitude allows to safely neglect its presence in codoped samples. The chemical composition has further been assessed by EDX, EELS and Raman spectroscopy. The structural analysis carried out by means of HR-XRD shows high crystallinity, and

1Hydrogen compensates Mg acceptors, and post-growth annealing is a must in order to obtain p-type material.

66 4.2 Formation of complexes in (Ga,Mn)N:Mg does not reveal the presence of secondary phases, confirmed by (HR)TEM. A targeted search for Mn with less then 4 3d electrons using magnetic resonance at various temperatures between 2 K and RT does not show any signals that couldn’t be traced back to magnetic contaminants in the sample substrate. Assuming that Mn4+ can be formed by transferring a hole from the acceptors to Mn, for an active acceptor concentration above the Mn concentration, it would be expected that holes are present in the valence band, and the samples should be conductive. Nevertheless, conductivity measurements reveal that samples with less than three times as much Mg2 as Mn are highly resistive. This leads to the conclusion, that the picture of isolated Mn and Mg impurities does not apply. To shed light on this situation, synchrotron XAS at the Mn K-edge has been measured in fluorescence mode at the BM08 beamline of the ESRF Grenoble. As in the non- codoped case, also in these samples Mn is incorporated as substitutional of Ga, with an experimental confidence of over 90%. In order to describe the observed spectra, a significant correlation between the position of Mn and Mg dopant ions in GaN has to be assumed. Simulated EXAFS spectra for various (relaxed) configurations, in which Mg is placed at the nearest Ga position from Mn, and several other possible scenarios including interstitial incorporation have been compared with the measured data. A modified reduced χ2 test has been employed to test models for their statistical usability (additional material of Ref. [31]). A standard EXAFS fitting procedure, which is starting with non-relaxed supercells, is then employed for the most probable model, which is found to be a pair of Mn and Mg, substituting for neighbouring Ga ions, which can describe all measured spectra reasonably well with only two fitting parameters changed between samples - the ratio between Mn and Mg concentration, and the distance between Mn and its surrounding N ions - while all other fitting parameters are chosen to be equal for all samples. The most notable result of this fitting procedure, the dependence of the Mg-Mn coordination number nMg as a function of the ratio of the Mg and Mn concentrations y = xMg/xMn, shows a linear dependence up to y = 3, where it saturates at a value of nMg = 3. A similar behaviour is obtained for the distance between Mn and the neighbouring N ions, which follows closely the values of the previously mentioned relaxed supercells. A sketch of the Mn-Mgx configuration is displayed in Fig. 4.5. To complement this structural information with chemical data, another technique that allows to assess the spin state of Mn has been employed, namely x-ray emission spectroscopy (XES), measured at ID26 of the ESRF. A first estimate of the Mn spin state 0 can be obtained by calculating the ratio between the Kβ1,3 and the Kβ emission line

2Which should be active since the hydrogen concentration is greatly lowered by the presence of Mn.

67 4 Donor and acceptor codoping of transition metal doped GaN

Figure 4.5: Illustration of the Mn-Mgx complexes as found by EXAFS. The energetically most favorable configurations are shown, based on DFT values. intensities, and the energy splitting between these transitions is proportional to the spin. Better accuracy on the change of the spin between samples can be obtained by inte- grating the difference of the normalised emission spectra, but quantitative information requires the comparison with simulated spectra or reference compounds [142]. In this case manganese oxides are used as reference, and comparison of the integrated absolute difference and linear extrapolation shows that the spin state as a function of y decreases from 2 down to 1, and saturates at y = 3, with a behaviour similar to the one found ≈ ≈ previously by EXAFS. The same change in the nominal spin value is obtained by ab-initio computations that allow also to calculate the magnetic moment distribution around the Mn ions. For non- codoped samples about 4.5µB are located on the Mn d shell, while 0.5µB are spread − around the neighbouring N ions. In codoped samples the magnetic moment distribution extends strongly to the N between Mn and Mg for complexes with one Mg ion, but localises back at Mn for complexes with two, and even more for those with three Mg ions. This means, that in principle the presence of single Mg neighbours could help mediating the magnetic interaction between Mn ions, yet this possibility is hindered if multiple Mg are close to Mn. Another finding is that the bond between Mn and N is shorter if Mg is bound to the same N ion. This shortening of the bond induces a uniaxial contribution to the crystal field, which is much stronger than the trigonal distortion along the wurtzite c-direction. Furthermore, the formation energy of a Mg-N bond does not vary much for the four N ions next to Mn, and the minor difference is definitely not noticeable at growth temperature, leading to a random distribution of the uniaxial crystal field along the Mn-N bond directions. These findings from ab-initio calculations match well with the observations from SQUID, where the anisotropy is reduced with increasing y, closely following the probability that

68 4.2 Formation of complexes in (Ga,Mn)N:Mg

Table 4.4: Shortening of the Mn-N bond in the presence of Mg. Values are taken from Ref. [31]. The bonds are labelled d1 to d4, where d1 is along the c-direction, and this is also the bond, at which the ﬁrst Mg atom is placed. Directly below the ﬁrst Mg atom is bond d2. The second Mg is added at d4, and the third at d3. These are, for each Mg, the lowest energy positions.

d1 [Å] d2 [Å] d3 [Å] d4 [Å] Mn 2.05 2.04 2.04 2.04 Mn-Mg 1.91 1.98 2.0 2.02 Mn-Mg2 1.84 1.87 1.92 1.84 Mn-Mg3 1.84 1.89 1.84 1.82

no Mg is bound to a Mn ion, which is given by (1 y/3)3. − The aforementioned dependence of the spatial distribution of the magnetic moment on the number of Mg ions next to Mn has consequences on the selection rules for optical transitions. For high values of y a pronounced optical emission can be observed in the infrared, with its strongest peak at 1.05 eV and several side peaks (cf. Fig. 4.6). Since ≈ all the peaks in this spectral range are related, it is likely that the same transition is observed here, for multiple sites (various possible plaements of Mg) and with phonon replicas. The integrated intensity of the luminescence as a function of the Mg/Mn ratio follows the lineshape of the probability to find three Mg ions next to Mn, which is given by 3 P3 (y) = (y/3) . This, combined with the previous data on the magnetic moment/spin indicates, that Mn5+, stabilised by the presence of the Mg ions in the first coordination shell around it, is likely the origin of the luminescence, which has previously been attributed to Mn4+ by others [95, 89, 87]. While for Mn3+ the intra-ion transition, as described in Chap. 3.1, is tricky to observe in PL, the luminescence of samples with y 3 ≥ is easily excited, strong and persists up to RT. This puzzling finding can be explained by the localisation of the spin on the Mn ions, that is more pronounced for y = 3 than for y = 0. This leads to an increase in the Huang-Rhys factor [143, 144], making it significantly easier to excite the luminescence through the phonon side peaks. The magnetic field dependence of the luminescence has been measured at 2 K, and the two peaks at 1.043 and 1.046 eV have been fitted with Lorentzians, in order to analyse the Zeeman splitting and to identify the energy levels that are involved. Upon application of a magnetic field, both peaks split in three subpeaks, and the splitting is slightly asymmetric for strong fields ( 10 T). A comparison with other elements of a 3d2 configuration in ≈

69 4 Donor and acceptor codoping of transition metal doped GaN

Figure 4.6: Photoluminescence of the samples codoped with Mn and Mg. [31]. (a) Lu- minescence as function of Mg/Mn ratio y. (c) PL of the sample with y = 4.1 as function of temperature. (b) Integrated intensity of the luminescence as a function of y and (d) temperature. In (b) the (scaled) probabilities to ﬁnd a certain number of Mg next to Mn are plotted as lines. Inset of (d): Energy levels involved in the transition and states nearby.

70 4.2 Formation of complexes in (Ga,Mn)N:Mg

GaN and AlN [145, 146] yields to the assignment of the ground state of this transition to 3 an A2 state with g-factor of ggr 2, as also expected from the Tanabe-Sugano diagram ≈ [53]. From the Tanabe-Sugano diagram two conﬁgurations would be possible for the 1 3 excited state of the transition: The E doublet or the T2 triplet. The slight asymmetry of the observed splitting hints towards 1E [145]. Our data can be ﬁtted well with ground state splitting parameters ggr = 2.01 0.08, D = 0.31 0.05 meV and an excited state ± ± splitting with gexc = 0.26 0.15. When comparing with values for Ti, the g-factors are ± very similar [145]. Our value of the D matrix is larger, and this fact can be explained by the local distortion around the Mn site caused by the Mg ions. According to Ref.

[147] the non-tetrahedral configuration of the crystal field in MnMg3 complexes can lead 3 1 to a significant admixture of T1 states to E, what shortens the lifetime of the excited states. This luminescence spans the important telecommunication wavelengths between 1550 and 1330 nm. For this reason, laser applications are a thrilling technological prospect [31, 33]. Preliminary measurements have been performed to search for amplified spontaneous emission, and Bragg reflectors based on the GaN/AlGaN material system suitable for wavelengths around 1240 nm are currently being developed.

