06 chapter1

21
1 CHAPTER 1 INTRODUCTION 1.1 INTRODUCTION In the world of quantum mechanics, the fundamental particle electron possess certain properties such as ‘mass’, ‘charge’ and ‘spin’ and these properties have contributed for the evolution of information technology, which has made tremendous changes in our day-to-day life. In conventional electronics, the charges are manipulated by electric fields but often the roles played by the spins are ignored. Electrical current is resultant of electrons interacting with each other and with electromagnetic fields through Coulomb and Lorentz forces respectively. The ability to generate, control and detect the motion of charges in either the free space (vacuum tubes) or in solid state (Si-based electronic devices) forms the basis of modern electronics. Further, the controlled transition/recombination of electrons between different energy levels lead to the absorption/generation of photons in the different range of the electromagnetic spectrum and it forms the basis of optoelectronics (e.g. light-emitting diodes and laser diodes). While in the case of information processing and storage, charge-based devices play a dominant role and in the case of information transmission, storage and display photonic devices are widely used. Recently a lot of interest on the development of spintronic devices has emerged in view of their potential application to the next generation electronic devices. Unlike conventional charge based electronic devices,

Transcript of 06 chapter1

Page 1: 06 chapter1

1

CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION

In the world of quantum mechanics, the fundamental particle

electron possess certain properties such as ‘mass’, ‘charge’ and ‘spin’ and

these properties have contributed for the evolution of information technology,

which has made tremendous changes in our day-to-day life. In conventional

electronics, the charges are manipulated by electric fields but often the roles

played by the spins are ignored. Electrical current is resultant of electrons

interacting with each other and with electromagnetic fields through Coulomb

and Lorentz forces respectively. The ability to generate, control and detect the

motion of charges in either the free space (vacuum tubes) or in solid state

(Si-based electronic devices) forms the basis of modern electronics. Further,

the controlled transition/recombination of electrons between different energy

levels lead to the absorption/generation of photons in the different range of

the electromagnetic spectrum and it forms the basis of optoelectronics

(e.g. light-emitting diodes and laser diodes). While in the case of information

processing and storage, charge-based devices play a dominant role and in the

case of information transmission, storage and display photonic devices are

widely used.

Recently a lot of interest on the development of spintronic devices

has emerged in view of their potential application to the next generation

electronic devices. Unlike conventional charge based electronic devices,

Page 2: 06 chapter1

2

which function on charge injection, transport and controlled manipulation,

spintronics devices specifically exploit spin properties. Spintronics is

expected to overplay the traditional electronic and photonic devices, allowing

for enhancement in the form of reduced power consumption, faster device

operation and new form of information computation.

1.2 SPINTRONICS

The discovery of giant magnetoresistance (GMR) effect is a

milestone in condensed matter physics for which both Fert and Grünberg

were awarded the Nobel Prize in Physics in the year 2007. From the study and

application of this effect, a new branch of solid state physics has emerged,

which is now called spintronics (name coined by Wolf) or spin electronics

(Wolf et al 2001, Zutic et al 2004, Prinz & Hathaway 1995, Sarma 2001).

Spintronics deals with the study of role played by electron spin in solid state

physics and its application to devices which will make use of the spin

properties instead of or in addition to its conventional charge degrees of

freedom. An electron is just like a spinning sphere of charge. It has an

intrinsic quantity of angular momentum (its "spin") and an associated

magnetic moment. In an ambient magnetic field, its energy depends on how

its spin vector is oriented. Every electron exists in one of the two states viz.

spin-up and spin-down with its spin either +1/2 or -1/2. In other words, an

electron can rotate either clockwise or anticlockwise around its own axis with

constant frequency. The two possible spin states naturally represent ‘0’ and

‘1’ states in logical operations.

In spintronics, in addition to the charge, electron spin is

manipulated to yield a desired outcome. The motion of spins, like the flow of

charge, can also carry information. The advantages of spin over charge are:

(i) the spins can be easily manipulated by applied magnetic fields and (ii) the

Page 3: 06 chapter1

3

spins have a long coherence or relaxation (Wolf et al 2001, Sarma 2001).

