Thesis Research Has Been a Collaborative Effort, and I Must Thank All Those That Have Made My Dissertation Work Complete

UNIVERSITY of CALIFORNIA Santa Barbara

Magnetism in Transition-Metal-Substituted Semiconducting Oxides

A Dissertation submitted in partial satisfaction of the requirements for the degree

Doctor of Philosophy in Materials

Aditi S. Risbud

Committee in charge:

Professor Ram Seshadri, Chair Professor Anthony K. Cheetham Professor Nicola A. Spaldin Professor Juergen Eckert

September 2005 The dissertation of Aditi S. Risbud is approved.

Professor Anthony K. Cheetham

Professor Nicola A. Spaldin

Professor Juergen Eckert

Professor Ram Seshadri, Committee Chair

August 2005 Magnetism in Transition-Metal-Substituted Semiconducting Oxides

Aditi S. Risbud

iii for my parents

iv Acknowledgements

Often as a chapter in one’s life comes to a close, an appreciation for what is about to be lost begins to surface. It is a credit to Santa Barbara that from the moment of my arrival, I was aware of how fortunate I would be to complete my Ph.D. work in such a beautiful environment. This work would not have been possible without the help of my advisor, Ram Seshadri, who I thank for being a wonderful advisor these past few years. Ram’s enthusiasm and re- lentless curiosity about science has been an inspiration, and I appreciate all his guidance over my time here. I must also (grudgingly) admit that I am now a

Linux user, and happy about it.

My thesis research has been a collaborative effort, and I must thank all those that have made my dissertation work complete. Nicola Spaldin’s support throughout my thesis has been invaluable; on top of that, she is probably the coolest professor I know. Thanks for the careful reading of my thesis.

Gavin Lawes’ straightforward and innovative description of the magnetic be-

v havior of my materials systems lent valuable insight into my research. Lauren

Snedeker was a fantastic intern, cheerily plugging away in the lab and helping my thesis work along. Mentoring is a highly rewarding part of science and

I was happy to work with Lauren, Margaret MacRae and Rey Honrada during my time here. Many thanks to my committee members Tony Cheetham,

Juergen Eckert, and David Clarke for their input and suggestions. I must also thank Z.Q. Chen, S. Stemmer, J.P. Attﬁeld, J. Ensling, C. Felser, M.M. Elcombe, and A.P. Ramirez for their contributions.

Before I began my Ph.D. work, there were a number of individuals who helped in the development of my science abilities. My undergraduate advisor at UC Davis, Alexandra Navrotsky, has an amazing devotion to science, and

I thank her for inspiring me to pursue my doctoral degree. I also thank Kate

Helean for her mentoring and friendship. My next research stint at Caltech was guided by Harry Atwater. Harry’s ability to communicate science effectively resounded with me and sparked the motivation for my current career goal. I also thank Regina Ragan for being a great mentor and role model during my time at Caltech. Upon my arrival at UCSB, the Lange group allowed me to make a seamless transition to the Materials department, and I thank

Fred Lange, Geoff & Denice Fair, Mark & Nicole Snyder, Biao and Zhou, Ryan

Bock, Scott Fillery, Haksung Moon, and Lars Loefﬂer for their support and

vi friendship. Dave Andeen is probably the best ofﬁcemate I have ever had, and

I will miss our conversations about Barry Switzer, the Raiders, Kings, and stay- ing cool, Lakers-style. The Seshadri group has seen a few members come and go in its relative youth, and I thank our post-docs K. Ramesha and Ombretta

Masala for their help with magnetic measurements and electron microscopy.

Eric Toberer and I have spent far too much time together being ofﬁcemates and the only graduate students in the Seshadri group, most memorably at MRS

Boston, home of the world’s best public transportation Kit Kat. As for MRS

San Francisco- I’m sorry about those contact lenses. I will miss our fashion and color scheme discussions. Someday we’ll compile that list of quotes and pass it on to future group members.

The best part of graduate school has been all the great people I have spent time with, both on and off the court. Jenny Andrew has been a source of endless friendship, replete with silly accents, Bollywood dance sequences, kothimbeer-laden meals, and lame materials science jokes. Tu kasli whooshaar ahes! Thanks for sitting through all my practice talks (and the real ones too).

Michael Pontin helped me see the conspiracies of the world, and even though he projects ’bitter old man,’ he is one of the kindest, most thoughtful people I know. David Follman has been a great housemate and friend. He is a talented writer and a tolerant individual, especially during basketball season. Adam

vii Pyzyna was a fun housemate and friend, and I will miss watching Chappelle and discussing the latest hip-hop scoop. Emily Parker has been a great friend, workout buddy (only a good friend would be willing to come to Sean’s brutal spin class and save seats) and sounding board for all my ridiculous drama.

Remember: You are a Genius. Seth Boeshore has been a ﬁne source of South

Park quotes and car bomb synergy. Over many a coffee, he has continually surprised me with his intellect (beyond just science) and sharp personal ob- servations. Weak. Thanks also to Garrett Cole for discussions on excitons, book hoarding, and general science enthusiasm. Katie Schaefer has been a great friend, shopping buddy (a convert, in fact) and listener, letting me whine about my day over a coffee (just not iced) or lunch. Justin Abramson is probably the worst ofﬁcemate but most interesting friend I’ve had- I will miss our discussions from science to life philosophies. You’ve certainly taught me a thing or two about myself, and I appreciate that. Also, thanks for all your help with SC. Larken Euliss was our favorite non-Materials person- thanks for in- troducing me to GVAC, bumble & bumble, and ‘thinking in chapters.’ Good luck at UT Arlington! I must also thank the Materials girls: Felicia Pitek, Lisa

Kinder, Meghan Kerner, Molly Gentleman and Lori Callaghan for a great time, whether it was dancing downtown or in Vegas.

There are a few people who let me ignore them for months and then are

viii willing to talk to me when we ﬁnally see each other. I call them long-distance friends. Stephanie Moore introduced me to Travis, dressing red, and Jude

Law. She’s a great friend and an Australian, but I don’t hold that against her.

Nils-Eric Snekkevik has been a great friend, e-mailing from all over the world and allowing me to vent about grad school, career paths, and singing along to Coldplay. Julie Casperson (now Brewer) has been a wonderful support through Caltech and grad school, managing to give me advice about school, shoes, and boys in a single afternoon. Thanks for including me in your wed- ding. Jason Holt has been a good friend over the years as well, in the homes of the Lakers, Warriors, and Kings. At least we can make fun of the Clippers together. I also thank Chelsea McClain, Malini Jain, Sean Chen, Sonia Dass, and Jay Young for their friendships over the years.

I must now thank the people without whom I wouldn’t have made it where

I am today. My cousin Sarita and I have grown up together, whether it was in one house or across continents. She has been there through every event (except when her phone dies) of my life, from our crazy family reunions to con- ventions and college experiences (unfortunately G Street cannot compete with

6th Street) with her own brand of sarcasm. She is the closest thing I have to a sister, and I hope that never changes. Thanks also to Seema, Raja, Vikram, and

Himaunshu for being sibling stand-ins and playing basketball (or football, it’s

ix hard to tell sometimes) in that crazy Oklahoma heat. Go Sooners! Finally, I thank my mom and dad, Smita and Subhash Risbud, for being my true best friends in this world. Dad has kept up with every science project or goal I have every pursued, often sending me articles or newspaper clippings to read, proofreading my work, patiently listening no matter what the situation, science or otherwise. Mom is tireless, and has always been willing to go have fun at any time of day or night, chat about friends and family, and told me what

I needed to hear (even if I didn’t want to hear it). She is deﬁnitely the genetic source of my sense of humor. I especially appreciate all the trips you guys have made to SLO, driving the entire day so that we could spend an afternoon together, bringing me Co-op cookies. I am a very lucky girl. As it comes to a close, I am happy to say that this chapter of my life has been one of the most rewarding and enjoyable, and I wouldn’t trade it for a thing.

x Curriculum Vitæ

Aditi S. Risbud

Education

1996-2000 B.S. in Materials Science and Engineering

University of California, Davis

Davis, CA

2001-2005 Ph.D. Materials

University of California, Santa Barbara

Santa Barbara, CA

Publications

A. S. Risbud, R. Seshadri, J. P. Ensling, and C. Felser.

Dilute Ferrimagnetic Semiconductors in Fe-substituted

Spinel ZnGa2O4. Journal of Physics: Condensed Matter, 17,

1003 (2005).

G. Lawes, A. S. Risbud, A. P. Ramirez, and R. Seshadri.

Absence of ferromagnetism in Co and Mn substituted

polycrystalline ZnO. Physical Review B, 71, 045201 (2005).

A. S. Risbud, L. P. Snedeker, M. Elcombe, A. K. Cheetham,

and R. Seshadri. Wurtzite CoO. Chemistry of Materials, 17,

xi 834 (2005).

A. S. Risbud, N. A. Spaldin, Z. Q. Chen, S. Stemmer,

and R. Seshadri. Magnetism in Polycrystalline Cobalt-

Substituted Zinc Oxide. Physical Review B 68, 205202

(2003).

A. S. Risbud, K. B. Helean, M. C. Wilding, P. Lu, and A.

Navrotsky. Enthalpies of Formation of Lanthanide Oxya-

patite Phases. Journal of Materials Research 16, 2780 (2001).

xii Abstract

Magnetism in Transition-Metal-Substituted Semiconducting Oxides

Aditi S. Risbud

The nascent ﬁeld of spintronics requires materials that exhibit room- temperature ferromagnetism while retaining their semiconducting properties.

A clever strategy for creating these materials is by substituting magnetic transition metals onto the cation sites of commonly used binary semiconductors in order to incorporate magnetic property (e.g. Mn-substituted GaAs). A materials system of great interest is transition-metal substituted ZnO, which was predicted by Dietl and co-workers[1] to be a room temperature ferromagnet with manganese substitution and hole doping. Despite a great deal of effort in preparing thin films of transition-metal substituted ZnO, there has not been reproducible evidence of ferromagnetism in this system; Curie temperatures and magnetic moments vary significantly between studies. In our work, bulk transition metal substituted ZnO samples were prepared and characterized in order to accurately determine their properties. We find no evidence for ferromagnetic behavior in either the Zn1−xCoxO nor the Zn1−xMnxO systems;

xiii rather the dominant nearest-neighbor interactions are antiferromagnetic. A similar behavior is observed in nanoparticulate analogs of the bulk materials. Along with substituted ZnO, the ‘end-member’ of the Zn1−xCoxO system, novel wurtzite CoO was also prepared and studied. Finally, solid solutions of a dilute ferrimagnetic semiconductor system, iron-substituted ZnGa2O4, were prepared and found to possess long-range magnetic ordering with ferromagnetic hysteresis at low temperatures. Optical spectroscopy indicates that the iron substitution does not greatly alter the position of the band edge, hence maintaining the semiconducting properties. Such promising results suggest that dilute ferrimagnetic semiconductors, which do not require conduction electrons to induce magnetism, are worthy of further investigation.

xiv Contents

Contents xv

List of Figures xvii

1 Spintronic Materials 1 1.1 Introduction ...... 1 1.2 Prior work ...... 7

2 Cobalt-substituted Zinc Oxide 14 2.1 Preparation ...... 15 2.2 Experimental Results ...... 16 2.3 Theory ...... 23

3 Magnetism in Substituted ZnO 32 3.1 Preparation ...... 33 3.2 Results ...... 34 3.3 Modeling ...... 41 3.4 Summary ...... 44

4 Wurtzite Cobalt Oxide 47 4.1 Previous work ...... 48 4.2 Preparation ...... 49

xv 4.3 Results ...... 51 4.4 Calculations ...... 58 4.5 Summary ...... 60

5 ZnO and Zn1−xCoxO Nanoparticles 62 5.1 Preparation ...... 66 5.2 Results ...... 68 5.3 Summary ...... 76

6 Iron-substituted Zinc Gallate 82 6.1 Preparation ...... 84 6.2 Results ...... 85 6.3 Summary ...... 92

Bibliography 96

xvi List of Figures

1.1 Schematic of a spin valve ...... 2 1.2 Ferromagnetic semiconductors and half-metals ...... 4 1.3 Datta-Das spin transistor ...... 5 1.4 Predicted Curie temperatures ...... 6

2.1 The wurtzite unit cell ...... 17

2.2 XRD data of Zn1−xCoxO ...... 18

2.3 Lattice parameters of Zn1−xCoxO ...... 19

2.4 TEM of Zn1−xCoxO ...... 21

2.5 Magnetic susceptibility of Zn1−xCoxO ...... 27 2.6 Unpaired electrons ...... 28 2.7 Magnetization as a function of ﬁeld ...... 29 2.8 Densities of state ...... 30 2.9 Relative stabilization of magnetic states ...... 31 2.10 Distribution of near neighbors ...... 31

3.1 XRD of Zn1−xMnxO ...... 34

3.2 Cell parameters of Zn1−xMnxO ...... 35 3.3 Specific heat ...... 37 3.4 Magnetization as a function of field ...... 39 3.5 Inverse susceptibility and fits ...... 40

xvii 3.6 Effective magnetic moments ...... 46

4.1 Diffraction data ...... 53 4.2 Wurtzite CoO crystal structure ...... 54 4.3 Wurtzite CoO magnetism ...... 56 4.4 Neutron patterns at different temperatures ...... 57 4.5 Electronic structure ...... 60

5.1 Crystal structures ...... 69 5.2 XRD of bulk and nano ZnO ...... 70 5.3 Electron diffraction ...... 71 5.4 Lattice image of nano-ZnO ...... 72 5.5 DIFFaX simulations ...... 73 5.6 XRD of nano-ZnO from zinc acetylacetonate ...... 77 5.7 Thermodiffractometry showing conversion to wurtzite ..... 78 5.8 Relative amounts of wurtzite and zinc blende ...... 79

5.9 XRD of Zn1−xCoxO nanoparticles ...... 80

5.10 Magnetism of Zn1−xCoxO nanoparticles ...... 81

6.1 Cation coordination of spinel ...... 83 6.2 XRD of substituted zinc gallates ...... 87 6.3 Optical properties ...... 88 6.4 Magnetization as function of temperature ...... 93 6.5 Magnetization as a function of ﬁeld ...... 94 6.6 Mossbauer¨ studies ...... 95

xviii Chapter 1

Spintronic Materials

1.1 Introduction

Starting in the second half of the 20th century, the control and manipula- tion of electronic charge in the solid state has motivated research efforts in both industrial and academic settings. The technological impact of these efforts is evident in the universality of computers that treat data as absence or presence of electronic charge. However, as devices become increasingly small, there has arisen a challenge that has aptly been described as the ‘end of the silicon road map.’[2] Rather than continue down this path, researchers have begun to investigate devices that utilize another property of the electron: its spin. Spin is a quantum mechanical concept associated with the splitting of electronic energy

1 levels in relation to a magnetic ﬁeld. Manipulating the spin of the electron instead of (or in addition to) its charge is the basis of spin-based electronics, or spintronics. The advantages of spin include non-volatility, increased data density and processing speed, decreased power consumption, and long coherence times. With the advent of the giant magnetoresistance (GMR) effect in 1988[3], the ﬁrst step towards incorporating spin into devices was taken. In GMR devices such as spin valves (diagrammed in Figure 1.1), a nonmagnetic metal layer is sandwiched between two ferromagnetic metal layers, with the resis- tance of current dependent on the relative orientation of the magnetic layers, allowing these devices to be used as switches or sensors.

ferromagnet 1

insulator

ferromagnet 2

Figure 1.1. Schematic of a spin valve. The current through the device depends on the relative orientation of spins in the two ferromagnets.