5 Synopsis and outlook

The magnetic and optical properties of GaN doped with Fe or Mn, and codoped with Mg acceptors and Si donors have been studied using EPR, FMR, PL, reflectivity, synchrotron XAS, and complementary measurement techniques, including but not limited to synchrotron and laboratory XRD, TEM, STEM, SIMS, SQUID magnetometry, synchrotron x-ray fluorescence, AFM, EELS. In the case of (Ga,Mn)N it has been found that the samples are dilute for all studied concentrations (up to 3% Mn cation concentration), and that Mn is predominantly in the 3+ valence state, which is very likely composed of a half filled 3d shell and a weakly bound hole whose wave function is spread over the surrounding N atoms. The high electric resistance, combined with the magnetic field and doping concentration dependence of the excitons hints towards a strong coupling between valence band holes and Mn 3d electrons. The bound hole state formed by this strong coupling hampers carrier mediated ferromagnetism, fitting well with the observation that the dominant magnetic interaction between Mn dopants is ferromagnetic superexchange, leading to Curie temperatures around 1 K for the Mn concentrations considered here, far below the predictions for carrier mediated magnetism, but also below values predicted by local density approximation based first principles calculations. When codoping with Si donors, the extra electrons supplied are found to be transferred to Mn, reducing the charge state to 2+, and magnetometry points to an antiferromagnetic interactions between Mn2+ ions. Codoping with Mn and Mg has been found to lead to an entireley different phenomenon, namely the formation of Mn-Mgx complexes with 1 x 3, where the Mg ≤ ≤ ions substitute for Ga positions right next to Mn. These complexes allow the stabilisa- tion of formal Mn valence states up to 5+ depending on the Mg/Mn ratio, and corre- spondingly also the spin state can be tuned. Furthermore, these complexes are found to enhance the Mn5+ internal near infrared PL by opening new excitation channels, making this material system an interesting candidate for optoelectronic functionalities in the telecommunications optical region. In Fe doped GaN on the other hand secondary phases are formed already at Fe cation

73 5 Synopsis and outlook concentrations as low as 0.4%, for conditions similar to those used to grow the dilute Mn doped samples. These secondary phases take the form of embedded NCs and have the tendency to arrange in planar arrays of NCs having a narrow size distribution, suggesting that the NC growth is a surface dominated process. The crystallographic phase and chemical composition of these NCs, and along with these also their magnetic properties can be tuned by controlling the growth conditions. Single layers of such NCs with a well defined phase can be produced at will by varying the doping profile. The magnetic anisotropy of such a planar array has been studied extensively, and while the uniaxial out-of-plane anisotropy is expected from the NC shape, surprisingly a hexagonal in- plane anisotropy is found for cubic GaxFe4−xN NCs, and several possible models have been proposed and compared to the observations. The most plausible explanation is that the measured hexagonal in-plane anisotropy is caused by the cubic crystal anisotropy of a minority of NCs which are oriented with their [111] direction along the [0001] direction of the host. Codoping with Si and Fe promotes the incorporation of dilute Fe in GaN by reducing the Fe charge state, and affecting the Coulomb interaction between Fe ions. In GaN, homogeneously codoped with Fe and Mg (i.e. (Ga,Fe)N:Mg) the dopants have been found to compete for incorporation, while in the case of digital Mg doping (i.e. (Ga,Fe)N:δMg) the overall Fe concentration and the variety of secondary phases gets enhanced. By comparing with first principles calculatiions, this effect of digital Mg codoping can be explained if the Fe incorporation is a bulk process. Currently the work on Mn doped GaN is going into several directions. One is the fabrication of spin-based devices, e.g. spin filters, by combining non-magnetic GaN with (Ga,Mn)N. As part of this effort, the spin-orbit coupling and localisation effects in GaN are under investigation [148]. Moreover, currently the polarity of GaN and AlGaN is exploited in order to promote carrier-mediated ferromagnetism at the interface with a highly Mn-doped GaN:Mn layer. Another idea is to utilise the magnetic field dependence of the near band gap optical properties for optics devices. The infrared PL signal of (Ga,Mn)N:Mg is under heavy investigation, and right now Bragg mirror structures based on AlxGa1−xN/GaN are being developed.

For Fe doped GaN, the next step is to combine samples with layers of Fe4N NCs with spin detectors (e.g. platinum electrodes) in order to measure spin pumping eﬀects by FMR of the crystals. Thinking further, with the knowledge of the magnetic anisotropy and preliminary data on the fabrication of elongated NCs in mind, magnetic storage applications can be envisioned. Electrical addressing of groups or individual NCs for electric charge storage is currently under consideration.

74 Acknowledgements

The research on which this thesis is based is a collaborative effort with many people involved. The contributions cannot be separated easily, and without the context of complementary data most of the measurements presented are without much informa- tive power. Therefore I would like to thank my coworkers here in Linz: Rajdeep Ad- hikari, Giulia Capuzzo, Thibaut Devillers, Bogdan Faina, Douglas Leite, Tian Li, Andrea Navarro-Quezada, Aitana Tarazaga Martín-Luengo, Mauro Rovezzi, Wolfgang Schlögel- hofer, David Auinger and Thomas Winkler, who were responsible for growing the samples and analysing the sample crystal and surface quality using XRD, TEM, Raman spectroscopy, AFM and several other techniques. My gratitude goes to the head of our research group, Alberta Bonanni, who is also the supervisor of this thesis, for standing up to the challenge of managing the contributions of everyone involved, putting together the jigsaw pieces of this research work to form a coherent picture, and for her continuous support during the creation of this thesis. Further thanks goes towards the coworkers from other institutions involved in the creation of this work. The persons I had the honor of working with personally were Jan Suffczynski, with whom the magnetic field dependent optical measurements were performed, and Nevill Gonzalez Szwacki, who tought me the basics of density funcional theory modelling, both from the University of Warsaw. A lot of my understanding of the theories behind DMS I learned while discussing with Dariusz Sztenkiel and Tomasz Dietl, both from IFPAN at the Polish Academy of Sciences, Warsaw. At the synchrotrons I would have been completely lost without the more experienced users that I spent the beamtimes with, Mauro Rovezzi at the ESRF and Christoph Cobet at BESSY, from whom I also learned how to interpret the acquired data. In addition to the list of people I directly worked with, there are many coworkers with whom I didn’t perform experiments together, but whose contribution to this work cannot be valued. The SQUID measurements were performed by Maciej Sawickis group at IFPAN, the SIMS measurements have been contributed by Rafał Jakieła, also from IFPAN. For their invaluable input given in discussions about physics during coffee breaks, I’d like to thank my colleagues Markus Humer and Lukas Nausner.

75 Acknowledgements

Last, but not least, I’d like to thank my parents, Rosa and Karl, for their love and support during my whole life, for teaching me many things about nature and for making it possible for me to study physics. Their help allowed me to become the person I am now. I cannot express how grateful I am to my love, Katharina, who enriches my life simply by being herself. I would not be complete without her.

76 Bibliography

[1] M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroﬀ, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas, “Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices,” Phys. Rev. Lett., vol. 61, pp. 2472–2475, Nov 1988. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevLett.61. 2472 [2] G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn, “Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange,” Phys. Rev. B, vol. 39, no. 7, pp. 4828–4830, Mar 1989. [Online]. Available: http://dx.doi.org/10.1103/PhysRevB.39.4828 [3] J. K. Spong, V. S. Speriosu, R. E. Fontana, M. M. Dovek, and T. L. Hylton, “Giant magnetoresistive spin valve bridge sensor,” Magnetics, IEEE Transactions on, vol. 32, no. 2, pp. 366–371, Mar 1996. [Online]. Available: http://dx.doi.org/10.1109/20.486520 [4] J. T. Vallin, G. A. Slack, S. Roberts, and A. E. Hughes, “Infrared Absorption in some II-VI compounds doped with Cr,” Phys. Rev. B, vol. 2, p. 4313, 1970. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.2.4313 [5] J. K. Furdyna, “Diluted magnetic semiconductors,” Journal of Applied Physics, vol. 64, no. 4, pp. R29–R64, 1988. [Online]. Available: http: //scitation.aip.org/content/aip/journal/jap/64/4/10.1063/1.341700 [6] T. Story, R. R. Gała¸zka, R. B. Frankel, and P. A. Wolﬀ, “Carrier-concentration- induced ferromagnetism in PbSnMnTe,” Phys. Rev. Lett., vol. 56, pp. 777–779, Feb 1986. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevLett.56.777 [7] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, and D. Ferrand, “Zener model description of ferromagnetism in zinc-blende magnetic semiconductors,” Science, vol. 287, no. 5455, pp. 1019–1022, 2000. [Online]. Available: http://www.sciencemag.org/cgi/content/abstract/287/5455/1019 [8] M. Wang, R. P. Campion, A. W. Rushforth, K. W. Edmonds, C. T. Foxon, and B. L. Gallagher, “Achieving high curie temperature in (Ga,Mn)As,” Applied Physics Letters, vol. 93, no. 13, p. 132103, 2008. [Online]. Available: http://link.aip.org/link/?APL/93/132103/1 [9] H. Ohno, “Making nonmagnetic semiconductors ferromagnetic,” Science, vol. 281, no. 5379, pp. 951–956, 1998. [Online]. Available: http://www.sciencemag.org/ content/281/5379/951.abstract

77 Bibliography

[10] K. Olejník, M. H. S. Owen, V. Novák, J. Mašek, A. C. Irvine, J. Wunderlich, and T. Jungwirth, “Enhanced annealing, high curie temperature, and low-voltage gating in (Ga,Mn)As: A surface oxide control study,” Phys. Rev. B, vol. 78, no. 5, p. 054403, Aug 2008. [Online]. Available: http: //dx.doi.org/10.1103/PhysRevB.78.054403

[11] R. P. Vaudo, X. Xu, and G. R. Brandes, “Semi-insulating GaN and method of making the same,” United States of America Patent 7,170,095, January 30, 2007. [Online]. Available: http://www.lens.org/lens/patent/US_7170095_B2

