ABSTRACT

AN EXPERIMENTAL STUDY ON THE MAGNETIC AND EXCHANGE BIAS PROPERTIES OF SELECTED MN RICH NI-MN-GA BASED HEUSLER ALLOYS

by Abdullah Mohamed Albagami

In this Thesis project, an experimental study on the magnetic and exchange bias properties of a series of polycrystalline Ni1.7-xMn1.7+xGa0.6 alloys have been investigated by x-ray diff raction, dc , and ac susceptibility measurements. X-ray diffraction measurement showed that all prepared samples have a tetragonal L10 martensitic structure at room temperature. Scanning microscopy measurements show that the compounds are single . With increasing Mn concentration x, the lattice parameters marginally increases. The temperature dependence of magnetization data show two distinct transitions in the alloys. At lower temperatures, a peak in the data is observed while the ferromagnetic to paramagnetic transition occurs at higher temperatures. With increasing Mn concentration, the temperature of both transitions increases. Thermomagnetic irreversibility is observed in the magnetization data of all alloys. The ac susceptibility measurements on the materials show the existence of frequency dependence, which suggest that the thermomagnetic irreversibility in the magnetization data is due to the glass like ground state in the alloys. The like ground state with competing magnetic interactions result in the observation of double-shifted hysteresis loop and exchange bias effects in the alloys. The magnitude of the exchange bias field is strongly dependent on the cooling field. AN EXPERIMENTAL STUDY ON THE MAGNETIC AND EXCHANGE BIAS PROPERTIES OF SELECTED MN RICH NI-MN-GA BASED HEUSLER ALLOYS

A Thesis Submitted to The Faculty of Miami University In partial fulfillment of The requirements for the degree of Master of Science Department of Physics by Abdullah Mohamed Albagami Miami University Oxford, Ohio 2016

Advisor: Prof. Mahmud Khan Reader: Prof. Herbert Jeager Reader: Prof. Khalid Eid

©2016 Abdullah Mohamed Albagami This Thesis titled

AN EXPERIMENTAL STUDY ON THE MAGNETIC AND EXCHANGE BIAS PROPERTIES OF SELECTED MN RICH NI-MN-GA BASED HEUSLER ALLOYS

by

Abdullah Mohamed Albagami

has been approved for publication by

The College of Arts and Science

and

Department of Physics

Prof. Mahmud Khan

Prof. Herbert Jeager

Prof. Khalid Eid

Contents

Chapter 1 Introduction and Motivation ...... 1

Chapter 2 Theory ...... 3 2.1 Physics of ...... 3 2.2 Types of magnetism ...... 4 2.2.1 Diamagnetism ...... 4 2.2.2 ...... 5 2.2.3 ...... 6 2.2.4 ...... 8 2.2.5 ...... 8 2.2.6 Spin glasses ...... 9 2.3 Magnetic interactions ...... 11 2.3.1 Direct exchange interaction ...... 11 2.3.2 Indirect exchange interaction ...... 13 2.3.3 Superexchange interaction ...... 13

Chapter 3 Experimental Techniques ...... 15 3.1 Sample preparation ...... 15 3.2 XRD measurements ...... 16 3.2.1 Bragg’s law of Diffraction ...... 16 3.2.2 Production of X-ray ...... 17 3.2.3 Experimental set up for XRD ...... 17 3.2.4 Analysis of XRD data ...... 18 3.3 Magnetization measurements ...... 19 3.3.1 Major Components of the PPMS ...... 19

iii 3.3.2 An introduction of VSM ...... 22 3.3.3 Operating principle of VSM: ...... 23 3.3.4 Overview of AC ...... 24 3.3.5 Design and working mechanism of PPMS ACMS option ...... 25

Chapter 4 Results and Discussion ...... 28 4.1 SEM and X-ray diffraction measurements ...... 28 4.3 dc Magnetization measurements ...... 31 4.3.1 Magnetization as a function of temperature ...... 31 4.2.2 Magnetization as a function of magnetizing field ...... 34 4.3 AC susceptibility measurements ...... 39 4.4 Discussion ...... 41

Chapter 5 Conclusion ...... 44

References ...... 46

iv

LIST OF FIGURES

Figure 1.1: HEB Vs. x data forNi2+xMn1.4-xGa0.6 system as obtained by Chapai et al… ...... 3 Figure 2.1: Arrangement of in diamagnetic materials ...... 6 Figure 2.2: Arrangement of magnetic moment in paramagnetic materials ...... 7 Figure 2.3: Arrangement of magnetic moment in ferromagnetic materials ...... 8 Figure 2.4: Unmagentized ferromagnetic domain (Left) Magnetized ferromagnetic domain (Right) ...... 9

Figure 2.5: Magnetization (M) as function of (H) at T

Figure 2.14: Superexchange in the interaction of the ferrimagnetic rare earth in a garnet………17

Figure 3.1: Graphical diagram showing Bragg’s law ...... 20 Figure 3.2: Graphical exemplification of conventional Coolidge tube technique of production of X-ray ...... 21 Figure 3.3: Major components of the diffractometer ...... 22 Figure 3.4: Block Diagram of PPMS showing major component ...... 24

Figure 3.5: Major components of the PPMS probe ...... 25 Figure 3.6: Major components for PPMS VSM system...... 27 Figure 3.7: The VSM system scheme ...... 28

v Figure 3.8: ACMS Insert and Coil Set...... 32

Figure 4.1: SEM micrograph of Ni1.7-xMn1.7+xGa0.6 (0  x  0.3) alloys ...... 35

Figure 4.2: X-ray diffraction patterns of Ni1.7-xMn1.7+xGa0.6 (0  x  0.3) obtained at room temperature ...... 36

Figure 4.3: The difference of lattice parameter “a” and “c” of Ni1.7-xMn1.7+xGa0.6 (0  x  0.3) obtained at room temperature ...... 36

Figure 4.4: Magnetization as a function of temperature measurements, M (T) of Ni1.7Mn1.7Ga0.6 (x =0) that obtained at a magnetic field of 100 Oe ...... 38

Figure 4.5 (a) - (f): Magnetization as a function of temperature measurements, M(T) of Ni1.7- xMn1.7+xGa0.6 (0.05  x  0.3) that obtained at a magnetic field of 100 Oe ...... 39

Figure 4.6: Variation of Tp and Tc of Ni1.7-xMn1.7+xGa0.6 as function of x. …………………..…………………………………………………………………..……………40

Figure 4.7: Magnetization as a function of filed, M(H), of Ni1.7-xMn1.7+xGa0.6 (x = 0) measured at 5 K after (a) zero field cooling; (b) field cooling at a field of 50 kOe ...... 42

Figure 4.8: Magnetization as a function of filed, M (H), of Ni1.7-xMn1.7+xGa0.6 (x = 0) measured at 5 K after zero field cooling ...... 43

Figure 4.9: Magnetization as a function of filed, M (H), of Ni1.7-xMn1.7+xGa0.6 (x = 0) measured at 5 K after field cooling at a field 50 kOe ...... 44

Figure 4.10: The variation of HEB (FC) as a function of excess Mn concentration x content ...... 45

Figure 4.11: Temperature dependence of the real and imaginary component of the ac susceptibility of Ni1.7-xMn1.7+xGa0.6 (x = 0) obtained in an ac field of 10 Oe and frequencies from 10 Hz to 10000 Hz ...... 47

Figure 4.12: Temperature dependence of the real component of the ac susceptibility of Ni1.7- xMn1.7+xGa0.6 (x > 0) obtained in an ac field of 10 Oe and frequencies from 10 Hz to 10000 Hz ...... 49

vi Figure 4.13: Temperature dependence of the imaginary component of the ac susceptibility of Ni1.7- xMn1.7+xGa0.6 (x > 0) obtained in an ac field of 10 Oe and frequencies from 10 Hz to 10000 Hz ...... 50

vii Chapter 1

Introduction and Motivation

The understanding of magnetic exchange interactions in magnetic materials is important for new innovations in science and technology. This is because magnetic materials have many multifunctional properties that are utilized in numerous technologies. The Exchange bias (EB) effect is one such property that is typically observed in materials where ferromagnetic (FM) and antiferromagnetic (AFM) interactions co-exist. Since the discovery of EB effect in CoO (AFM) coated Co (FM) nanoparticles by Meikle john and Bean in 1956,1 a significant amount of research efforts have been made on this subject. Eventually it was discovered that materials exhibiting EB phenomena can be utilized in several technologies including spin valves, magnetic recording read 2 heads, and giant magnetoresistive sensors.

