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Introduction To Half Metals

1 INTRODUCTION On the basis of electrical properties materials are classified into three main categories.

These are conductors, insulators and semiconductors. Conductors fall in the category of those

materials which have high conductivity and low resistivity and conduct electricity. Insulators fall

in the 2nd category of materials which have low conductivity and high resistivity and they do not

conduct electricity. Semiconductors are materials which exhibit characteristics of conductors at

high temperature and characteristics of insulators at low temperature. Here of our concern are the

conductors. In periodic table, all the metals are conductors. All metals are conductors because

they have free electrons in them. These free electrons move randomly in these conductors but the

current setup by these electrons is zero due to the random motion because due to random motion

they cancel the effect of each other but when a battery is applied across the ends of the

conductors an electric field is setup inside the conductor and electrons move in such a direction

that their direction is always opposite to the electric field and a current is setup in the conductor.

To explain why some materials are conductors, some are insulators and some are

semiconductors many theories have been put forward like free electron theory, molecular orbital

theory (band theory). The most important of them is the band theory. According to this theory,

when we consider an individual atom, the electrons are arranged in different discrete energy

levels. When these atoms approach each other in a solid, the atomic orbitals of these atoms

overlaps with one another to form molecular orbitals. We are taking Li as an example for

explanation. Imagine the step by step formation of a chain of Li-atoms, Li-Li-Li……Li-LI-Li. In

the formation of this chain of Li-atoms first of all two Li-atoms will form a Li2-molecule. In the

formation of this molecule the two 2s-AOs (each having one electron, Li → 2s1 ), one from each

Li-atom, combine to give two MOs. The lower energy MO is completely filled with two

electrons and the higher energy MO is vacant [Fig. (A)]. Attaching another Li-atom to Li2-

molecule gives the linear Li3-molecule. Li3-molecule is formed when three 2s-AOs combine to

give three MOs [Fig. (B)].


Now as the length of chain increases by increasing the number of Li-atoms we get a large

number of MOs closely spaced together. The number of MOs is same as that of AOs responsible

for their formation. As the number of Li-atoms increases, the energy levels get closer and closer

and ultimately become continuous. Such a group of continuous energy levels is known as a band

and consequently the molecular orbital theory is called band model.


Since 2s AOs of each Li-atom has only one electron, lower half of total MOs formed is

completely filled and the upper half is vacant. The upper half of the band has higher energy than

the lower half. Thus the band in Li-Li-Li……..Li-Li-Li chain is half filled provided we consider

a three dimensional arrow of Li-atoms.

Band model can readily explain the metallic properties. When a crystal of Li is placed in

an electric field, a few electrons acquire energy and are excited to higher vacant MOs. The

higher energy electrons carry current with them. The higher conductivity of metals is thus due to

the presence of large number of higher energy vacant MOs. Thus we see that the electrons in the

lower energy MOs are not localized. These delocalized absorb and re-emit light and thus render

the metal surface shiny and lustrous. Since the bonding electrons are not localized at any

particular atom in the metal crystal, the metal can be deformed easily which explains the

malleability and ductility of metals.

When the band is formed, the electrons are re-distributed in the band such that half of the band is

filled and half is empty. The energy gap between the two states i.e. between filled and empty

states is negligibly small and electrons go very easily from the filled states into the empty states

and in these empty states, they can move freely.

These metals are very important in our life. They are used nowadays in every field of life

and life without them now is impossible. In these conductors the charge degree of freedom of

metals is used to carry information from one place to another. In these materials electrons with

both up spin and down spin takes place in the process of conduction. Now such materials have

been developed in which the spin degree of electrons is also used for carrying information along

with the charge. These materials are called half metals.

1.1 Fermi Level:For a single atom, by the use of ionization energy value of electrons we can find the at least

tightly held electrons. As far as solids are concerned there is no ionization energy for electrons

because it is defined for electrons in the gaseous state of matter. So now the question arises how

to find the least tightly held electrons in solids, the answer is Fermi level. For solids we can find

the at least tightly held electrons by the use of Fermi level. Fermi level is also known as the total

chemical potential or electrochemical potential of electrons. Fermi level got the name of that


scientist who for the first time proposed it (Enrico Fermi). Fermi level is one of the

thermodynamic quantity of a body, and its importance is the thermodynamics work required for

the addition of an electron to a solid. Different solid have different thermal and chemical

properties, Fermi level play an important role in determining these properties for different solids.

The Fermi level can have different values at different temperatures, but when we measures the

value of the Fermi level at absolute zero then it is known as “Fermi energy”. As Fermi level can

have different values for different temperatures, so the value of Fermi level changes when a solid

is warmed or when electrons are added or removed from the solid. The concept of Fermi level

comes from the Fermi-Dirac Statistics. Fermions are the particles which obeys the Fermi-Dirac

Statistics and also Pauli Exclusion Principle. Electrons are also fermions, so they also obey the

above principle and statistics. Pauli Exclusion Principle states that fermions cannot occupy the

states having identical energy. A distinct energy with in a solid with which an electron can be

made held with in a solid is known as the energy level. Quantum mechanics laws states that each

energy level can have a limited number of electrons. By using the formula of Fermi-Dirac

Statistics which gives the probability of an electron to be in a state having energy E, the formula

is given below

f (E )= 1e(E−μ)/(kT )+1

In which T is the absolute temperature and k is the Boltzmann’s Constant. For defining the Fermi

level from this formula, consider a state at the Fermi level i.e. E=µ so the formula would result 12

. Then from this we can define the Fermi level like this, that it is the energy level that has the

probability to be exactly half filled with electrons. Below the Fermi level all the levels are full

filled while there are empty levels above the Fermi level. The location of µ is important in

determining different properties of solids. Different materials have different Fermi level. When

the contact of materials, having different Fermi levels, is made so a change in the resultant Fermi

levels happens, the level with higher Fermi level is lowered and the level with the low Fermi

level value becomes high and a result the equilibrium of these two different Fermi levels

happens. This change in the Fermi level is very important in different electronic devices. As we

know that at ordinary temperature the electrons do not respond very much to the specific heat of

solids while the play an important role in thermal and electrical conductivities of solids.


1.2 HALF METALS:Half metals are those materials which behave like conductor for the electrons of one spin and as

insulators or semiconductors for the electrons of other spin. In these materials, the band gap is

zero for one spin orientation and larger for another spin orientation of electrons and due to which

the electrons of one spin takes part in the process of conduction.

1.2.1 Material Examples of Half Metals:Half metallic materials include Oxides, Heusler Alloys both full and Half Heusler and many

other materials. These are

1.2.1.1 Heusler Alloys: Examples of Heusler half metallic compounds are given below.

Co2MnSi, Co2MnGa, Co2MnGe Pd2MnAl, Pd2MnIn

1.2.1.2 Oxides: Some oxides are also having half metallic character. These are chromium dioxide

(CrO2), Magnetite (Fe3O4), mixed valence magnetite and double pervoskites etc. are the

examples of half metallic ferromagnetic oxides.