[12] G. T. Thaler, M. E. Overberg, B. Gila, R. Frazier, C. R. Abernathy, S. J. Pearton, J. S. Lee, S. Y. Lee, Y. D. Park, Z. G. Khim, J. Kim, and F. Ren, “Magnetic properties of n-GaMnN thin ﬁlms,” Applied Physics Letters, vol. 80, no. 21, pp. 3964–3966, 2002. [Online]. Available: http://scitation.aip.org/content/aip/journal/apl/80/21/10.1063/1.1481533

[13] M. Park, K. Huh, J. Myoung, J. Lee, J. Chang, K. Lee, S. Han, and W. Lee, “Room temperature ferromagnetic (Ga,Mn)N epitaxial ﬁlms with low Mn concentration grown by plasma-enhanced molecular beam epitaxy,” Solid State Communications, vol. 124, no. 1-2, pp. 11–14, 2002. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0038109802004714

[14] K. H. Kim, K. J. Lee, D. J. Kim, H. J. Kim, Y. E. Ihm, D. Djayaprawira, M. Takahashi, C. S. Kim, C. G. Kim, and S. H. Yoo, “Magnetotransport of p-type GaMnN assisted by highly conductive precipitates,” Applied Physics Letters, vol. 82, no. 11, pp. 1775–1777, 2003. [Online]. Available: http://scitation.aip.org/content/aip/journal/apl/82/11/10.1063/1.1561580

[15] S. Sonoda, S. Shimizu, T. Sasaki, Y. Yamamoto, and H. Hori, “Molecular beam epitaxy of wurtzite (Ga,Mn)N ﬁlms on sapphire (0001) showing the ferromagnetic behaviour at room temperature,” Journal of Crystal Growth, vol. 237-239, Part 2, no. 0, pp. 1358–1362, 2002. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0022024801021832

[16] E. Sarigiannidou, F. Wilhelm, E. Monroy, R. M. Galera, E. Bellet-Amalric, A. Rogalev, J. Goulon, J. Cibert, and H. Mariette, “Intrinsic ferromagnetism in wurtzite (Ga,Mn)N semiconductor,” Phys. Rev. B, vol. 74, no. 4, p. 041306, Jul 2006. [Online]. Available: http://dx.doi.org/10.1103/PhysRevB.74.041306

[17] M. L. Reed, N. A. El-Masry, H. H. Stadelmaier, M. K. Ritums, M. J. Reed, C. A. Parker, J. C. Roberts, and S. M. Bedair, “Room temperature ferromagnetic properties of (Ga,Mn)N,” Applied Physics Letters, vol. 79, no. 21, pp. 3473–3475, 2001. [Online]. Available: http://scitation.aip.org/content/aip/journal/apl/79/21/ 10.1063/1.1419231

[18] N. Theodoropoulou, A. F. Hebard, M. E. Overberg, C. R. Abernathy, S. J. Pearton, S. N. G. Chu, and R. G. Wilson, “Magnetic and structural properties

78 of Mn-implanted GaN,” Applied Physics Letters, vol. 78, no. 22, pp. 3475–3477, 2001. [Online]. Available: http://scitation.aip.org/content/aip/journal/apl/78/22/ 10.1063/1.1376659

[19] J. I. Hwang, M. Kobayashi, G. S. Song, A. Fujimori, A. Tanaka, Z. S. Yang, H. J. Lin, D. J. Huang, C. T. Chen, H. C. Jeon, and T. W. Kang, “X-ray magnetic circular dichroism characterization of GaN/Ga1−xMnxN digital ferromagnetic heterostructure,” Applied Physics Letters, vol. 91, no. 7, p. 072507, 2007. [Online]. Available: http: //scitation.aip.org/content/aip/journal/apl/91/7/10.1063/1.2769944

[20] Y. Shon, Y. H. Kwon, Y. S. Park, S. U. Yuldashev, S. J. Lee, C. S. Park, K. J. Chung, S. J. Yoon, H. J. Kim, W. C. Lee, D. J. Fu, T. W. Kang, X. J. Fan, Y. J. Park, and H. T. Oh, “Ferromagnetic behavior of p-type GaN epilayer implanted with Fe+ ions,” Journal of Applied Physics, vol. 95, no. 2, pp. 761–763, 2004. [Online]. Available: http://scitation.aip.org/content/aip/journal/jap/95/2/10.1063/1.1630364

[21] S. Granville, B. J. Ruck, F. Budde, H. J. Trodahl, and G. V. M. Williams, “Nearest-neighbor Mn antiferromagnetic exchange in Ga1−xMnxN,” Phys. Rev. B, vol. 81, p. 184425, May 2010. [Online]. Available: http: //link.aps.org/doi/10.1103/PhysRevB.81.184425

[22] M. Zając, J. Gosk, M. Kamińska, A. Twardowski, T. Szyszko, and S. Podsiadło, “Paramagnetism and antiferromagnetic d-d coupling in GaMnN magnetic semiconductor,” Applied Physics Letters, vol. 79, no. 15, pp. 2432–2434, 2001. [Online]. Available: http://scitation.aip.org/content/aip/journal/apl/79/15/10. 1063/1.1406558

[23] A. Bonanni, “Ferromagnetic nitride-based semiconductors doped with transition metals and rare earths,” Semiconductor Science and Technology, vol. 22, no. 9, pp. R41–R56, 2007. [Online]. Available: http://stacks.iop.org/0268-1242/22/R41

[24] K. W. Edmonds, S. V. Novikov, M. Sawicki, R. P. Campion, C. R. Staddon, A. D. Giddings, L. X. Zhao, K. Y. Wang, T. Dietl, C. T. Foxon, and B. L. Gallagher, “p-type conductivity in cubic (Ga,Mn)N thin ﬁlms,” Applied Physics Letters, vol. 86, no. 15, p. 152114, 2005. [Online]. Available: http://scitation.aip.org/content/aip/journal/apl/86/15/10.1063/1.1900924

[25] K. Sato, L. Bergqvist, J. Kudrnovský, P. H. Dederichs, O. Eriksson, I. Turek, B. Sanyal, G. Bouzerar, H. Katayama-Yoshida, V. A. Dinh, T. Fukushima, H. Kizaki, and R. Zeller, “First-principles theory of dilute magnetic semiconductors,” Rev. Mod. Phys., vol. 82, pp. 1633–1690, May 2010. [Online]. Available: http://link.aps.org/doi/10.1103/RevModPhys.82.1633

79 Bibliography

[26] T. Dietl, “Hole states in wide band-gap diluted magnetic semiconductors and oxides,” Phys. Rev. B, vol. 77, no. 8, p. 085208, Feb 2008. [Online]. Available: http://dx.doi.org/10.1103/PhysRevB.77.085208

[27] A. Bonanni, M. Sawicki, T. Devillers, W. Stefanowicz, B. Faina, T. Li, T. E. Winkler, D. Sztenkiel, A. Navarro-Quezada, M. Rovezzi, R. Jakieła, A. Grois, M. Wegscheider, W. Jantsch, J. Suﬀczyński, F. D’Acapito, A. Meingast, G. Kothleitner, and T. Dietl, “Experimental probing of exchange interactions between localized spins in the dilute magnetic insulator (Ga,Mn)N,” Phys. Rev. B, vol. 84, p. 035206, Jul 2011. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.84.035206

[28] A. Navarro-Quezada, N. Gonzalez Szwacki, W. Stefanowicz, T. Li, A. Grois, T. Devillers, M. Rovezzi, R. Jakieła, B. Faina, J. A. Majewski, M. Sawicki, T. Dietl, and A. Bonanni, “Fe-Mg interplay and the eﬀect of deposition mode in (Ga,Fe)N doped with Mg,” Phys. Rev. B, vol. 84, p. 155321, Oct 2011. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.84.155321

[29] J. Suﬀczyński, A. Grois, W. Pacuski, A. Golnik, J. A. Gaj, A. Navarro- Quezada, B. Faina, T. Devillers, and A. Bonanni, “Eﬀects of s,p-d and s-p exchange interactions probed by exciton magnetospectroscopy in (Ga,Mn)N,” Phys. Rev. B, vol. 83, no. 9, p. 094421, Mar 2011. [Online]. Available: http://dx.doi.org/10.1103/PhysRevB.83.094421

[30] M. Sawicki, T. Devillers, S. Gałęski, C. Simserides, S. Dobkowska, B. Faina, A. Grois, A. Navarro-Quezada, K. N. Trohidou, J. A. Majewski, T. Dietl, and A. Bonanni, “Origin of low-temperature magnetic ordering in Ga1−xMnxN,” Phys. Rev. B, vol. 85, p. 205204, May 2012. [Online]. Available: http: //link.aps.org/doi/10.1103/PhysRevB.85.205204

[31] T. Devillers, M. Rovezzi, N. G. Szwacki, S. Dobkowska, W. Stefanowicz, D. Sztenkiel, A. Grois, J. Suﬀczyński, A. Navarro-Quezada, B. Faina, T. Li, P. Glatzel, F. d’Acapito, R. Jakieła, M. Sawicki, J. A. Majewski, T. Dietl, and A. Bonanni, “Manipulating Mn-Mgk cation complexes to control the charge- and spin-state of Mn in GaN,” Sci. Rep., vol. 2, p. 722, Oct. 2012. [Online]. Available: http://dx.doi.org/10.1038/srep00722

[32] A. Grois, T. Devillers, T. Li, and A. Bonanni, “Planar array of self- assembled GaxFe4−xN nanocrystals in GaN: magnetic anisotropy determined via ferromagnetic resonance,” Nanotechnology, vol. 25, no. 39, p. 395704, 2014. [Online]. Available: http://stacks.iop.org/0957-4484/25/i=39/a=395704

[33] A. Bonanni, A. Grois, T. Devillers, T. Dietl, and J. Suﬀczyński, “Semiconductor laser,” Austrian Patent AT512 938, 2012.