The EB phenomena is described as a shift of the magnetic hysteresis loop along the magnetic field axis.1The loop shifts because of a unidirectional exchange anisotropy, which is induced in the FM layer at the interface of the FM/AFM system when the system is cooled in a static magnetic field to below the Neel temperature of the AFM layer.1,3 Ideally the EB effect is always observed in systems consisting of ferromagnetic (FM) and antiferromagnetic (AFM) interfaces. For instance, small coated particles, inhomogeneous materials, and thin films.2 However, the phenomena has been observed recently in many bulk materials including several Mn rich Ni-Mn-X (X= Sb, Sn, 4, 5, 6, 7 and In) based Heusler alloys.

In the off-stoichiometric Mn-rich Ni-Mn-X Heusler alloys, the Mn atoms may occupy three different sites. The exchange interaction between Mn atoms on the regular Mn sites is FM. The excess Mn atoms that occupy the Ni or X sites couple antiferromagnetically with the Mn atoms on the regular Mn sites. Thus, in the Mn rich Heusler alloys competing FM and AFM exchange interactions generate inhomogeneous magnetic behavior. These competing interactions are believed to be responsible for the EB effects in this alloys.4, 5, 6 Traditionally the EB effect is usually observed after the material is cooled in the presence of a magnetic field to temperatures below the Neel temperature of the AFM layer, as mentioned earlier. In contrary to this traditional behavior, the EB effect after zero magnetic field cooling (ZFC) has been observed in several Heusler alloys.6,7 .These observations could not be explained based on FM/AFM interfaces and a new

1 explanation based on spin glass (SG), super spin glass (SSG), ferrimagnetism (FI), super 7 paramagnetic (SPM) domains, and super ferromagnetic (SFM) domains was proposed. From the above discussion it can suggested that by manipulating the Mn concentration in the Ni-Mn-X Heusler alloys, the magnetic ground state and the associated EB effects can be controlled. Taking this into consideration, Chapai et al. have recently investigated the magnetic properties and EB phenomena in Ni2-xMn1.4+xGa0.6 (x=0.05-0.3). In this study, he found that the system exhibit interesting EB behaviors, as shown in Fig. 1.As we can see in the figure, the ZFC

HEB for the Mn rich Ni2-xMn1.4+xGa0.6system decreases to zero with increasing x. On the other hand the magnitude if the FC HEB increases with increasing Mn concentration. Chapai et al. concluded his study on the Ni2-xMn1.4+xGa0.6 system with x = 0.3. However, Fig. 1 indicates that the FC EB can be further increased by increasing the Mn concentration. Keeping the above discussion in mind, I have performed an experimental study on the EB phenomena in Ni1.7-xMn1.7+xGa0.6 alloy system. The goal is to explore the effects of Mn on the magnetic and exchange bias properties of the alloys.

8 Figure 1.1: HEB Vs. x data for Ni2+xMn1.4-xGa0.6 system as obtained by Chapai et al.

2

Chapter 2

Theory

As far as the existing literature is concerned, magnetism started with the discovery of the natural ferric ferrite (Fe3O4) stones, also none as loadstones, in 600 BC by the Greek philosophers. Guan Zhong, a chinse writer, described lodestones as “loving stones” in one of his literature.9 Somewhere around 1175, found its first application in compasses. In the 1600’s, William Gilbert made a significant progress on the study of magnetism and wrote the book “De magnete”.10 Although electricity and magnetism have been applied in technologies for many years between the 1600’s and the 1800’s, the fundamental physics that governs magnetism in materials could only be explained by in the early 1900’s. In this chapter, the fundamentals of magnetism are discussed briefly.

2.1 Physics of Magnetism: Magnetism of atoms is governed by their , each of which has two types of magnetic moment. The first one is the orbital moment that is due to the orbital motion of the electron around the nucleus. The second moment, which is usually larger than the orbital moment, is a quantum mechanically derived moment called the spin of the electron. To better understand the way orbital and the spin momentum couples together to give a net magnetic moment, it is important to know how the electrons occupy different shells in an atom.

In an atom, each electron occupies a specific orbit which is defined by the four quantum numbers n, l, lz and sz. This means that each orbit defined by the four quantum numbers can accept only one electron, as described by the Pauli principle. The maximum number of electrons that belong to the electron shell with principal quantum number n is given by 2n 2 . For example, the maximum number of electrons is 2 for the K shell (n = 1), 8 for the L shell (n = 2), and 18 for the M shell (n = 3). The number of electrons increases with the increase of the atomic number Z, and the electrons fill up the states from the lowest energy state to the higher energy ones. As the number of electrons increases, the shells are filled in a specific order, where the numbers 1, 2, 3,

3 etc. signifies the principle quantum number n of one orbit. As the atomic number increases from Z = 1 () to Z =18 () the electrons fill up in the order of 1s, 2s, 2p, 3s, and 3p. As Z increases further it results in an occupation of 4s levels leaving vacant orbits in the 3d shells. As the number of electrons increase further in a series of elements from Z =19 to Z = 29, the 3d levels are gradually filled up with increasing Z. These elements are known as the transition elements.

Since n =3 for all 3d electrons and they have same orbital configuration, all their orbital states have the same energy. When there are a number of electrons in the 3d shell the spin vectors si of individual electrons are coupled through the spin-spin interactions and the resultant spin vector is:

n

S   si . i1

Similarly, the orbital vectors li of the electrons combine to give the resultant orbital vector:

n

L   li . i 1

The resultant total angular momentum J results from the spin-orbit interaction and is given by:

J = L + S.

2.2 Types of magnetism: Since all materials are made of atoms, they all exhibit some kind of magnetism. The materials can be classified based on their susceptibility (χ) and temperature dependence of magnetization.13 A brief description of the basic types of magnetism are given below. 2.2.1 Diamagnetism: Diamagnetism is the most common type of magnetism that is exhibited by all matter. The phenomenon results due to the electrons orbiting the nucleus forming circular currents that results in a magnetic field that opposes the applied magnetic field. The does not exist in diamagnetic materials as a result of paired atomic electrons. It is usually very weak in many materials due to the interaction between the orbiting electrons and an applied magnetic field according to Lenz’s low (see figure 2.1). Therefore, the magnetization and susceptibility of

4 diamagnetic materials are negative. Diamagnetism is considered to be the induced magnetic dipole which are produced due to the applied magnetic field. The behavior of diamagnetic material is not affected by temperature due to the orbital motion of an electron cannot be affected by the motion of the atoms.

Figure 2.1: Arrangement of magnetic moment in diamagnetic materials14

2.2.2 Paramagnetism: Paramagnetic materials show a linear dependence of the magnetization M on the applied magnetic field H, and M disappears when H is removed. At finite temperatures, the spins of a paramagnetic material are thermally agitated and are randomly oriented. When an external magnetic field is applied, the average orientations of the spins are slightly changed that results in a weak induced magnetization parallel to the applied magnetic field (see figure 2.2). When the external magnetic field is removed, the magnetic dipoles go back to their initial random positions.

Figure 2.2: Arrangement of magnetic moment in paramagnetic14

5

Above a critical temperature, known as the Curie temperature, all ferromagnetic materials become paramagnetic and their susceptibility depends on the temperature. The reciprocal of the susceptibility depends linearly on the temperature, and has a T-intercept at the paramagnetic Curie temperature (P) on the positive temperature axis. This relation of susceptibility and temperature follow the Curie-Weiss law, and can be expressed with the equation:

C  

(T   P )

2.2.3 Ferromagnetism:

In ferromagnetic materials the neighboring spins are aligned parallel to each other as a result of a strong exchange interaction between them. When the temperature is increased, the arrangement of the spins is disturbed by the thermal agitation and results in a temperature dependence of spontaneous magnetization. Above the Curie point, TC, the susceptibility varies according to the Curie-Weiss law. Although there is a presence of spontaneous magnetization, ferromagnetic materials are normally in a demagnetized state. This is because the material is divided into many magnetic domains, each of which is spontaneously magnetized in different direction resulting in a zero net magnetization. When an external magnetic field is applied, the magnetization of the material increases with the increasing applied field and reaches the saturation magnetization (see figure 2.4).