Control of electrical properties and modification of information by spin

manipulation are the two main goals of this field. A significant proportion of

present solid state research has been devoted to developing, understanding

and discovering materials for spintronics.

1.2.1 Spintronic Devices

Spintronic devices are based on careful manipulation of the

electron spin. In general, the scheme of spin manipulation mechanism is

based on: (1) generation of spin-polarized electron or spin-polarized current

(2) injection and transportation of the spin-polarized electron and

(3) detection of the spin-polarized carriers with information.

Spintronics based devices offer several advantages over

conventional charge based devices. Spin orientation of conduction electrons

survives for a relatively longer period of time and hence the magnetised

materials maintain their spin even without power. The non-volatile nature of

spintronic devices make them particularly attractive for memory storage,

magnetic sensors applications and potentially for quantum computing, where

electron spin would represent a bit (called qubit) of information. Energy

efficiency is another important virtue of these devices as spin can be

manipulated by low-power external magnetic field. Miniaturisation is also an

added advantage since spintronics can be coupled with conventional

semiconductor and optoelectronic devices. All spintronic devices perform

according to the simple scheme: (1) information is stored (written) in the form

of spins i.e., as a particular spin orientation (up or down), (2) the spins, being

attached to mobile electrons, carry the information along a wire and (3) the

information is read at a terminal.

Page 4: 06 chapter1

4

Generally, spintronics based devices are classified into three types:

1) ferromagnetic metal alloy based devices, 2) semiconductor based devices

and 3) the devices that manipulate the quantum spin states of individual

electrons for information processing e.g. Quantum computers (Awschalom

et al 2002).

1) Ferromagnetic metal alloy based devices are mainly used in

memory and information storage. They are also termed as

magnetoelectronic devices. They rely on the GMR effect.

Magnetic interaction is well understood in this category of

devices (Oestreich et al 2002). A typical GMR device consists

of at least two layers of ferromagnetic materials separated by a

spacer layer. When the two magnetization vectors of the

ferromagnetic layers are aligned, the electrical resistance will

be lesser (so a higher current flows at constant voltage)

compared to the situation when magnetic vectors of the

ferromagnetic layers are anti-aligned. This constitutes a

magnetic field sensor. Two variants of GMR have been

applied in these devices:

(a) current-in-plane (CIP), where the electric current flows

parallel to the layers and

(b) current-perpendicular-to-plane (CPP), where the electric

current flows in a direction perpendicular to the layers.

At present, computer hard disks, read heads and magnetoresistive

random access memory (MRAM) chips are produced based on the

ferromagnetic metal alloys.

Page 5: 06 chapter1

5

Other metal-based spintronic devices:

• In tunnel magnetoresistance (TMR), CPP transport is achieved

by using quantum-mechanical tunneling of electrons through a

thin insulator separating ferromagnetic layers.

• In spin-transfer torque, a current of spin-polarized electrons is

used to control the magnetization direction of ferromagnetic

electrodes in the device.

• In case of spin-wave logic devices, orientations of spins are

used to carry information to perform logical operations.

2) Semiconductor based spintronic devices combine the

advantages of semiconductor with the concept of

magnetoelectronics. This category of devices includes spin

diodes, spin filter and spin FET (Wolf et al 2001). In order to

make use of semiconductor based spintronic devices, certain

issues need to be addressed. The first issue is creation of an

different spin distribution which is called as spin-polarization

or spin injection. Spin-polarized current is the primary

requirement in the fabrication of semiconductor based

spintronic devices. It is also very fragile state. The second

problem is achieving transport of spin-polarized electrons

maintaining their spin-orientation. Final issue is relaxation

time which is related to application i.e., the spin comes to

equilibrium by a phenomenon called spin relaxation. It is

important to create longer relaxation time for effective spin

manipulation, which will allow additional spin degree of

freedom to spintronic devices with the electron charge.

Utilizing the spin degree of freedom independently or along

Page 6: 06 chapter1

6

with mainstream electronics will significantly improve the

performance with higher capabilities.