80 [34] I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” Journal of Applied Physics, vol. 94, no. 6, pp. 3675–3696, 2003. [Online]. Available: http://dx.doi.org/10.1063/1.1600519

[35] H. Morkoç, Handbook of Nitride Semiconductors and Devices, Volume 1: Materials Properties, Physics and Growth. WILEY-VCH Verlag GmbH & Co. KGaA, 2008.

[36] K. Itoh, T. Kawamoto, H. Amano, K. Hiramatsu, and I. Akasaki, “Metalorganic vapor phase epitaxial growth and properties of GaN/Al0.1Ga0.9N layered structures,” Japanese Journal of Applied Physics, vol. 30, no. 9R, p. 1924, 1991. [Online]. Available: http://stacks.iop.org/1347-4065/30/i=9R/a=1924

[37] H. Amano, N. Sawaki, I. Akasaki, and Y. Toyoda, “Metalorganic vapor phase epitaxial growth of a high quality GaN ﬁlm using an AlN buﬀer layer,” Applied Physics Letters, vol. 48, no. 5, pp. 353–355, 1986. [Online]. Available: http://scitation.aip.org/content/aip/journal/apl/48/5/10.1063/1.96549

[38] S. Nakamura, T. Mukai, and M. Senoh, “Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes,” Applied Physics Letters, vol. 64, no. 13, pp. 1687–1689, 1994. [Online]. Available: http: //scitation.aip.org/content/aip/journal/apl/64/13/10.1063/1.111832

[39] T. Paskova, V. Darakchieva, P. Paskov, U. Södervall, and B. Monemar, “Growth and separation related properties of HVPE-GaN free-standing ﬁlms,” Journal of Crystal Growth, vol. 246, no. 3 - 4, pp. 207 – 214, 2002. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0022024802017438

[40] S. S. Park, I.-W. Park, and S. H. Choh, “Free-standing GaN substrates by hydride vapor phase epitaxy,” Japanese Journal of Applied Physics, vol. 39, no. Part 2, No. 11B, pp. L1141–L1142, 2000. [Online]. Available: http://jjap.jsap.jp/link?JJAP/39/L1141/

[41] I. Grzegory, M. Boćkowski, B. Łucznik, S. Krukowski, Z. Romanowski, M. Wróblewski, and S. Porowski, “Mechanisms of crystallization of bulk GaN from the solution under high N2 pressure,” Journal of Crystal Growth, vol. 246, no. 3-4, pp. 177–186, 2002. [Online]. Available: http: //www.sciencedirect.com/science/article/pii/S0022024802017402

[42] T. Hashimoto, F. Wu, J. S. Speck, and S. Nakamura, “A GaN bulk crystal with improved structural quality grown by the ammonothermal method,” Nat Mater, vol. 6, no. 8, pp. 568–571, Aug. 2007. [Online]. Available: http://dx.doi.org/10.1038/nmat1955

[43] C. Rawn and J. Chaudhuri, “Lattice parameters of gallium nitride at high temperatures and resulting epitaxial misﬁts with alumina and silicon carbide substrates,” Advances in X-ray analysis, vol. 43, pp. 338–343, 2000. [Online]. Available: http://www.icdd.com/resources/axabrowse/axa_vol43.htm

81 Bibliography

[44] R. St¸epniewski, M. Potemski, A. Wysmołek, K. Pakuła, J. M. Baranowski, J. Łusakowski, I. Grzegory, S. Porowski, G. Martinez, and P. Wyder, “Symmetry of excitons in GaN,” Phys. Rev. B, vol. 60, pp. 4438–4441, Aug 1999. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.60.4438

[45] W. J. Fan, M. F. Li, T. C. Chong, and J. B. Xia, “Electronic properties of zincblende GaN, AlN, and their alloys Ga1−xAlxN,” Journal of Applied Physics, vol. 79, no. 1, pp. 188–194, 1996. [Online]. Available: http://scitation.aip.org/content/aip/journal/jap/79/1/10.1063/1.360930

[46] M. Leszczynski, H. Teisseyre, T. Suski, I. Grzegory, M. Bockowski, J. Jun, S. Porowski, K. Pakula, J. M. Baranowski, C. T. Foxon, and T. S. Cheng, “Lattice parameters of gallium nitride,” Applied Physics Letters, vol. 69, no. 1, pp. 73–75, 1996. [Online]. Available: http: //scitation.aip.org/content/aip/journal/apl/69/1/10.1063/1.118123

[47] S. Rumyantsev, M. S. Shur, and M. Levinshtein, Handbook series on semiconductor parameters. Singapore: World Scientiﬁc, 1996.

[48] D. Fritsch, H. Schmidt, and M. Grundmann, “Band-structure pseudopotential calculation of zinc-blende and wurtzite AlN, GaN, and InN,” Phys. Rev. B, vol. 67, p. 235205, Jun 2003. [Online]. Available: http://link.aps.org/doi/10.1103/ PhysRevB.67.235205

[49] M. J. Paisley, Z. Sitar, J. B. Posthill, and R. F. Davis, “Growth of cubic phase gallium nitride by modiﬁed molecular-beam epitaxy,” Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, vol. 7, no. 3, pp. 701–705, 1989. [Online]. Available: http://link.aip.org/link/?JVA/7/701/1

[50] B. Faina, “The correlation between growth parameters, structural and magnetic properties in dilute (Ga,Mn)N.” Ph.D. dissertation, Johannes Kepler Universität Linz, May 2011.

[51] A. Navarro-Quezada, “Control of transition metal ion aggregation in (Ga,Fe)n,” Ph.D. dissertation, Johannes Kepler Universität Linz, 2009.

[52] N. Bohr, “Studier over metallernes elektrontheori,” Ph.D. dissertation, Københavns Universitet, 1911.

[53] A. Abragam and B. Bleaney, Electron paramagnetic resonance of transition ions, ser. International Series of Monographs on Physics, W. Marshall and D. H. Wilkin- son, Eds. Clarendon Press, 1970.

[54] J. Smit and H. Beljers, “Ferromagnetic resonance absorption in BaFe12O19, a highly anisotropic crystal,” Philips Research Reports, vol. 10, pp. 113–130, 1955.

[55] L. Baselgia, M. Warden, F. Waldner, S. L. Hutton, J. E. Drumheller, Y. Q. He, P. E. Wigen, and M. Maryško, “Derivation of the resonance frequency from the

82 free energy of ferromagnets,” Phys. Rev. B, vol. 38, pp. 2237–2242, Aug 1988. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.38.2237

[56] X. H. Huang and M. Pardavi-Horvath, “Local demagnetizing tensor calculation for arbitrary non-ellipsoidal bodies,” Magnetics, IEEE Transactions on, vol. 32, no. 5, pp. 4180–4182, Sep 1996. [Online]. Available: http://dx.doi.org/10.1109/20.539330

[57] A. F. Kip and R. D. Arnold, “Ferromagnetic resonance at microwave frequencies in an iron single crystal,” Phys. Rev., vol. 75, pp. 1556–1560, May 1949. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRev.75.1556

[58] S. Misra, C. Poole, and H. Farach, “A review of spin Hamiltonian forms for various point-group site symmetries,” Applied Magnetic Resonance, vol. 11, pp. 29–46, 1996, 10.1007/BF03163526. [Online]. Available: http: //dx.doi.org/10.1007/BF03163526

[59] C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics. Wiley- Interscience, 1977.

[60] J. A. Weil and J. R. Bolton, Electron Paramagnetic Resonance; Elementary Theory and Practical Applications, 2nd ed. Wiley-Interscience, 2006.

[61] A. Bonanni, M. Kiecana, C. Simbrunner, T. Li, M. Sawicki, M. Wegscheider, M. Quast, H. Przybylińska, A. Navarro-Quezada, R. Jakieła, A. Wołoś, W. Jantsch, and T. Dietl, “Paramagnetic GaN:Fe and ferromagnetic (Ga,Fe)N : The relationship between structural, electronic, and magnetic properties,” Phys. Rev. B, vol. 75, no. 12, p. 125210, Mar 2007. [Online]. Available: http://dx.doi.org/10.1103/PhysRevB.75.125210

[62] H. A. Jahn and E. Teller, “Stability of polyatomic molecules in degenerate electronic states. i. orbital degeneracy,” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 161, no. 905, pp. 220–235, 1937. [Online]. Available: http://www.jstor.org/stable/96911

[63] J. T. Vallin and G. D. Watkins, “EPR of Cr2+ in II-VI lattices,” Phys. Rev. B, vol. 9, p. 2051, 1974. [Online]. Available: http://link.aps.org/doi/10.1103/ PhysRevB.9.2051

[64] A. Wołoś, A. Wysmolek, M. Kaminska, A. Twardowski, M. Bockowski, I. Grzegory, S. Porowski, and M. Potemski, “Neutral Mn acceptor in bulk GaN in high magnetic ﬁelds,” Phys. Rev. B, vol. 70, no. 24, p. 245202, Dec 2004. [Online]. Available: http://dx.doi.org/10.1103/PhysRevB.70.245202