Figure 2.3: Arrangement of magnetic moment in ferromagnetic14

6 As the applied field is reduced, the magnetization decreases but does not come back to the original value. This irreversible process of magnetization is called hysteresis, as shown in figure 2.5.

Figure 2.4: Unmagentized ferromagnetic domain (Left) magnetized ferromagnetic

domain15

At H=0 the magnetization reaches a non-zero value that is called the residual magnetization or the remanence. As the magnetization is decreased further (increased in a negative sense) the intensity of magnetization decreases and finally reaches zero. The absolute value of this field is known as the coercive field. Now if the magnetic field is increased further in a negative sense it will result in an increase of magnetization in a negative way and it will finally reach the negative saturation magnetization. The entire loop is called the hysteresis loop as discussed earlier.

17 Figure 2.5: Magnetization (M) as function of magnetic field (H) at T

7 2.2.4 Antiferromagnetism: In antiferromagnetic materials, the ordering of the spins are in antiparallel arrangement (see figure 2.6). Therefore, the net moment is zero at the magnetic ordering temperature known as the Néel temperature. However, the antiferromagnetic crystal will be paramagnetic above the Néel temperature. As shown figure 2.6, for an antiferromagnetic material, the susceptibility increases with increasing temperature until the Néel temperature, and decreases with increasing temperature above this temperature. On the other hand for all temperatures, the paramagnetic susceptibility decreases with increasing temperature.

Figure 2.6: Arrangement of magnetic moment in antiferromagnetic materials (Left) Susceptibility vs Temperature18 (Right)

2.2.5 Ferrimagnetism: Ferrimagnetism is considered to be a combination of ferromagnetism and antiferromagnetism . Ferrimagnetism takes place in when some atoms arrange themselves in the same direction of the filed as in ferromagnetic materials, and others in opposite directions of the filed like in antiferromagnetic materials as shown in figure 2.7. Ferrimagnetism is unique because the value of one spin is larger than the other one. As result of that the net magnetization does not equal zero.

8 This kind of material have high and positive susceptibility depending on temperature. The behavior of ferromagnetic materials is similar to ferromagnetic materials but they become paramagnetic above the Neel temperature. The magnetization of ferromagnetic crystal decreases with increasing 19 the temperature.

Figure 2.7: Arrangement of magnetic moment in ferrimagnetic materials

2.2.6 Spin glasses: Spin glasses are an interesting type of magnetic materials because they have properties quite different from those of ferromagnetic and antiferromagnetic materials.20 They are disordered magnetic materials.21 The magnetic moment of atoms in these materials are not aligned in a regular orientation. The spin glass type states arises in a materials due to the coexistence of ferromagnetic and antiferromagnetic interactions. As shown in figure 2.8, the red lines indicate to the FM and the green ones indicate to the AFM. They do not change and are stuck similarly to conventional glass molecules which cannot make much movement but the direction of their spin can alter. According to figure 2.8, the spin in the top and bottom rows want to make the middle spin point up, but the left and right spin want to make it point down. Therefore, it is difficult to know what to do to reduce the system energy. As a consequence, the spin in the middle of the system will be always frustrated.

9

Figure 2.8: Arrangement in spin glass; the green lines denote FM interaction and red lines denote AFM interaction.22

In most cases, the lattice geometry is responsible for the magnetic frustration in a spin glass system. As an example, the triangle of the antiferromagnet is located similar to frustrated geometrically system as it can be seen in figure 2.9. In the figure geometry, when the red and blue spins on the primary triangle are pointed in an opposite direction to fulfill the antiferromagnetic interactions, the third spin cannot be anti-aligned with the other two spins. So, the geometry of the triangular lattice is conflicting with the antiferromagnetic interactions, and is called geometrical frustration. Geometrical frustration ideally to the ground state of a degenerate manifold instead of a single stable ground state arrangement.

Figure 2.9: (a) Antiferromagnetic un-frustration on a23 square lattice (b) on equilibrium triangular lattice.

At low temperature the material state is disordered and similar to regular glasses which are quenched or stuck. So, we cannot utilize the same tools to recognize the state of the crystal because there is no obvious ordering. This type of quenched disorder can be listed under the spin

10 glasses. However, the disorder here is not structural but magnetic. The spin glasses start to be complex systems which are not in equilibrium and preserve themselves at the boundary condition of chaotic flow and rigid ordering. So they do not shape themselves in any obvious arrangements. The complex structures, which are inside the spin glasses, are metastable due to the unstable arrangement.23, 24 The spin glasses have modern theory, which suggest that the foundation of spin glasses in physics is in their microscopic interactions and the competition between ferromagnetic 25 and antiferromagnetic interactions. On the experimental part, the spin glasses exhibit some interesting unbalanced behaviors. Because it has the timescales of relaxation or equilibration and has the ability to remember particular properties from its past history. Moreover, at low temperature, the spin glass can show a that does not have long-range order of magnetization. Above the critical temperature (Tc), the spin glasses can show normal magnetic properties but below the Tc the spin glasses will be frozen in some random arrangement and then the spin glasses show featured transport properties, which depend on the cooling condition of the sample weather is field cooled (FCC) or zero field cooled (ZFC). The Spin glass system has a at TC which is a phase 26 transition indicator and displays a featured kink. 2.3 Magnetic interactions: The magnetism of a material is governed by the spin concept which is the coupling of magnetic moments in the material. This concept was developed in a short time from 1925 to 1928 by Pauli and Dirac.9 They developed it by quantum theory. The magnetism is created by different exchange interaction mechanisms such as ferromagnetic, ferrimagnetic, antiferromagnetic and spin glasses systems. The different types of exchange interactions can be classified as direct exchange interaction, indirect exchange interaction, super exchange and double exchange interactions. A brief detail of these interactions are given in the following sections. 2.3.1 Direct exchange interaction: In a direct exchange interaction the atoms are close enough so that the wave functions of the electrons overlap. As a result a strong and short range coupling of the magnetic spins occur which decreases quickly with the separation of the ions. There is an easy way to understand the direct exchange interaction which is to have two atoms and one electron from each atom. The Coulomb interaction can be minimal if the atoms become very close to each other and then the electrons stay in between the nuclei for most of their time. As the electrons should be located at the same area in

11 space at the same time, Pauli's exclusion principle says that they have to obtain opposite spins. As reported by Bethe and Slater most of the electrons time are spent in between nearby atoms when the distance between the atoms is small. As a consequence for that the spins are antiparallel alignment and then we have negative exchange which are antiferromagnetism (see Figure 2.10)

Figure 2.10: Antiparallel alignment for small interatomic separations.

When the electrons are far away from the atoms and spend most of their time far apart from each other to decrease the repulsion between the electrons. The result of that is to have parallel alignment or positive exchange which is ferromagnetism (see figure 2.11).

Figure 2.11: Parallel alignment for large interatomic separations.

The direct exchange for inter-atomic j can be positive or negative depending on the equilibrium between the Coulomb energy and the kinetic energy. Figure 2.12 shows the Bethe-Slater curve. As shown in the figure, the curve represents the value of direct exchange parameter as a functions of the interatomic distance. The transition element Co is located at the side of the peak of this curve, while Cr and Mn are situated at the negative exchange. The exchange interaction in Fe depends on the crystal structures and it might be near the zero-crossing of the curve.