From this beginning, the efforts to create spintronic devices has led nat- urally to the need for materials that combine both ferromagnetic and semiconducting properties for ease of integration into existing technology. Such ferromagnetic semiconductors would ideally have Curie temperatures above

2 room temperature and be able to support both p- and n-type doping, but most importantly would require a large spin-carrier polarization. For large spin- polarization to occur in semiconductors, the densities of states must exhibit

‘half-metallic’ behavior[4]; the Fermi level must intersect one of the two spin bands (spin up or spin down), whereas for the other, the Fermi level lies in a band gap. Examples of this half-metallic behavior include oxides such as

CrO2 and double perovskites[5]. Ferromagnetic semiconductors are also spin- polarized; candidate materials include dilute magnetic semiconductors (DMS) with a certain fraction of transition metal substitution (Mn, Co, Fe) on the cation site of a semiconductor to add the property of magnetism. A schematic illustrating typical densities of states for both ferromagnetic semiconductors and half-metallic ferromagnets is illustrated in Figure 1.2.

The results of this research are integral to a variety of novel technologies, including spin transistors[6] (a schematic of which is displayed in Fig- ure 1.3) and magneto-optical devices based on room temperature ferromagnetism. With worldwide efforts to ﬁnd new structures and chemistries, enhancement of the capability and performance of existing and newly proposed devices is imminent, with the ultimate goal of completely integrating electronic, magnetic, and photonic device technologies.

The search for dilute magnetic semiconductors has led to numerous studies

3 ferromagnetic half−metallic semiconductor ferromagnet

Figure 1.2. Densities of states comparing ferromagnetic semiconductors and half-metallic ferromagnets. EF is the Fermi energy. on candidate materials. Investigations on bulk, thin film, and nanostructured materials, along with theoretical predictions, have been undertaken primarily in the last five years in the hopes of finding a room temperature ferromagnetic semiconductor. Within the realm of DMS, ZnO and GaN are wide bandgap semiconductors with unusual optical and electronic properties, exhibiting a high degree of optical transparency along with semiconducting behavior, and hence are desirable host materials. Cobalt- and manganese-substituted ZnO have been of particular interest, after a series of theoretical predictions[1, 7] emerged, suggesting that ZnO could be rendered ferromagnetic with a certain fraction of transition metal substitution and significant hole doping (as shown in Figure 1.4). Unfortunately, hole doping in ZnO is difficult due to its intrin-

4 (a) (b)

AlGaAs AlGaAs

2DEG 2DEG

Source InGaAs Drain Source InGaAs Drain

Figure 1.3. Schematic of the proposed Datta-Das spin transistor, which uses the orienta-

tion of spins in a 2-D electron gas to control the ﬂow of current.

sically n-type behavior, although there have been reports of p-type behavior,

for example, through co-doping of gallium and nitrogen in ZnO[8]. A ﬁrst-

principles investigation by van de Walle[9] suggests that the simultaneous in-

corporation of nitrogen and hydrogen may be beneﬁcial for achieving p-type doping in ZnO. Most experimental investigations involve the epitaxial growth of Co- or Mn-substituted ZnO thin ﬁlms on sapphire substrates via pulsed laser deposition. Other studies prepare bulk polycrystalline Zn1−xCoxO or

Zn1−xMnxO using solid-state oxide reactions or precursor decomposition. A few attempts to create nanostructures of Mn-doped ZnO have also been undertaken.

Despite these efforts in theory, bulk materials preparation, and thin ﬁlm growth, there is a marked discrepancy in the properties observed in these materials, not only across but even within preparation methods as well as in the theoretical predictions. At the most fundamental level, many groups measure

5 Figure 1.4. Predicted Curie temperatures for typical semiconductors, determined using a Zener model assuming ﬁve percent Mn substitution and a hole doping concentration of

1020/cm3. Reprinted with permission from [1]. Copyright [2000] AAAS.

ferromagnetic behavior in substituted ZnO, while others do not see any ferro-

magnetic behavior. Even amongst those who ﬁnd ferromagnetism, reported

Curie temperatures range from 10 K to well above room temperature, with

the magnetic moments per transition metal ion consistently varying over a

wide range. These discrepancies yield a number of questions for the careful

researcher; most revolve around the nature of substitution. For example, is

the transition metal truly substituting on the cation site (e.g. is Co2+ on the

Zn2+ site)? If not, are there secondary phases that are contributing to the mag-

netic behavior? These questions can be addressed through x-ray diffraction

as well as other probes such as (for example) energy dispersive x-ray spec-

troscopy in bulk samples. Next, why is there a difference between the ex-

6 pected and measured values of the magnetic moment in these materials? Is there more than one type of interaction involved when a small fraction of transition metal ions are sprinkled into the zinc oxide lattice? How then does hole doping affect these interactions? Finally, are these systems worthy dilute magnetic semiconductor systems, or are there other systems potentially of more interest and higher impact? These questions have been addressed in this dissertation work, through studies of transition metal substituted ZnO in both bulk and nanoparticle morphologies, along with novel wurtzite CoO, and Fe- substituted ZnGa2O4.

1.2 Prior work

Theoretical studies on transition-metal-substituted ZnO began with a report by Dietl and co-workers[1] suggesting that a variety of compound and elemental semiconductors would become ferromagnetic when substituted with

ﬁve percent manganese and hole-doped to the extent of 1020 holes per cm3.

These researchers considered hole-mediated ferromagnetism in substituted semiconductors through a simple mean ﬁeld model, which describes ferromagnetism as being driven by the exchange interaction between carriers and localized spins. The results of this study indicated that both ZnO and GaN could be room temperature ferromagnets with the suggested substitution and

7 doping values. Subsequent work[7, 10] considered a ZnO supercell consist-

ing of eight ZnO pairs per cell (the traditional ZnO wurtzite unit cell con-

sists of two ZnO pairs per unit cell) to predict the magnetism of II-VI com-

pound DMSs. Two of the eight Zn atoms in this supercell were systemati-

cally replaced with TM atoms. In addition, the effects of hole doping with

N and electron-doping with Ga were also considered. A report by Sato and

Katayama-Yoshida[7] found that if no carriers are introduced into the system, antiferromagnetic ordering is the stable ground state conﬁguration. The addition of holes leads to a transition from antiferromagnetic to ferromagnetic behavior, while the addition of electrons leads to no change in the magnetic behavior of the system (remains antiferromagnetic). The predicted trend for

3d transition metals in ZnO was that the ground state for all transition metals (except Mn, which should be antiferromagnetic) should be ferromagnetic.

More speciﬁcally, these authors report that ferromagnetic ordering is stabilized by the addition of electrons, while the addition of holes results in a transition from ferromagnetic to antiferromagnetic ordering (an opposite result to that for Mn substitution). Another report[11] suggested the possi-

bility of co-substituting, i.e. substituting more than one transition metal on

the Zn site, with ferrimagnetic behavior predicted for (Fe,Cu) co-substituted

ZnO. More accurate density-functional theory-based calculations performed

by Spaldin[12, 13] take into consideration both Co2+ atoms that are separated

8 and those that are nearer to one another, in order to study clustering effects.

This ﬁnding shows that in contrast to previous predictions[7, 10], robust fer-

romagnetism can only be obtained in transition-metal-substituted ZnO with

hole doping.

The majority of research efforts on Co-substituted ZnO and Mn-substituted

ZnO involves thin ﬁlm growth, usually via pulsed laser deposition (PLD) of a ceramic target onto a sapphire substrate[14, 15, 16, 17, 18, 19, 20, 21, 22, 23].

Pulsed laser deposition is a valuable technique for transition-metal-substituted

ZnO thin ﬁlm growth because it allows for a high solubility of magnetic atoms

into the ZnO lattice. A typical study, such as a 2004 report by Venkatesan

and co-workers[17], uses a KrF excimer laser and a ceramic target consisting

of a mechanical mixture of ZnO and MO powders (where M is a transition

metal) to deposit Zn1−xMxO on a sapphire substrate. The substrate is held

at 600◦C and the oxygen pressure during deposition is maintained between

1 and 10−4 mbar, with resulting ﬁlm thicknesses between 60-120 nm. Mag-

netic measurements on Zn1−xMxO ﬁlms with M = Co indicate a magnetic

moment per cobalt ion between 0.8 and 2.6 µB, depending on the orienta-

tion of the applied magnetic ﬁeld. The moment is highest when the ﬁeld is

applied parallel to the edge of the sapphire substrate. These ﬁlms also ex-

hibit room temperature ferromagnetism. Other routes for preparing thin ﬁlms

9 of substituted ZnO include the sol-gel method[24, 25, 26], radio frequency magnetron sputtering[16, 27, 28, 29, 30, 31], and vapor transport with ion implantation[32, 33]. Although many of these investigations appear to yield promising results, there is, as mentioned previously, quite a distribution in the reported Curie temperatures (in the cases where ferromagnetism is observed) and magnetic moments. For example, Co2+ in a tetrahedral environment should have a moment of 3 µB; reported values range from 0.02-2.6 µB per Co ion.

The origin of ferromagnetic behavior seen in ZnO thin films is controver- sial. If one considers a film on the order of nanometers in thickness, the substitution of a small percentage of Zn atoms with Mn or Co implies that the overall number of magnetic atoms in the system will be rather small. Measuring the location and properties of a small number of atoms distributed throughout a thin film requires a great deal of precision, which is difficult to achieve with conventional diffraction and microscopy methods. As an example, a review by

Pearton[34] indicates that the local structure determined by EXAFS (extended x-ray absorption fine structure) in Mn-substituted GaN thin films reveals a significant fraction of Mn atoms present as small Mn clusters. In most studies, it is proposed that ferromagnetic ordering in these materials should arise from a competition between the antiferromagnetic superexchange interactions (in

10 which adjacent transition metal atoms, separated by a spin-polarized oxygen atom, must align antiferromagnetically to satisfy Hund’s rule) and the ferromagnetic double exchange interactions (in which carriers have spin memory and their hopping causes transition metal moments to align). However, direct evidence is lacking for this mechanism being the sole source of ferromagnetic behavior in transition metal substituted ZnO; transition metal micro-clusters and/or other transition metal oxide phases could easily contribute to or be the cause of observed ferromagnetic behavior. Since stoichiometry and phase purity are difﬁcult to determine in thin ﬁlms, the exact nature of the magnetic interactions is often quite ambiguous. Bulk samples with well-characterized phase purity, structure, and crystallite size are needed for detailed investigations of the exact origin of ferromagnetism (or lack thereof) in ZnO-based dilute magnetic semiconductors. These experimental data will also facilitate the development of conceptual models that can be linked to theoretical predictions about useful magnetic properties.

Aside from our own work[12], which will be discussed in Chapter 2, a few groups have explored the preparation and characterization of the bulk Zn1−xCoxO system. A metastability study[35] determined the solubility of cobalt in zinc oxide to be 65 percent via a hydrolysis route; another investigation[36] using a spray pyrolysis route pushed this limit to 70 per-

11 cent before evidence of phase segregation became apparent. Nearly all bulk studies[37, 38, 39, 40, 41, 42, 43] involve the sintering of starting oxides (e.g.

MnO2 and ZnO) in appropriate ratios to prepare polycrystalline Zn1−xMnxO or Zn1−xCoxO. A study by Sharma and co-workers[42] began with the mixing, calcining, and sintering of high-purity MnO2 and ZnO powders in order to make Zn0.98Mn0.02O. This resultant powder was then pressed into a pellet and sintered at various temperatures (500-900◦C) to determine the effect on its magnetic behavior. Magnetic measurements on these materials yielded room temperature and higher ferromagnetic behavior when the pellet sinter-

◦ ing temperature was held under 700 C, with a magnetic moment of 0.16 µB per Mn ion. X-ray diffraction data, crucial to the determination of secondary phases in these systems, was not reported. A follow-up study by Kundaliya and co-workers[40] attempted to replicate these ﬁndings, and determined that ferromagnetism does persist in these materials up to approximately 700◦C; however, this is due to a metastable oxygen-vacancy stabilized Mn2−xZnxO3−δ phase. This study concludes that ‘a uniform solid solution of Mn in ZnO does not form under low-temperature processing.’