3) The devices falling under the third category are being

considered for building quantum computers. Quantum

information processing and quantum computation is the most

ambitious goal of spintronics research. The spins of electrons

and nuclei are the perfect candidates for quantum bits or

qubits. A qubit (quantum bit) is the fundamental particle of

spin-based computing and its quantum mechanical spin state

carries the information. The qubit has to maintain a

well-defined spin state long enough for a digital operation to

be carried out (Ohno 1998). Therefore, electron spin and

nuclear based hardwares are some of the important candidates

being considered for quantum computers.

In fact, the dream of spintronics scholars is the seamless integration

of electronic, optoelectronic and magnetoelectronic multifunctionality on a

single device that can perform more efficiently than today’s microelectronic

devices. Thus, spintronics technology is expected to produce new

multifunctional devices such as spin-field-effect-transistor, spin-light-

emitting-diode, spin-resonant tunneling-diode, optical switches operating at

terahertz frequency, modulators, encoders, decoders, and quantum bits for

quantum computation and communication (Datta & Das 1990, Schiliemann

et al 2003, Johnston-Halperin et al 2002, Flatte & Vignale 2001, Koga et al

2002). Spintronics has also successfully given rise to new kind of devices for

memory/data storage application, e.g. MRAM.

Page 7: 06 chapter1

7

Nominally, highly spin-polarized materials could provide both

effective spin injection into nonmagnetic materials and large

magnetoresistance effects, important for non-volatile applications. Thus an

efficient spin electrode must either have conductivity comparable to that of

semiconductors or have a spin-polarization near 100%. Schmidt et al (2000)

proposed that two categories of materials namely dilute magnetic

semiconductors (DMS) and half-metals (HM), can act as efficient spin

electrodes. A lot of research has been carried out to study these two types of

materials.

DMS is obtained by doping conventional compound

semiconductors with small concentration of magnetic transition metals. They

are believed to be potential candidates for spin electrodes, since their

conductivity is comparable to that of semiconductors (Ohno 1998). At

present, various families of DMSs have been proposed theoretically (Sato &

Katayama-Yoshida 2000 & 2001, Zutic et al 2004, Ivanov et al 2004).

Experimentally, much more improved spin-polarization has been observed in

some DMS based spin electrodes (Schmidt & Molenkamp 2001).

1.3 HALF-METALLIC FERROMAGNETIC MATERIALS

From the above analysis, it is observed that an essential component

of any kind of spintronic devices, i.e., the exploitation of spin-dependent

electron transport phenomena (Wolf et al 2001, Zutic et al 2004) is the

realization of highly spin-polarized materials. Half-metallic ferromagnets

(HMF’s) are considered ideal candidates for spintronic applications since they

possess 100% polarization of carriers at Fermi level. The concept of HM was

first established from electronic structure calculations of half-Heusler

NiMnSb alloy by de Groot et al (1983).

Page 8: 06 chapter1

8

In general, HMF’s can essentially be treated as hybrids of metals

and semiconductors. In other words, the spin resolved bands have a special

behaviour i.e., majority (minority) spin band shows metallic-like behaviour

whereas the minority (majority) spin band shows semiconductor-like

behaviour with a gap at Fermi level EF. HMF’s should satisfy the following

two conditions.

i) They should exhibit 100% spin-polarization at EF and it is due

to existence of metallic and semiconducting nature in their

opposite spin states. A schematic representation of the density

of states of a half-metal, a normal metal, and a semiconductor

is shown in Figure 1.1 for comparison.

Figure 1.1 Schematic representation of the density of states for a

half-metal compared to a normal metal and a

semiconductor

The spin-polarization P at EF is expressed in terms of the majority

spin and minority spin density of states, n (EF) and n (EF), as

F F

F F

n E n EP

n E n E (1.1)

Page 9: 06 chapter1

9

For ideal HMF’s, P = 1; it can conduct current which exhibits

100% spin-polarization.

ii) The total magnetic moment/unit cell should be an integer.