1.2.2 Explanation of Half Metals: The big advantage of these materials is that both the properties that are conduction

and insulation are found in a single material. The property of half metallicity can be found in

magnetic materials because magnetic materials have rich variety of spin alignments, for example

all parallel (ferromagnetism), periodic arrangements with equal and opposite spins (anti-

ferromagnetism), several spins up and some down (ferrimagnetism), and more.

As earlier we have stated that for half metallicity we need a material with full spin

polarized electrons. A half metallic ferromagnetic phenomenon is not found in pure elemental

form. There are some elements which have 3d bands at Fermi level with full spin polarization,

but the 4s bands formed by the 4s electrons also cross the Fermi level and as a result at Fermi

level we are having both spin up (↑) and spin down (↓) electrons. We need to make this material

with the full spin polarization of electrons at the Fermi level. To do so we have to make an alloy

of this for pushing the 4s band bottom above the Fermi level or make such alloy in which we by

contact of different materials make the Fermi level of this lowered i.e. to depress the Fermi level


below the 4s bands. So alloy formation is necessary for achieving full spin polarization or

making such compounds which have oxygen in them i.e. half metallic ferromagnetic oxides.

Thus Half Metallic ferromagnetic material is not found in single pure elemental form; it should

contain more than one element to be called “Half metallic ferromagnetic”.

Below is the formula given which is used for finding the spin polarization of materials.

P=N ↑−N↓N↑+N ↓

In which N ↑ is the number of up spin electrons while N↓ is the number of down spin electrons.

Half metallic density of states are given in the above fig, (a) there are only up spin electron at the

Fermi level in type IA and (b) while there are only down spin electrons at Fermi level in type IB.

the states at Fermi level may be localized in narrow d bands.

In the above diagram, it can be seen that there is a density of states of electrons for only one spin

at the Fermi level. This diagram is only for the two types of the Half Metals i.e. for type IA and

IB. In type IA at Fermi level EF the up spin electrons are itinerant while none of the down spin

electrons are there. While in type IB none of the up spin electrons are there at Fermi level E F

while the down spin electrons are itinerant as shown in the above figure.

There are several consequences of half metallic ferromagnetic properties. For consideration let

take an example, as in half metallic ferromagnets there are spin polarized electrons so only one


spin oriented electrons will take part in the electrical conduction exclusively. which suggest the

usage of the spin of electrons as another degree of freedom for different purpose, especially in

logical devices.

As the difference in materials is made on the basis of band gaps as mentioned earlier the

difference in metals, semiconductors and insulators. But also the half metallic ferromagnetic

materials can also be further classified on the basis of their band gap nature. These categories of

half metallic ferromagnets are as follows.

1st category is that in which the half metals have a covalent band gap

2nd category is that in which the half metals are having a charge transfer band gaps

3rd category is the one in which the half metals possess a d-d band gap

1.3 APPLICATIONS: Following are the different applications of half metals.

1.3.1 GMR (Giant Magneto résistance): GMR is a way to control electrical resistance at the Nano scale using magnetic field.

In this device a nonmagnetic metal is sandwiched between two magnetic layers. The value of the

resistance can be lowered by applying external magnetic field while having parallel

magnetization; while its value can be increased by applying external magnetic field and having

antiparallel magnetization. It is given by the following formula.

GMR=R↑↓−R↑↑R↑↑

First of all OMR (Ordinary Magneto résistance) was discovered by Lord Kelvin in 1856. In this

device resistance was changed with the application of external magnetic field but this change

was very small up to 5%. Later on progress in MR effect was made and in 1980 GMR was

developed. In GMR resistance was changed up to 50% by applying external magnetic field. The

phenomenon of MR is nowadays used in Spin-Valve sensors, Hard Drives, IBM Spin-Valve

Sensors and Magnetic RAM (MRAM).

1.3.2 Memory Devices: These half metals can also be used for making memory devices. The basic

phenomena on which the memory devices works is the Anomalous Hall Effect, the anomalous


Hall Effect phenomena happens in ferromagnetic materials where is very larger than the normal

Hall Effect. And we need no external magnetic field due to Hall Effect. As Half metal have spin

polarized electrons at Fermi level so in memory devices for switching mechanism these spin

polarized electrons are used due to the Hall Voltage which comes as a result of Anomalous Hall

Effect Phenomena.

1.3.3 Spin Injector: Spin injector are those devices which we can use for the spin polarized electrons

injection. For the injection of electrons into a sink which is usually a semiconductor from a

source which is a ferromagnetic material, we have to make suitable combination of the half

metallic source and the active material i.e. semiconductor. Every combination of half metal and

semiconductor may have not good performance/result.

1.3.4 Spin injection methods: Spin polarized electrons can be injected to other material by using different methods

some of they are given below.

Injection of polarized electrons using polarized light i.e. optical method

Injection of polarized electrons using electron source (Direct Method) i.e. Electrical

Method

As it is clear from name of first method i.e. optical indicates this method involves light in this

method. We know how to make polarized light and if use circular polarized light to irradiate a

semiconductor then we can excite one spin electrons and hence we can make injection of spin

polarized electrons. The reverse method/phenomena can be used for the detection of spin

polarization.

Another method of injection of polarized electrons is to directly inject it into metals, or we can

use an electron source with comparable conductivity for the injection of electrons i.e.

ferromagnetically doped semiconductor. But it needs a very low temperature and high external

magnetic field for considerable operation. Spin injection can also be performed if we make the

resistance between the half metallic ferromagnetic and semiconductor to be depend on the spin

of electrons by using different methods i.e. tunnel barriers etc. It is still unclear that which


method can be used for the 100% spin polarized electron injection. There is a possibility that it

may be a totally different method from the ones I have mentioned.


2 LITERATURE REVIEW:Here in this chapter we are going to discuss some of the work done by different scientists

in the field of half metals in different period of time. It is given by year wise in the following

sections.