An intrinsic problem with this type of solid-state ceramic processing is that the reaction must initially occur at the point of contact between two particles; in order to further the reaction, one must have increasingly longer diffusion

12 paths, which reduces the overall reaction rate. This makes it difficult to determine when the reaction has reached completion, hindering the chances of obtaining a compositionally homogeneous product. In light of these findings, it would be beneficial to have a preparation route that creates a random mixture of zinc and cobalt (or manganese) atoms on the zinc site, ensuring a truly dilute magnetic semiconductor material. The development of such a route and its decomposition to obtain stoichiometric bulk Zn1−xCoxO is the topic of the following chapter. In the third chapter, both Zn1−xCoxO and Zn1−xMnxO are studied to analyze the magnetic interactions present in each system. Chapter

4 explores the development of an ‘end-member’ of the metastable Zn1−xCoxO phase, novel wurtzite CoO, and its structural and magnetic properties. As a nanoscale analog to the bulk materials developed in the ﬁrst few chapters,

Chapter 5 will focus on the preparation of ZnO and Zn1−xCoxO nanoparticles and their properties. Chapter 6 will conclude this work by investigating another potentially more exciting system, dilute ferrimagnetic Fe-substituted

ZnGa2O4.

13 Chapter 2

Cobalt-substituted Zinc Oxide

The search for a dilute magnetic semiconductor within the Zn1−xCoxO sys-

tem has piqued our interest in creating a bulk analog to the Zn1−xCoxO thin

ﬁlms previously studied. In order to make a bulk dilute magnetic semiconduc-

tor material whose properties can be readily measured, we began with a route

which produced a suitable quantity of material, allowing characterization to

readily be performed. The route selected to prepare bulk Zn1−xCoxO allows for any quantity of material desired to be made, with an ease of reproducibility and translation to other ﬁrst row transition metal oxide systems. Our proposed route uses a single-source precursor, where transition metal ions are intimately mixed on lattice sites prior to decomposition.

14 2.1 Preparation

Polycrystalline bulk Zn1−xCoxO was prepared using an oxalate

[Zn1−xCox(C2O4)·2H2O] precursor decomposition technique with x = 0,

0.05, 0.10, 0.15, 0.20, 0.25, and 0.30. Due to the intrinsic metastability of the

Zn1−xCoxO system, crystalline oxalates are suitable precursors, creating a random and intimate mixing of Zn2+ and Co2+ ions on lattice sites prior to decomposition, along with the removal of carbon as CO and CO2 during decomposition, leaving a phase pure oxide product. Oxalates were prepared by mixing 0.4 M solutions of zinc and cobalt acetates with a 0.4 M solution of oxalic acid. The resulting precipitates were collected and rinsed extensively with deionized water, then dried in air at 60◦C. These oxalates were then ground and decomposed in air by placing in a pre-heated furnace for the des- ignated time. Decompositions of these oxalates to oxides were performed at temperatures as low as 300◦C, but for a higher degree of crystallinity, samples were decomposed in air at 900◦C for 15 minutes, and removed (‘quenched’) from the furnace. The resulting oxides were dark green in color, with the color deepening as the cobalt concentration increased. Characterization of these samples was performed via powder x-ray diffraction, transmission electron microscopy, and DC magnetization measurements.

15 2.2 Experimental Results

Powder x-ray diffraction patterns were acquired on a Scintag X2 diffractometer operating in the Bragg-Brentano geometry using Cu Kα radiation.

Data were collected at a step size of 0.02◦ in 2θ. Subsequent Rietveld re-

ﬁnement of these patterns was performed using the XND Rietveld code. Ri- etveld reﬁnement was also used to determine accurate lattice parameters for the wurtzite structure (illustrated in Figure 2.1) as a function of starting cobalt concentration. It is important to note that the difference in effective ionic radii between Zn2+ and Co2+ in tetrahedral coordination is nearly negligible (Zn2+

= 0.60 A˚ while Co2+ = 0.58 A);˚ hence signiﬁcant changes in the lattice constants are not evident. Due to the poor contrast between Co and Zn ions in x-ray diffraction, a more quantitative estimate of the relative amounts of each ion in the wurtzite lattice could not be determined solely through x-ray diffraction.

This was remedied by using transmission electron microscopy and energy dispersive x-ray spectroscopy for the x = 0.15 and 0.25 samples to obtain more accurate elemental analyses. These samples were dispersed on a carbon-coated copper grid and studied using a JEOL JEM 2000FX microscope equipped with an energy dispersive x-ray spectrometer. From these studies, a solubility limit for Co in ZnO was determined. Magnetic measurements were performed on the Zn1−xCoxO samples with x = 0.05, 0.1, and 0.15 using a Quantum De-

16 sign MPMS XL magnetometer. Susceptibility as a function of temperature was

measured by warming samples in a ﬁeld of 1000 Oe after cooling in zero ﬁeld.

Figure 2.1. The wurtzite unit cell. The cations (grey) can be substituted by other (mag-

netic) cations indicated by the blue sphere. Anions are orange.

Powder x-ray diffraction patterns of the Zn1−xCoxO samples with 0 ≤

x ≤ 0.3 are shown in Figure 2.2. The data are shown as points while the

Rietveld ﬁts are solid lines. The vertical markers above the ﬁgure represent

expected peak positions for the wurtzite ZnO and spinel Co3O4 phases; the latter emerges as a secondary phase at higher starting x values. As seen in the

Rietveld ﬁt, the spinel phase appears as an impurity in the x = 0.25 and 0.30 samples; consequently we can state that a single phase solid solution is obtained up to x = 0.20. For the x = 0.25 and 0.30 samples, Rietveld analysis was performed using a two-phase ﬁt to accommodate both the spinel and wurtzite

17 components of the structure.

◦ Figure 2.2. Powder x-ray diﬀraction data for Zn1−xCoxO decomposed at 900 C. Starting

◦ values of x = 0.25 and x = 0.30 yield peaks at 2θ = 37 indicative of a spinel Co3O4 impurity phase.

Rietveld analysis also allows the extraction of accurate hexagonal lattice parameters a and c, along with the unit cell volume as a function of starting x, as depicted in Figure 2.3. As mentioned previously, since the difference in radii between Zn2+ and Co2+ is nearly negligible, signiﬁcant changes in the lattice constants are not expected. However, the general trend shows that

18 as the a-parameter increases the c-parameter decreases, leaving the cell volume essentially constant. If Co2+ were in an octahedral environment, it would

be reﬂected as a dramatic change in the lattice parameter as a function of x; octahedral Co2+ has an effective ionic radius between 0.65 A(low˚ spin) and

0.74 A(high˚ spin), again versus 0.60 Afor˚ Zn2+.

3.260

3.255 (Å) a 3.250

3.245 0 0.1 0.2 0.3

5.208

5.204 (Å) c 5.200

0 0.1 0.2 0.3 47.8

) 47.7 3 (Å

V 47.6

47.5 0 0.1 0.2 0.3 starting x

Figure 2.3. Hexagonal lattice parameters a and c, along with unit cell volume V as a

function of x for Zn1−xCoxO.

Although x-ray diffraction provides evidence for a solubility limit at x =

19 0.20, it could miss small precipitates of a secondary phase (phases under one percent of the total composition would be missed by x-ray diffraction). In order to determine the exact solubility limit of the Zn1−xCoxO system, transmission electron microscopy (TEM) was employed, allowing the detection of small precipitates of secondary phases. The x = 0.15 and x = 0.25 samples were selected for study in order to ‘bookend’ the solubility limit suggested by x-ray diffraction. The TEM analysis for x = 0.15 indicates single crystals of

Zn0.85Co0.15O, with individual crystallites between 50 and 200 nm in size. De- spite the appearance of defects (as indicated by the arrows in Figure 2.4), the composition determined by energy dispersive x-ray spectroscopy (EDS) was uniformly Zn0.85Co0.15O throughout the sample. In comparison, the x = 0.25 sample has larger crystallites with a large number of structural defects. The composition determined by EDS does indeed suggest regions of impurities, with signiﬁcant variations in the Zn:Co ratio between crystallites (up to 80%

Co in certain instances).

From these structural studies, it is reasonable to assume that the x = 0.05,

0.10, and 0.15 samples have Co2+ uniformly substituting for Zn2+ in the wurtzite lattice; a magnetic study of these samples was deemed appropriate.

Magnetic data were acquired on warming in a field of 1000 Oe after cooling in zero field (ZFC); data taken on warming after field cooling (FC) showed iden-

20 Figure 2.4. Transmission electron micrographs of (a) Zn0.85Co0.15O and (b) Zn0.75Co0.25O.

The scale bars are 200 nm.

tical behavior. The traces of inverse susceptibility (1/χ) versus temperature followed a Curie-Weiss (antiferromagnetic) behavior at temperatures between

300 and 400 K, as shown in Figure 2.5.

These data can be ﬁt to a straight line and extrapolated to the temperature axis to determine the Curie-Weiss θ, which is an indicator of the type and strength of magnetic coupling between Co2+ ions in the structure; for x = 0.10 and 0.15, θ = 60 and 90 K, respectively. However, for x = 0.05, θ is slightly positive, indicating a slightly ferromagnetic behavior. The magnitudes of θ are larger due to the higher concentrations of magnetic ions in the lattice as x increases. In addition, the effective magnetic moment per mole of Zn1−xCoxO

21 was calculated as a function of starting x from the susceptibility data. The

slope C from χ = C/(T − θ) can be related to the effective magnetic moment

1/2 µe f f through µe f f = (3kBC/NA) where kB is the Boltzmann constant and

NA is Avogadro’s number. From µe f f , we can calculate the number of unpaired

electrons per formula unit of Zn1−xCoxO through the Lande´ g-factor, which re-

lates an ion’s number of unpaired electrons to its effective magnetic moment.

These are plotted in Figure 2.6 as a function of starting x in Zn1−xCoxO. The

dashed line corresponds to the expected values of the number of unpaired elec-

trons per formula unit assuming all the cobalt in the structure is tetrahedrally

coordinated in the high-spin conﬁguration. The correspondence between ob-

served and expected values corroborates our belief that the samples are truly

Zn1−xCoxO with speciﬁed x.

Subsequently, low temperature (2 K) magnetization as a function of magnetic ﬁeld was measured for Zn1−xCoxO with x = 0.05, 0.10, and 0.15. This is plotted in Figure 2.7 as magnetization in bohr magnetons as a function of

ﬁeld scaled by the temperature. For all three samples, no ferromagnetic ordering is present, with no evidence of hysteresis. Included for comparison is the Brillouin function for an ideal paramagnet, again demonstrating that the x = 0.05 sample most closely approximates paramagnetic behavior. For larger

x values, the concentrations of magnetic atoms are larger and hence the anti-

22 ferromagnetic interactions are more pronounced, leading to a deviation from ideal paramagnetic behavior. Saturation of the x = 0.10 and 0.15 samples occurs at smaller values but the saturation behavior for all three samples begins at approximately the same H/T value as the Brillouin function. A further analysis of this magnetic data is investigated in the following chapter.

2.3 Theory

To explore the possibility of ferromagnetism in transition metal substituted ZnO, ﬁrst-principle total energy calculations were performed by Pro- fessor Nicola Spaldin using density functional theory based on pseudopoten- tials with localized atomic orbital basis sets. The code SIESTA was used as it provides accuracy with small computational cost versus other approaches. A

32-atom wurtzite lattice supercell was constructed with 16 ZnO formula units, created by doubling the conventional four-atom wurtzite unit cell along each axis, giving a hexagonal lattice parameter a = 12.28 au and the ratio c/a =

1.6024. The densities of states for such a supercell are displayed in Figure

2.8(a), with Zn d states concentrated within a region centered around -7 eV with a dispersion of approximately 2 eV. Oxygen p states are concentrated between -6 and -2 eV.When one cobalt atom is substituted on a zinc site (resulting in a cobalt concentration of 6.25%) in each supercell, the ordering of spins is

23 forced to be ferromagnetic. The calculated magnetic moment per unit cell is

2+ 3.10 µB, quite similar to the 3 µB predicted for strictly ionic Co with three unpaired electrons. The density of states for this situation (Zn15CoO16) is shown in Figure 2.8(b). This density of states is almost identical to pure ZnO, aside

from the localized and well-deﬁned Co states (shaded with a thick solid line)

within the band gap. This implies that the spin polarization of the Co atom

hardly affects the Zn and O states.

However, with two cobalt atoms substituted in the supercell (giving a

12.5% cobalt concentration with the formula Zn14Co2O16), several different

positional as well as magnetic conﬁgurations are possible. Two different po-

sitional conﬁgurations were considered: a ‘near’ conﬁguration in which the

cobalt atoms in a unit cell are separated by a single oxygen atom, and a ‘sepa-

rated’ conﬁguration, in which the cobalt atoms are connected through -O-Zn-

O- bonds. For both ‘near’ and ‘separate’ conﬁgurations, the relative energies

of ferromagnetic and antiferromagnetic spin alignments were calculated. Our

results indicated that for both conﬁgurations, the separations in energies be-

tween the ferromagnetic and antiferromagnetic are very small, with the ferro-

magnetic spin alignment being slightly lower; i.e., the energy of the ‘separated’

ferromagnetic conﬁguration is 4 meV lower than that of the ‘separated’ antifer-

romagnetic conﬁguration while the ‘near’ ferromagnetic conﬁguration is only

24 1 meV lower than that the ‘near’ antiferromagnetic conﬁguration.

