Chapter 5 June 25 man - INFLIBNETshodhganga.inflibnet.ac.in/bitstream/10603/35685/34/12... · 2018-07-02 · 107 Chapter 5 5.1 Introduction The eccentric materials that are characterized

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Chapter 5

5.1 Introduction

The eccentric materials that are characterized by an imbalance in number of

majority and minority charge carriers are the prerequisite of spintronics. A half-metallic

(HM) ferro-/ferri-magnet is a prototype material in which one spin channel is metallic

while the other one is semiconducting with an energy gap at Fermi level (EF). The

Heusler alloys with this property accomplish the requirement of spintronics very

impressively because these systems exhibit robust d-electrons-arbitrated electronic and

magnetic properties which suit the aforementioned field. HM Heusler alloys are expected

to play a key role in realistic applications due to their very high Curie temperatures and

their structural similarity to the widely used binary semiconductors crystallizing in the

zinc-blende structure [1-5]. Half-metallicity is very delicate property strongly dependent

on the positions of various constituent atoms of a HM Heusler alloy. In other words, one

can say that this character solely attributed to the prevalence of order in a particular

Heusler structure. Since the real materials always contain some degree of disorders,

therefore for the sake of realistic prediction of the materials for practical applications, it is

necessary to access the effect of disorder on HM property of Heusler alloys.

The electronic and magnetic properties of the perfectly ordered Heusler alloys

have been extensively studied in recent past [6-18]. In order to control precisely the

properties of these alloys, one has to study the effects susceptible of inducing states

within the minority-spin gap and thus destroying the half-metallicity. States at the

interfaces of these alloys with semiconductors [19-22] as well as temperature-driven

excitations [23-26] seem to destroy half-metallicity. In addition to interface states and

temperature, the third main effect which can destroy half-metallicity is the appearance of

defects and disorder [27-28].

It is established that small amounts of disorder within the distribution of the atoms

on the lattice sites can lead to the appreciable changes in their electronic structure, which

results in distinct alteration of their magnetic and transport properties [29-31]. This may

further lead to loss of half-metallicity or spin polarization [32]. Since properties of

Heusler alloys are strongly dependent on the atomic arrangement of the constituent

Chapter 5

108

atoms, therefore a careful analysis of crystal structure is essential to understand the

structure-to-property relation of Heusler alloys. The most prominent disorder in L21-type

Heusler structure is the B2-type disorder. The other noticeable disorders [1, 33-36] which

frequently occur in L21-type Heusler alloys are shown in Fig. 5.1.

Fig. 5.1 Schematic representation of (a) ordered L21-type Heusler structure and most prominent disordered in this: (b) B2-type disorder, (c) DO3-type disorder and (d) A2-type disorder.

In B2-type disorder, CsCl-type structure, the Y and Z atoms are equally

distributed and consequently the 4a and 4b positions become equivalent which reduces

the symmetry of original L21-type structure and the resulting space group is Pm3m. The

mixing of the position of an X atom by a Z atom results in the DO3-type disorder or BiF3-

type disorder. A very less common kind of disorder (not shown here) is B32a-type

Mn2CoSi and NiCoMnGa Heusler alloys: Disorder effect

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disorder (space group no. 227, Fd3m). In this disorder, the X-atoms, which occupy one of

the fcc sublattices, are mixed with the Y atoms, whereas the X atoms on the second

sublattice are mixed with the Z atoms. On the other hand, the all positions of L21-ype

structure become equivalent in the tungsten-type structure leading to a bcc lattice and

reduced symmetry Im3m. Generally, the A2-type disorder occurs when the disordering

between the X and YZ sublattices take place [37]. It should be noted that some types of

disorder can not be easily detected by XRD, as the scattering coefficients of the 3d-

transition metals are very similar [36].

There are various studies of disorder existing in the literature for L21-type

structure. On theoretical front, it has been predicted that spin polarization of Co-based

Heusler alloys is sensitive to this site disorder. It has been shown that while the half-

metallicity is retained for Mn antisite disorder, the Co antisite disorder destroy the half

metallicity due to a sharp peak located just in the proximity of the Fermi level EF. The

other defects, consisting of Co-Mn and Mn-Si swaps do not destroy the half-metallicity

[31]. Miura et al. [29] investigated the effects of atomic disorder on the half-metallicity

of the full-Heusler Co2CrAl and showed that the Co-Cr disorder significantly reduces the

total magnetic moment and the spin polarization at EF owing to an intense peak of the Co

3d states, while the Cr-Al disorder gives practically no effect on the spin polarization.