2.1 Discovery of Half Metals: Half metals were introduced by de Groot and his co-workers in 1983. Half metals were

discovered at the same time with the development of computers. The discovery of half metals

introduced a new branch of science. The newly discovered branch of science at that time is

known as “Material Science” nowadays. In this the approach which was adopted for solving

different problems was an approach of numerical. A theory known as local density

approximation (theory used to find the state of a system) was used and it was known by them

that in NiMnSb, which was a Heusler Alloy also, the Fermi level EF was made crossed only by

electrons with single spin orientation called the majority electrons while in between the valence

and conduction band, for the spin orientation there is a gap which is semiconducting. It means

that for one spin orientation the behavior of the material would be like that of conductor while

having insulator or semiconducting behavior for another spin orientation. That is why these

materials are called half metals. When a potential difference is applied at the ends of these

materials, a spin polarized current start to flow in these materials that is a current which is due to

only electrons of one spin and this current is called 100% spin polarized current. The discovery

of these materials increased the importance of band structure theory but at the same time these

results introduced some limitations to this theory. For example, the calculations done for

majority of band structures are based on single electron and these calculations have been made at

absolute zero temperature (T = 0 K), whereas, the experiments for the confirmation of the half

metals are done at temperatures greater than absolute zero. This raises an important question that

will the phenomena of half metallicity exist at finite temperatures? The answer to this question is

no because for most of the metals and Half metallic oxides, the spin polarization range at

temperatures below the curie temperature and this is not limited by band gap. Another question

which can be raised is that will the half metal be stable if substitutions are added to it or there is

some sort of disorder in the material and also what is the behavior of these materials at the

surface or nearer to the surface, where as we know due crystal defects the symmetry of


translation vanishes. It is well known that when there is a small coordination number for a

material at the surface, so due to this the band narrowing effect happens on the electronic

structures. There possibility for happening of surface reconstruction effect is also there at the

surface. A converse question to the previous can also be asked that is there is any material which

have different properties at different considerations i.e. to be having a half metallic character at

the surface and no half metallic character in the bulk? The possibility of this question is also

there that what will be the effect on half metallic properties at the interface, if a material with

more complex band structure is joined with it. The high concentration of defects can also affect

this. The answer to these questions cannot be a single one because all these questions depend

from material to material.

2.2 Some of the work done after the discovery: After their discovery, many experiments were done in the laboratories to study different

properties of half metals under different conditions. The work of some of the scientists is

discussed below.

2.2.1 In 2004: In March 2004, J M D Coey and S Sanvito studied many ferromagnetic metals, semi

metals and semiconductors which have fully spin polarized electronic structures. They tried to

classify these materials into six extended categories. These materials were classified into these

categories or groups on the basis of their chemical systematics or on the calculations done for

these materials on the basis of density functional theory. The main purpose of their work was to

classify these materials on the basis of simple properties so that they are easy to study.

In their course of study, they investigated a group of those materials which has a fully

spin polarized current and if not fully spin polarized current then at least they should have a

current in which the charge carriers are strongly of only one spin. This discussion is only about

those spin-split electronic structures which are at absolute zero temperature, i-e, T = 0K. This

discussion is not about those spin-split electronic structures which are at finite temperatures

because waves of spin mixes densities of states of up ↑ and down ↓ spin at finite temperature.

The attempt of these scientists to arrange these magnetic materials into these new six categories

can be very useful and this can lead the scientists to the new ferromagnetic materials discovery


due to which the combination of spin polarization and mobility can be done, needed for the

spintronics future.

2.2.2 In 2006: In February 2006 Galanakis, Ph. Mavropoulos and P.H. Dederichs studied the

properties of interatomic Heusler alloys and published a paper. These materials are very

important because they have very high Curie temperature and having similarity of structure

between them and binary semiconductors. Basic electronic and magnetic properties of Heusler

Alloys including both types i.e. half-Heusler alloys e.g. NiMnSb and full-Heusler alloys e.g.

Co2MnGe is presented by them. The initial results show that minority spin gap presence makes

both their electronic properties and magnetic properties. The relation between the valence

electrons “Z” and the total spin magnetic moment is linear i.e. as the number of valence electrons

“Z” is increased so as the magnetic moment also increases and thus we can make new half-

metallic alloys in the laboratory with our required magnetic properties.

The usage of local density functional theory was made in order to calculate the Heusler

Alloys Electronic structure and magnetic properties and after analyzing these calculations

carefully, we came to know the basic mechanism of gap formation and also about the valence

charge and spin moment correlation. Heusler alloys having a composition of transition atoms, is

essential for the gap formation at Fermi level (EF) due to their Hybridization of d-d orbitals. In

NiMnSb which is a half Heusler alloy the gap is created by the hybridization as well as the

bonding and antibonding splitting between the Mn d and Ni d states. The gap origin is again the

hybridization which is between the two Co atoms and after this hybridization their interaction

with the Mn d states.

2.2.3 In 2007: In July 2007, Warren E Pickett and Helmut Eschrig used the collinear density

functional theory at the basic level to find the state of half metallic ferromagnets and they found

the representation of complete different state of matter by these materials. For these materials

they have founded that the system is spin polarized but still the spin degree of freedom is absent.

but still it is spin polarized for low energy physics. This discovery made these materials very

attractive in the field of spintronics and also it introduced a new type of superconducting

phenomena in which the spin pairing of electrons is not present. To explain this phenomenon, a


fully relativistic theory was presented which introduced the phenomenon of spin-orbit coupling

in these materials and this theory destroyed the half metallic aspect of these materials. This does

not mean that half metals are not present in real sense, but if we see qualitatively then Half

Metallicity is a distinct state while spin orbit coupling is a perturbative effect. It was suggested

that under suitable conditions, these materials can overcome the spin-orbit coupling and can

remain as half metals.

It has been made clear that the state of half metallic ferromagnetic and that of normal

ferromagnetic are totally different. This statement was explained briefly with the help of

different viewpoints. First of all, the non-relativistic spin density functional theory for finding the

state of the material was ignored and a relativistic theory of spin-orbit coupling was introduced.

The half metallic character of these materials vanishes due to this spin orbit coupling, but this

effect is very small for small magnetic atoms, i.e. those atoms whose atomic number is less than

30. It was also shown that under suitable conditions like appropriate electronic structure and

band filling of electrons even heavier atoms can behave like half metals. A discussion of the

possibility of those half metals whose net orbital moment is zero was also made. Those half

metals whose net orbital moment value is zero were then called as “half metallic anti-

ferromagnets” and can also be called compensated half metals. There are many types of half

metals present and also many types are predicted by the scientists with different values of orbital

moments but still there is no good sign of a half metallic anti-ferromagnets with net orbital

moment equal to zero. The predicted compound Mn2Ga is a good possibility of anti-

ferromagnetic half metal but this material is yet to be synthesized in the laboratory. There is a

large number of ferromagnets in intermetallic compounds and oxides is present, so we can

expect that half metallic anti-ferromagnets are also present but they are not discovered yet and

there is big need to discover these compounds. There is a possibility of a new type of

superconductivity in these anti-ferromagnetic materials, a superconductivity which may be

similar to the ferromagnetic materials Superconductivity, but the evaporation of minority bands

may also be made which also takes their superconducting gap with them .

In July 2007, R Skomski investigated the dependence of spin polarization on temperature of the

half metallic ferromagnets with a covalent band gap and then compared the results with those of

other magnetic materials like semimetals, strong and weak ferromagnets and exchange enhanced


Pauli magnets. The density of states at finite temperature is non-zero for the minority spins

electrons due to the exchange of spin within the atom. This mixing of density of states for

different spins due to temperature means that there is some conductivity due to the electrons of

minority spin electrons and current is not 100% polarized and we cannot say that this is a half

metal. When the temperature is decreased to zero kelvins then due to inter sub-lattice

interactions, spin-orbit coupling and crystal imperfections. The moment jumps from one atom to

the other atom and this moment becomes unstable and as a result spin polarization is reduced due

to stoner-type thermal excitations.