[65] B. Monemar, P. P. Paskov, J. P. Bergman, A. A. Toropov, T. V. Shubina, T. Malinauskas, and A. Usui, “Recombination of free and bound excitons in GaN,” physica status solidi (b), vol. 245, no. 9, pp. 1723–1740, 2008. [Online]. Available: http://dx.doi.org/10.1002/pssb.200844059

83 Bibliography

[66] K. Korona, J. Kuhl, J. Baranowski, and S. Porowski, “Excitonic thermalization and recombination in homoepitaxial gallium nitride,” physica status solidi (b), vol. 216, no. 1, pp. 85–89, 1999. [Online]. Available: http://dx.doi.org/10.1002/(SICI) 1521-3951(199911)216:1<85::AID-PSSB85>3.0.CO;2-T

[67] D. Chtchekine, G. Gilliland, Z. Feng, S. Chua, D. Wolford, S. Ralph, M. Schurman, and I. Ferguson, “Temperature dependence of bound exciton emissions in GaN,” MRS Internet J. Nitride Semicond. Res., vol. 4S1, p. G6.47, 1999. [Online]. Available: http://nsr.mij.mrs.org/4S1/G6.47/

[68] S. Marcet, D. Ferrand, D. Halley, S. Kuroda, H. Mariette, E. Gheeraert, F. J. Teran, M. L. Sadowski, R. M. Galera, and J. Cibert, “Magneto-optical spectroscopy of (Ga,Mn)N epilayers,” Phys. Rev. B, vol. 74, no. 12, p. 125201, Sep 2006. [Online]. Available: http://dx.doi.org/10.1103/PhysRevB.74.125201

[69] W. Pacuski, P. Kossacki, D. Ferrand, A. Golnik, J. Cibert, M. Wegscheider, A. Navarro-Quezada, A. Bonanni, M. Kiecana, M. Sawicki, and T. Dietl, “Observation of strong-coupling eﬀects in a diluted magnetic semiconductor Ga1−xFexN,” Phys. Rev. Lett., vol. 100, no. 3, p. 037204, Jan 2008. [Online]. Available: http://dx.doi.org/10.1103/PhysRevLett.100.037204

[70] W. Pacuski, D. Ferrand, J. Cibert, J. A. Gaj, A. Golnik, P. Kossacki, S. Marcet, E. Sarigiannidou, and H. Mariette, “Excitonic giant zeeman eﬀect in GaN:Mn3+,” Phys. Rev. B, vol. 76, p. 165304, Oct 2007. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.76.165304

[71] M. Julier, J. Campo, B. Gil, J. P. Lascaray, and S. Nakamura, “Determination of the spin-exchange interaction constant in wurtzite GaN,” Phys. Rev. B, vol. 57, pp. R6791–R6794, Mar 1998. [Online]. Available: http://link.aps.org/doi/10.1103/ PhysRevB.57.R6791

[72] R. St¸epniewski, K. P. Korona, A. Wysmołek, J. M. Baranowski, K. Pakuła, M. Potemski, G. Martinez, I. Grzegory, and S. Porowski, “Polariton eﬀects in reﬂectance and emission spectra of homoepitaxial GaN,” Phys. Rev. B, vol. 56, pp. 15 151–15 156, Dec 1997. [Online]. Available: http: //link.aps.org/doi/10.1103/PhysRevB.56.15151

[73] B. Gil, O. Briot, and R.-L. Aulombard, “Valence-band physics and the optical properties of GaN epilayers grown onto sapphire with wurtzite symmetry,” Phys. Rev. B, vol. 52, no. 24, pp. R17 028–R17 031, Dec 1995. [Online]. Available: http://dx.doi.org/10.1103/PhysRevB.52.R17028

[74] J. M. Luttinger, “Quantum theory of cyclotron resonance in semiconductors: General theory,” Phys. Rev., vol. 102, pp. 1030–1041, May 1956. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRev.102.1030

84 [75] E. F. Schubert and W. T. Tsang, “Photoluminescence line shape of excitons in alloy semiconductors,” Phys. Rev. B, vol. 34, no. 4, pp. 2991–2994, Aug 1986. [Online]. Available: http://dx.doi.org/10.1103/PhysRevB.34.2991

[76] A. Djurišić, Y. Chan, and E. Li, “Novel model for the optical function of GaN,” Applied Physics A: Materials Science & Processing, vol. 74, no. 5, pp. 669–674, May 2002. [Online]. Available: http://dx.doi.org/10.1007/s003390100936

[77] W. Pacuski, D. Ferrand, J. Cibert, C. Deparis, J. A. Gaj, P. Kossacki, and C. Morhain, “Eﬀect of the s, p-d exchange interaction on the excitons in Zn1−xCoxO epilayers,” Phys. Rev. B, vol. 73, p. 035214, Jan 2006. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.73.035214

[78] C. Tanguy, “Optical dispersion by Wannier excitons,” Phys. Rev. Lett., vol. 75, no. 22, pp. 4090–4093, Nov 1995. [Online]. Available: http: //dx.doi.org/10.1103/PhysRevLett.75.4090

[79] W. Pacuski, “Optical spectroscopy of wide gap diluted magnetic semiconductors based on ZnO and GaN,” Ph.D. dissertation, Université Joseph Fourier - Grenoble 1, University of Warsaw, 2008. [Online]. Available: http: //www.fuw.edu.pl/~wmpac/

[80] H. Müller, “Memorandum on the polarization optics of the photo-elastic shutter.” Report of the OSRD Project OEMsr-576, vol. 2, 1943.

[81] C. C. Katsidis and D. I. Siapkas, “General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference,” Appl. Opt., vol. 41, no. 19, pp. 3978–3987, Jul 2002. [Online]. Available: http://ao.osa.org/abstract.cfm?URI=ao-41-19-3978

[82] J. Schnakenberg, Elektrodynamik. Wiley-VCH, 2003.

[83] A. Zunger, S. Lany, and H. Raebiger, “The quest for dilute ferromagnetism in semiconductors: Guides and misguides by theory,” Physics, vol. 3, p. 53, Jun 2010. [Online]. Available: http://link.aps.org/doi/10.1103/Physics.3.53

[84] W. Stefanowicz, D. Sztenkiel, B. Faina, A. Grois, M. Rovezzi, T. Devillers, F. d’Acapito, A. Navarro-Quezada, T. Li, R. Jakieła, M. Sawicki, T. Dietl, and A. Bonanni, “Structural and paramagnetic properties of dilute Ga1−xMnxN,” Phys. Rev. B, vol. 81, no. 23, p. 235210, Jun 2010. [Online]. Available: http://dx.doi.org/10.1103/PhysRevB.81.235210

[85] T. Graf, M. Gjukic, M. S. Brandt, M. Stutzmann, and O. Ambacher, “The Mn3+/2+ acceptor level in group III nitrides,” Applied Physics Letters, vol. 81, no. 27, pp. 5159–5161, 2002. [Online]. Available: http://link.aip.org/link/?APL/81/5159/1

[86] T. Graf, M. Gjukic, L. Görgens, O. Ambacher, M. S. Brandt, and M. Stutzmann, “Charge transfer at the Mn acceptor level in GaN,”

85 Bibliography

Journal of Superconductivity, vol. 16, pp. 83–86, 2003. [Online]. Available: http://dx.doi.org/10.1023/A:1023288718903

[87] B. Han, B. W. Wessels, and M. P. Ulmer, “Optical investigation of electronic states of Mn4+ ions in p-type GaN,” Applied Physics Letters, vol. 86, no. 4, p. 042505, 2005. [Online]. Available: http://link.aip.org/link/?APL/86/042505/1

[88] O. Sancho-Juan, A. Cantarero, N. Garro, A. Cros, G. Martinez-Criado, M. Salome, J. Susini, D. Olguin, and S. Dhar, “X-ray absorption near-edge structure of GaN with high Mn concentration grown on SiC,” Journal of Physics: Condensed Matter, vol. 21, no. 29, p. 295801 (8pp), 2009. [Online]. Available: http://stacks.iop.org/0953-8984/21/295801

[89] R. Y. Korotkov, J. M. Gregie, and B. W. Wessels, “Mn-related absorption and PL bands in GaN grown by metal organic vapor phase epitaxy,” Physica B: Condensed Matter, vol. 308-310, pp. 30 – 33, 2001. [Online]. Available: http://www.sciencedirect.com/science/article/B6TVH-459MSV1-7/2/ 711fdf1a4096d0c8d9e3c7bb8dd6485d

[90] A. Titov, “Propriétés électroniques des semiconducteurs magnétiques dilués: Ga1−xMnxN, Ga1−xMnxAs, Ge1−xMnx,” Ph.D. dissertation, Université Joseph- Fourier - Grenoble 1, 12 2006. [Online]. Available: http://tel.archives-ouvertes.fr/ tel-00113864/en/

[91] T. Yamamoto, “Assignment of pre-edge peaks in K-edge x-ray absorption spectra of 3d transition metal compounds: electric dipole or quadrupole?” X-Ray Spectrometry, vol. 37, no. 6, pp. 572–584, 2008. [Online]. Available: http://dx.doi.org/10.1002/xrs.1103

[92] A. Titov, X. Biquard, D. Halley, S. Kuroda, E. Bellet-Amalric, H. Mariette, J. Cibert, A. E. Merad, G. Merad, M. B. Kanoun, E. Kulatov, and Y. A. Uspenskii, “X-ray absorption near-edge structure and valence state of Mn in (Ga,Mn)N,” Phys. Rev. B, vol. 72, p. 115209, Sep 2005. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.72.115209