Figure 2.12: The Bethe-Slater curve.13

12 2.3.2 Indirect exchange interaction: The indirect exchange interaction occurs when moments are separated at relatively larger distances. The indirect exchange is the leading interaction in , where there are no direct overlaps between the neighboring electrons. So, it occurs via an intermediary, which in metals are the itinerant electrons. This kind of exchange is well known Ruderman, Kittel, Kasuya and Yoshida (RKKY) interaction. The coefficient of the RKKY exchange (j) swings from positive to negative as the distances between the ions alter and behaves like a damped oscillation as shown in Figure 2.13. The magnetic ions could be ferromagnetic or antiferromagnetic depending on the distance between the pair of ions. The magnetic ion generates a spin polarization in the itinerant electrons in its range. This polarization in the itinerant electrons is detected by the moments of other magnetic ions in the neighborhood giving rise to an indirect coupling.

Figure 2.13: A graph of the indirect coefficient (RKKY) exchange vs. the interatomic

separation.23

2.3.3 Superexchange interaction: Superexchange interaction can be explained as the interaction between moments on ions when they are separated far away from each other and then make them connected via the direct exchange. However, they interact with each other in a long distance through a non-magnetic substance. To make it clear, an example is shown in figure 2.14, where the magnetic moments of a pair of cations are separated by a diatomic anion. For the ferric ion, the 3d shell is partially filled and charge distribution is a spherically symmetric. On the other hand, the triply rare-earth ion is not

13 symmetric. The spin-orbit of the coupled ion is strong and the charge distribution is coupled to its moment. The moments of the ions are connected by superexchange. Therefore, turning the Fe moment changes the R cation overlap in the molecule. This alters the Coulomb and exchange interactions magnitude between the cations, giving rise to a coupling, which relies on the moment's orientation.

Figure 2.14: Superexchange in the interaction of the ferrimagnetic rare earth in a garnet.26

14 Chapter 3

Experimental Techniques The goal of this project is to study the structural and magnetic properties of Heusler alloy

materials Ni1.7-xMn1.7+xGa0.6 (0  x  0.3). The experimental work was done in three steps which are sample preparation, structural characterization, and characterization of the magnetic properties. Samples were prepared by arc melting technique. X-ray diffraction (XRD) measurements were done to analyze the crystal structure, and the magnetic properties of the samples were measured by using a Physical Property Measurement System (PPMS) made by Quantum Design Inc. The experimental detail of this work will be described in the following sections. 3.1 Sample preparation:

Polycrystalline Ni1.7-xMn1.7+xGa0.6 (0  x  0.3) samples were prepared by arc melting technique in an argon atmosphere. The constituent elements were weighed in proportion on a digital balance. Then the elements were melted together in an arc melting chamber in high purity argon atmosphere. For assuring proper melting, the alloys were flipped and re-melted at least three times. Following the melting, the samples are sealed in vycor tubes in partial and argon using oxy-propane torch and annealed at 850 0C for 72 hours in a high temperature tube furnace. I have prepared 7 samples by this technique. A complete list of the samples is given in Table 1. To measure the magnetic properties, the samples were cut in to small pieces by using a slow speed wheel cutter.

Ni1.7-xMn1.7+xGa0.6 The Value of x

Ni1.7Mn1.7Ga0.6 x = 0

Ni1.65Mn1.75Ga0.6 x = 0.05

Ni1.6Mn1.8Ga0.6 x = 0.1

Ni1.55Mn1.85Ga0.6 x = 0.15

Ni1.5Mn1.9Ga0.6 x= 0.2

Ni1.45Mn1.95Ga0.6 x = 0.25

Ni1.4Mn2Ga0.6 x = 0.3 Table 1: The list of samples prepared by arc melting technique.

15 3.2 XRD measurements: In order to properly investigate the magnetic properties of the alloys, the identification of the phase purity and crystal structure is important. The crystal structures of the samples were determined by XRD measurements. In this measurement, x-rays of a fixed wavelength are shined on the crystal while we measure the intensity of the reflected x-ray beam from the crystal as a function of angle governed by Bragg’s law. We used an x-ray source originated from line with wavelength,  =1.54056 Å. 3.2.1 Bragg’s law of Diffraction: Bragg’s law is defined as the relationship between the position of atomic planes in crystals and the angles of the incident x-ray where these planes can generate the strongest reflected electromagnetic radiations. The aim of Bragg’s law is to measure the wavelength and the lattice spacing of the crystal. Let us assume that the x-rays are shined on a crystalline sample and are reflected back, as schematically shown in Figure 3.1. The reflected beams superposition takes place when the path difference is an integer multiple of the x-ray wavelength λ. If we know the angle θ between the incident beam and the atomic planes, as described by the Miller indices (hkl), the reflected neighboring beams difference is 2dhklsinθ, where dhkl is the spacing between the scattering planes. This gives arise to the Bragg’s equation which is

2dhkl sinθ = nλ (3.1)

Figure 3.1: Graphical diagram showing Bragg’s law.28

In the XRD measurements, samples are studied as powders with grains in random arrangements to make sure that all crystallographic directions are sampled by the incident beam. By analyzing the reflected beam the crystal structure of the sample can be estimated.

16 3.2.2 Production of X-ray: X-rays are generated when electrons of high energy hit a heavy target with high atomic number. When electrons hit the metal target, the energy of the incident electron might be enough to take out the electron from inner shell of the atoms in the target. Once this occurs, electron position are generated there. In order to make these position full of electrons, electron from outer shell of the target atom jump to the inner shell there by producing radiation that makes X-rays called characteristic X-rays. The typical way to get an X-ray is by the Coolidge tube technique as shown in figure 7. It is made up of a tube of highly evacuated glass tube with pressure of about 10-5 mm of Hg. The electrons beam released from the source (heated cathode) are accelerated by a potential difference located between anode and cathode. X-rays are supplied if the electron beam strikes the metal target with enough energy. The target temperature is controlled by providing cold underneath the target. When the metals have high atomic number, we can have energetic and intense x-ray.

Figure 3.2: Graphical exemplification of conventional Coolidge tube technique of

production of X-ray.29

3.2.3 Experimental set up for XRD: An x-ray experiment requires an x ray source to produce an x-ray, a high voltage power supply to run the tool and a detector to pick up the diffraction x-rays (as shown in figure 3.3).

17

Figure 3.3: Major components of the diffractometer.28

In this measurement, an x-ray of a fixed wavelength are shined on the crystal and at the same time we measure the intensity of the reflected x-ray beam from the crystal as a function of angle governed by Bragg’s law. We used X-ray source originated from copper line with wavelength equal 1.54056 A. 3.2.4 Analysis of XRD data: The XRD measurements were performed on a Scintag Pad X-ray powder diffractometer that employed Cu-Kα radiation. The diffraction patterns were indexed using a computer program known as Powder Cell. 27 Small pieces of the samples were crushed into powder form using mortar and pestle and were used for XRD measurements. Since the samples were polycrystalline, crushing them down to powder form allows formation of fine grains of single crystals. The measurements were done in the 2 range of 20-100 degrees at room temperature. The data was recorded by automated computer software. Using the peak values (hkl) and the value of d, obtained from Bragg’s equation, the following equations were used to evaluate the lattice parameters of the samples.

2 2 2 1 h  k  l Cubic:  d 2 a 2

2 2 2 1 h  k l Tetragonal:   d 2 a 2 c 2

Here a, b, and c represents the lattice parameters.

18 3.3 Magnetization measurements: The magnetic properties of the samples were measured by using a Physical Property Measurement System (PPMS) made by Quantum Design Inc. The PPMS system contains a superconducting that can generate a magnetic field of up to 90 kOe. Various measurements including electrical resistivity, dc magnetization and ac susceptibility measurements. The measurements can be performed both as a function of temperature and magnetic field. The temperature can be varied from 1.8 K to 400 K, while a magnetic field of up to 90 kOe can be generated. In this research, magnetization as a function of temperature (M vs. T) is performed in temperature range from 5 K to 400 K and a constant magnetic field of 100 Oe and 1 kOe. Magnetization as a function of field (M vs. H) measurements are performed at various temperatures in magnetic fields of up to 50 kOe. The dc magnetization measurements were performed under zero fields cooled (ZFC) and field cooled (FCC) conditions. For the ZFC measurements the samples were cooled down from 300 K to 5 K at zero magnetic fields. For the FC measurements the samples were cooled down to 5 K at a magnetic field of 50 kOe. AC magnetic susceptibility measurements are also performed on all samples using the PPMS. All measurement and data collection ate automated by the windows software known as the PPMS MultiVu. The following sections discuss the components of PPMS including the Vibrating sample magnetometer (VSM) and ac magnetic susceptibility (ACMS) options. 3.3.1 Major Components of the PPMS: The major components of the PPMS are shown in figure 3.4. The system is rather complex, and in this we only present a brief discussion on the various components of PPMS system.