In July 2007, a review of the results of half metallic Heusler Alloys electronic properties was

also made by other scientists like Galanakis and Ph Mavropoulos. They discussed the connection

between the magnetic properties and gap, also with the discussion of the origin of the gap. Fermi

level slightly shifts when a change in the lattice parameter is made. States within the gap are

induced due to spin-orbit coupling but still at Fermi Level these half metallic alloys have a spin

polarization of high degree. When the doping of these materials is made with some other

material or defects of low formation energy are created in these materials, then the properties of

gap are affected slightly, whereas the effect of temperature on these materials is very high and a

total loss to the half metallic character of these materials can be made due to temperature.


In this chapter we are going to study some of the structural properties of different types of half

metallic compounds. There are many types of half-metallic compounds in nature. First of all we

are going to study Heusler alloys.

3 HEUSLER ALLOYS: Heusler alloys are considered to be the most attractive compounds for half metallicity

because these compounds have a very high curie temperature and the structure of these

compounds is related to the structure of conventional semiconductors. The first compound

discovered by de Groot in 1983 was also a half-Heusler alloy NiMnSb. The richness in half

metallic character gives these compounds a full spin polarization of 100% at Fermi level EF. The

Co2FeSi is a Heusler alloy having the highest value of Curie temperature among all the known

Half Metals. The value is 1100 K.

These materials are named Heusler Alloy in order to honor Friedrich Heusler, a German

mining engineer also a chemist, who for the first time studied such an alloy in 1903. The

compound he studied was Cu2MnSn. More half-metallic Heusler alloys are given below.

a) Cu2MnAl, Co2MnSi, Cu2MnIn, Cu2MnSn,

b) Ni2MnAl, Ni2MnIn, , Ni2MnSb, Ni2MnGa

c) Co2MnAl, Ni2MnSn, Co2MnGa, Co2MnGe

d) Pd2MnAl, , Pd2MnSn, Pd2MnSb

e) Co2FeSi, Pd2MnIn, Co2FeAl

f) Co2FeGe, Fe2VAl, Mn2VGa,

These Heusler alloys are then again classified into two types.

1) Full-Heusler alloys 2) Half-Heusler alloys

1) Full-Heusler alloys are those which are of the form X2YZ and they crystallizes in the L21

Structural form consisting of four sub-lattices of FCC among which the occupation of

two sub-lattices is made by the of X-atoms of the same type.

2) Half-Heusler alloys are those which are in the form of XYZ and having a C1b structural

form. In these compounds, one sub-lattice remains unoccupied.

Now we discuss different types of properties of these materials.


3.1 Electronic and Magnetic Properties of the Heusler Alloys: As mentioned above that Heusler Alloys are of two categories. One is Full Heusler Alloys

and the other is half Heusler Alloys. Explanation of both of these is given below one after the

other.

3.1.1 Half-Heusler Alloys Band Structural Explanation: We represent here the results of some of the Half-Heusler Alloys belonging to C1 b

structure. These calculations have been done by using density functional theory. Here we are

going to discuss the properties of NiMnSb as an example. The density of states are shown in the

left side of the below given Fig (A) for NiMnSb in a non-spin polarized calculation while on the

right side a polarized calculation of the density of states of NiMnSb is given in Fig (A).

Local contribution of the density of states by the Ni site is given in the figure by the

dashed line, while in the Fig (A), for Sb and Mn, the dotted and full lines shows their Local

contribution of density of states. Four different bands have contributions to the DOS of NiMnSb.

First is the deep lying s band introduced by Sb with atomic configuration of 5s2 5p3. This s band

is located at about -12 eV which is not shown in the Fig. Second are the three p-bands of Sb,

which are located in the region between -5.5 eV and -3 eV. Third are the five d-bands of Ni

which are located in the region between -3 eV and -1 eV and these are separated by the Mn five

d-bands. Hybridization between the atomic orbitals of these entire atoms happens i.e. the Ni d,

Figure (A)

Density of States for non-polarized calculation is on the left side while for polarized calculation it is given on the


Mn d and Sb sp orbitals gets hybridize with each other. This hybridization is either of bonding or

non-bonding type.

This configuration is not stable for the compound NiMnSb because in the middle of the

anti-bonding band, there lies the Fermi Energy, and also the formation of the magnetic moment

by the Mn atom increases it exchange energy by a considerable amount. As we have mentioned

earlier that the results for polarized NiMnSb compound is given on the right side of Fig (A). It is

clear in the diagram that the Mn d states are shifted to lower energies in the majority (spin ↑)

band and with the d states of Ni it forms a common d band, whereas the Mn states are shifted to

higher energies and are unoccupied in the minority band (spin ↓) and at EF a Band gap is formed

which separates the d bonding occupied states from the anti-bonding unoccupied d-type states.

That is why NiMnSb is a half metal at EF with a band gap in the minority band and a sp metallic

like density of states in the minority band at EF.

The location of the total magnetic moment in one single unit cell is mostly at the

Manganese (Mn) atom the estimation for the total magnetic moment is 4µB exactly. As we know

that there are a total of 22 valence electrons for NiMnSb in each unit cell. The contribution of

these 22 electrons from the three atoms are as follows, out of 22 valence electrons 10 electrons

contribution is made from Ni, Mn atom makes a contribution of 7 electrons while the rest of the

5 electrons contribution is from Sb. At Fermi level EF, due to the gap, 9 bands are fully occupied

in the minority band, and these 9 bands are 1 s band Sb like, 3 p bands Sb like while the rest of

the 5 bands are Ni like and a unit cell accommodates 9 electrons. As there are a total of 22

electrons per unit cell and 9 electrons are in the minority band so for the majority band the

number of electrons can be found as 22 – 9 = 13 electrons, whereas 22 are the total number for

electrons in a unit cell and 9 is the number of electron in the minority band. So 9 electrons are in

minority band (spin ↓) and 13 are in majority band (spin ↑), so 13 – 9 = 4, that is why this

compound has a moment of 4µB. The total moment can be found by using a rule which is very

simple and is as follows: Mt = Zt – 18, where in the aforementioned stated rule, M t shows the

total moment while the total number of valence electrons per unit cell is shown by Zt.

3.1.2 Full Heusler Alloys Band Structural Explanation: As we know and also we have mentioned earlier in this chapter as well as in the

previous chapter that the Heusler Alloys are of two types. One is Half Heusler Alloys while the


other one is Full Heusler Alloys. A discussion upon the band structure of the Half Heusler Alloys

is made in the previous section of this chapter. Now we are going to explain the band structure

for the Full Heusler Alloys. The structure of Full-Heusler alloys is L21 structure. Here we are

going to discuss the electronic structure of the compounds like Co2MnZ, whereas Z can be Al,

Si, Ga, Ge and Sn. All these Z compounds have sp hybridization. These compounds are full

Heusler alloys and all these Full Heusler Alloys are strong ferromagnets with high Curie

temperatures. There Curie temperature values are more than 600 K and these compounds also

have the advantage that they show very little disorder. In these full-Heusler compounds, each Mn

atom or there will be a sp atom which will be surrounded by four atoms of Cobalt (Co) forming

an octahedral symmetry, while there are four Manganese (Mn) atoms or sp atoms which

surrounds a single Cobalt (Co) atom forming a tetrahedral symmetry.