[93] A. Wołoś and M. Kaminska, “Magnetic Impurities in Wide Band-gap III-V Semiconductors,” in Spintronics, ser. Semiconductors and Semimetals, E. Weber, Ed. Elsevier, 2008, vol. 82, ch. 8, pp. 325 – 369. [Online]. Available: http://www.sciencedirect.com/science/article/B7W5P-4V0MG7F-C/ 2/7bfd1ﬀ81dfa316a252fa26d366f49c2

[94] J. Zenneck, T. Niermann, D. Mai, M. Roever, M. Kocan, J. Malindretos, M. Seibt, A. Rizzi, N. Kaluza, and H. Hardtdegen, “Intra-atomic photoluminescence at 1.41 eV of substitutional Mn in GaMnN of high optical quality,” Journal of Applied Physics, vol. 101, no. 6, p. 063504, 2007. [Online]. Available: http://link.aip.org/link/?JAP/101/063504/1

86 [95] E. Malguth, A. Hoﬀmann, W. Gehlhoﬀ, M. Kane, and I. Ferguson, “Mn charge states in GaMnN as a function of Mn concentration and co-doping,” Mater. Res. Soc. Symp. Proc., vol. 1040, pp. Q09–18, 2008. [Online]. Available: http://www. mrs.org/s_mrs/sec_subscribe.asp?CID=11340&DID=208936&action=detail

[96] A. Grois, “Optical studies of manganese doped gallium nitride,” Master’s thesis, Johannes Kepler Universität Linz, 2010.

[97] Q. Yan, P. Rinke, M. Scheﬄer, and C. G. V. de Walle, “Strain eﬀects in group-III nitrides: Deformation potentials for AlN, GaN, and InN,” Applied Physics Letters, vol. 95, no. 12, p. 121111, 2009. [Online]. Available: http://link.aip.org/link/?APL/95/121111/1

[98] J. Tworzydło, “Model of magnetic and chemical disorder in dilute magnetic semiconductors,” Phys. Rev. B, vol. 50, no. 19, pp. 14 591–14 594, Nov 1994. [Online]. Available: http://dx.doi.org/10.1103/PhysRevB.50.14591

[99] A. Twardowski, D. Heiman, M. T. Liu, Y. Shapira, and M. Demianiuk, “Raman spectroscopy of Cd1−xCrxs,” Phys. Rev. B, vol. 53, pp. 10 728–10 731, Apr 1996. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.53.10728

[100] M. Herbich, W. Mac, A. Twardowski, K. Ando, Y. Shapira, and M. Demianiuk, “Magnetization and exciton spectroscopy of the diluted magnetic semiconductor Cd1−xCrxS,” Phys. Rev. B, vol. 58, pp. 1912–1921, Jul 1998. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.58.1912

[101] M. Nawrocki, J. P. Lascaray, D. Coquillat, and M. Demianiuk, “Diluted magnetic (semimagnetic) semiconductors,” in MRS Symposia Proceedings, R. L. Aggarwal, J. K. Furdyna, and S. von Molnar, Eds., vol. 89. Materials Research Society, Pittsburgh, 1987, p. 65.

[102] N. P. Stern, R. C. Myers, M. Poggio, A. C. Gossard, and D. D. Awschalom, “Con- ﬁnement engineering of s-d exchange interactions in Ga1−xMnxAs/AlyGa1−yAs quantum wells,” Phys. Rev. B, vol. 75, p. 045329, Jan 2007. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.75.045329

[103] C. Śliwa and T. Dietl, “Electron-hole contribution to the apparent s-d exchange interaction in III-V dilute magnetic semiconductors,” Phys. Rev. B, vol. 78, p. 165205, Oct 2008. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB. 78.165205

[104] J. I. Hwang, Y. Ishida, M. Kobayashi, H. Hirata, K. Takubo, T. Mizokawa, A. Fujimori, J. Okamoto, K. Mamiya, Y. Saito, Y. Muramatsu, H. Ott, A. Tanaka, T. Kondo, and H. Munekata, “High-energy spectroscopic study of the III-V nitride-based diluted magnetic semiconductor Ga1−xMnxN,” Phys. Rev. B, vol. 72, p. 085216, Aug 2005. [Online]. Available: http: //link.aps.org/doi/10.1103/PhysRevB.72.085216

87 Bibliography

[105] A. Bonanni and T. Dietl, “A story of high-temperature ferromagnetism in semiconductors,” Chem. Soc. Rev., vol. 39, pp. 528–539, 2010. [Online]. Available: http://dx.doi.org/10.1039/B905352M

[106] A. Navarro-Quezada, W. Stefanowicz, T. Li, B. Faina, M. Rovezzi, R. T. Lechner, T. Devillers, F. d’Acapito, G. Bauer, M. Sawicki, T. Dietl, and A. Bonanni, “Embedded magnetic phases in (Ga,Fe)N: Key role of growth temperature,” Phys. Rev. B, vol. 81, no. 20, p. 205206, May 2010. [Online]. Available: http://dx.doi.org/10.1103/PhysRevB.81.205206

[107] A. Navarro-Quezada, T. Devillers, T. Li, and A. Bonanni, “Planar arrays of magnetic nanocrystals embedded in GaN,” Applied Physics Letters, vol. 101, no. 8, p. 081911, 2012. [Online]. Available: http://scitation.aip.org/content/aip/journal/ apl/101/8/10.1063/1.4747809

[108] A. Bonanni, A. Navarro-Quezada, T. Li, M. Wegscheider, Z. Matěj, V. Holý, R. T. Lechner, G. Bauer, M. Rovezzi, F. D’Acapito, M. Kiecana, M. Sawicki, and T. Dietl, “Controlled aggregation of magnetic ions in a semiconductor: An experimental demonstration,” Phys. Rev. Lett., vol. 101, no. 13, p. 135502, Sep 2008. [Online]. Available: http://dx.doi.org/10.1103/PhysRevLett.101.135502

[109] K. H. Jack, “The occurrence and the crystal structure of α00-iron nitride; a new type of interstitial alloy formed during the tempering of nitrogen-martensite,” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol. 208, no. 1093, pp. 216–224, 1951. [Online]. Available: http://rspa.royalsocietypublishing.org/content/208/1093/216.abstract

[110] T. K. Kim and M. Takahashi, “New magnetic material having ultrahigh magnetic moment,” Applied Physics Letters, vol. 20, no. 12, pp. 492–494, 1972. [Online]. Available: http://scitation.aip.org/content/aip/journal/apl/20/12/ 10.1063/1.1654030

[111] J. Coey and P. Smith, “Magnetic nitrides,” Journal of Magnetism and Magnetic Materials, vol. 200, no. 1-3, pp. 405 – 424, 1999. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0304885399004291

00 [112] M. Takahashi and H. Shoji, “α -Fe16N2 problem - giant magnetic moment or not,” Journal of Magnetism and Magnetic Materials, vol. 208, no. 3, pp. 145 – 157, 2000. [Online]. Available: http://www.sciencedirect.com/science/article/pii/ S0304885399005363

[113] S. Kokado, N. Fujima, K. Harigaya, H. Shimizu, and A. Sakuma, “Theoretical analysis of highly spin-polarized transport in the iron nitride Fe4N,” Phys. Rev. B, vol. 73, p. 172410, May 2006. [Online]. Available: http://link.aps.org/doi/10. 1103/PhysRevB.73.172410

88 [114] M. Tsunoda, H. Takahashi, S. Kokado, Y. Komasaki, A. Sakuma, and M. Takahashi, “Anomalous anisotropic magnetoresistance in pseudo-single-crystal 0 γ -Fe4N ﬁlms,” Applied Physics Express, vol. 3, no. 11, p. 113003, 2010. [Online]. Available: http://stacks.iop.org/1882-0786/3/i=11/a=113003

[115] M. Tsunoda, Y. Komasaki, S. Kokado, S. Isogami, C.-C. Chen, and M. Takahashi, “Negative anisotropic magnetoresistance in Fe4N ﬁlm,” Applied Physics Express, vol. 2, no. 8, p. 083001, 2009. [Online]. Available: http://stacks.iop.org/1882-0786/2/i=8/a=083001

[116] K. Ito, K. Kabara, H. Takahashi, T. Sanai, K. Toko, T. Suemasu, and 0 M. Tsunoda, “Negative anisotropic magnetoresistance in γ -Fe4N epitaxial ﬁlms on SrTiO3 (001) grown by molecular beam epitaxy,” Japanese Journal of Applied Physics, vol. 51, no. 6R, p. 068001, 2012. [Online]. Available: http://stacks.iop.org/1347-4065/51/i=6R/a=068001

[117] K. Ando, S. Takahashi, J. Ieda, H. Kurebayashi, T. Trypiniotis, C. H. W. Barnes, S. Maekawa, and E. Saitoh, “Electrically tunable spin injector free from the impedance mismatch problem,” Nat Mater, vol. 10, no. 9, pp. 655–659, Sep. 2011. [Online]. Available: http://dx.doi.org/10.1038/nmat3052

[118] A. Brataas, Y. Tserkovnyak, G. E. W. Bauer, and B. I. Halperin, “Spin battery operated by ferromagnetic resonance,” Phys. Rev. B, vol. 66, p. 060404, Aug 2002. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.66.060404

[119] H. J. von Bardeleben, N. Jedrecy, and J. L. Cantin, “Ferromagnetic resonance signature of metallic Co clusters in ferromagnetic ZnCoO thin ﬁlms,” Applied Physics Letters, vol. 93, no. 14, p. 142505, 2008. [Online]. Available: http://scitation.aip.org/content/aip/journal/apl/93/14/10.1063/1.2998309

[120] M. Charilaou, J. Kind, I. García-Rubio, D. Schüler, and A. U. Gehring, “Magnetic anisotropy of non-interacting collinear nanocrystal-chains,” Applied Physics Letters, vol. 104, no. 11, p. 112406, 2014. [Online]. Available: http://scitation.aip.org/content/aip/journal/apl/104/11/10.1063/1.4869092

[121] J. A. Osborn, “Demagnetizing factors of the general ellipsoid,” Phys. Rev., vol. 67, pp. 351–357, Jun 1945. [Online]. Available: http://link.aps.org/doi/10. 1103/PhysRev.67.351

[122] P. J. Jensen and G. M. Pastor, “Low-energy properties of two-dimensional magnetic nanostructures: interparticle interactions and disorder eﬀects,” New Journal of Physics, vol. 5, no. 1, p. 68, 2003. [Online]. Available: http://stacks.iop.org/1367-2630/5/i=1/a=368

[123] J. M. Coey, Magnetism and magnetic materials. Cambridge University Press, 2010.