This second condition should be strictly satisfied for theoretical

calculations (Slater-Pauling rule or Slater Pauling curve). Slater (1936) and

Pauling (1938) independently discovered that the magnetic moment (Mt) of

the 3d elements and their binary alloys can be estimated on the basis of the

average number of valence electrons per atom. According to this rule the total

magnetic moment (Mt) can be calculated in the following manner:

Let the total number of valence electrons/unit cell be Zt which is an

integer and it can also be expressed as the sum of the number of spin-up (N )

and spin-down electrons (N )

tZ N N (1.2)

The total magnetic moment is the difference between N and N

electrons

( )t BM N N (1.3)

Combining these two equations, Mt can be written as

( 2 )t t BM Z N (1.4)

This is the general expression for total magnetic moment. For the

half-metallic full-Heusler compounds/(half-Heusler), it is shown that the four

Page 10: 06 chapter1

10

atoms/(three atoms) in the unit cell have a constant number of 12/(9) spin

minority electrons. The magnetization depends linearly on the number of

valence electrons. Therefore, for full-Heusler alloys, the total magnetic

moment is expressed as, Mt = (Zt 24) B and for half-Heusler alloys

Mt = (Zt 18) B.

For the compounds in zinc-blende structure, the total magnetic

moment is Mt = (Zt 8) B, since the minority state valence band

accommodate 4 electrons (Galanakis et al 2006). In all cases, it is evident that

the moments are integers.

1.3.1 Literature Review on Half-Metallic Ferromagnetism

1.3.1.1 HM ferromagnetism with transition metal

In order to have HM property, materials are required to possess

proper magnetic exchange splitting of the electronic states with different

spins, which would push the Fermi level into the gap of one spin channel. The

gap may develop because of the crystal field or the complete occupation of

certain atomic orbitals. After the prediction of half-metallic ferromagnetism

(HMF) in half-Heusler NiMnSb (de Groot et al 1983), different class of

HMF’s have been predicted theoretically or synthesized experimentally. Most

known HM compounds are oxides, sulfides and Heusler alloys. For example,

HMF has been observed in full-Heusler compounds such as Co2MnSi and

Co2MnGe (Ishida et al 1995), in metallic oxides such as CrO2 (Schwarz 1986)

and Fe3O4 (Dedkov et al 2002), in perovskite compounds such as

La0.7Sr0.3MnO3 (Soulen et al 1998) and Sr2FeMoO6 (Kobayashi et al 1998),

and in diluted magnetic semiconductors (DMSs) such as Mn-doped GaN

(Kronik et al 2002) and Mn-doped Ge (Liu & Liu 2006).

Page 11: 06 chapter1

11

In the last one decade, much attention has been paid to the

transition metal pnictides and chalcogenides with zinc blende (ZB) structures

due to their compatible lattice structure with conventional semiconductors. It

has already been predicted theoretically that the ZB CrAs (Galanakis 2002),

ZB CrTe (Liu et al 2010), and ZB MnBi (Xu et al 2002) are HMF’s with

finite HM gaps. These binary compounds do not exist in nature but the

non-equilibrium growth by molecular beam epitaxial method (MBE) has

facilitated the creation of these compounds. Akinaga et al (2000) have grown

thin films of CrAs on GaAs substrates by MBE and found that CrAs is

ferromagnet with a Curie temperature (TC) higher than 400 K.

Among the above mentioned HMF materials, Heusler alloys

remains an attractive for technological applications, because they exhibit

much higher ferromagnetic TC than other HM materials (Webster & Ziebeck

1988). Also, another property of these materials which is useful for industrial

applications is their crystal structure and lattice matching with

zinc-blende semiconductors (Xie et al 2001, Kurfiss & Anton 2003).

Heusler compounds are a typical class of HMF’s and have been

intensively studied. The theoretical and experimental studies on Co2-, Mn2-

and Fe2- based full-Heusler compounds show that these compounds exhibit

half-metallic property. Co2MX (M = Mn, Fe and Cr; X = Si, Ge and Sn)

compounds in full-Heusler structure have been found to be HMF’s by some

theoretical and experimental research groups (Galanakis et al 2002, Picozzi

et al 2002, Yang et al 2002, Branford et al 2007). The measured TC’s are

985 K for Co2MnSi, 905 K for Co2MnGe (Kawakami et al 1987) and 1100 K

for Co2FeSi (Wurmehl et al 2005).