In addition to modeling cobalt substitution in the ZnO wurtzite lattice,

electron and hole doping were also considered. Hole doping was modeled

by removing a zinc atom from the supercell to form Zn13Co2O16, where represents a vacancy. This p-type doping strongly stabilizes the ferromagnetic ground state; in both ‘near’ and ‘separated’ conﬁgurations, the ferromagnetic state is now 60 meV lower in energy than the antiferromagnetic state. Con- versely, if electron doping is modeled by removing an oxygen atom to create

Zn14Co2O15, the antiferromagnetic state is now 4 meV lower in energy than the ferromagnetic state for the ‘separated’ configuration while for the ‘near’ configuration the antiferromagnetic state is 1 meV lower than the ferromagnetic state. Small (less than 10 meV) differences in the energies of the different ground states are not significant; the most striking result of the calculations is that robust ferromagnetism in Zn1−xCoxO is only possible in the present of substantial hole doping. These results are summarized in Figure 2.9.

From these calculations, a trend is observed that aids the understanding of

the magnetic data: when the cobalt atoms are separated, the tendency for these

atoms to align ferromagnetically is enhanced. As mentioned above, while the x

= 0.05 sample showed evidence for ferromagnetic interactions between cobalt

atoms (Curie-Weiss θ = 20 K), the x = 0.10 and 0.15 samples imply a nearest-

25 neighbor antiferromagnetic ordering with θ = -60 K and 90 K, respectively. To interpret these results, one can consider the fraction of transition metal ions in the wurtzite lattice that have other metal nearest-neighbors (ignoring the oxygen anion), as a function of x, as plotted in Figure 2.10. When x = 0.05, over half (about 55%) of the Co2+ have no nearest-neighbor Co2+. This implies that a large fraction of the Co2+ ions in the x = 0.05 sample correspond to the ‘separated’ case, where magnetism occurs from coupling through intervening zinc ions. As x increases, the fraction of Co2+ that have Co2+ nearest-neighbors increases, and the dominant magnetic interaction, enhanced by the shrinking distances between one cobalt ion and another, begins to resemble the ‘near’ scenario. In all three samples (x = 0.05, 0.10, and 0.15), one can consider two kinds of magnetic ions: ones that have nearest neighbors that are cobalt, and ones that do not. The cobalt ions with other cobalt nearest neighbors couple antiferromagnetically, so as the cobalt loading in Zn1−xCoxO increases, the saturation moments at 2 K are reduced. The cobalt ions without nearest neighbors

(’isolated’) act as paramagnets, with χ → ∞ as T → 0. Although the afore- mentioned description of the magnetic behavior in this system is qualitatively satisfying, it would be useful to ﬁt the magnetic data to a function that can describe both the ‘near’ and ‘separated’ interactions while illuminating the rea- sons why no ferromagnetic order is observed in transition-metal-substituted

ZnO samples. This is the topic of the following chapter.

26 0.04 (a)

) 0.03 −1 Oe −1 0.02

0.01 (emu mol χ 0 0 100 200 300 400 4000 (b) 3000 mol Oe)

−1 2000 (emu

χ 1000 1/

0 −100 0 100 200 300 400 T (K)

Figure 2.5. Susceptibility versus temperature (a) for x = 0.05, 0.10, and 0.15 in

Zn1−xCoxO. Inverse susceptibility versus temperature (b) for the same samples; the high-

temperature portions of the data have been extrapolated to the temperature axis to deter-

mine the Curie-Weiss θ.

27 0.5

) 0.4 −1 mol B µ 0.3

0.2

experiment 0.1 spin−only magnetic moment (

0 0 0.05 0.1 0.15 0.2

x in Zn1−xCoxO

Figure 2.6. The number of unpaired electrons per formula unit Zn1−xCoxO as a function of starting x, obtained from the Curie-Weiss ﬁt of the high temperature susceptibility.

28 3

2 x=0.05

) 1 x=0.10 2+ x=0.15

Co 0 per

B µ −1 M (

−2

−3 −4 −2 0 2 4 H/T (T K−1)

Figure 2.7. Magnetization as a function of applied ﬁeld (scaled by the temperature) at

2 K. The dashed line represents the Brillouin function for a Co2+ ion with three unpaired electrons.

29 80 (a) 40

0 −8 −6 −4 −2 0 2 4 6 8 ) −1 80

cell (b) −1 40 Co 3d total spin

−1 0

80 −8 −6 −4 −2 0 2 4 6 8 DOS (states eV 80 (c) 40 Co 3d total 0

80 −8 −6 −4 −2 0 2 4 6 8 Energy (eV)

Figure 2.8. Densities of states for a supercell of ZnO (a); Zn15CoO16 (b); and Zn14Co2O16

(c). In panels (b) and (c), the upper portions represent spin up states while the lower portions represent spin down states.

30 Zn14Co2O16 FM AFM “near” -1 0 “separated” -4 0

Zn13Co2O16 “near” -60 0 “separated” -60 0

Zn14Co2O15 “near” 0 -1 “separated” 0 -4

Figure 2.9. Relative stabilization energies (in meV) of the diﬀerent magnetic ground states.

Zn1−xMxO 0.8 x = 0.05 x = 0.10 x = 0.15 0.6 x = 0.20

0.4 frequency of NN

0.2

0 0 1 2 3 4 5 6 7 8 9 10 11 12 number of NN

Figure 2.10. Distribution of the number of M near-neighbors (NN) for each M atom for diﬀerent values of x in Zn1−xMxO.

31 Chapter 3

Magnetism in Substituted ZnO

The magnetism explored in the previous chapter began to describe the interactions between magnetic ions in the diluted magnetic semiconductor

Zn1−xCoxO when these ions are spaced either by a single oxygen atom in the wurtzite structure (‘near’) or by a -O-Zn-O- spacer (‘separated’). Along with this system, one can also consider the behavior of Zn1−xMnxO, with x between 0.02 and 0.15, to develop a general understanding of the magnetic behavior of transition metal ions in ZnO. In this chapter, the magnetic properties of both systems are measured as a function of temperature and magnetic

field in order to fit the behavior to known interactions from room temperature to low temperature (T=2 K). As mentioned in Chapter 1, certain studies find room temperature ferromagnetism in Zn1−xMnxO in both bulk and thin film

32 conﬁrmations[42]; others do not[14, 44]. Due to this disparity, our study of bulk

Zn1−xMnxO can help lead to a resolution of some of these mixed results.

3.1 Preparation

Using the same single-source oxalate precursor method described in Chap- ter 2, bulk [Zn1−xMnx(C2O4)·2H2O] samples were prepared with 0.02 ≤ x ≤

0.15. These materials were decomposed at 1100◦C for 15 minutes in air to form Zn1−xMnxO. Powder x-ray diffraction patterns of these materials were recorded on a Scintag X2 diffractometer in the Bragg-Brentano conﬁguration using CuKα radiation. X-ray data were collected using a step size of 0.015◦ in

2θ, as shown in Figure 3.1. None of these samples showed impurity phases as the Mn loading increased to 15%. There is evidence of linewidth broadening, suggesting a decrease in grain size/crystal correlation. This is reasonable in keeping with the low expected solubility of Mn2+ in the ZnO lattice; Mn2+ has an effective ionic radius of 0.66 Ain˚ tetrahedral coordination whereas Zn2+ has an effective ionic radius of 0.60 A.˚ Higher substitution values were not investigated due to an apparent solubility limit at higher x values; x-ray diffraction

(not shown) suggests an Mn3O4 impurity arises at these higher Mn concentrations.

33 Figure 3.1. Powder x-ray diﬀraction data for Zn1−xMnxO. Data are circles; the lines are

Rietveld simulations.

3.2 Results

Subsequent Rietveld reﬁnement of the x-ray data gives hexagonal lattice

cell parameters a and c for the wurtzite structure. The evolution of each lattice

parameter as a function of Mn concentration, x, is shown in Figure 3.2, along

with the unit cell volume. Unlike Co-substituted ZnO, the cell parameter evo-

lution is not straightforward in this Mn-substituted ZnO system. The a cell

parameter increases linearly with x only until x = 0.08; the c cell parameter

follows a slightly more complicated path that eventually reaches a maximum,

again at x = 0.08. As expected when substituting a larger Mn2+ ion for a Zn2+

ion, the unit cell volume increases systematically as a function of x, until x =

0.08.

34 Figure 3.2. Lattice cell parameters (above) and unit cell volume (below) for Zn1−xMnxO.

Our results differ slightly from a previous report on bulk Mn-substituted

ZnO[41], which showed a linear increase in the a and c lattice parameters,

as a function of starting x until x = 0.15, which is their observed solubility

limit. This resulted in an increase in the unit cell volume V. With these results

in mind, we restrict our magnetic measurements on samples with x ≤ 0.10

for Zn1−xMnxO, along with Zn1−xCoxO. Magnetization measurements were performed using a commercial superconducting quantum interference device

(SQUID) magnetometer (Quantum Design MPMS). In order to minimize sample holder effects, each measurement was performed using approximately 30 mg of sample material; this yielded a signal over three orders of magnitude greater than the magnetic background of the sample holder. Magnetization

35 was measured as a function of applied ﬁeld at a single (ﬁxed) temperature; additionally, magnetic susceptibility was measured as a function of temperature.

To obtain the intrinsic magnetization of our samples as a function of temperature, the differential susceptibility was measured by subtracting the magnetic moment measured at 1 T from the magnetic moment measured at 2 T at each temperature. Although ZnO should (in theory) exhibit diamagnetic behavior, the background susceptibility of the x = 0.00 sample (pure ZnO) was also measured separately and subtracted from the data for substituted samples. This

‘baseline’ contribution was determined to be approximately ten percent of the total susceptibility at higher temperatures.

In previous work[21], impurity effects had been attributed to intrinsic behavior, making it all the more important that we detect any impurity in our samples that could contribute to the magnetic behavior. X-ray diffraction indicates that any impurity, if present, remains under the one percent level. Addi- tionally, low magnetic field susceptibility measurements as a function of magnetic field, at a fixed temperature, show no deviation from linear behavior.

This indicates that there are no impurities present at this detection level; we can feel confident that all the transition metal ions are substituting for Zn2+ in the ZnO lattice. As a final bulk probe of magnetic order, the specific heat

(heat capacity per unit mass) of the x = 0.15 sample was measured for Mn-

36 substituted ZnO. In order to obtain decent thermal conductivity in the sample,

30 mg of the Zn0.85Mn0.15O sample was mixed with 30 mg of micron-sized sil- ver powder (to obtain roughly a 1:1 ratio by weight), and cold-pressed into a sintered pellet. The x = 0.15 sample was chosen as it would have the greatest potential impurity contribution to the magnetization. As shown in Figure 3.3, the absence of any long-range order in magnetic impurities manifests itself as a lack of any signal in speciﬁc heat; we can now be quite sure that the intrinsic effects of the substituted ZnO are indeed being probed. Consideration of these measurements, along with the differential susceptibility mentioned previously, solidiﬁes our assertion that there is no spurious contribution to the observed magnetic behavior from ferromagnetic impurity clusters.

2.5

2.0 ) 2 1.5

1.0 Mn Zn O + Ag .15 .85

C/T (mJ/g K 0.5

0.0 0 20406080 Temperature (K)

Figure 3.3. Speciﬁc heat (heat capacity per unit mass) measured for Zn0.85Mn0.15O.

37 Magnetization as a function of applied ﬁeld, depicted in Figure 3.4 was measured for the Zn1−xMnxO samples with x = 0.02, 0.04, and 0.08. These data were measured at 2 K, and suggest that there are contributions to the magnetic signal, both from free spins and from spins within antiferromagnetic clusters.

The moment is large for the lower concentrations of Mn substitution (indicated as circles for x = 0.02 and triangles for x = 0.04 in Figure 3.4) but decreases as the

Mn loading increases. This can be explained as follows. Initially, the magnetic moment emerges primarily from free spins in each system. As x increases, the number of Mn ions that belong to antiferromagnetic clusters increases, and these clusters, in turn, do not contribute to the magnetic signal. This reduces the net magnetization, and is similar to the behavior exhibited by Zn1−xCoxO

(as described in Chapter 2). It is important to note that there is no evidence of ferromagnetic hysteresis, even at 2 K. Our observation is in direct contrast to a report suggesting room temperature ferromagnetism in Zn0.98Mn0.02O[42], which found a very small ferromagnetic moment in samples prepared under relatively low temperature conditions. The reason for such a discrepancy may be attributed to unreacted starting manganese oxides[41].

The inverse susceptibility as a function of temperature is plotted for both

Zn1−xCoxO and Zn1−xMnxO in Figure 3.5 with x = 0.05, 0.10, and 0.15 for Co substitution and x = 0.02, 0.04, and 0.08 for Mn substitution. These data show

38 Figure 3.4. Magnetization as a function of applied ﬁeld for Zn1−xMnxO at 2 K.

behavior characteristic of other transition-metal-substituted ZnO samples: a

high temperature portion that is nearly linear, followed by a signiﬁcant curva-

ture at lower temperatures. Additionally, there is a systematic variation in the

high temperature magnetization as a function of starting x. The samples with

lower starting x have larger values; the inverse susceptibility decreases mono- tonically with increasing x. The analysis of such data is typically performed by ﬁtting the high temperature portion of the 1/χ plot to a linear Curie-Weiss

behavior expected for an antiferromagnetic material. Previous work[45] on

II-VI dilute magnetic semiconductor systems predicted that the high tempera-

ture susceptibility should follow a modiﬁed Curie-Weiss law, where the Curie

39 constant C and the Curie-Weiss temperature are scaled by the substituent con-

centration x. Although this model works well for manganese-substituted cad-

mium and mercury selenides and tellurides, discrepancies arise when we try

to apply this model to our Mn-substituted ZnO materials.