Figure 3.4: Block Diagram of PPMS showing major component.31

19

Liquid Dewar: The helium Dewar hosts the and the sample chamber. The Dewar is surrounded by a vacuum space, which is again surrounded by the outermost liquid jacket. The vacuum space and the liquid nitrogen jacket helps minimize the liquid helium boil off. The nitrogen-jacket has a 40 L liquid nitrogen capacity and the main Dewar has a 30 L liquid helium capacity. The liquid helium is used to cool the superconducting magnet and the sample chamber for low temperature measurements. Sample Probe: The main parts of the probe are the sample chamber, impedance assembly, superconducting magnet, baffled rods, and probe head, which can be shown in figure 3.5. The sample chamber is located between two vacuum tubes inside the probe. The foundation of sample chamber includes a 12-pin connection to make contact with the installed sample puck bottom. The cooling annulus can be indicated by the area between the sample chamber and inside vacuum tube. The liquid-helium is withdrawn by the impedance tube so the sample chamber can be warmed and cooled. The probe has the impedance assembly that can control the liquid helium to go into the cooling annulus from the Dewar. The superconducting magnet is made of niobium titanium alloys and is located at the outer part of the probe. The magnet circuit can be controlled by the persistence switch, so the magnetic field could be altered. Once the heater is closed, the entire magnet will be superconducting, which means the current source is not needed in the constant field operation.

20

Figure 3.5: Major components of the PPMS probe. 31

Model 6000 PPMS Controller: The Model 6000 PPMS Controller is the integrated user interface that keep the electronics and the gas-control valves for the PPMS device. The Model 6000 PPMS Controller is consist of the CPU board, motherboard, and bridgeboard system. The CPU board is serves as the system processor. The system integration can be managed by the motherboard. The bridgeboard system is provided for reading the temperature. Gas valves and gas lines are located inside the Model 6000 and are used to control the temperature. Vacuum pump: The vacuum pump works continually to manage the pressure of the sample chamber and to assist thermal control. It has pipes in the Model 6000 to adjust the vacuum and the gas-flow rates. The pump is located under in the electronics cabinet. To save the system from the pollution, the pump has an oil-mist filter which linked with an exhaust line and a foreline trap. The oil-mist filter can be found inside the electronics cabinet. Electronic cabinet: The electronics cabinet carries three component: the Model 600, the vacuum pump, and a power strip. There is also an additional empty space inside the electronics cabinet

21 which can be used for more hardware and electronics that might be needed. To obtain all the PPMS requirements, we need to have PPMS MultiVu which is windows based control software. With the PPMS MultiVu we will be able to control the system parameters and make our measurement sequences which can operate the system automatically. 3.3.2 An introduction of VSM: Vibrating sample magnetometer (VSM) is used to measure the magnetic properties of the samples. The sensitivity of the VSM option is such even a small change in the magnetic moment from 10-5 to 10-6 emu would be detected. The design of VSM is straightforward but has the ability to produce an exact magnetic moment measurement which is needed to be done in a uniform magnetic field as a function of different parameter such as temperature, magnetic field, and crystallographic orientation. The measurement is performed by oscillating the sample close to a detection coil while concurrently adjusting the induced voltage. The system has the ability to fix magnetization changes below 10-6 emu at 1 Hz due to the use of a compact gradiometer coil configuration, large oscillation amplitude (1–3 mm peak) and a 40 Hz frequency. The VSM application contains a VSM linear motor transport to vibrate the sample, a coil set puck for detection, and electronics to drive the VSM linear motor transport and detect the reaction from the coils. There is also a software option, which is “The MultiVu”, is provided to automate and manage the whole system. A simple scheme of the VSM system is shown in figure 3.6.

Figure 3.6: Major components for PPMS VSM system. 32

22 3.3.3 Operating principle of VSM: A vibrating sample magnetometer is able to change the magnetic flux which aid to generate a voltage in the pickup coil which is ruled via the magnitude of the Faraday’s equation. The

Faraday’s equation can be written as Vcoil = dΦ /dt = (dΦ/ dz). (dz/ dt) where, Φ is the magnetic flux enclosed by the pickup coil, z is the perpendicular position of the sample in respect to the coil. When the sample position is oscillating sinusoidally, then the voltage equation can be written as

Vcoil = 2πfCmAsin (2πft), where C is a coupling constant, m is the DC magnetic moment of the sample, A is the amplitude of oscillation, and f is the frequency of oscillation. To perform magnetic measurements, the coefficient of the sinusoidal voltage signal from the detector of the coil has to be measured. Figure 3.7 shows how this operates with the VSM application.

Figure 3.7: The VSM system scheme.31

The sample is linked to the end of a sample rod which goes sinusoidally. The midst of the oscillation is located at the perpendicular center of the gradiometer pickup coil. The position and amplitude of oscillation can be controlled by the VSM motor module that uses an optical linear

23 encoder signal to read back from the VSM linear motor transport. The voltage which is generated in the pickup coil is expanded and detected by the VSM detector module. The position encoder signal can be used as a reference point to aid the VSM detector module for the synchronous detection. The VSM motor module can provide the encoder signal that clarifies the raw encoder. The detection of VSM module can adjust the in-phase and the quadric phase signals which come from the encoder and the amplified voltage from the pickup coil. These signals will be rated and sent to the controlling network which is the CAN bus and taken to the VSM application. 3.3.4 Overview of AC Magnetometer: The alternate current magnetic susceptibility (ACMS) option on the PPMS can provide AC susceptibility measurement that can determine the time dependent moment of a sample. There will be induced current in the pickup coils that is created by the field of the time-dependent moment, which allow measurements without sample motion. By the description of this measurement technique, some important substance properties can be investigated. Since a time-dependent moment is induced, the magnetization dynamics data can be obtained by AC measurements, where the sample moment is still the same while the measurement is performed. On the other hand, some interesting materials can be well described through the AC magnetic measurements and some other techniques, for example DC magnetization. The AC measurement can detect any small changes in M (H), so it can detect small magnetic shifts even though the absolute value of the moment is very large. The AC moment in the sample at higher frequency case cannot go along with the DC magnetization curve because the sample has dynamic effects. Thus, the AC susceptibility measurement is named as the dynamic susceptibility. At higher frequencies, the sample magnetization might beyond the drive field that can be adjusted by the magnetometer circuitry. So, there are two quantities for the AC susceptibility measurement which are the magnitude of the susceptibility, χ and the phase shift, Φ, The AC susceptibility can have an in-phase, or real part χ’ and an out-of-phase, or imaginary part χ”. At the low frequency limit, where the DC and AC measurement are almost the same, the real part χ’ of the AC susceptibility is the slope of the M (H) curve. The imaginary part, χ” can assist us to specify dissipative processes which occurs in the sample such as the dissipative processes of conductive samples is because of eddy currents. When the value of χ” is not zero, the relaxation and irreversibility of the sample can show up in spin-glasses that can give rise to the irreversible domain wall movement in ferromagnetism because of the permanent moment. Moreover, both the

24 real and imaginary part are highly sensitive to the thermodynamic phase alterations, and are utilized to scale the transition temperatures. AC magnetometry can aid to provide these interesting phenomena to the probe. Typical measurements to get this data are χ vs. temperature, driving frequency, and DC field bias, harmonic measurements, and χ’ vs. AC field’s amplitude. Due to its precision, it has ability to isolate between in real and imaginary parts in the AC moment reaction, the AC susceptibility measurement is widely utilized in substance description techniques. For instance; AC susceptibility has been one of the most important tools to define the superconductors in physics, especially to measure the critical temperature. In like manner, spin-glass behavior is often described through AC susceptibility measurements.32 Furthermore, the AC susceptibility measurements are a standard tool for the description of ferromagnetic particles that behave as super paramagnetism. The dynamic of AC susceptibility is also used to investigate the nature of magnetic phase transitions, for example ferromagnetic transitions.33 In our study, we used the ACMS which are compatible with the PPMS to measure the magnetic susceptibility of the samples.