89 Bibliography

[124] C. Guillaud and H. Creveaux, “Préparation et propriétés magnétiques du composé déﬁni Fe4N,” Comptes rendus hebdomadaires des séances de l’Académie des Sciences, vol. 222, p. 1170, 1946. [Online]. Available: http://gallica.bnf.fr/ark:/12148/cb343481087/date.langFR

[125] B. C. Frazer, “Magnetic structure of Fe4N,” Phys. Rev., vol. 112, pp. 751–754, Nov 1958. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRev.112.751

[126] S. K. Chen, S. Jin, T. H. Tiefel, Y. F. Hsieh, E. M. Gyorgy, and D. W. Johnson, “Magnetic properties and microstructure of Fe4N and (Fe,Ni)4N,” Journal of Applied Physics, vol. 70, no. 10, pp. 6247–6249, 1991. [Online]. Available: http://scitation.aip.org/content/aip/journal/jap/70/10/10.1063/1.350010

[127] T. Nakamura, T. Takahashi, N. Takahashi, T. Kato, K. Furukawa, G. M. Smith, C. J. Oates, and P. C. Riedi, “High-ﬁeld FMR investigation of epitaxially grown Fe4N ﬁlms on a MgO(001) substrate,” Electrochemical and Solid-State Letters, vol. 6, no. 10, pp. C146–C148, 2003. [Online]. Available: http://esl.ecsdl.org/content/6/10/C146.abstract

[128] T. Gressmann, M. Wohlschlögel, S. Shang, U. Welzel, A. Leineweber, E. Mittemeijer, and Z.-K. Liu, “Elastic anisotropy of γ’-Fe4N and elastic grain interaction in γ’-Fe4N1−y layers on α-Fe: First-principles calculations and diﬀraction stress measurements,” Acta Materialia, vol. 55, no. 17, pp. 5833 – 5843, 2007. [Online]. Available: http://www.sciencedirect.com/science/article/pii/ S1359645407004569

[129] E. Zhao, H. Xiang, J. Meng, and Z. Wu, “First-principles investigation on the elastic, magnetic and electronic properties of MFe3N (M=Fe, Ru, Os),” Chemical Physics Letters, vol. 449, no. 1-3, pp. 96–100, 2007. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0009261407013930

[130] T. Takahashi, J. Burghaus, D. Music, R. Dronskowski, and J. M. Schneider, “Elastic properties of γ’-Fe4N probed by nanoindentation and ab initio calculation,” Acta Materialia, vol. 60, no. 5, pp. 2054 – 2060, 2012. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S1359645412000079

[131] A. Yurkova, A. Byakova, A. Belots’ky, Y. Milman, and S. N. Dub, “Mechanical behaviour of nanostructured iron fabricated by severe plastic deformation under diffusion flow of nitrogen,” Materials Science Forum, vol. 503-504, p. 645, 2006. [Online]. Available: http://dx.doi.org/10.4028/www.scientific.net/MSF.503-504. 645

[132] S. Zheng, Y. Sun, A. Bloyce, and T. Bell, “Characterization of plasma nitrided and PVD-TiN duplex treated Armco Iron and En40B steel by nanoindentation,” Materials and Manufacturing Processes, vol. 10, no. 4, pp. 815–824, 1995. [Online]. Available: http://www.tandfonline.com/doi/abs/10.1080/10426919508935068

90 [133] L. Chen, F. Matsukura, and H. Ohno, “Direct-current voltages in (Ga,Mn)As structures induced by ferromagnetic resonance,” Nat Commun, vol. 4, p. 2055, June 2013. [Online]. Available: http://dx.doi.org/10.1038/ncomms3055

[134] R. C. Jeﬀ, M. Yun, B. Ramalingam, B. Lee, V. Misra, G. Triplett, and S. Gangopadhyay, “Charge storage characteristics of ultra-small Pt nanoparticle embedded GaAs based non-volatile memory,” Applied Physics Letters, vol. 99, no. 7, p. 072104, 2011. [Online]. Available: http: //scitation.aip.org/content/aip/journal/apl/99/7/10.1063/1.3625426

[135] F. Li, S. H. Cho, D. I. Son, K. H. Park, and T. W. Kim, “Multilevel nonvolatile memory eﬀects in hybrid devices containing CdSe/ZnS nanoparticle double arrays embedded in the C60 matrices,” Applied Physics Letters, vol. 92, no. 10, p. 102110, 2008. [Online]. Available: http://scitation.aip.org/content/aip/journal/apl/92/10/ 10.1063/1.2898163

[136] T. Dietl, “From our readers: Self-organized growth controlled by charge states of magnetic impurities,” Nature Materials, vol. 5, no. 9, pp. 673–673, Sep. 2006. [Online]. Available: http://dx.doi.org/10.1038/nmat1721

[137] M. Rovezzi, F. D’Acapito, A. Navarro-Quezada, B. Faina, T. Li, A. Bonanni, F. Filippone, A. A. Bonapasta, and T. Dietl, “Local structure of (Ga,Fe)N and (Ga,Fe)N:Si investigated by x-ray absorption ﬁne structure spectroscopy,” Physical Review B, vol. 79, no. 19, p. 195209, 2009. [Online]. Available: http://link.aps.org/abstract/PRB/v79/e195209

[138] E. G. Sharoyan, O. S. Torosyan, E. A. Markosyan, and V. T. Gabrielyan, “EPR and spin-lattice relaxation of Mo3+ ions in corundum,” physica status solidi (b), vol. 65, no. 2, pp. 773–778, 1974. [Online]. Available: http://dx.doi.org/10.1002/pssb.2220650238

[139] D. Bletskan, V. Bratus’, A. Luk’yanchuk, V. Maslyuk, and O. Parlag, “Determining residual impurities in sapphire by means of electron paramagnetic resonance and nuclear activation analysis,” Technical Physics Letters, vol. 34, pp. 612–614, 2008. [Online]. Available: http://dx.doi.org/10.1134/S1063785008070237

[140] N. Gonzalez Szwacki, J. A. Majewski, and T. Dietl, “Aggregation and magnetism of Cr, Mn, and Fe cations in GaN,” Phys. Rev. B, vol. 83, p. 184417, May 2011. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.83.184417

[141] G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Applied Physics Letters, vol. 70, no. 24, pp. 3209–3211, 1997. [Online]. Available: http://link.aip.org/link/?APL/70/3209/1

91 Bibliography

[142] G. Vankó, J.-P. Rueﬀ, A. Mattila, Z. Németh, and A. Shukla, “Temperature- and pressure-induced spin-state transitions in LaCoO3,” Phys. Rev. B, vol. 73, p. 024424, Jan 2006. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB. 73.024424

[143] K. Huang and A. Rhys, “Theory of light absorption and non-radiative transitions in F-centres,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 204, no. 1078, pp. 406–423, 1950. [Online]. Available: http://dx.doi.org/10.1098/rspa.1950.0184

[144] H. Zhao and H. Kalt, “Energy-dependent Huang-Rhys factor of free excitons,” Phys. Rev. B, vol. 68, p. 125309, Sep 2003. [Online]. Available: http: //link.aps.org/doi/10.1103/PhysRevB.68.125309

[145] R. Heitz, P. Thurian, I. Loa, L. Eckey, A. Hoﬀmann, I. Broser, K. Pressel, B. K. Meyer, and E. N. Mokhov, “Identiﬁcation of the 1.19-eV luminescence in hexagonal GaN,” Phys. Rev. B, vol. 52, pp. 16 508–16 515, Dec 1995. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.52.16508

[146] P. Thurian, I. Loa, P. Maxim, A. Hoﬀmann, C. Thomsen, and K. Pressel, “The V3+ center in AlN,” Applied Physics Letters, vol. 71, no. 20, pp. 2993–2995, 1997. [Online]. Available: http://scitation.aip.org/content/aip/journal/apl/71/20/ 10.1063/1.120240

[147] Y. Shen and K. L. Bray, “Inﬂuence of low-symmetry distortions on the luminescence of Cr4+-doped forsterite,” Phys. Rev. Lett., vol. 84, pp. 3990–3993, Apr 2000. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevLett.84.3990