Among the Mn2-based Heusler alloys, Mn2VAl was the first to be

proposed as HMF and was studied in detail both experimentally and

Page 12: 06 chapter1

12

theoretically (Ishida et al 1984, Itoh et al 1983). Later, a series of Mn2VZ

alloys (Z = Al, Ga, In, Si, Ge and Sn) (Ozdogan et al 2006) were investigated

by means of band structure calculations. Among them, Mn2VZ (Z = Al, Ga,

In and Sn) were found to be nearly half-metallic at their equilibrium lattice

constant. Later, Mn2FeZ (Z = Al, Si) and Mn2NiZ (Z=Ga, In, Sn, Sb and Al)

are found to be HM materials by theoretical and experimental studies

(Wurmehl et al 2006, Barman & Chakrabarti 2008).

In 2007, HM property was predicted in Fe2YSi (Y = Cr, Mn, Fe,

Co, Ni) Heusler alloys theoretically and also was confirmed experimentally

(Hongzhi et al 2007). HM properties of the Fe2-based compounds such as

Fe2TiAl, Fe2MnP and Fe2MnSi compounds have been studied by first

principles calculations (Shreder et al 2008, Kervan & Kervan 2012) and all

these compounds are predicted to be HMF’s. Recently, first principle

calculation have been carried out on Fe-based alloys such as Fe2TiZ (Z = Ga,

Ge, P, As, In, Sn and Sb) and it show that HM property is exhibited in Fe2TiP,

Fe2TiAs and Fe2TiSb compounds (Luo et al 2012, Kervan & Kervan 2013).

Apart from the above mentioned full-Heusler alloys, HM properties of Cr

based alloys Cr2MnZ (Z = P, As, Sb, and Bi) (Galanakis et al 2007),

Vanadium based alloys V2YSb (Y = Cr, Mn, Fe and Co) (Xing et al 2009)

have also been studied. The HMF property of Ti-based Heusler alloys with

Hg2CuTi-type structure, such as Ti2CoAl, Ti2NiAl and Ti2CoGa, has been

reported recently (Bayar et al 2011, Lei et al 2011, Kervan & Kervan 2012a).

Several groups have veri ed the HMF character of bulk NiMnSb

using rst-principles calculations (Galanakis et al 2000, Orgassa et al 1999,

Kubler et al 1983) and showed that the magnetism in NiMnSb is mainly due

to the hybridization of higher valent 3d Ni atom with Mn and the indirect

exchange of the 3d electrons through the sp atom namely Sb. Experimental

studies on ferromagnetism in half-Heusler NiMnZ (Z = Pd, Pt and Sb) has

Page 13: 06 chapter1

13

been reported and the measured TC’s are found to range between 500 K and

730 K (Webster & Ziebeck 2001).

Recently, HMF with very high TC has been predicted in a new

class of half-Heusler alloys NiMnZ (Z = Si, P, Ge, As, Te) (particularly,

TC = 1000 K for NiMnSi) (Dinh et al 2008). NiCrM (M = P, As, Sb, S, Se and

Te) and NiVM (M= P, As, Sb, S, Se, and Te) compounds have also been

predicted to be HMF’s (Zhang et al 2003, Zhang et al 2004). Theoretically,

the above room temperature ferromagnetism in NiCrM (M = P, Se and Te)

and NiVAs were observed by Sasioglu et al (2005). In addition to these

compounds, many half-Heusler alloys such as CoMnX (X = P, As and Sb),

FeMnSb and FeCrSb also predicted to be HM from ab-initio calculations.

(Nanda & Das gupta 2003, Xu & Zhang 2011).

1.3.1.2 HM ferromagnetism without transition metal

Magnetism in the above mentioned compounds is due to the

presence of localized d or f electrons. The magnetic moment in these

materials results mainly from transition metals and hence, they are known as

HM-3d compounds. However, recently, an unusual class of ferromagnetic

materials, which do not contain transition-metal or rare-earth atoms have been

found and analyzed theoretically by ab-initio calculations. It has been

observed that the magnetism in these materials is mainly originates from the

anionic p-like orbitals. Generally, the p-orbitals are believed to be delocalized

and magnetism is usually not expected.