3.3.5 Design and working mechanism of PPMS ACMS option: The Physical Property Measurement System (PPMS) has an AC Measurement System (ACMS) option that is a DC magnetometer and AC susceptometer. The ACMS technology provides inclusive susceptibility and magnetization abilities when detained environment as a friendly user. While the ACMS are connected to the automated temperature and magnetic field controlling in the PPMS, the ACMS option gives completely automatic magnetic workstation. The ACMS system contains the AC-drive and detection coils, thermometer, and electrical connections. The AC-drive coil provides an alternating excitation field and the detection coil inductively reacts to the sample moment and excitation field. The copper AC-drive and detection coil are located within the ACMS sets, in the center of the DC superconducting magnet that is in the PPMS device. The ACMS sets are directly suitable with the PPMS sample chamber and obtains the sample area that makes the sample receives a uniform magnetic field. Thus the DC field and temperature control is done with traditional PPMS ways. The sample can be caught within the coil set by the rigid sample rod. In the ACMS sample transport assembly, there is a DC servo motor used to longitudinally translate the sample holder. The DC servo motor can aid to give us the longitude of the sample motion. The ACMS sample, which are transported assembly, can be found on the top of the PPMS probe. The detection coils are oriented to be as a first-order

25 gradiometer arrangement. Therefore, the sample’s signal will be covered from uniform background sources by this arrangement.

Figure 3.8: ACMS Insert and Coil Set.34

The ACMS insert and the Coil assembly are illustrated in Figure 3.8. There are 12-pin connector located at the PPMS sample chamber to connect the ACMS drive and detection coils with the PPMS electronics. This makes use of the normal PPMS hardware, so the extra wiring and connectors are not needed on the subsystem of the ACMS probe. A Digital Signal Processor board (DSP), that is located in the Model 6000 PPMS Controller, is utilized in the ACMS to produce the stimulation waveforms and save the detected reaction of the signal. While an AC susceptibility measurement are obtained, an alternating or a constant magnetic field is applied automatically to the measurement zone by the superconducting magnet in the PPMS. The AC board’s DSP can help to synthesize this alternating magnetic field and send it to a digital- to-analog adapter. The signal of the analog can be magnified with a view to stimulate the compensation and drive coils. A small alternating magnetic field can be add to the large applied magnetic field that comes from the superconducting magnet of the PPMS by the AC susceptibility

26 option in the ACMS and then measures the reaction of a sample’s magnetic moment. The response amplitude and phase are saved. An AC measurement is performed, when the sample is located in the middle the detection coil and a signal is put in an application for the drive coil. Then, the voltage from one side to the other of the detection coils can be recorded for a specified amount of time by the DSP. To reduce noise, the average of doubled AC waveforms can be calculated point-by-point. The sample is consecutively located in the other detection coil, then the response of the time range is once more measured. There is imponderables between the drive coil and the counter-wound sense coils which can affects the measurement, so the difference between the two average waveforms are calculated to eradicate this imponderables. One of the PPMS feature is digital filtering due to utilizing a DSP chip instead of a locker in amplifier. This feature can vastly improve the rendering of the signal-to-noise through analog filters.

27 Chapter 4

Results and Discussion

In this thesis project we have measured the structural and magnetic properties of a series of selected

Ni1.7-xMn1.7+xGa0.6 (0 x  0.3) Heusler alloys. This chapter presents the experimental results and related discussion.

4.1 SEM and X-ray diffraction measurements:

The SEM images, obtained at room temperature, of the Ni1.7-xMn1.7+xGa0.6 alloys are shown in Figure 4.1. The images confirms that the alloys are single phase and contains no impurities or secondary phases. In addition, a careful observation reveals the twin boundaries of the martensitic phase. The twinning microstructures are comparable to those obtained in other Ni-Mn-Ga alloys.35

Figure 4.2 shows the room temperature XRD patterns of the polycrystalline Ni1.7-xMn1.7+xGa0.6 samples. The patterns indicate that the alloys exhibit the L10 martensitic tetragonal structure with the space group I4/mmm and space group number 139. The lattice parameters as a function of concentration x is shown in figure 4.3. The lattice parameters “a” and “b” are equal but the lattice parameters “a” and “c” are different. As we can see in the figure, with increasing Mn concentration, both a and c marginally decreases from a =7.5995 Å (c =6.844 Å) to a =7.541 Å (c = 6.691 Å) for the alloy with x = 0 and x = 0.3, respectively. The marginal change in lattice parameters can be attributed to the similarity between the radius of manganese and ions, [1.246 Å for Ni ion and 1.264 Å for Mn ion considering the coordination number of 12]36.

28

Figure 4.1: SEM micrograph of Ni1.7-xMn1.7+xGa0.6 (0  x  0.3) alloys.

29

Figure 4.2: X-ray diffraction patterns of Ni1.7-xMn1.7+xGa0.6 (0  x  0.3) obtained at room temperature.

Figure 4.3: The difference of lattice parameter “a” and “c” of Ni1.7-xMn1.7+xGa0.6 (0  x  0.3) obtained at room temperature.

30

4.3 dc Magnetization measurements: We have performed dc magnetization measurements on all the Ni1.7+xMn1.7-xGa0.6 samples. The measurements were performed as a function of field and temperature. By performing the magnetization measurements we intended to determine the ferromagnetic Curie temperature, TC, and other magnetic properties including the exchange bias. The M (H) measurements were performed at 5 K (and higher temperatures for some samples) under both ZFC and FC conditions.

The temperature dependence of magnetization, M (T), measurements were also performed under

ZFC and FCC conditions at a constant field of 100 Oe and 1 kOe. In this section we present and discuss the experimental data.

4.3.1 Magnetization as a function of temperature:

Figure 4.4 show the M (T) data of the Ni1.7+xMn1.7-xGa0.6 alloys measured at a magnetic field of

100 Oe. As shown in figure 4.4a, the ZFC magnetization of Ni1.7+xMn1.7-xGa0.6 (x = 0) initially increases with increasing temperature. As the temperature nearly approaches 100 K, a change in slope in the ZFC M (T) data is observed. With further increase of temperature the magnetization sharply increases until it reaches a peak at a particular temperature, which we refer to as the peak temperature (TP). Above TP, the magnetization changes at a slower rate until it sharply drops at

TC. The FCC M (T) data exhibit different behavior. As the temperature is reduced from the highest temperature above TC, the FCC M (T) data follow the same path as that of the ZFC M (T) data until TC. Below TC a large thermomagnetic irreversibility is observed in the FCC and ZFC M (T) data for all samples, as clearly shown in figure 4.4. The observed behavior in the M (T) data of

8 Ni1.7+xMn1.7-xGa0.6 (x = 0) is consistent with that reported by Ramakanta et al.

31 The M (T) data for the Ni1.7+xMn1.7-xGa0.6 (x > 0) materials are shown in figure 4.5. Although, the

ZFC M (T) data show minor variations with increasing Mn concentration, the FCC M (T) data show nearly identical behavior for all Ni1.7+xMn1.7-xGa0.6 alloys. Like the alloy with x = 0, thermomagnetic irreversibility is observed in all materials. The thermomagnetic irreversibility in the Ni1.7+xMn1.7-xGa0.6 alloys may be attributed to several factors including magnetic blocking or spin-glass like states in the samples, where freezing or pinning of the magnetic domains occur when the material is cooled in the presence of a magnetic field. Competing magnetic interactions can also result in such observation.

The values of TC and TP for the Ni1.7+xMn1.7-xGa0.6 samples were estimated from the derivative

(dM/dT) of the ZFC M (T) curves. The variation of these temperatures versus the Mn concentration x are shown in figure 4.5. With increasing Mn concentration both TC and TP increases, as shown in the figure. The increase of the transition temperatures indicates that the ferromagnetic exchange interaction in the Ni1.7+xMn1.7-xGa0.6 systems increases with increasing Mn concentration.