Figure 3.5. Inverse susceptibility as a function of temperature for Zn1−xCoxO (above) and

Zn1−xMnxO (below). The solid lines are ﬁts to the functional form of the susceptibility.

40 3.3 Modeling

As such, a model proposed by Professor Gavin Lawes[46] describes the

complete susceptibility behavior based on two sets of substituent transition

metal spins, as suggested by the magnetization behavior shown in Figure 3.4.

Returning to the concept of ‘near’ and ‘separated’ spins outlined in Chapter 2, this model assumes one subset of spins (those substituent ions with no nearest- neighbor substituent ion) is completely ‘free,’ and hence follows a simple paramagnetic Curie behavior. The second set of spins (those substituent ions with at least one substituent nearest-neighbor) is affected by mean ﬁeld interactions, resulting in a susceptibility that can be expressed as a Curie-Weiss function.

Separating the substituent ions into these two noninteracting subsets (meant to represent isolated and clustered spins) yields an excellent ﬁt to the susceptibility data over our entire measured temperature range. One can also allow for the possibility of different Curie constants for each term. In particular, this model assumes:

C C χ = 1 + 2 (3.1) T T + θ

to ﬁt the magnetic susceptibility data for our Zn1−xMnxO and Zn1−xCoxO systems. As depicted in Figure 3.5, the solid lines show the ﬁt to Equation

41 3.1, which accurately describes the behavior of these materials over the en-

tire temperature range from the high temperature linear behavior through the

curvature of the low-temperature regime. It is noteworthy that only a subset

of the spins participate in the magnetic behavior of these materials. For ex-

ample, in Mn-substituted ZnO, the values of θ range from 190 K to 360 K for

the samples studied. This implies that the spins in transition metal clusters

are affected by antiferromagnetic mean ﬁeld interactions, in keeping with the

behavior shown in Figure 3.4. Similar results are observed for Co-substituted

ZnO; in this system, the values of θ lie between 160 K and 250 K.

As noted in Chapter 2, the Curie constant C can be related to the effective magnetic moment of an ion, or more speciﬁcally, to the effective magnetic moment of a substituent transition metal ion in our ZnO systems. Considering

Equation 3.1, we can use the ﬁt values of C1 and C2 to extract the effective moment for the transition metal spins. Assuming C1 arises from substituent transition metal ions with no nearest-neighbor substituent transition metal ions, C1 must be scaled with the fraction of transition metal ions meeting this condition.

The relative fraction of transition metal ions with no nearest neighbors was computed as a function of x by assuming random substitution of transition metals on the Zn site. The effective magnetic moment of the isolated spins was then determined from C1 scaled by the fraction of transition metal ions with

42 no nearest neighbors. Likewise, the effective moment of the clustered spins was calculated from the value of C2 scaled by the fraction of clustered spins.

These calculations are summarized in Figure 3.6 for Co- and Mn-substituted

ZnO. The error bars capture the uncertainty in determining the value of x, and show the expected values of the effective magnetic moments. Representative

2+ 2+ expected spin moments are 5.9µB for Mn and 4.8µB for Co [47]. The results shown in Figure 3.6 yield an average effective moment (taken as the intermediate point between isolated and clustered spin contributions) close to the expected values. For small x, the effective moment is larger for the clustered spins than for the isolated ones; the reason for this is not entirely clear.

Our study on a series of transition-metal-substituted ZnO systems reveals several noteworthy features. Analysis of compounds with varying amounts of substituent ions gives evidence for a systematic clustering of spins as the fraction of magnetic ions is increased. Furthermore, in keeping with our[12] and other[44] prior results, we ﬁnd that the dominant spin-spin interactions are antiferromagnetic in these clusters. This work also leads to an explanation for why such antiferromagnetic interactions do not lead to long-range spin ordering, as seen in other transition metal oxide systems. Assuming the spins in these systems are localized and non-migratory, we suggest that the lack of magnetic order arises from geometrical considerations. In diluted magnets,

43 the percolation concentration, pc, plays an important role[48]. This percola-

tion concentration, or threshold, represents a critical bond or site concentra-

tion such that a system has sufﬁcient linkage paths extending across its whole.

The value of pc depends on the type of lattice being randomly diluted, on the

range of the exchange interactions (nearest-neighbors or next-nearest neigh-

bors), and whether the dilution is of site or bond type. Site dilution is more

effective than bond dilution in disconnecting the lattice, such that for a given

lattice, the critical concentration pc for site dilution is less than that for bond dilution. For the wurtzite lattice, the critical concentration, or percolation threshold, is 19.5%[48]. (This quoted threshold is actually for a fcc lattice, which has

the same number of nearest-neighbors as the wurtzite lattice.) From this we

can see that the concentration of magnetic ions in our study- which at maxi-

mum is 10%- is well below the percolation threshold, implying that long-range

magnetic order should not be expected in these materials.

3.4 Summary

In conclusion, our efforts in the preparation and characterization of

Zn1−xCoxO and Zn1−xMnxO materials have led to several remarkable out-

comes. We ﬁnd no evidence for a ferromagnetic transition in these systems

above T = 2 K for 0.02 < x < 0.15 for either the Co or Mn substituent in ZnO.

44 Additionally, the dependence of the magnetization on applied ﬁeld (at low

temperature) indicates that the dominant interaction between spins is antifer-

romagnetic, as mentioned in the previous chapter. The ﬁt to our magnetic sus-

ceptibility data by Lawes effectively describes the behavior of these materials

over a large temperature range as the sum of two Curie-Weiss terms. The ﬁt

can be described as a high-temperature (θ > 100 K) antiferromagnetic interac-

tion, which is associated with nearest-neighbor interactions between magnetic

clusters, and a low-temperature Curie function that isolated spins participate

in.

In light of these ﬁndings, it becomes increasingly difﬁcult to imagine a sit-

uation in which substituting either Co or Mn for Zn in ZnO would produce a

ferromagnetic semiconductor that would be useful in devices (i.e. exhibit fer-

romagnetism above a few K). These results are substantiated by recent work

stressing the importance of hole-doping in substituted ZnO to achieve carrier-

mediated ferromagnetism[13]. The next chapter will investigate the struc-

tural and magnetic properties of the ‘end-member’ of the Zn1−xCoxO system, wurtzite CoO.

45 Figure 3.6. Eﬀective moments for the isolated (open symbols) and clustered (ﬁlled symbols) Co2+ (upper panel) and Mn2+ spins (lower panel). The dotted lines show the expected values of the spin-only and full-spin moments for the Co ions and the spin-only moment appropriate for the Mn ions. The error bars yield an uncertainty in x of ±0.005.

46 Chapter 4

Wurtzite Cobalt Oxide

In order to complete our magnetic and structural study of Zn1−xCoxO, it is useful to try to prepare the ‘end-member’ of the system, CoO, in the wurtzite structure. Cobalt oxide typically crystallizes in one of two stable phases: CoO, which has the rocksalt crystal structure (space group Fm3¯m) or Co3O4 which has the normal spinel structure (space group Fd3¯m). These crystal structures are cubic, with an octahedral arrangement of oxygen atoms

2+ around the Co ion. This leads to both CoO and Co3O4 exhibiting antiferromagnetic behavior[49]. Recently, materials garnering attention are those with tetrahedrally coordinated structures such as GaAs, ZnO, and GaN, which crystallize in either the cubic zinc blende (space group F43¯ m) or the hexagonal wurtzite (space group P63mc) structures. In addition to their semiconducting

47 properties, these materials are studied as potential ferromagnetic semiconduc-

tors, made by adding several percent of a magnetic ion to the lattice, as in

Ga1−xMnxAs[50]. There is also a possibility for the coupling of structure with magnetic properties in this potentially piezoelectric material; piezomagnetic

behavior has been predicted in the hypothetical wurtzite MnO[51]. As such, it

is of great interest to prepare cobalt oxide in a tetrahedrally coordinated conﬁg-

uration to determine its structural, magnetic, electronic, and optical properties.

4.1 Previous work

CoO in the zinc blende structure was ﬁrst prepared by decomposition of

Co acetate in a nitrogen atmosphere[52] with approximately four percent each

of carbon and cobalt metal resulting as impurity phases, conﬁrmed by x-ray

diffraction. More recently[53], the decomposition of cobalt acetate tetrahy-

drate in argon was studied using time-resolved neutron diffraction and ther-

mogravimetric analysis; in a parallel study, electron microscopy and atomic

simulation calculations were utilized to determine crystal morphologies and

predict lattice energies for the rocksalt, zinc blende, and wurtzite polymorphs

of CoO[54], respectively. The decomposition was determined to consist of a

loss of water at 150◦C, followed by crystallization of the anhydrous acetate at

200◦C. Subsequent heating led to the formation of either zinc blende CoO at

48 290◦C or a mixture of zinc blende and wurtzite at 310◦C. It is important to

note that the wurtzite phase was never formed without the zinc blende phase

present[54], implying the wurtzite polymorph nucleates from zinc blende, per-

haps as a stacking fault. At 320◦C, a transformation to rocksalt CoO occurs, sta-

bilizing an octahedral coordination. The lattice energy calculations[53], along

with an investigation of the thermodynamic activity-composition relations in

the CoO-ZnO system[55] suggest that when the total lattice energies are com-

pared (the total lattice energy is the sum of ionic cohesive energy and octa-

hedral site preference energy), the rocksalt structure is more stable than the

wurtzite structure, although only by a small amount (v0.27 eV per mol).

4.2 Preparation

Due to the narrow temperature range in which wurtzite CoO will trans-

form to rocksalt CoO, we suggest an entirely novel precursor route for the

formation of tetrahedrally coordinated CoO involving the decomposition of

cobalt acetylacetonate, Co(CH3COCH2COCH3)2, in reﬂuxing dibenzyl ether.

Specifically, one gram of cobalt acetylacetonate was added to v40 grams of benzyl ether in a three-necked flask equipped with a magnetic stir bar; a water condenser was inserted into the center neck for refluxing. The other two necks were used for a thermocouple and nitrogen flow. This solution was heated to

49 reﬂux to between 290 and 293◦C, with magnetic stirring. During heating, the solution progresses from pink through purple to a brownish black. The mixture was cooled for one hour and centrifuged, allowing for the solid product to be collected. This product was then washed in toluene and dried in air at

80◦C overnight. The resultant powder was a deep moss green in color, akin to the Co-substituted ZnO materials, which grew increasingly darker green as a function of Co loading. X-ray diffraction data of this powder was collected on a Scintag X2 diffractometer in the Bragg-Brentano conﬁguration (Cu Kα radiation, 45 kV, 35 mA) with a step size of 0.01◦ for 6 hours between 30 and 90◦

2θ.

Neutron diffraction data were collected on the Strain Scanner at the Aus- tralian Nuclear Science and Technology Organization (ANSTO) reactor HI-

FAR. This instrument has a well-shielded, small 32-wire area detector and gives a better signal-to-noise ratio when the detector is in the close-in position, compared with standard powder instruments at ANSTO. Data were collected for 80 minutes at each detector position in the 4.2 K run; this was reduced to

40 minutes per detector in the 450 K run. The sample was contained in an aluminum foil tube ﬁve millimeters in diameter and v10 millimeters in length.

One end of this tube was press-sealed with a fold of cadmium and the other was ﬁtted with a ﬁve millimeter diameter aluminum pin, which was screwed

50 to the cold head of the cryofurnace. Despite being masked with cadmium,

the foil can give rise to peaks in the neutron diffraction pattern. The reported

temperature is that of the head to which the aluminum pin was attached.

4.3 Results

Neutron diffraction is a powerful tool for structural analyses because the

intensity of neutron scattering varies quite irregularly with the atomic number

of a scattering atom. Hence, unlike x-ray diffraction, it is possible to differenti-

ate between neighboring elements on the periodic table, or between light and

heavy elements, such as oxygen and cobalt. Additionally, neutrons interact

with the magnetic moment of the scattering atoms, helping to disclose any in-

formation about the magnetic structure. Room temperature powder x-ray and

neutron diffraction data for CoO is shown in Figure 4.1. Due to the small sam-

ple amount and Co fluorescence in the presence of Cu Kα radiation, the x-ray and neutron data are noisy. In order to determine the structure of our novel compound, we used the XND Rietveld code to refine the neutron and x-ray data simultaneously. The 300 K neutron data did not yield any peaks corresponding to any magnetic phase. In order to accurately assess all potential phases in the sample, the neutron data was refined against expected patterns for wurtzite CoO, fcc-Co (determined to be a small impurity in the sample) and

51 fcc-Al (from the sample can for neutron measurements). The x-ray reﬁnement

did not include the aluminum can. In Cu Kα radiation, Co scatters anoma- lously; hence the appropriate f 0 and f 00 terms were included in the reﬁnement.

The relative coherent neutron scattering cross-sections are 5.80 fm for O and

2.49 fm for Co. This means that the neutron diffraction pattern will be dominated by scattering by oxygen while the x-ray pattern will be dominated by scattering from cobalt. Due to the site symmetry in the wurtzite unit cell for Co and O, the neutron and x-ray ﬁts to CoO are quite similar, apart from the typical form-factor decay in the x-ray data (Figure 4.1). This combined reﬁnement

gives an RBragg of nine percent for the CoO phase. From this ﬁt, the wurtzite

˚ ˚ 1 2 lattice parameters are a = 3.244 A, and c = 5.203 A, with Co at ( 3 , 3 ,0) and O at

1 2 ( 3 , 3 ,0.416). The relative amount of fcc-Co was determined to be v 12 mol%.