First, Kusakabe et al (2004) predicted that ZB Ca pnictides (CaP,

CaAs, and CaSb) are HMF’s and found that the ferromagnetic characteristic is

due to the hybridization of the localized Ca d and As p-states. After this,

many efforts have been made to study the magnetism in these types of

Page 14: 06 chapter1

14

compounds in different lattice structures. In this regard, some research groups

have investigated I-IV, I-V, I-VI, II-V and II-IV compounds in different

structures. Gao et al (2007), Gao & Yao (2007a) studied MC (M= Mg, Ca, Sr,

and Ba) compounds in ZB structure and SrC and BaC in rocksalt (RS)

structure. They observed that CaC, SrC, and BaC compounds in ZB structure

and SrC and BaC in RS structure are HMF’s and the calculated TC’s are

higher than the room temperature. Also they calculated the exchange constant

using frozen-magnon approximation. Moreover, Zhang (2008) has reported

that ZB LiC, NaC, and KC compounds are HMF’s ferromagnets, but these

compounds in RS structure show nearly HM ferromagnetic properties.

Further, I–N compounds (Li, Na, K) (N, P, As) have also been analysed in

which nitrides have been found to be HMF’s (Gao et al 2009).

Recently, Gao et al (2011) have carried out theoretical investigation

of alkali-metal compounds MS (M = Li, Na, and K) and found that all the

compounds in ZB and RS-type structure (except RS-LiS) are HMF with an

integer magnetic moment of 1 B/f.u. Nitride-based compounds with alkali

and alkaline earth metals are found to be HMF’s by Geshi

et al (2007), Lakdja et al (2013) in various structures.

From the discussions of HM-3d compounds, it is observed that the

magnetic moment of these compounds is usually 3 B or 4 B (Galanakis &

Mavropoulos 2003), which is larger than 1 B or 2 B of ZB-HM sp

ferromagnets. In real-time applications, conventional ferromagnets create

larger stray fields, which result in considerable undesirable energy losses.

Therefore, the HM sp ferromagnets are more meaningful due to their smaller

values of magnetic moment. These compounds do not contain transition-metal

atoms and therefore the mechanism of ferromagnetism is different from both

the double exchange and the p–d exchange that are important in magnetic 3d

compounds. The explanation for the presence of non-vanishing

Page 15: 06 chapter1

15

spin-polarization in sp HM compounds is due to the effect of strong

spin-polarization of energy states of light elements (C, N) near the Fermi level

in which a strong Hund’s coupling take place. The spin-polarization is not

destroyed by the formation of bonds in the crystal. In other words, the atomic

polarization is stronger than hybridization effects. Here the crucial role is

played by the spin-polarization of the p-like states of the anoins. These are

widely known in literature with various names like d0 ferromagnetism or

p-ferromagnetism or sp-ferromagnetism (Coey 2005). There are several ways

to create sp-electron ferromagnetism and in this context, an extensive review

has been made by Volnianska & Boguslawski (2010).

Moreover, few studies have been made on the surface properties of

CaC and Ca and Sr nitrides and their interfaces with binary semiconductors

(Gao et al 2009 & 2011). Recently, Laref et al (2011) have calculated

exchange constants, spin wave stiffness constants and Curie temperatures for

ZB HM sp CaZ (Z = N, P, As, and Sb) ferromagnets. The estimated Curie

temperature of HM-CaN is considerably higher than room temperature when

compared with the other compounds.

One of the most promising routes to half-metallic sp electron

ferromagnets is the growth of I/II–IV/V nanostructures in metastable lattice

structures similar to the case of transition-metal pnictides and chalcogenides

in the metastable zincblende structure (Mavropoulos & Galanakis 2007).

Evidence for the growth of such nanostructures has been provided by Liu et al

(2008), whom have also reported successful self assembly growth of ultrathin

CaN in the rocksalt structure on top of Cu (001).

Page 16: 06 chapter1

16

1.4 MOTIVATION AND OBJECTIVE OF THE PRESENT

WORK

Attempts to replace present-day microelectronic devices with

nanoscale spintronic devices have led to a search for new materials with

multifunctional properties (multitasking materials that can be manipulated by

independent sources). A major hindrance for the practical implementation of

spintronic devices is that they require efficient spin-polarized carrier injection

and transport. In principle, HMF materials are ideal spin injectors and

detectors. Some of the half-metals have been successfully synthesized

experimentally (Akinaga et al 2000). This success has encouraged scientists

to further explore and understand other half-metallic materials. Also, these

materials are an impressive tool for the rational design of new materials based

on computational studies.