Figure 4.4: Magnetization as a function of temperature, M (T), of Ni1.7Mn1.7Ga0.6 (x =0) obtained at a magnetic field of 100 Oe.

32

Figure 4.5 (a) – (f): Magnetization as a function of temperature, M (T), of

Ni1.7-xMn1.7+xGa0.6 (0.05  x  0.3) obtained at a magnetic field of 100 Oe.

33

Figure 4.6: Variation of Tp and Tc of Ni1.7-xMn1.7+xGa0.6 as function of x.

4.2.2 Magnetization as a function of magnetizing field:

In order to explore the exchange bias properties of our samples, we have measured the M (H) data of our samples under both ZFC and FC conditions. The ZFC and FC M (H) data of

Ni1.7+xMn1.7-xGa0.6 (x = 0) obtained at 5 K are shown in figure 4.7. The insets of the figures show the complete hysteresis loops measured in magnetic fields from -50 kOe to 50 kOe. For clearer visualization of the lower field region, the magnetization curves from –2 kOe to 2 kOe are shown in the main figure. As shown in the figure, initially the magnetization increases linearly with increasing magnetic field until 1 kOe, and beyond this field the magnetization increases abruptly with further increase in field. Above 21 kOe the magnetization nearly saturates reaching a value of 28 emu/g at 50 kOe. It is also clear in figure 4.7, that ZFC M (H) loop obtained at 5 K, exhibits a double shifted hysteresis loop. Such double-shifted features in the

ZFC M (H) loops are usually observed when the AFM interactions in the material are divided

34 into two types of region that are locally oriented in the opposite directions. During the measurement process, each of these regions couples in opposite way to the FM regions, resulting in double-shifted hysteresis loops.

Figure 4.7b show the FC M (H) data of the Ni1.7+xMn1.7-xGa0.6 (x = 0) alloy. Before the measurement, the sample was cooled from 300 K to 5 K in presence of a 50 kOe external field.

As shown in the figure, the FC M (H) data is significantly different than the ZFC one. The FC data resembles a typical ferromagnetic hysteresis loop with the center shifted along the negative field axis. This is a typical exchange bias behavior. Figure 4.8 and 4.9, show the ZFC and FC M

(H) data for the rest of the Ni1.7+xMn1.7-xGa0.6 alloys. As shown in figure 4.8, the double shifted behavior enhances with increasing Mn concentration, with the alloy with x = 0.3 showing the most clear double-shifted hysteresis loop. On the other hand, the shape of the FC M (H) loops don’t vary much with increasing Mn concentration. However the coercivity and the exchange bias field do vary with increasing Mn concertation.

The exchange bias (EB) phenomena takes a place because of the exchange interaction between

FM and AFM components at the interface. As we discussed earlier, our system exhibit spin-glass type ground state where the AFM and FM interactions have various domains as a result of the magnetic ions configuration and the competing interactions between them. When an antiferromagnetic substance is powerfully exchange coupled to a ferromagnetic substance, then the ferromagnetic substance will obtain its interfacial spins pinned because of the unidirectional anisotropy where is created at the interface.38 When the moment of the ferromagnetic layer invert, the cost of the energy will be increased at least corresponding to the required energy to make a

Neel domain wall in the AFM substance. The increased energy term results is a shift in the converting field of the FM. Consequently, the exchange bias curve of a ferromagnetic substance

35 will resemble to the normal ferromagnet except when the curve is shifted away from zero through a value of HEB known as the exchange bias field and its value robustly depends on the spin orientation at the interface. As seen in figure 4.7b and 4.9, our samples showed the exchange bias phenomena that alters with changing Ni/Mn concentration. From the FC M (H) data of the samples

HEB 411 Oe has been obtained for the sample with x = 0. The observed data corresponds well

7 with the literature. As shown in figure 4.9, with increasing x HEB of the Ni1.7-xMn1.7+xGa0.6 system increases from 411 Oe (x = 0) to 600 Oe (x = 0.3). This behavior suggest that with increasing

Mn content the magnetic ground state of the Ni1.7-xMn1.7+xGa0.6 system changes dramatically.

Figure 4.7: Magnetization as a function of filed, M(H), of Ni1.7-xMn1.7+xGa0.6 (x = 0) measured at 5 K after (a) zero field cooling and (b) field cooling at a field of 50 kOe.

36

Figure 4.8: Magnetization as a function of filed, M(H), of Ni1.7-xMn1.7+xGa0.6 (0.05  x  0.3) measured at 5 K after zero field cooling.

37

Figure 4.9: Magnetization as a function of filed, M(H), of Ni1.7-xMn1.7+xGa0.6 (0.05  x  0.3) measured at 5 K after field cooling at a field of 50 kOe.

38

Figure 4.10: The variation of HEB (FC) as a function of excess Mn concentration x.

4.3 AC susceptibility measurements: The EB in Heusler alloys can be explained by the spin glass kind frustrated nature of the ground state. Such ground states can be detected by the ACMS measurements. The magnetization dynamics of a system can be probed by ACMS measurements, which is not possible to obtain by dc magnetization measurements. Another advantage of the AMCS measurements is that the value of susceptibility and the phase shift can be obtained at higher frequency, and close to the driving signal. Thus, we can get a real part (in phase part, χ) and an imaginary part (out of phase part, χ).

The real part of the susceptibility is associated with the M (H) slope and is highly responsive to even a small alteration in the M (H) but the imaginary part gives information about the dissipative procedures in the sample. When the χ (T) is not zero, the spin-glasses will have relaxation and

39 irreversibility 39. Considering these thoughts, ac susceptibility measurements have been done on the Ni1.7-xMn1.7+xGa0.6 samples in order to inspect the nature of the ground state and to investigate more possible reasons behind the observation of the EB phenomena in this system.

Figure 4.11 shows the (T) and (T) data for the Ni1.7-xMn1.7+xGa0.6 (x = 0) samples measured in an ac field of 10 Oe and frequencies (f) of 100 Hz, 500 Hz, 1000 Hz, and 10000 Hz. As shown in the figure, (T) increases linearly with increasing temperature until 75 K when a change in slope is observed. Beyond 75 K, (T) increases exponentially peaking at 150 K and then increases at a slower rate until 180 K, and peaks again at ~210 K. Beyond this temperature, (T) finally decreases to zero demonstrating a TC of ~220 K, which is consistent with the M(T) data (see figure

4.4). Between 75 K and 185 K, frequency dependence is observed in the (T) data. The (T) data (figure 4.11b) exhibit a different interesting behavior. Two sharp peaks at 125 K and 200 K are observed in the data. The interesting feature to notice is that the peak at 125 K shifts to higher temperature with increasing frequency while the peak at 200 K does no shift with frequency.

Figure 4.11: Temperature dependence of the real and imaginary part of the ac susceptibility of Ni1.7Mn1.7Ga0.6 (x = 0) obtained in an ac field of 10 Oe and frequencies from 10 Hz to 10000 Hz.

40 As shown in figure 4.12 and 4.13, the (T) and (T) data for the Ni1.7-xMn1.7+xGa0.6 (x > 0) changes dramatically with increasing Mn content. For nearly all samples with x > 0, the (T) data exhibit a frequency independent peak near TC, along with a minor anomaly at TP. A closer look at the anomaly near TP reveals a strong frequency dependence in that region. The (T) data of the samples with x > 0 also exhibit similar behavior.

4.4 Discussion: The experimental results for the Ni1.7-xMn1.7+xGa0.6 samples presented above suggest that the ground state of the system is strongly dependent on the Mn content. The observed behavior can be explained considering a model by Lázpita et al. that describes the moment distribution in Ni-

Mn-Ga based alloys.41 According to the model, depending on the stoichiometry of the alloy, the

Mn atoms are allowed to occupy the regular Mn sites, Ni sites, and Ga sites. The respective Mn atoms are described as the Mn/Mn (for regular site), Mn/Ni (for Ni site) and the Mn/Ga (for Ga site) atoms. In the absence of the Mn/Ni atoms, the coupling between the Mn/Mn atoms and the

Mn/Ga atoms is typically AFM. When the excess Mn atoms occupy the Ni sites, the Mn/Ni atoms become the closest neighbor to the Mn/Mn atoms, and therefore a stronger AFM coupling between the Mn/Ni and Mn/Mn atoms overcome the AFM coupling between the Mn/Mn and

Mn/Ga atoms. Thus resulting in FM coupling between the Mn/Mn and the Mn/Ga atoms.