Rietveld reﬁnement of wurtzite CoO also yields bond distances and va-

lences for this novel material. As shown in Figure 4.2, wurtzite CoO has a

rather long axial bond distance of 2.162 A,˚ and three shorter ‘equatorial’ dis-

tances of 1.923 A,˚ with a ratio of 1.13. For comparison, pure wurtzite ZnO gives an axial bond distance of 2.009 A,˚ with equatorial distances of 1.968 A,˚ yielding

a ratio of 1.02. Additionally, a bond valence sum of 1.9 is calculated for Co. Un-

fortunately, we have yet to be able to prepare CoO without an accompanying

Co metal impurity. From previous work on transition metal nanoparticles[56],

52 Figure 4.1. Powder neutron (above) and x-ray (below) diﬀraction data patterns of wurtzite

CoO. The points are data and the lines are the Rietveld fits. it has been shown that cobalt acetate is easily reduced to cobalt metal in refluxing organic solvents in the presence of organic alcohols. Although we have not added any extraneous reducing agents to our route, it is possible that the decomposition products of the acetylacetonate serve to create sufficiently reducing conditions such that a portion of the cobalt is reduced. Unfortunately, due to the fine-grained nature of the CoO powder, we have not been able to separate Co from the CoO magnetically.

Magnetization measurements were taken on a Quantum Design MPMS

53 Figure 4.2. Crystal structure of wurtzite CoO drawn using parameters obtained from

Rietveld reﬁnement. The light spheres are O; the dark spheres are Co.

5XL magnetometer between 5 and 400 K. Magnetic susceptibility as a func-

tion of temperature and as a function of applied magnetic ﬁeld were recorded,

as displayed in Figure 4.3. In order to saturate the ferromagnetic contribu-

tion from the fcc-Co, magnetic susceptibility as a function of temperature was recorded under a ﬁeld of H = 2T. In keeping with the antiferromagnetic behavior exhibited by rocksalt CoO[57], one would expect wurtzite CoO to display

similar behavior. However, as displayed in the top panel of Figure 4.3, there is

no evidence for ordering in this system; the reason for such behavior may be

due to magnetic frustration in this system, which will be elaborated upon later

in the chapter.

54 Magnetization as a function of temperature is plotted in the lower panel of Figure 4.3. Data were acquired at seven different temperatures, using 50 K intervals between 5 and 305 K. The magnetization is clearly dominated by the ferromagnetic Co metal impurity. As expected for the high Curie temperature of Co metal (v 1400 K), no large change is evident in the M-H loops in the measured temperature range. Additionally, most of the traces collapse on one another, and saturate at H = 1 T with a saturation magnetization value of

0.24µB per Co ion. Comparing this with a typical saturation value of 1.74µB for Co metal, we calculate the relative amount of cobalt metal in the sample to be v14 mol%, which is comparable to the value determined via Rietveld reﬁnement.

In order to further investigate the possibility of magnetic ordering in this system, magnetic neutron scattering was performed at various temperatures between 15 and 450 K, as detailed in Figure 4.4. Neutrons with λ = 1.401 Awere˚ used. The data indicate that there are no new magnetic reﬂections at low an- gles, even down to 15 K, aside from a small ‘bump’ in the data at 4π sin θ/λ =

2π/d = 1.3 A˚ −1, indicated by the arrow. With six unpaired d electrons expected per unit cell of CoO and a small unit cell volume, one would expect peaks associated with long-range magnetic order to be quite pronounced. The lack of evidence for magnetic ordering in neutron diffraction, magnetic susceptibility,

55 0.074

) (a)

−1 0.073

Oe 0.072 −1

0.071

0.070 (emu mol χ 0.069 0 100 200 300 400 T (K)

0.4

0.2 Co)

per 0.0

B µ ( −0.2 M (b) −0.4 −6 −3 0 3 6 H (T)

Figure 4.3. Magnetic susceptibility as a function of temperature for CoO, above. The ‘+’ represent zero-field cooled data; the ‘◦’ are field-cooled data. Magnetization as a function of temperature acquired at seven different temperatures between 5 and 305 K, below. and magnetization measurements suggests that CoO in the wurtzite structure may in fact be a magnetically frustrated system. In magnetically frustrated systems, a large fraction of magnetic sites in a lattice are subject to competing or contradictory constraints. When frustration occurs solely due to the geometry or topology of the lattice, it is termed ‘geometric frustration[58].’ Many transition metal oxides crystallize in magnetic structures that are prone to ge-

56 ometric frustration, such as corner- or edge-sharing triangular or tetrahedral lattices. When these types of lattices (exempliﬁed by the wurtzite structure) are coupled with antiferromagnetic interactions, magnetic frustration occurs.

Hence it is likely that frustration and short-range order could be the source of the bump observed at 2θ/d = 1.3 A˚ −1.

2500 * T = 450 K 2000 *

1500 T = 400 K

counts 1000 T = 300 K

500 T = 15 K

1.0 1.5 2.0 2.5 3.0 3.5 4.0 −1 4π sinθ/λ (Å )

Figure 4.4. Neutron diﬀraction data for CoO acquired at temperatures ranging from 15 to 450 K. Asterisks mark the reﬂections from the aluminum sample holder. The arrow under the 15 K data points out a potential ‘bump’ in the data indicative of short-range antiferromagnetic ordering.

Another possible explanation for the lack of magnetic order may be the

57 small particle size of the wurtzite CoO. From Scherrer broadening analysis, which uses the x-ray linewidth of a peak at full-width half-maximum to determine the particle size, we determine the CoO crystallites to be less than 20 nm in size. In general, wurtzite-based antiferromagnets are associated with large magnetic unit cells. Hence the broadening of superstructure reﬂections would be quite exaggerated in small crystallites, and would result in peak intensity comparable to the background. In the future, larger sample quantities could remedy this situation to determine the intrinsic magnetic ordering in this system.

4.4 Calculations

To further our understanding of this material, it was deemed useful to determine the electronic structure of wurtzite CoO. First principles electronic structure calculations using density functional theory were performed on wurtzite CoO using structural parameters obtained from Rietveld analysis.

Both nonmagnetic and ferromagnetic unit cells were considered; calculations show that the ferromagnetic spin-polarization stabilizes the CoO unit cell by v0.4 eV per CoO versus nonmagnetic CoO. Antiferromagnetic supercells were not considered at this stage. Obtaining the correct magnetic ground state may require the additional consideration of electron-electron interactions, of-

58 ten described in terms of a Hubbard U. In the Hubbard model, electrons on

a lattice are assumed to possess an onsite-only repulsive interaction that in-

ﬂuences electron hopping between adjacent sites. The Hubbard U is the pa-

rameter deﬁned as the Coulomb-energy cost to place two electrons on the

same site[59]. These interactions have been shown to be important in rock-

salt CoO[60], where a Hubbard U of 5.3 eV was determined.

Figure 4.5 details the LMTO (linear mufﬁn tin orbital) densities of states of

O p and Co d states in the two spin conﬁgurations (up and down) for spin-

polarized CoO. The O p states are centered around -6 eV with respect to the

Fermi energy, signiﬁcantly separated from the Co d states. Such a separation

between p and d states is to be expected for a divalent transition metal com-

pound. However, there is signiﬁcant metal-oxygen covalency, as illustrated

by the strong exchange splitting of O p states. The electronic conﬁguration

of Co2+ in a tetrahedral environment can be expected to be high spin, with

a small crystal ﬁeld splitting. In agreement with this suggestion, the DOS

2 2 shown in Figure 4.5 exhibits the following d orbital ﬁlling: e (↑), t2(↑), e (↓),

t2(↓). Since the widths of the different d bands are slightly large, wurtzite CoO is found to be a metal, unlike what would be expected for a material that is green in color. If the bandwidths were narrower, we would obtain an insulating, antiferromagnetic ground state[12].

59 15

O p majority spin 10 Co d ) −1

cell 5 −1 spin

−1 0

DOS (states eV 10 minority spin

15 −8 −6 −4 −2 0 2 4 energy (eV)

Figure 4.5. Densities of O p and Co d states in spin up and spin down conﬁgurations obtained from spin-polarized LMTO calculations on wurtzite CoO using an experimentally determined crystal structure. The origin on the x-axis is the Fermi energy.

4.5 Summary

In summary, we have prepared CoO in the wurtzite structure using a non-

aqueous solution route, and determined its crystal structure using powder x-

ray and neutron diffraction. The magnetic behavior of CoO was studied via

SQUID magnetization measurements and low-temperature neutron diffrac-

tion, with no evidence for long-range magnetic ordering. This system is a

likely candidate for magnetic frustration, a property inherent to the wurtzite

60 lattice. Our initial efforts at determining the electronic structure implies that further investigations into the electron-electron interactions must be explored in order to fully describe this novel material. With an extensive study of the bulk metastable Zn1−xCoxO system complete, we can now turn our attention to the nanoscale analogs of this material system and explore their properties. As such, the preparation and characterization of ZnO and Zn1−xCoxO nanoparticles is the topic of the next chapter.

61 Chapter 5

ZnO and Zn1−xCoxO Nanoparticles

In recent decades, a shift in the evolution of materials science has led to the study of nanoscale materials. These materials exhibit properties which, unlike their bulk analogs, can be tailored as a function of size or other characteristic length scale, such as exciton radius, electron mean free path, or magnetic domain size. In its bulk form, wurtzite-structured zinc oxide is of interest due to its wide band gap (Eg = 3.3 eV)[61], making it a transparent, piezoelectric semiconductor with a high exciton binding energy (60 meV). As such, bulk ZnO is utilized in a variety of electronic, optical, and acoustic devices.

ZnO nanoparticles are of interest in applications requiring a high degree of optical transparency along with UV absorption. ZnO nanoparticles have been prepared using many different techniques, including hydrolytic and sol-gel

62 routes[62, 63]. In recent years, ZnO nanoparticles have been prepared using several methods, including hydrolysis of zinc acetate in a polyol medium[64]

and sol-gel routes using the reaction of alkylzinc with ethanol, t-butanol, and

water[65].

In our route, we use an organic-phase, thermolytic conversion of bulk ZnO powder to nanophase ZnO, through the intermediate formation and decomposition of zinc 2,4-pentanedionate (or acetylacetonate). This intermediate is the same precursor used to form wurtzite CoO in the previous chapter. Such an organic phase conversion is quite versatile; we also demonstrate decomposition of bulk Zn1−xCoxO (formed using the route detailed in Chapter 2) into nanophase Zn1−xCoxO, and anticipate such a general route to be useful for the bulk to nanophase conversion of various oxide materials.

The most noteworthy result of this preparation has been the structure of the resulting nanophase material: when decomposed using our thermolytic route, ZnO is found to be partially in the zinc blende structure. This is quite curious; although nearly all semiconducting II-VI compounds of divalent elements crystallize in tetrahedral structures, the more ionic of these (e.g. ZnO,

GaN, AlN) prefer the hexagonal P63mc wurtzite structure while the more co- valent (e.g. GaAs or InSb) prefer the cubic F43¯ m zinc blende structure. The two

structures are related by a stacking polytype (i.e., hcp to fcc stacking). Wurtzite

63 is stabilized for the more ionic compounds due to decreased repulsions between like ions in this structure type, which is reﬂected in the slightly larger

Madelung constant of wurtzite (1.641) versus that of zinc blende (1.638)[66].

Classically, the Madelung constant is used in determining the energy of a single ion in a crystal; more specifically, the constant represents the relationship of the distance between ions due to a specific type of crystal, independent of lattice dimensions. As ZnO is the most polar of these tetrahedral compounds, it has a strong tendency to crystallize in the wurtzite structure. This is reflected in the absence of a zinc blende ZnO phase in either the Powder Diffraction File

(JCPDS-ICDD, 2000) or Inorganic Crystal Structure Database (FIZ-Karlsruhe,

1997). There has been a lone report of ZnO in the zinc blende structure formed via oxidation of thin ﬁlms of zinc in air, with electron diffraction yielding a lattice parameter of a = 4.62 A[˚ 67].

At high pressures (9.1 GPa), ZnO transforms into a rocksalt phase[68]. Us- ing electronic structure calculations, the cohesive energies per formula unit

ZnO have been determined to be 7.692 eV for the wurtzite structure, versus

7.679 eV for the zinc blende structure[69], yielding an energy difference of

0.013 eV. In comparison, the difference in cohesive energies for ZnS, which fre- quently exhibits a wurtzite/zinc blende structural duality, is 0.00019 eV[70], with the zinc blende structure being favored. This polytypism is at the crux

64 of the ‘fcc-hcp dilemma’[71], which predicts, using molecular dynamic simu-

lations, that a Lennard-Jones solid may be fcc, despite the hcp structure be-

ing energetically favorable. The Lennard-Jones potential describes the inter-

action between two uncharged molecules or atoms, such as atoms in a noble

gas, in order to calculate their properties[47]. Experiments on large clusters of

argon[72] indicate that the fcc and hcp structures often co-exist, as evidenced by electron diffraction of the Ar clusters. Our own study on the low-temperature formation of CoO, discussed in the previous chapter, showed the formation of fcc Co metal clusters, despite this metal’s preference for the hcp structure[73].

A signiﬁcant contributor to this behavior is that the metastable zinc blende

phase may nucleate before the more stable wurtzite phase, in line with the

Ostwald Step Rule[74], which suggests that crystallization from a solution occurs in steps in such a way that phases which are often thermodynamically unfavorable occur ﬁrst. van Santen showed that Ostwald’s step rule can be related to irreversible thermodynamics, minimizing entropy production through a multiple step process[75]. A recent example of such behavior is seen in the

formation of ice in the atmosphere[76]. In this case, the cubic form crystal-

lizes initially and then rapidly converts to the hexagonal form. Interestingly,

the ambient pressure cubic and hexagonal forms of ice are nearly isostructural

with zinc blende and wurtzite. Aside from a scientiﬁc curiosity, researchers

65 have noted the importance of trapping metastable phases in the early stages of solid formation as a method for generating novel materials with unusual structures.