In the figure below, the spin resolved DOS for different full-Heusler compounds has been

shown. As we have mentioned in the discussion upon the Half Heusler Alloys like NiMnSb that

the Mn have a much localized spin moment because of the spin-down electrons exclusion at the

Mn site and the approximate value of this moment is 3.7µB, while in CoMnSb, the spin moment

further decreases to 3.2 µB due to the increased hybridization of the Cobalt (Co) and Manganese

(Mn) spin-down electrons. Each Mn atom is surrounded by eight Co atoms and there is a strong

hybridization between the electrons of these atoms and this strong hybridization further

decreases the value of spin-moment which is then less than 3 µB.

The Co atoms are coupled to the spin moments of Mn ferromagnetically and the value of their

spin moment varies from ~0.7 to 1.0 µB. The Co moment is large as well as positive and

basically arises because in the minority conduction band there are two unoccupied bands of Co.

Therefore the moment is 2 µB for both the Co atoms, for the case that all the majority states are

Atom resolved Density of States for the Co2MnZ compounds withZ = Al, Si, Ge, Ga elements.


occupied. We can find the moment of full-Heusler alloys by a rule which is a little different from

the case of Half Heusler Alloys. The rule for finding the spin moment for Full Heusler Alloys is

Mt = Zt – 24, like the spin moment finding rule for Half Heusler Alloys, here also Z t shows the

number of valence electrons and Mt shows the total moment. For the compounds containing Al

and Ga as their elements have 28 valence electrons so according to the above rule they have a

moment of 4 µB, whereas, for the compounds containing Silicon (Si), Germanium (Ge) and tin

(Sn) as their constituents, they have 29 valence electrons with a moment of 5 µB.

Beside these Heusler alloys there are many other types of compounds which are half-

metallic in nature. Some of the properties of these compounds are given below.

3.2 Half Metallic Ferromagnetic Oxides: There are also some oxides which have half metallic nature. This includes oxides having

rutile, spinel, inverse spinal and many other structures. Some of the oxides and their structural

explanations are given below.

3.2.1 CHROMIUM DIOXIDE (CrO2): CrO2 is a very important compound used very commonly in our daily life in many

applications. It is the simplest oxide with high spin polarization.

3.2.1.1 Structure of CrO2: CrO2 has a Rutile Structure. Rutile is a non-cubic close pack structure. The diagreme

of a general rutile structure is as follow.

Rutile Structure usually comes for the compounds having general formula AX2. In which

for consideration the Light Black ones are atoms A, while the dark Black ones are the X atoms.

For the given compound CrO2 as we see that A = Cr and X = O so it means the Cr ions are

located at the corners as well as in the center of the unit cell.

Cr (24) [Ar]

3d 4s

O (8) [He]

2s 2p


3.2.1.2 Coordination Number of Chromium and Oxygen in CrO2:

It is clear from the structure that every Cr cation is surrounded by six oxygen anions.

As each Cr cation is surrounded by six oxygen anion so its coordination number is six while

oxygen atom is attached to 3 Cr ions so its coordination number is 3. Oxygen is attached to 3 Cr

ions at a time so it means it shares 1/3 of its part to every Cr ion and there are total 6 oxygen

atom attached to Cr ion. There is one Chromium ion and 13×6=2 oxygen ions to make the

compound. That is why the formula of the compound is given by CrO2.

3.2.1.3 Electronic Configuration of Chromium, Oxygen and their ions in CrO2:

CrO2 is a half metallic oxide with a curie temperature of 398K. In this compound we

have a constituent Cr which is also a transition metal. As there are many rows of transition

metals in the periodic table. So of all the transition metals, this metal belongs to first row of

transition metals. Cr has an atomic number of 24 with electronic configuration as follows,

1s2, 2s2, 2p6, 3s2, 3p6, 3d5, and 4s1. It is obvious from the configuration of electrons for Cr that

there is a half-filled 3d orbital as well as half-filled 4s orbital. If we look at the oxidation state of

chromium and oxygen in CrO2 we come to know that for chromium it is +4 while oxygen is in its

normal oxidation state of -2. If we draw the electronic configuration of chromium and oxygen in

a picture so it would be like this

If we consider the oxidation state of these two elements in CrO2 there electronic configuration

would be

Cr4+ (20) [Ar] 3d 4s

O2-(10) [He] 2s 2p


It means that each oxygen ion is filling their p-state by acquiring 2 electrons from the

chromium metal. As in the molecular formula of CrO2, it is obvious that oxygen ions are twice in

number than the chromium ion. Therefore the O ion will be in its nominal -2 valence state while

the Cr is in +4 nominal valence state.

The oxygen atom surrounds the Cr ion in the Rutile structure like Octahedral. The first

effect that would be on Cr because of the six oxygen ions that surrounds it is the splitting of the

Cr d-orbitals in accordance with the crystal field theory. The explanation of the crystal field

splitting is as follows: the Cr d-orbitals will split in t2g triplet (three of the 5 d orbitals energy will

be lower and they are known as the triply degenerate orbitals) and eg doublet (two of the 5 d

orbitals energy will be higher than the other 3 and they are known as doubly degenerate orbitals).

The d-orbitals splitting are in according to the crystal field theory. The value for this splitting of

d-orbital is about 1.5 eV. This splitting occurs per Cr ion in the structure. As the energy of the

triplet becomes lowers so they overlaps slightly with the oxygen majority p-states. In a tight

bonding model, the overlap between the majority O-p and Cr-d states requires some interaction

between the d-state of Cr. The formation of bands in CrO2 is the result of the overlaps of the 3d

orbitals, the dxy orbitals overlaps slightly therefore they forms a nonbonding level which is

occupied with a localized Core spin having a value ½ i.e. S=1/2. Besides the d xy orbitals the t2g

contains other d-orbitals also i.e. t2g (dxy, dyz, dzx). So a broader half-filled band is form by the

mixing of these d-orbitals of t2g.


3.2.2 MAGNETITE (Fe3O4): Magnetite (Fe3O4) is the oldest known magnetic material and also a half metal with a

curie temperature of 860K. Its formula is Fe3O4. We can also write this formula like (FeO.Fe2O3)

or like Fe (FeO2)2.