This peculiar property (HM) is exhibited by several transition-metal

based alloys but lately, half-metallic ferromagnetism has been observed for

several alloys which do not include transition-metal atoms. These compounds

have the advantage of being energy-efficient for applications since they create

weak external magnetic fields and thus lead to minimal energy losses.

From the literature review on sp ferromagnets, it is observed that

these materials are very promising candidate for spintronic applications since;

(i) they have a small spin magnetic moment per formula unit and

thus create small external magnetic fields,

(ii) they present very stable half-metallicity upon hydrostatic

pressure,

Page 17: 06 chapter1

17

(iii) their equilibrium lattice constants are close to that of

semiconductors,

(iv) results of the ZB and RS structures suggest high values of

Curie temperature,

(v) the half-metallic gaps are wide,

(vi) interfaces with semiconductors retain half-metallicity.

Nowadays attention has also been drawn to potential sp-electron

HMF in full-Heusler and half-Heusler structures. This is mainly because the

Heusler-based materials have TC much higher than room temperature

(Wurmehl et al 2005). High TC is very important for application to spintronic

devices since it stabilizes the half-metallicity of the material through a small

reduction of the spin-polarization at room temperature. Therefore it is of great

interest to merge the magnetic properties of the sp-HM compounds with the

properties of Heusler-type structure.

As far as, HMF in compounds with Heusler-type structure

excluding transition metals are concerned, to the best of our knowledge, only

less work has been reported so far. From first-principles calculations, GeKCa

and SnKCa were found to be HMF’s in the half-Heusler (C1b)-type structure

by Chen et al (2011). Recent first principles calculations of XCsBa (X = C, Si

and Ge) by Lakdja et al (2013a), RbSrX (X = C, Si and Ge) by Rozale et al

(2013a) and XRbCs (X = N, P and As) by Lakdja et al (2014) predict the

existence of HMF in these systems. Rozale et al (2013) studied the HMF

property of KCaX2 (X = C,N,O) compounds in full-Heusler (L21)-type

structure and predicted that KCaN2 and KCaO2 exhibit HMF property with

total magnetic moment of 3.0 B/f.u. and 1.0 B/f.u. respectively. These

interesting predictions motivated us to search for new HMF’s without any

transition metals in Heusler type structure.

Page 18: 06 chapter1

18

1.4.1 Crystal Structure of Heusler Compounds

Heusler-type alloys were discovered by the German miner and

chemist Friedrich Heusler. The most important property of the Heusler type

alloys is that they show ferromagnetic behavior even though the constituting

elements are not magnetic one. These remarkable properties of Heusler alloys

have contributed to the magnetic properties of some materials such as

magneto-optical, magneto-caloric, magneto-structural and magneto-electrical

materials.

There are two kinds of Heusler alloys: the full-Heusler alloy and

the half-Heusler alloy. The first study on Heusler alloy was materialized with

the full-Heusler alloy symbolized by the formula X2YZ. The X2YZ Heusler

compounds are ternary intermetallics with a 2:1:1 stoichiometry. These

compounds crystallize in the cubic structure (Fm3m, space group no. 225)

with Cu2MnAl (L21) as prototype and the crystal structure shown in

Figure 1.2. The unit cell consists of four interpenetrating face centred cubic

(fcc) sublattices with the Wyckoff positions (1/4, 1/4, 1/4) for X1, (3/4, 3/4,

3/4) for X2, (0, 0, 0) for Y and (1/2, 1/2, 1/2) for Z atoms respectively.

The Half-Heusler compounds (XYZ) crystallize in a

non-centrosymmetric cubic MgAgAs-type structure (space group no. 216,

F-43m, C1b) which is a ternary ordered variant of the CaF2 structure and can

be derived from the tetrahedral ZnS-type structure by filling the octahedral

lattice sites (Figure 1.3). The unit cell consists of three interpenetrating fcc

sublattices, each of which are occupied by the X, Y and Z atoms. The

corresponding occupied Wyckoff positions are (1/4, 1/4, 1/4), (0, 0, 0) and

(1/2, 1/2, 1/2). The full-Heusler L21-type structure becomes C1b-type structure

of half-Heusler XYZ compounds (also known as Nowotny-Juza compounds)

when one of the X position is vacant.