5.1 Preparation

For the bulk to nanophase conversion of ZnO and Zn1−xCoxO, all chemi- cals were used without any further puriﬁcation. Bulk ZnO powder (1 gram,

12.3 mmol, Aldrich 99.999%) was added to 2,4-pentanedionate (10 grams, 99.9 mmol, Aldrich, 99+%) in a three-necked round bottom ﬂask under N2. This solution was stirred continuously with a magnetic stir bar for v 2.5 hours at

483 K. After this time, the mixture was cooled to room temperature and a solid coral precipitate was collected by centrifugation. This precipitate was determined to be a 2,4-pentanedionate of zinc [Zn(acac)2], formed via the following reaction:

ZnO + 2C5H7O2 −→ Zn(C5H6O2)2 + H2O(↑)

1 gram of this precipitate was placed in a clean three-necked round-bottom

3 ﬂask and dissolved under N2 with dibenzylether (31 cm , 0.16 mmol). This solution was heated to 573 K for 1 hour, during which time the solution went

66 from a clear yellow to an opaque brown. Upon cooling this solution to room

temperature, a grayish-white powder was collected by centrifugation at 3000

rpm for 15 minutes and dried in air. ZnO nanoparticles formed from com-

mercial zinc 2,4-pentanedionate (0.432 g, 1.6 mmol, Aldrich) were prepared by

mixing the zinc 2,4-pentanedionate with dibenzyl ether (20 cm3, 0.1 mmol) un-

der N2 in a three-necked round-bottom ﬂask. This clear mixture was magneti-

cally stirred and heated to 553 K for 1 hour. Upon cooling to room temperature,

the resulting brown suspension was centrifuged at 3000 rpm for 10 minutes,

washed in ethanol, and centrifuged for another 10 minutes at 3000 rpm before

drying for 12 hours in air at 333 K. A similar procedure was followed to pre-

pare Zn1−xCoxO using appropriate amounts of either bulk Zn1−xCoxO (for the bulk-to-nano route) or zinc and cobalt 2,4-pentanedionates (for the commercial route).

X-ray diffraction of these materials was performed on a Scintag X2 diffractometer (Cu Kα radiation, 35 mA, 45 kV) in the Bragg-Brentano reﬂection geometry using a step size of 0.01◦ for 1 hour with 2θ between 20 and 80◦.

Thermodiffractometry was obtained on a Bruker D8 Advanced diffractometer with a platinum heating stage and a Braun position sensitive detector. High- resolution transmission electron microscopy was carried out on a FEI Tecnai

FEG microscope operating with an accelerating voltage of 300 kV. Samples

67 were prepared by dispersing nanoparticles in acetone; a drop of this dispersion was placed on a holey carbon-coated copper grid, allowing the solvent to evaporate.

5.2 Results

Powder x-ray diffraction data and corresponding Rietveld ﬁts for the (a) bulk starting ZnO and (b) nanophase ZnO obtained via the intermediate 2,4- pentanedionate are shown in Figure 5.2. Structural reﬁnement of this x-ray data was performed using the XND Rietveld code, and shows the product phase to be a mixture of (c) wurtzite and (d) zinc blende phases of ZnO. Verti- cal lines at the top of the plot indicate expected peak positions for the wurtzite

(W) and zinc blende (ZB) phases. From this reﬁnement, the following structural parameters are obtained:

3 Wurtzite: P63mc, a = 3.252(3) A,˚ c = 5.219(5) A,˚ V/2 = 23.90(4) A˚ ;

1 2 1 2 Zn at ( 3 , 3 ,0) and O at ( 3 , 3 ,0.404)

Zinc Blende: F43¯ m, a = 4.568(3) A,˚ V/4 = 23.83(3) A˚ 3;

1 1 1 Zn at ( 4 , 4 , 4 ) and O at (0,0,0).

The reﬁned lattice parameters for nanophase wurtzite match closely with those of the bulk phase, aside from the free z parameter for O, which we ﬁnd

68 (a)

(c)

(b)

Figure 5.1. Crystal structures of (a) zinc blende and (b) wurtzite ZnO. Black spheres are zinc and the small gray spheres are oxygen. Zinc blende ZnO described in a hexagonal unit cell is shown in (c). Depicted structures represent data from Rietveld reﬁnement of the x-ray data of the ZnO nanoparticles, and are to scale. to be 0.404(7) as opposed to the bulk value of 0.385(1). Figure 5.1 shows the unit cells for the zinc blende and wurtzite structures from these reﬁned values. This discrepancy is most likely due to the limited data on the nanophase sample. The volume per formula unit of ZnO is v 0.3% larger for the more stable wurtzite phase. Quantitative phase analysis using Rietveld scale factors indicate that the relative amounts of the two phases are 64% zinc blende and

36% wurtzite. Particle size was determined by the Scherrer formula to be 25 nm for the wurtzite phase, using the (002) reﬂection, and 20 nm for the zinc

69 blende phase, using the (111) peak.

Figure 5.2. X-ray diffraction data (filled circles) and Rietveld fits (gray lines) for (a) bulk wurtzite ZnO, and (b) nanophase ZnO (wurtzite and zinc blende) obtained from the bulk sample. Contributions to the Rietveld fit of the nanophase ZnO from (c) wurtzite and

(d) zinc blende are included. The diﬀerence proﬁle for the nanophase ZnO is shown (e).

Vertical lines at the top of the ﬁgure indicate expected peak positions.

Selected area electron diffraction patterns are depicted in Figure 5.3 from different regions of the nanophase ZnO. By performing a series of tilting experiments, regions were identiﬁed in the sample as being (a) purely hexagonal wurtzite, projected down [001]W, and (b) cubic zinc blende projected down

[110]ZB. It is noteworthy that the zinc blende regions of the sample exhibit stacking faults, leading to streaks in the diffraction pattern. The wurtzite re-

70 gions, on the other hand, are more crystalline, as evidenced by the sharper diffraction spots in Figure 5.3(b).

Figure 5.3. Selected area electron diﬀraction patterns for nanophase ZnO showing (a) wurtzite and (b) zinc blende domains.

High resolution lattice imaging, as shown in Figure 5.4, confirms that the sample makeup is not individual wurtzite or zinc blende grains but rather a continuous mixture of the two phases. The samples exhibit either hcp or faulted fcc stacking within a 30 nm by 30 nm field. In order to simulate the atypical stacking of our ZnO nanoparticles, the DIFFaX code[77], which gener- ates x-ray diffraction patterns from pre-defined structural units, was utilized.

Using the results from Rietveld reﬁnement of our powder x-ray data, we can deﬁne a structural unit with lattice parameters a = b = 3.2301 A,˚ c = 7.9120 A,˚

◦ 1 and γ = 120 , with Zn at (0,0,0) and O at (0,0, 4 ). Two stacking vectors were

71 considered:

−→ 2 1 1 R1 = ( 3 , 3 , 3 )

−→ 1 2 1 R2 = ( 3 , 3 , 3 )

Figure 5.4. High resolution transmission electron microscope image of the nanophase ZnO

lattice, projected perpendicular to the stacking direction.

−→ Continuous application of R1 leads to fcc zinc blende stacking; alternating −→ −→ R1 with R2 produces the hcp wurtzite structure. Hence stacking faults can be generated by mixing these two vectors. An x-ray pattern generated by stacking 30 nm of ZnO layers with 60 zinc blende planes with 80 wurtzite planes

72 and 5 stacking faults in the fcc region is shown in Figure 5.5. This simulation was run to give a wurtzite to zinc blende ratio of 1:2, as implied by the Rietveld reﬁnement, which gave relative values of 36% wurtzite and 64% zinc blende.

Although the agreement between experiment and simulation is only qualita- tive, our analysis gives results more consistent with microscopy (as opposed to a two-phase Rietveld reﬁnement).

Figure 5.5. X-ray diﬀraction data of ZnO nanoparticles (a) and DIFFaX simulation (b) of a ﬁnite crystal with hcp and faulted fcc domains. Vertical lines indicate expected peak positions.

73 In addition to the bulk-to-nanophase conversion, we have confirmed that commercial zinc acetylacetonate can also be decomposed to form ZnO nanoparticles. These experiments were done to rule out the possibility that the bulk-to-nanophase conversion was merely an ‘etching down’ of the starting bulk ZnO material. ZnO nanoparticles were formed by decomposing commercial zinc 2,4-pentanedionate in refluxing dibenzyl ether. X-ray diffraction data, depicted in Figure 5.6, and subsequent Rietveld refinement suggests that the product phase is once again a combination of wurtzite and zinc blende phases, but with the percentage of each phase reversed; the decomposition of the commercial material yields 64% wurtzite and 36% zinc blende. These nanoparticles (as calculated from Scherrer broadening) are 10 nm (wurtzite) and 8.1 nm

(zinc blende). We cannot suggest an explanation for these nanoparticles being smaller than the ones obtained through the bulk-to-nanophase route, as the decomposition temperatures are identical.

In order to investigate the conversion of zinc blende to the wurtzite phase in these nanoparticles, we performed temperature-dependent x-ray diffrac- tometry, or thermodiffractometry, on these materials. Heating of samples on a platinum stage while obtaining x-ray diffraction data allows for the determination of a transition from zinc blende to wurtzite. Data were acquired at 100 K intervals between 473 and 973 K and at 20 K intervals between 673 and 973 K,

74 as shown in Figure 5.7. Analysis of this data indicates that the rapid conversion of zinc blende domains to wurtzite begins at around 700 K. Relative amounts of the two phases have been determined through the Rietveld scale factors at each temperature for which data was taken. These relative amounts, plotted in

Figure 5.8, indicate that there is a negligible amount of the zinc blende phase by 973 K.

The preparation of Zn1−xCoxO nanoparticles was also explored using this same thermolytic route. For the bulk-to-nanophase conversion, bulk

Zn1−xCoxO (made using the route described in Chapter 2) was decomposed in reﬂuxing dibenzylether to form Zn1−xCoxO nanoparticles, with 0 ≤ x ≤ 0.15.

X-ray diffraction data, shown in Figure 5.9, indicates clean phases up to x =

0.15.

Susceptibility as a function of temperature was measured for these

nanoparticles in order to determine their magnetic behavior. In contrast to

a study reporting room temperature ferromagnetism in Co-substituted ZnO

quantum dots[78], we ﬁnd no evidence for ferromagnetic behavior in this system, as shown in Figure 5.10. Although the study by Schwartz and co-

workers ﬁnds ferromagnetism, they report a magnetic moment of 0.3 µB per

2+ Co ion, versus the 3 µB per ion expected if all spins participating in mag-

netism. They believe most spins were hence rendered ‘magnetically silent,’ an

75 observation that suggests any ferromagnetic behavior could be due to inter-

dopant magnetic coupling between interfaces that form when these quantum

dots aggregate[78].

5.3 Summary

In conclusion, we demonstrate an all-organic phase conversion of bulk

ZnO and Zn1−xCoxO to nanophase ZnO and Zn1−xCoxO through an interme- diary 2,4-pentanedionate decomposition. Decomposition of bulk ZnO yields both zinc blende and wurtzite structure ZnO nanoparticles; in the presence of cobalt, only the wurtzite phase is stabilized. This thermolytic route is some- what general and could potentially be applied to other oxide systems. The most noteworthy results of this chapter are the stabilization of zinc blende ZnO up to 700 K and the complete absence of ferromagnetism in the Co-substituted

ZnO nanoparticles, ruling out any chance of room-temperature DMS-type behavior in this materials system. In the next chapter, we turn to an as-yet un- explored materials system, the dilute ferrimagnetic semiconductor. This is the topic of the following (and ﬁnal) chapter.

76 Figure 5.6. X-ray diffraction data (filled circles) and Rietveld fits (gray lines) for nanophase

ZnO via thermolytic decomposition of commercial zinc acetylacetonate (a). Contributions to the fit from wurtzite (b) and zinc blende (c) are included, along with the difference profile (d).

77 (a) 973 K

693 K 673 K 573 K 473 K 30 32 34 36 38 40 42 44 46 48 50 (b)

973 K W(973 K) ZB(973 K)

473 K W(473 K) ZB(473 K)

30 32 34 36 38 40 42 44 46 48 50 o CuKα 2θ ( )

Figure 5.7. Thermodiﬀractometry results for nanophase ZnO (a), with Rietveld analysis of the data taken at 973 and 473 K (b), showing the various wurtzite and zinc blende contributions.

78 Figure 5.8. Scaled relative amounts of wurtzite and zinc blende ZnO as a function of temperature, obtained from Rietveld scale factors.

79 5 % 10

10 %

log (counts) 5 15 %

0 30 40 50 60 70 80 o CuKα 2θ ( )

Figure 5.9. Powder x-ray diﬀraction data for Zn1−xCoxO nanoparticles, with 0 ≤ x ≤ 0.15.

80 800 5 % 10 % 15 % 600

400 mole Oe) [1000 Oe] −1

200 (emu χ 1/

0 0 100 200 300 400 T (K)

Figure 5.10. Inverse susceptibility as a function of temperature for Zn1−xCoxO nanoparticles, with 0 ≤ x ≤ 0.15.