3.2.2.1 Structure: Magnetite has an inverse spinal structure. Inverse spinal structure is a mixed metal

structure with a general formula [(M+2)T,(M+2, M+3)O,(O2-)4]. In the above mentioned general

formula ‘M’ means metal and ‘O’ is for Oxygen because spinal or inverse spinal structures are

mixed metal oxides and the Superscripts are their oxidation or valence state while in subscript

‘T’ for tetrahedral ‘O’ for octahedral and 4 is the number of Oxygen ions. Inverse spinal

structure generally is given below.

The oxygen ion in the magnetite (Fe3O4) forms the close pack face centered cubic (FCC)

structure. The Fe2+ ion is octahedral and Fe3+ is tetrahedral and in the remaining octahedral holes

or for convenience we can also say that the iron (Fe) atoms occupy the interstitial sites.

Fe3+ occupies the A-site as labeled in the figure while equal number of Fe3+ and Fe2+ ions

occupies the B-site as labeled also. In the consideration of the aforementioned paragraph we can

say that A-site has a tetrahedral oxygen coordination and B-site has and octahedral oxygen

coordination.

Fe (26) [Ar]

3d 4s

O (8) [He]

2s 2p

Fe+2(24) [Ar] 3d 4s

Fe+3(23) [Ar] 3d 4s

O2-(10) [He] 2s 2p


3.2.2.2 Electronic Configuration of Iron, oxygen and their ions in Fe3O4: Fe (26) has an electronic configuration which is given below.

While that of oxygen is

As we see from the general formula of the inverse spinal structure Metal i.e. iron has an

oxidation or valence state of +2 and +3 while oxygen has -2.

Following are the electronic configuration of Fe2+, Fe3+ and O2- ions.

Oxygen is in its nominal -2 valence state while Fe has two different valence states i.e. +2 & +3.

3d 4s

3d 4s


3.2.2.3 Effect of oxygen ions on iron and their electron arrangement after contact: As Fe2+ has octahedral oxygen coordination. So its d orbitals splits according to

octahedral crystal field splitting due to O2- ligands. Oxygen O-2 is a weak ligand. So by coming

near the iron atoms it cannot make the electron in the d state of iron to pair up and that is why

after splitting of the d states their electronic arrangements are in the High spin. High spin means

that 1 electron will be filled in the triplet degenerate states t2g with parallel spin and then the

doublet eg degenerate states will be filled with the parallel spin of 1 electron place in each of

them. After that if there is an electron for configuration then place it in t2g states for pairing.

In the spinal structure of magnetite Fe3O4, on the octahedral site it is a ferromagnetic crystalizing

with an 3d↓ electron among the 3d↑ cores which is given below in configuration.

After the crystal field splitting the high spin configuration of electrons is t2g (↑↓,↑ ,↑¿ and

eg (↑ ,↑).

And for Fe3+ its electronic arrangement is given below before crystal field splitting

It has got five d orbitals electrons with parallel one electron in each orbital.

The crystal field splitting of Fe3+ has got two aspects one is that if we consider the Fe3+ ion which

is with the Fe2+ i.e. at B-site so it has an octahedral coordination of oxygen ions therefore it will

split like the above one (Fe3+) with a high spin electronic configuration of t2g (↑ ,↑ ,↑¿ and eg(↑ , ↑)

in which t2g have low energy while eg has relatively high. And if we consider the Fe3+ ion which

is present at A-site having tetrahedral oxygen ions coordination. So it will also split into two and

three different degenerate orbitals but their energies are in reverse order i.e. t2g will have

relatively high energy that eg and they will also have high spin configuration of eg(↑ ,↑) and t2g

↑ ,↑ ,↑¿.


3.2.2.4 Alignment and Ionic Dipole moment of ferrous and ferric ions: This is a ferrous ferrite molecule because it has ferrous and ferrite ions. These ferrous

and ferrite ion are align antiparallel. There anti parallel alignment is suggested after calculating

their dipole moment. When Fe2+ loses 2 electrons then they have 6 electrons with d orbital

having paired electrons and 4 d orbital with unpaired electrons, and also 1 electron have a

magnetic moment of 1μB so in the 6 electrons the paired electrons cancel out their magnetic

moment due to opposite nature or sign. Then the total ionic magnetic moment of Fe2+ is4 μB.

Similarly the ionic magnetic moment of Fe3+ is 5 μB because it has five electrons in the d state

with parallel due to loss of two 4s and 1 3d electron. If parallel alignment of ferrous and ferric

ions is considered then by calculating their total magnetic dipole moment is

4+2 (5 )=14 μB

And by considering their anti-parallel alignment the total ionic magnetic moment is

¿

The ionic magnetic moment is like above because one Fe3+ ion in A-site is in antiparallel

alignment with the Fe3+ ion of B- site. So {(5∗1 )+4 } is the ionic magnetic moment of B-site and ¿

is the ionic magnetic moment of A-site and their result is4 μB. This calculated ionic magnetic

moment of Fe3O4 and the one which is measured experimentally are in good agreement with each

other that is why we say that the ferrous and ferric ions have antiparallel alignment.


4 Applications of half metals:

Half metals are of great importance in our daily life and they have many practical

applications and there applications are increasing day by day. Some of the applications are

discussed here below.

4.1 Magneto-optical effects:

In these materials a very large Kerr effect has been observed. The types of Magneto-optical

effects includes an effect which is known as Magneto optic Kerr effect (Moke) also known

Surface magneto-optic Kerr effect (SMOKE) name. If a material sample is subjected to a

magnetic field and a polarized light reflects from that surface so this polarized light study is

known as Magneto-optical Kerr effect. This effect describes the changes to light reflected from a

magnetized surface. Magnetization structure of different materials is investigated by using this

effect in a subject known as “Material Science”.

When light is incident on a magnetic material then it is reflected from the surface. As a result of

reflection of light the polarization and the reflected intensity changes. As dielectric tensor has

two components i.e. the diagonal and off diagonal components but the responsibility of this

effect is on the off diagonal component. And as a result an anisotropic permittivity is given by

the off diagonal component to the magneto-optical material, which means it has different

permittivity in different directions. The relation between the permittivity of a material and speed

of light in that material is given by the following equation.

vp=1

√ϵμ

In the above equation vp shows the velocity of light in the material, is the permittivity of the

material, and µ shows the magnetic permeability; and so speed of light also depends upon the

orientation of light. Due to this fluctuation occurs in the polarized incident light phase.

4.1.1 Geometries for MOKE Experiment:

For Performing MOKE Experiment there are three Geometries. These Geometries arises from

the direction of magnetic field with respect to the plane of incidence and sample surface. These


Moke Geometries are Polar, longitudinal and Transverses. Further Brief details of these Moke

Geometries are given below.

4.1.1.1 Polar Moke: For Polar Moke Geometry the magnetic vector is normal to the reflection surface

and having a parallel direction to the plane of incidence, the name “Polar Kerr Effect” is given to

this due to the usage of Polar Moke Geometry. The diagram for the Polar Moke Geometry is

given below.

Polar Moke Geometry

The study of Polar Moke is usually done at near normal angles of incidence and reflection to the

reflecting surface. In this both beams must pass through a hole in one pole of a magnet. Polar

Geometry got the distinction only of where Moke can be observed at normal incidence.