Page 19: 06 chapter1

19

Figure 1.2 Structure of the X2YZ Heusler compounds. X atoms (black) are at (1/4, 1/4, 1/4), (3/4, 3/4, 3/4), Y atoms (white) at (1/2, 1/2, 1/2) and Z atoms (grey) at (0, 0, 0)

Figure 1.3 Structure of the XYZ Heusler compounds. X atoms (black) are at (1/4, 1/4, 1/4), Y atoms (white) at (1/2, 1/2, 1/2) and Z atoms (grey) at (0, 0, 0)

Page 20: 06 chapter1

20

The goal of our work is to predict new HM compounds without any

transition metal in Heuler structure with a high degree of spin-polarization

and also to demonstrate that the origin of ferromagnetism is due to the

spin-polarization of p orbitals. Apart from the technological applications,

these systems are model objects for the study of new mechanisms of

formation of ferromagnetism. So far, no detailed electronic band structure

calculation has been reported for the titled compounds. In this work, the

detailed electronic band structure calculation of XYZ, XYZ2 and XMO-type

compounds in Heusler structure has been carried out. Cumulative efforts in

this research area will surely lead to the development of new materials with

desired physical properties, with a greater impact on the industry of spintronic

devices.

1.5 OUTLINE OF THE THESIS

In the present work, structural, electronic and magnetic properties

of XYZ (X = Li, Na, K and Rb; Y = Mg, Ca, Sr and Ba; Z = B, Al and Ga)

and XYZ (X = Li, Na, K and Rb; Y = Mg, Ca, Sr and Ba; Z = C, Si, Ge and

Sn) compounds in half-Heusler cubic (C1b)-type structure, XYZ2 (X = Li, Na,

K and Rb; Y = Mg, Ca and Sr; Z = N, O) compounds in full-Heusler cubic

(L21)-type structure and XMO (X = Li, Na, K and Rb; M = Cu and Ag)

compounds in tetragonal KAgO-type structure and half-Heusler cubic

(C1b)-type structure were calculated. The TB-LMTO-ASA program is used

for this purpose. Even though this method has limitations like shape

approximation, it is advantageous when compared to other linear methods. It

requires minimal basis set and is computationally fast.

The thesis is organized into seven chapters. The structure of the

thesis is as follows:

Page 21: 06 chapter1

21

Chapter 1 provides a general overview of spintronics. Also provides a brief introduction and review on d0-HMF’s.

Chapter 2 presents the basics of methodology used in this work, i.e., Density Functional Theory (DFT) together with the details of electronic band structure calculations (LMTO and TB-LMTO methods).

Chapter 3 describes structural, electronic and magnetic properties of hypothetical XYZ (X = Li, Na, K and Rb; Y = Mg, Ca, Sr and Ba; Z = B, Al and Ga) compounds in half-Heusler (C1b)-type structure. Spin-polarized electronic band structures and density of states of these systems are calculated to reveal the mechanism of ferromagnetism. The results show that some of the compounds in this series exhibit HMF property.

Chapter 4 deals with structural, electronic and magnetic properties of hypothetical XYZ (X = Li, Na, K and Rb; Y = Mg, Ca, Sr and Ba; Z = C, Si, Ge and Sn) compounds in half-Heusler (C1b)-type structure. Most of the compounds in this series exhibit HMF property.

In chapter 5, structural, electronic and magnetic properties of hypothetical XYZ2 (X = Li, Na, K and Rb; Y = Mg, Ca and Sr; Z = N and O) compounds in full-Heusler (L21)-type structure are discussed. The calculations show HMF property in these compounds.

In chapter 6, the detailed study of structural and electronic properties of XMO (X = Li-Rb; M = Cu and Ag) compounds in tetragonal KAgO-type structure and half-Heusler cubic (C1b)-type structure are described. The spin-polarized calculations in half-Heusler (C1b)-type structure show that these compounds do not show any magnetic behaviour.

Finally, chapter 7 summarizes the work and gives the suggestions for future work in the related field.