Considering that this model is valid, replacing Ni with Mn in the Ni1.7-xMn1.7+xGa0.6 materials results in a variation of Mn atoms on the 3 possible sites, causing a redistribution of the AFM and FM interactions in the system. This redistribution causes a variation in the competition between the different interactions which results in the variation in the observed behavior in the experimental results.

41

Figure 4.12: Temperature dependence of the real component of the ac susceptibility of Ni1.7-xMn1.7+xGa0.6 (x > 0) obtained in an ac field of 10 Oe and frequencies from 10 Hz to 10000 Hz.

42

Figure 4.13: Temperature dependence of the imaginary component of the ac susceptibility of Ni1.7-xMn1.7+xGa0.6 (x > 0) obtained in an ac field of 10 Oe and frequencies from 10 Hz to 10000 Hz.

43 Chapter 5

Conclusion

We have experimentally investigated the magnetic and associated exchange bias properties of

Ni1.7-xMn1.7+xGa0.6 (0  x  0.3) alloys. The XRD and SEM measurement illustrate that the alloys have single phase exhibit the tetragonal L10 structure (martensitic phase) at room temperature. The lattice parameters (a = b ≠ c) changes marginally with increasing Mn concentration due to the small differences in the atomic radii of Ni and Mn.

For all Mn concentration x, the ZFC and FCC M (T) data obtained in an applied magnetic field of 100 Oe of the Ni1.7-xMn1.7+xGa0.6 alloys exhibit thermomagnetic irreversibility. Ac magnetic susceptibility data suggest that the irreversibility is due to the presence of spin glass like ground state in the alloys. With increasing Mn concentration both TC and the low temperature anomaly at TP increases, suggesting an enhancement of FM exchange interaction in the system. The M(H) data obtained under ZFC conditions exhibit double-shifted hysteresis behavior suggesting that the AFM interactions in the materials are divided into two types of region that are locally oriented in the opposite directions and each of these regions couples in opposite way to the FM regions, resulting in double-shifted hysteresis loops. The FC M (H) loops show that all samples exhibit exchange bias behavior and the magnitude of the exchange bias field increases with increasing Mn concentration.

The observed magnetic properties of Ni1.7-xMn1.7+xGa0.6 alloys are explained on the basis of magnetic moment distribution in them. The exchange interaction between Mn atoms on the regular

Mn sites is FM. The excess Mn atoms that occupy the Ni or Ga sites couple antiferromagnetically with the Mn atoms on the regular Mn sites. Thus, in the Mn rich Heusler alloys competing FM and

44 AFM exchange interactions generate inhomogeneous magnetic behavior. These competing interactions are believed to be responsible for the glassy like ground state and the observation of the exchange bias effects in the Ni1.7-xMn1.7+xGa0.6 alloys.

45 References: 1 W. H. Meikles john and C. P. Bean, Phys. Rev. 102, 1413 (1956). 2 J. Nogués and I. K. Schuller, J. Magn. Mater. 192, 203(1999). 3 T. Lin, C. Tsang, R.E. Fontana, and J. k. Howard, IEEE Trans. Magn. 31, 2585 (1995). 4 B. M. Wang, Y. Liu, P. Ren, B. Xia, K. B. Ruan, J. B. Yi, J. Ding, X. G. Li, and L. Wang, Phys. Rev. Lett. 106, 077203 (2011). 5A.K. Pathak, D. Paudyal, W.T. Jayasekara, S. Calder, A. Kreyssig, A.I. Goldman, K.A. Gschneidner Jr., V.K. Pecharsky, Phys. Rev. B, 89 (2014), 224411. 6A. K. Nayak, M. Nicklas, S. Chadov, C. Shekhar, Y. Skourski, J. Winterlik, and C. Felser, Phys. Rev. Lett. 110 (2013), 127204.

7 Z. D. Han, B. Qian, D. H. Wang, P. Zhang, X. F. Jiang, C. L. Zhang, and Y. W. Du, Appl. Phys. Lett. 103, 17

8 “Exchange bias phenomena in Ni2−xMn1.4+xGa0.6” Mahmud Khan and Ramakanta Chapai, J. All. Comp., 647, 935 (2015). 9 J. Stohr, H.C.Siegmann, Magnetism from fundamentals to nanoscale dynamics, Springer (2006). 10 B.D. Cullity and C.D. Grahm, Introduction to Magnetic Materials, Second Edition, Wiley publication (2009). 11 H. Kronmuller and S. Parkin, Handbook of Magnetism and Advanced Magnetic Materials. Edited Volume 1, John Wiley & Sons, Ltd, (2007). 12 D. C. Agrawal, Introduction to Nanoscience and Nanomaterials, World Scientific (2013). 13 K. C. Barua, Introduction to , Alpha science (2007). 14 http://www.madsci.org/posts/archives/2008-08/1219953614.Ph.r.html 15 http://202.141.40.218/wiki/index.php/Ferromagnetism. 16 D. Jile, Introduction to Magnetism and Magnetic Materials, Chapman and Hall (1991). 17 http://ischuller.ucsd.edu/research/exchange_bias.php. 18 http://electrons.wikidot.com/magnetism-iron-oxide-magnetite. 19 C. Kittle, Introduction to solid state physics, Wiley publication, (2007). 20 D. Sussman, the Replica Approach Spin and Structural Glasses, (2008). 21 D. L. Stein, C. M. Newman, Spin Glasses and Complexity, Princeton University Press (2013). 22 S.T. Bramwell, M. J. P. Gingras, Science 294, 1495 (2001).

46 23 P. J. Ford, Spin Glasses, CONTEMP. PHYS., VOL.23, NO. 2,141-168 (1982). 24 D. L. Stein, C. M. Newman, Spin Glasses and complexity. Princeton University Press (2013). 25 S F Edwards and P W Anderson, Theory of spin glasses, J. Phys. F: Met. Phys.5 965 (1975). 26 J. A. Mydosh, Spin glasses: An experimental Introduction, Taylor and Francis (1993). 27 C. Zener, Phys. Rev. 82, 403 (1951). 28 http://nptel.ac.in/courses/103103026/module2/lec12/2.html. 29 http://people.senecac.on.ca/marg.brown/RAD212CH104.htm#slide0066.htm. 30 Y. Waseda, E. Matsubara, K. Shinoda, X-Ray Diffraction , Springer publication (2011). 31 PPMS Hardware Manual, 1070-150, Rev. B5, Quantum Design, Inc. (2008). 32 C. A. M. Mulder, A. J. van Duyneveldt, J. A. Mydosh, Phys. Rev. B 23, 1384 (1981). 33A. G. Berndt, X. Chen, H. P. Kunkel, G. Williams, Phys. Rev. B52, 10160 (1995). 34AC Measurement System (ACMS) Option User’s Manual, Part Number 1084-100 C-1 Quantum Design Inc. (2008). 35C.B. Jiang, Y. Mahammad, L.F. Deng, W. Wu, H.B. Xu, Acta Matar. 52 (2007) 2779. 36 W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys, Wiley Inter-science, New-York, pp.146–148 (1972). 37 G. Bertotti, Hysteresis in Magnetism, Academic Press, (1998). 38 J. Nogue & s, I.K. Schuller. Journal of Magnetism and Magnetic Materials 192 203-232 (1999). 39 J. A. Mydosh, J. Magn. Mater. 157/158, 606 (1996). 40 P. Liao, C. Jing, X.L. Wang, Y.J. Yang, D. Zheng, Z. Li, B.J. Kang, D.M. Deng, S.X. Cao, J.C. Zhang, B. Lu, Appl. Phys. Lett., 104 ,092410 5 (2014). 41 P Lázpita, J M Barandiarán, J Feuchtwanger, J Gutiérrez, I Rodriguez, V A Chernenko, A Stunault and C Mondelli, J. Phys: Conf. Series 325 (2011), 012016.

47