4.1.1.2 Longitudinal Moke: In the longitudinal geometry for Moke, the magnetic vector is parallel to both the

sample surface and the plane of incidence. The diagram for the longitudinal geometry for Moke

is as given.


.

Longitudinal Moke Geometry

The light reflected from the sample surface is not normal to it rather it reflects with an angle.

When a light incident on the sample surface, having a linearly polarized light nature, it

polarization nature changes from linearly to elliptical nature. The change in polarization nature is

directly proportional to that component of magnetic vector which is parallel to both the reflection

surface and plane of incidence.

4.1.1.3 Transversal Moke: When the magnetic vector is perpendicular to the plane of incidence and parallel

to the sample surface then this type of geometry is known as Transverse Moke or Transverse

Moke Geometry. The diagram for the Transvers Moke Geometry is given below.

Transverse Moke Geometry

The light reflected from the surface of the sample surface is also not normal to it like that of the

Longitudinal Moke, but in Longitudinal Moke we measure the change in polarization while in

Transverse Moke we measure the reflectivity of the incident light. The reflectivity of the incident


light has a direct relation to that component of magnetic vector which is perpendicular to the

plane of incidence and parallel to the sample surface.

4.1.2 Applications of MOKE:There are many applications of this magneto optic Kerr effect in physics. Some are given

below.

4.1.2.1 Microscopy: The well-established technique which we use for studying the materials magnetization

properties is the technique of “Magneto-Optical Kerr Effect” which is in short also can be

written as “Moke”. By using the Moke effect we have established a Magneto-Optical

Microscope through which we get the magnetization images for materials and can also study

them. The technique for studying the magnetization properties is known as Magneto-Optical

Microscopy. Through this we can also made the development and characterization of different

materials. This magneto Optical Kerr microscope can also be called as the “Polarization

Microscope”. By using the Moke Microscope we can image the Magneto Microstructures with

the lateral resolution in the range from nanometer to millimeters.

In the aforementioned paragraph we have mentioned some of the uses of the Magneto Optical

Microscopy. Now we are going to explain the principle on which the Magneto Optical

Microscopy works, and also how it works. The principle on which it works is the “Magneto

Optical Kerr Effect” and the explanation of its working is given in the coming paragraph.

In the Moke Microscopy the light passes through two filters. Before the interaction with the

sample material the light passes through the polarizer filter and then interact with the sample

material. After the interaction of the light with the sample material it the passes through the

analyzer polarizing filter. After passing through these two filters the light is then passed through

the regular “Optical Microscope”. The requirement of the polarized light depends upon the

geometries i.e. for different Moke geometries we require light with different polarization. The

polarizer filter can change the nature of the incident light to any nature i.e. to linear, circular or

elliptical it has all the choices depends upon the requirement of the experiment. When an

incident light makes an interaction with the sample material so after the interaction it reflects

which result a change in the light. It may can change the Kerr rotation, Kerr ellipticity or a

change in the polarized amplitude can occur. Then in the path of the reflected light there is an


analyzer which converts these changes in the polarization of light into the light intensity. After

this conversion it becomes visible and can be seen and study. From these changes in the

polarization of light a magnetic field image can be created by using a computer system.

4.1.2.2 Magnetic Media: The introduction of Magneto Optical (MO) Drives was made in 1985. When they introduce

Magneto Optical (MO) Drives for the first time, they were WORM originally. The WORM

means that “write once and read many” i.e. data can be added only one time and cannot be erased

but it can be read many times. Now a day, there use is not wide. These Magneto Optical Drives

are reliable in accurate writing and also in consistent data retention. The typical range of the

sizes of these Magneto Optical Drivers is from Megabytes to gigabytes i.e. from 100 megabytes

(MB) to 9.2 gigabytes (GB). Magneto Optical Drives checked the data like it was being written

on the Drives due to this it takes longer than typical CDs or DVDs. However in this, increase

data integrity is allowed.

The above paragraph was just an introduction to the Magnetic Optical Drives. Now we come to

the principle on which it works. The basic principle on which the Magneto Optical (MO) drives

works i.e. write and read data is the “Magneto Optical Effect”. As it is clear from the name that it

uses both the technologies for the operation of the “Magneto Optical disk drive” i.e. the magnetic

as well as optical (Laser) technologies are employed for this.

The principle of writing and reading is as follows: a magnetic field and a laser are needed for the

operation i.e. for reading and writing data. For writing we need both the magnetic field as well as

the laser, while we need only laser for reading the data. The design of the Magneto Optical (MO)

disk drive are made so that upon inserting it for writing, the label side of this MO disk is exposed

to the magnetic field while the other side is exposed to the laser light. The coating of this MO

disk is made with such a material which can be magnetized as a specific temperature known as

the Curie temperature usually around 300oC, the change in the Curie temperature can occur by

using different materials for composition of the MO disk drives. The coating of the MO disk

drive is made so that it cannot be magnetized at any temperature and it is extremely stable at

room temperature. We use Laser light for targeting specific regions of the Magnetic Optical

(MO) disk drives instead of heating the entire disk. Due to this targeting of specific regions of

the Magnetic Optical (MO) disk drive, we heat up the magnetic particles or magnetic domains


present in the MO film and due to this their temperature increases to curie temperature and now

they can be easily affected by the magnetic field generated by the read/write head. And through

this change of direction we store the data on the disk. This technique is very accurate and enables

the Magneto Optical (MO) disk drive to pack a lot of information on it. This packing of

information for Magneto Optical disk drive is more than the other magnetic devices because of

the use of this technique.

For reading the data on the Magneto Optical (MO) disk drive we use a less power laser. The

reading is done by the use of Kerr Effect, in which as we know a change in polarization of light

depending upon the orientation of the magnetic particles. In the process of writing, that spot

where the laser did not touch it represent a zero 0 and 1 represents that part of the Magneto

Optical (Mo) disk drive where the laser touches it. And by this we reads the data on the Magneto

Optical (MO) disk drives.

4.2 GMR applications:

Magneto Resistance (MR) is the ratio of the resistance of a conductor without the magnetic field

to the resistance of that conductor in the magnetic field. Now a day a large change in the

electrical resistance of a material by applying magnetic field to it is of great importance in

technologies like magnetic switching devices and magnetic memories etc. The following

equation we use for finding the Magneto Resistance effect value. It can’t exceed the 100%. The

equation for Magnetoresistance (MR) is given below.

∆ RR

=R↑↑−R↑↓R↑↓

Where ∆ RR is the change in electrical resistance per unit electrical resistance i.e. Magneto

Resistance. And R↑↑ and R↑↓ are the resistivity’s for the parallel and antiparallel alignment of

magnetization in two magnetic layers which are adjacent to each other. Lord Kelvin, a British

physicist for the first time reported the Magneto Resistance effect known as the “Anisotropic

Magneto Resistance effect”. The discovery of this effect was made in 1857. This Anisotropic

effect is small approximately up to 3% and it depends upon the Fermi surface of the material as

well.