81 Chapter 6

Iron-substituted Zinc Gallate

After a thorough study of transition metal substituted ZnO, as described in Chapters 2 and 3, and Zn1−xCoxO nanoparticles (Chapter 5), we find a complete absence of long-range magnetic ordering in well-characterized samples. Our findings are validated by other studies, both experimental[41] and theoretical[13], that point out difficulties in stimulating ferromagnetism through transition metal substitution of ZnO. A promising alternative to inducing ferromagnetism in a wide bandgap semiconductor oxide is to consider a material that has two host cation sites. This would lead to an anti-alignment of spins, as is the natural tendency of spins in insulating oxides, without the need for conduction electrons to promote magnetism. If the cations on each site were different (e.g. Fe2+ and Fe3+), it could then lead to a net

82 ferrimagnetism. A natural structure for inducing ferrimagnetism is thus spinel structure, AB2O4, shown in Figure 6.1, in which spins in the tetrahdral (A) and octahedral (B) cation sites are usually anti-aligned with respect to one another. The high effective cation coordination in the spinel structure suggests that even with a low concentration of transition metal substitution, extensive magnetic coupling can be expected. Additionally, with 2 B sites for every A site, there exists a possibility for a net ferrimagnetic moment.

Figure 6.1. Cation coordination in the spinel structure, AB2O4. The lighter spheres are the tetrahedral (A) atoms; the darker spheres are the octahedral (B) atoms.

A spinel of interest is the wide bandgap oxide zinc gallate, or ZnGa2O4,

83 which has a direct bandgap of 4.1 eV[79]. This material also shows potential for incorporation into devices, as ZnGa2O4 can be grown epitaxially on spinel

MgAl2O4 substrates[80, 81]. We have chosen to substitute ZnGa2O4 with iron by creating solid solutions of [ZnGa2O4]1−x[Fe3O4]x with 0 ≤ x ≤ 0.15, in the hopes of creating a dilute ferrimagnetic semiconductor. X-ray diffraction, transmission electron microscopy, magnetic measurements, Mossbauer¨ spectroscopy, and UV/Visible spectroscopy were performed on these samples, in order to determine their structural, magnetic, and optical properties.

6.1 Preparation

Using the same precursor route (described in Chapters 2 and 3) used to make polycrystalline Zn1−xMxO, precursor oxalates Zn1−xFex(C2O4)·2H2O were prepared with x = 0.00, 0.02, 0.05, 0.10, and 0.15 through precipita- tion from an aqueous solution. Polycrystalline [ZnGa2O4]1−x[Fe3O4]x samples were made by grinding the relevant oxalate with appropriate amounts of

Ga2O3 and decomposing in air at 1473 K for 18 hours, with an intermediate regrinding step. Samples were inserted and removed from the furnace at temperature. The pure ZnGa2O4 sample (x = 0.00) sample is white; as x increases, samples range from beige to auburn in color. For samples with larger x values, longer sintering times are required, suggesting the presence of a solubility

84 limit. X-ray diffraction data were collected on a Scintag X2 diffractometer oper-

ated in the θ − 2θ geometry. Transmission electron microscopy (TEM), coupled

with energy dispersive x-ray spectroscopy (EDX) analysis, was performed on

a JEOL JEM 2010 microscope, with the sample powder dispersed from a sol-

vent onto a carbon-coated copper grid. UV/Visible diffuse reﬂectance spectra

were collected by sprinkling powder onto Scotch tape. Magnetization mea-

surements were carried out on a Quantum Design MPMS 5XL SQUID mag-

netometer at temperatures between 2 and 400 K. Mossbauer¨ spectra were obtained at 4.2 and 293 K using a constant-acceleration spectrometer equipped with a 1024-channel analyzer and operated in the timescale mode. The γ source was 25 mCi57 Co/Rh, and the spectra were analyzed using the EFFINO computer program[82].

6.2 Results

As shown in Figure 6.2a, powder x-ray diffraction indicates a very small

impurity phase at 2θ = 34.2◦ in all the samples, including the nonmagnetic

host ZnGa2O4. Additionally, the x = 0.15 sample has a monoclinic Ga2O3

impurity. Other than these nonmagnetic impurities, the samples are clean

with only the spinel phase present. Rietveld reﬁnement of the x-ray data

was performed using the XND program. The variation of the lattice pa-

85 rameter, shown in Figure 6.2b, is linear as a function of Fe loading. Data

are in circles, with a line connecting published lattice parameter values for

pure ZnGa2O4 with Fe3O4 (off the plot). Under our preparation conditions,

Fe3O4 is stable, implying that our material system should be a solid solution

[ZnGa2O4]1−x[Fe3O4]x. However, our Mossbauer¨ data indicates the presence of only Fe2+, which means the stoichiometry is slightly different than expected

3+ 2+ (Fe3O4 can be thought of as [Fe ][Fe2 ]O4). There is a small broadening of the x-ray linewidths as a function of substitution, characteristic of an increase in the number of elements on the lattice. Unfortunately, the x-ray form factors of iron, zinc, and gallium are too similar to readily distinguish relative amounts of each element present in the spinel. In order to determine the ratio of elements within the system, the x = 0.15 sample was chosen to per- form TEM/EDX analysis. Systematic data collection suggested that the ratio of

Fe:Zn:Ga was nearer to 1:3:6 rather than the 1:2:4 ratio expected for spinel (as calculated from the nominal composition). This ratio remains homogeneous over the length scale of the EDX spot size (v3 nm).

Although pure ZnGa2O4 is a wide bandgap semiconductor, we wanted to

conﬁrm that Fe substitution would not hamper the semiconducting nature of

this material system. UV/Vis diffuse reﬂectance spectroscopy, displayed in

Figure 6.3, was used to determine the effects of substitution on the bandgap of

86 (a) x = 0.00

x = 0.05

log(counts) x = 0.10

x = 0.15

15 20 25 30 35 40 45 50 o CuKα 2θ ( ) 8.35 (b)

(Å) 8.34 a

8.33 0 0.05 0.1 0.15 0.2 0.25 x

Figure 6.2. Powder x-ray diﬀraction (a) of the [ZnGa2O4]1−x[Fe3O4]x (0 ≤ x ≤ 0.15) samples displayed on a log scale. Points are data and the lines are Rietveld ﬁts to the spinel structure. The vertical dashed lines indicate a Ga2O3 impurity. Lattice parameter evolution of the spinel solid solution (b) are shown as open circles; a line connects the published values for ZnGa2O4 (x = 0) and Fe3O4 (x = 1).

these materials. As conﬁrmed by the sharp band edge absorption, ZnGa2O4

is a direct bandgap semiconductor. However, our samples yield a bandgap of

3.1 eV, rather than the reported value of 4.1 eV. Due to the sensitivity of the

ZnGa2O4 optical absorption edge on composition[79], a very small concentra-

tion of cation vacancies are enough to shift the band edge towards the red.

We ﬁnd that substitution with iron leaves the band edge unchanged; however,

87 new features linked to atomic transitions arise in the visible region. The relative increase of these features in the visible region of the spectra results in an effective (relative) decrease in the intensity of the band edge absorption.

Figure 6.3. Diffuse reflectance UV/Vis spectra of [ZnGa2O4]1−x[Fe3O4]x for the various x in the near UV and visible regions of the spectrum. Data have been offset along the reflectance axis for clarity; asterisks are associated with absorption of the Scotch tape.

The magnetic behavior of the x = 0.05, 0.10, and 0.15 samples are plotted in Figure 6.4; Figure 6.4a depicts the magnetization as a function of temperature, while Figure 6.4b shows the magnetization as a function of applied ﬁeld.

88 In the magnetization as a function of ﬁeld plots, the magnetization has been scaled to a per mole Fe3O4 basis, implying that in the absence of long-range interactions, the three curves should overlap onto a single one. Such behavior is not evident, even at 400 K. Additionally, plots of inverse magnetization as a function of temperature are not linear for any of the samples under 400 K, conﬁrming the lack of long-range interactions.

As shown in Figure 6.4a, there is a separation between the zero-ﬁeld cooled

(dashed curves) and ﬁeld-cooled traces (solid curves); this separation is clearly visible for the x = 0.10 and 0.15 samples at around 100 K. At 5 K, all the samples display hysteretic behavior without magnetic saturation. This implies that a certain fraction of the spins are ‘free,’ and not participating in the magnetic ordering. Assuming iron substitutes in ZnGa2O4 as a solid solution with Fe3O4, the saturation magnetization is expected to be 4µB per Fe3O4. If we take the saturation of the x = 0.15, for example, to be at the value where the hysteresis loop closes, we ﬁnd a saturation value of v 1µB at 5 K. This value suggests about 25% of the substituted Fe is participating in the bulk ferrimagnetism.

Figure 6.5 depicts magnetization as a function of scaled ﬁeld (H/T) at three different temperatures: 2 K (a), 50 K (b), and 200 K (c). Hysteresis behavior is exhibited at the two lower temperatures, but even at 200 K, the magnetization as a function of scaled applied ﬁeld indicates long-range ordering. The

89 nature of the 200 K trace suggests superparamagnetic behavior with a block-

ing temperature around 100 K; however, superparamagnetic behavior would

mean that the traces of M versus H/T should collapse onto a single curve (as

previously mentioned); we do not see this. In Figure 6.5d, the temperature de-

pendence of the magnetic coercivity is plotted for the x = 0.15 sample, which rises in a near-exponential fashion as the temperature decreases. The 5 K coercivity is v 250 Oe, versus a published value of 420 Oe for Fe3O4[83].

Finally, Mossbauer¨ spectroscopy was performed on the x = 0.05 and x =

0.15 samples in order to determine the amount and valency of iron present

in the samples. Mossbauer¨ spectroscopy is a spectroscopic technique based

on the Mossbauer¨ effect[84]. In its most common form, a sample is exposed

to a beam of γ-radiation, and a detector measures the intensity of the beam

transmitted through the sample. The γ-ray energy is varied by accelerating

the γ-ray source through a range of velocities. The relative motion between

the source and sample results in an energy shift. γ-ray intensity is then plotted

as a function of the source velocity. At velocities corresponding to the reso-

nant energy levels of the sample, some of the γ-rays are absorbed, resulting

in a drop in the measured intensity and a corresponding dip (or peak) in the

spectrum. The number, positions, and intensities of the peaks provide infor-

mation about the chemical environment of the absorbing nuclei. However, in

90 order for Mossbauer¨ absorption of γ-rays to occur, the γ-ray must be of the appropriate energy for the nuclear transitions of the atoms being probed. Only a few elemental isotopes exist for which these criteria are met, so Mossbauer¨ spectroscopy can only be applied to a relatively small group of atoms. These include 57Co, 57Fe, 129I, 119Sn, and 121Sb. Of these, 57Fe is by far the most common element studied. For both samples the isomer shift with respect to iron metal was 0.32 mm s−1 and the quadrupolar splitting was 0.52.

As shown in Figure 6.6, neither sample exhibits the six-peak pattern characteristic of magnetic ordering at 293 K. At 4.2 K, the x = 0.15 sample showed a doublet peak corresponding to paramagnetic Fe3+ and a six-peak pattern corresponding to magnetically ordered Fe3+. The internal ﬁeld is between

250 and 510 Oe, consistent with the magnetization data. We ﬁnd, from the

Mossbauer¨ ﬁt to the paramagnetic and ferromagnetic phases at 4.2 K, a relative ratio of 10% paramagnetic to 90% ferromagnetic phases. Although we assumed our sample to be a solid solution of with ZnGa2O4 with Fe3O4, there is no evidence for the presence of Fe2+ from our Mossbauer¨ data. Rather, it is more likely that our solid solution is between ZnGa2O4 and γ-Fe2O3; the latter is a distorted spinel that has only Fe3+ ions present.

91 6.3 Summary

In conclusion, we ﬁnd that the Fe-substituted ZnGa2O4 compounds, with x

= 0.05 - 0.15, do exhibit long-range magnetic ordering and ferromagnetic hys-

teresis at low temperatures; Mossbauer¨ spectroscopy conﬁrms this ordering at

4.2 K. The addition of magnetic substituent ions has not signiﬁcantly affected the semiconducting properties of the ZnGa2O4 material, with the band edge

position essentially unchanged up to x = 0.15 Fe loading. We can assume the

3+ Fe-substituted ZnGa2O4 compounds have random substitution of Fe ions

on both the tetrahedral and octahedral sites in the spinel lattice. In the future,

it would be useful to conduct further Mossbauer¨ studies, as well as powder

neutron diffraction measurements in order to further characterize these com-

pounds.

Our success in obtaining a dilute ferrimagnetic semiconductor in the Fe-

substituted ZnGa2O4 system suggests the promise of exploiting the intrinsic anti-alignment of spins in transition metal oxides in order to create a material that will exhibit ferromagnetism while retaining its semiconducting properties. These systems have the added benefit of not requiring conduction electrons, a problem to date in the ZnO-based dilute magnetic semiconductor system. Having this novel materials system at our disposal is beneficial towards the ultimate goal of finding a room-temperature ferromagnetic semiconductor.

92 Figure 6.4. Magnetization as a function of temperature (a) under a 100 Oe ﬁeld for

[ZnGa2O4]1−x[Fe3O4]x with x = 0.05, 0.10, and 0.15; magnetization as a function of applied field (b) at 5 K for the x = 0.05, 0.10, and 0.15 samples. Data were collected upon warming after cooling under zero field (dashed lines) and after cooling under a 100 Oe field

(solid lines).

93 Figure 6.5. Magnetization as a function of H/T of [ZnGa2O4]1−x[Fe3O4]x with x = 0.15 at varying temperatures (a-c). Coercive ﬁeld (d) scaled by the temperature at various temperatures for the x = 0.15 sample.

94 Figure 6.6. M¨ossbauer spectra obtained at 293 K (above) and 4.2 K (below) for the

[ZnGa2O4]1−x[Fe3O4]x sample with x = 0.15.

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