[148] W. Stefanowicz, R. Adhikari, T. Andrearczyk, B. Faina, M. Sawicki, J. A. Majewski, T. Dietl, and A. Bonanni, “Experimental determination of Rashba spin-orbit coupling in wurtzite n-GaN:Si,” Phys. Rev. B, vol. 89, p. 205201, May 2014. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.89.205201

92 Acronyms

AFM atomic force microscopy. 7, 73, 75

AFMR antiferromagnetic resonance. 9

DBE donor bound excitons. 27, 28, 42

DFT density functional theory. 44, 52, 55, 59, 62, 68

DMS dilute magnetic semiconductors. 1, 75

EDX energy-dispersive x-ray spectroscopy. 35, 66

EELS electron energy loss spectroscopy. 35, 39, 64, 66, 73

EPR electron paramagnetic resonance. 9, 15, 17, 20, 24, 25, 36, 38, 46, 47, 55–60, 64, 73

EXAFS extended x-ray absorption ﬁne structure. 33, 35, 37, 40, 63, 66–68

FMR ferromagnetic resonance. 9, 12, 46–50, 52, 73, 74

FXA free exciton A. 28, 40–42

FXB free exciton B. 28, 41

FXC free exciton C. 28, 39, 41

HAADF high angle annular dark ﬁeld. 35, 64

MOVPE metalorganic vapour phase epitaxy. 3, 7, 27, 33, 45, 55, 62

NC nanocrystals. 35, 45–53, 61, 62, 74

NMR nuclear magnetic resonance. 9, 10, 15

PL photoluminescence. 2, 7, 27, 28, 30, 40, 42, 69, 70, 73, 74

RT room temperature. 1–4, 45–48, 50, 55, 67, 69 sccm standard cubic centimetres per minute. 7, 33, 34, 46, 56–58, 60, 63, 66

SIMS secondary ion mass spectroscopy. 7, 35, 56–58, 64, 66, 73, 75

93 Acronyms

SQUID superconducting quantum interference device. 7, 8, 34, 36, 38, 55–60, 68, 73, 75

STEM scanning transmission electron microscopy. 33–35, 63, 64, 73

SXRD synchrotron x-ray diﬀraction. 7, 33, 55, 56, 63

TEM transmission electron microscopy. 7, 33, 46, 48, 50–52, 55, 56, 62, 63, 67, 73, 75

TM transition metal. 2, 7, 8, 24, 26, 28, 29, 33, 40, 41, 44, 55

XANES x-ray absorption near edge structure. 35–37, 55

XAS x-ray absorption spectroscopy. 2, 7, 55, 63, 67, 73

XES x-ray emission spectroscopy. 67

XRD x-ray diﬀraction. 7, 33, 40, 46–48, 50, 52, 56, 58, 63, 66, 73, 75

94 Andreas Grois Freistädter Straße 205/4 4040 Linz Austria

Born on September 14th, 1984 in Ried i/I, Austria Curriculum Vitae Education

1999 to 2004 HTL on computer science in industry • Technical Paper (Fachbereichsarbeit) on building and main- taining the IT-network for a school in Neukirchen 2004 to 2009 Major in Technical Physics at Johannes Kepler Univer- • sity, Linz, Austria 2009 to 2010 Diploma Thesis: • “Optical studies of manganese doped gallium nitride” at the Institute of Semiconductor and Solid State Physics, Johannes Kepler University, Linz, Austria, in the group of Assoc. Prof. Dr. Alberta Bonanni 2010 to 2015 PhD thesis: • “Modulated (Ga,TM)N structures: optics & magnetism” at the Institute of Semiconductor and Solid State Physics, Johannes Kepler University, Linz, Austria, in the group of Assoc. Prof. Dr. Alberta Bonanni

Skills

Primary Experimental Physics: Photoluminescence, (Magneto-) • Reflectivity, X-ray Photoelectron Spectroscopy, Magnetic Resonance Theory and Modelling: Crystal Field Modelling of EPR spectra, Density Funcional Theory based modelling of optical properties, magnetic anisotropy modelling Software: LATEX, C, C++, OpenCL, GNU Scientific Li- brary, Python, GNU Octave, Maxima, gnuplot, fityk Secondary Experimental Physics: Raman-Spectroscopy, X-ray and • electron diffraction, X-ray Absorption Finestructure, scanning probe microscopy, electical transport measurements, metalorganic chemical vapour deposition Languages German (native), English (fluent) •

95 International experience

2009-09 ESRF Grenoble: Experiment HS-3919: “Where do holes • reside in (Ga,Fe)N doped with Mg” by M. Rovezzi, A Grois, F. d’Acapito, A. Navarro-Quezada and A. Bonani at beamline BM-08 2010-01 ESRF Grenoble: Experiment HS-4015: “Mn Local struc- • ture in GaN: a systematic investigation from dilution to clusterization” by M. Rovezzi, F. d’Acapito, A. Navarro- Quezada and A. Bonanni at beamline BM-08 2010-01 University Warsaw: Magneto-reﬂectivity measurements 2010-11 • on manganese doped gallium nitride in the frame of ÖAD project PL 13/2010 2011-12 University Warsaw: Infrared photoluminescence on gal- • lium nitride codoped with manganese and magnesium in the frame of ÖAD project PL 13/2010 2012-11 University Warsaw: Measurements of the magnetisation • dynamics of manganese doped gallium nitride and work on density functional theory simulations of this material in the frame of ÖAD project PL05/2012 2012-12 BESSY II Berlin: Experiment 2012-2-120261: “Com- • plex dielectric function and eﬀects of p-d hybridization in (Ga,Fe)N and (Ga,Mn)N in correlation with the charge state of the transition metal ions” by A. Bonanni, C. Cobet and N. Esser

Presentations at conferences

2011-06 MORIS 2011: Poster Presentation: “Eﬀects of s,p-d and • s-p exchange interactions probed by exciton magnetospectroscopy in Ga1 xMnxN” − 2011-11 Joint Polish-Japanese Workshop: Spintronics - from • new materials to applications: Poster and oral presentation: “Electron paramagnetic resonance on transition metals in GaN” 2012-09 JEMS 2012: Oral presentation: “Mechanisms of exchange • interactions in dilute Ga1 xMnxN - experiment and mod- − elling” 2013-02 European School on Magnetism: Poster with oral in- • troduction: “Dilute and condensed transition-metal-doped GaN: Phase diagrams and magnetic interactions” 2014-09 EMRS Fall Meeting 2014: Oral presentation: “On the • trail of room temperature antiferromagnetism in (Fe,Ga)N nanocrystals embedded in GaN”

96 Internships

2000 to 2008 Vishay Telefunken, GEA Happel, Werzalit •

Publications

W. Stefanowicz, D. Sztenkiel, B. Faina, A. Grois, M. Rovezzi, T. Dev- • illers, F. d’Acapito, A. Navarro-Quezada, T. Li, R. Jakiela, M. Sawicki, T. Dietl, and A. Bonanni, Structural and paramagnetic properties of dilute Ga1 xMnxN, Phys. Rev. B, vol. 81, p. 235210, June 2010 − J. Suﬀczyński, A. Grois, W. Pacuski, A. Golnik, J. A. Gaj, A. Navarro- • Quezada, B. Faina, T. Devillers, and A. Bonanni, Eﬀects of s,p-d and s- p exchange interactions probed by exciton magnetospectroscopy in (Ga,Mn)N, Phys. Rev. B, vol. 83, p. 94421, March 2011

A. Bonanni, M. Sawicki, T. Devillers, W. Stefanowicz, B. Faina, Tian Li, • T. E. Winkler, D. Sztenkiel, A. Navarro-Quezada, M. Rovezzi, R. Jakieła, A. Grois, M. Wegscheider, W. Jantsch, J. Suﬀczyński, F. D’Acapito, A. Meingast, G. Kothleitner, and T. Dietl, Experimental probing of exchange interactions between localized spins in the dilute magnetic insulator (Ga,Mn)N, Phys. Rev. B, vol. 84, p. 035206, July 2011

A. Navarro-Quezada, N. Gonzalez Szwacki, W. Stefanowicz, Tian Li, A. • Grois, T. Devillers, R. Jakieła, B. Faina, J. A. Majewski, M. Sawicki, T. Dietl, and A. Bonanni, The Fe-Mg interplay and the eﬀect of deposition mode in (Ga,Fe)N doped with Mg, Phys. Rev. B, vol 84, p. 155321, October 2011

M. Sawicki, T. Devillers, S. Gałęski, C. Simserides, S. Dobkowska, B. • Faina, A. Grois, A. Navarro-Quezada, K. N. Trohidou, J. A. Majewski, T. Dietl, A. Bonanni, Origin of low-temperature magnetic ordering in Ga1 xMnxN, Phys. Rev. B, vol 85, p. 205204, May 2012 − T. Devillers, M. Rovezzi, N. Gonzalez Szwacki, S. Dobkowska, W. Ste- • fanowicz, D. Sztenkiel, A. Grois, J. Suﬀczyński, A. Navarro-Quezada, B. Faina, Tian Li, P. Glatzel, F. d’Acapito, R. Jakieła, M. Sawicki, J. A. Majewski, T. Dietl, A. Bonanni, Manipulating Mn-Mgk cation complexes to control the charge- and spin-state of Mn in GaN, Scientiﬁc Reports, vol 2, p. 722, October 2012

97 Publications (continued)

A. Grois, T. Devillers, T. Li, and A. Bonanni, Planar array • of self-assembled GaxFe4 xN nanocrystals in GaN: magnetic − anisotropy determined via ferromagnetic resonance, Nanotech- nology, vol 25, p. 395704, September 2014