Another effect was discovered in 1988 which is ten times larger than this “anisotropic effect”.

This effect is known as “Giant Magneto Resistance effect”. was discovered in 1988. The

discovery was made by two research groups independently. Albert Fert and Peter Grünberg are

the scientists who discovered this effect independently. Giant magneto resistance effect is

observed in a system which consists of multilayers having interleaved layers of magnetic and

non-magnetic materials. The use of Giant Magnetoresistance (GMR) effect is made in magnetic

sensors and nearly in the read head of every the hard disks. For half metals the value of bulk

magneto resistance is low. And when manganite losses its half metallicity property i.e. it is no

longer half metal, then close to its curie temperature TC the colossal Magneto Resistance (CMR)

is presented by it. As we have stated above that the Giant Magneto Resistance (GMR) effect is

observed in multilayer systems and also in half metals we have a property which we called the

vanishing down spin density. This vanishing of the down spin density of the half metals is useful

in multilayer spin valve systems. There are two geometries of GMR. These are CPP and CIP

which means conduction perpendicular to the plane and conduction in the plane respectively. In

the multilayer system of the Giant magneto resistance (GMR) effect, we have some important

factors; these are the spin diffusion length and the resistance of the magnetic layer for both types

of electronic spin. The diagram for the two geometries of the GMR is given below.

In the case of half metallic materials a non-magnetic material is sandwiched between two half

metallic layers for the Giant Magneto Resistance effect. This non-magnetic material is known as

the spacer. If we give the half metals a ferromagnetic (FM) alignment so then some current will

The figure shows the geometries for measurement of the Giant Magneto Resistance (GMR) effect in which the arrows indicates the current or conduction perpendicular to the plane and current or conduction in the plane.


pass through this multilayer system. This passage of current may be due to the metallic

conduction (GMR) or tunneling of spin up electrons (TMR). And if we align the half metals anti-

ferromagnetically (AF) so current can pass through the junction because for one spin direction no

current enters the junction and for other spin direction no current leaves the junction and hence

no current passes. This is the case of the ideal spin valve (an application of GMR which is a

device in which the value of the electrical resistance can change between two values depending

upon the relative alignment of the magnetization in the layers). A spin valve consist of two or

more conducting materials. If we provide a configuration having a conduction perpendicular to

the plane (CPP) geometry to a spin valve system, so then we can expect the largest effects

because the non-magnetic material known as spacer which is sandwiched between two magnetic

materials provides no short-circuit for current and hence for the antiparallel configuration of the

magnetic layers a complete switch-off is possible.

4.3 Spin electronics, Injection of polarized carriers:

As we know that electron can have one spin at a time, and also we know that the

density of states for the half metallic ferromagnetic is spin polarized. So the current which

tunnels out of a ferromagnetic material is spin polarized in nature. And the largest polarization

will be obtained by using half metals. The usage of this can be made in different ways.

i) Information on the spin diffusion length of a metal can be obtained by spin injection

in that metal.

ii) If we inject a spin polarized current in a superconductor, so this injection in the

superconductor can act as a pair breaking agent. In yttrium barium copper oxide

(YBaCuO), a huge decrease in the superconducting current is led by a the injection of

a current which is 100% polarized in nature.

iii) Building a spin transistor using half metals is also counts as an application of the half

metals, which indeed can act as a source of a current which has polarized nature and

also the use of this spin transistor can be made as an analyzing filter. So spin

transistor built with the use of a half metal can be used for both purposes.

As we know that in the specialized application of Scanning Tunneling Microscopy (STM) i.e. in

spin polarized scanning tunneling microscopy (SP-STM), we need sharp magnetic tip for gaining


detailed information of magnetic phenomena on a single atom. If a tip is used which is made

from a simple magnetic material then this tip produces a stray field due to its magnetization

which can modify the domain patterns. So the use of half metals can also be made in this. If we

use a half metal having a vanishing magnetization for making the tip, so the problem of the stray

field can be solved the patterns of the magnetic domains cannot be changed i.e. cannot be

modified.

4.3.1 Spin injection Schemes: There are many methods used for injecting electrons in a material which are spin

polarized in nature. Some of them are mentioned below.

4.3.1.1 The First Method: At some instance we need a device through which we can inject spin polarized electrons

or we can polarized carriers into other materials. For this we use a suitable combination of a half

metallic ferromagnetic material and a semiconductor but a suitable one. By considering every

combination of half metallic source and the active material (semiconductor or metal) there occur

different problems.

If the modification of a thin film is performed likely to make a sharp corner in the thin film

where the mobile carriers will accumulate, then this new device made can act like a spin injector

of spin polarized electrons.

The diagram of such a device is as follows.

In the figure shown above a thin film made up of CrAs is grown on a substrate and

there we made a sharp corner for the accumulation of the mobile charge carriers. At top their

present Doped GaAs which act like spin polarized electrons collector. There are three axis


mentioned in above fig i.e. x-axis is pointing towards the right side, y-axis is pointing upward

while the z-axis points out of the paper.

Phenomenon which is responsible for the spin injection of electrons is Anomalous Hall effect. In

the above fig as we see that the x-axis if the direction of the magnetization. In the direction of the

z-axis we applied the electric field and in the y-axis mobile carriers will accumulate through the

sharp corner in the GaAs. As there is a corner present in the y-axis direction so the accumulated

electrons will be forced out of the sample due to this corner shaped area. The injection of these

electrons can be made then into the doped GaAs where they will carry their spin moments in the

direction of the Magnetization.

4.3.1.2 The Second Method:

Another way to inject spin polarized electrons is the direct injection of these from a

ferromagnetic into a semiconductor. The polarization of current at the interface is given below

P=P0

1+(1−P02 ) σ F ⅄SCσ SC ⅄F

Where P0 is the polarization far inside the ferromagnetic material, and σ Fare σ SC respectively the

conductivities of Ferromagnetic and semiconductor material while ⅄F∧⅄SC are their mean

distance travels by spin carries before a spin flipping scattering occur. The term σFσSC

in the

formula is very important, which is the ratio of the conductivities of the ferromagnetic material

to the semiconducting material. As typically Ferromagnets have large conductivities than

semiconductors so the denominator in the formula becomes very large and as a result the

polarization approaches to zero. This is known as ‘conductivity mismatch’. This method is not

very efficient and has an efficiency of 1-2%.

4.3.1.3 The Third Method: If we doped a semiconductor with ferromagnetic material and use it i.e. if we use Ferro

magnetically doped material instead of just ferromagnetic material then the conductivity

mismatch problem can be solved. Because the FMDM and semiconductor have got comparable


conductivities so there will be no polarization i.e. conductivity mismatches. But the problem here

arises is that we need very low temperature and High external electric field. Due to these

problems this method has also got some limitations.

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