Ishida et al. [38] investigated the effect of chemical disorder on the half-metallicity of

Fe2CrZ and analyzed the chemical disorder level dependence of the total energy, spin

polarization and magnetic moment. Fe-Cr disorder is energetically more likely to occur.

They further showed that a high degree of spin polarization may be maintained even if

there are Fe–Cr and Cr–Z disorders in this alloy, whereas the Fe–Z disorder may degrade

the spin polarization. Kogachi et al. [39], using thermodynamic approach based on the

Bragg–Williams approximation, showed that the Co-type disorder leads to degradation of

the magnetism as observed in Co2MnSi and Co2MnGe, while the Mn–Z-type disorder

affects hardly the magnetism as in Co2MnSn. Gercsi et al. [40] investigated the effect of

structural disorder in Co2FeSi Heusler alloy using ab initio calculations and showed that

there is a possibility of obtaining a material with high spin polarization even in the

presence of disorder; however the A2-type disorder should be completely avoided.

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110

On the other hand, experimentally, Raphael et al. [41] utilized neutron diffraction

to measure significant levels of Co-Mn disorder in the polycrystalline bulk samples of

Co2MnSi Heusler alloy. They showed that the antisite disorder may serve as the dominant

electron scattering mechanism in this alloy. They further asserted that this is an indirect

evidence of disorder and emphasized on the importance of finding a technique which can

be used to characterize antisite disorder in thin-film Heusler alloys. Takamura et al. [42]

developed a new methodology for assessment of atomic ordering in full-Heusler alloys,

which is the extension of the commonly used Webster model. They applied the proposed

model to thin films of Co2FeSi full-Heusler alloy and showed a high degree of L21

ordering. Kudryavtsev et al. [43] synthesized the Co2CrAl Heusler alloy thin film

exhibiting the magnetic, the transport, and the optical properties close to those of the bulk

ordered sample. It was shown that the L21-type Co2CrAl Heusler alloy films are

ferromagnetically ordered with a TC close to that of the bulk sample. The increase in

structural disorder of L21→B2→A2 →amorphous state causes the reduction in TC down

to the paramagnetic state for amorphous films.

Besides in the L21-type structure, studies also exist in literature regarding the

effect of disorder in semi-Heusler alloys (C1b-type structure). Helmholdt et al. [44] with

neutron diffraction experiment showed that the compound IrMnGa has a crystal structure

similar to the C1b-type but shows a considerable atomic disorder between the Ir and Mn

atoms. The spin polarization measured using Point contact spectroscopy on arc melted

specimens of NiMnSb was found to be 58%, which indicates that the lack of half-

metallicity in these materials is indeed a bulk effect [45]. Using band structure

calculations Orgassa et al. [46] showed that antisite disorder of only a few percent can

destroy the HM nature of NiMnSb semi-Heusler alloy.

A recent study [47] on the crystal structures of Co2−xRhxMnZ (Z = Ga, Sn, Sb)

quaternary Heusler alloys revealed the existence of different types of anti-site disorder in

these alloys. This study emphasized that the quaternary Heusler alloys seem to be more

susceptible for anti-site disorder as compared to their ternary relatives. The magnetic

moments of the disordered compounds deviate from the Slater-Pauling rule indicating

that 100% spin polarization can not be realized in disordered alloys.


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While there is plethora of studies existing in the literature for the effect of

disorders and defects on the physical properties of conventional Heusler alloys, we found

a lack of such studies for inverse Heusler alloys and quaternary Heusler alloys. These

alloys, as described in previous chapters, show a great potential in spintronics

applications and deserve a thorough study to understand the relation between spin

polarization, magnetism and various possible disorders. So, we have highly motivated to

study such alloys under the effects of various possible disorders. In first part of this

chapter, we have discussed in details the various antisite disorders prone to occur in

inverse Heusler alloy, Mn2CoSi, and its effects on half-metallicity and magnetism. We

have selected Mn2CoSi inverse ternary Heusler for this study due to its sustainable half-

metallicity for wide range of lattice constant (5.4 Å-5.9 Å) [48] and also because such

type of alloys has already been synthesised [49]. In the second part, quaternary Heusler

alloys, NiCoMnGa have been studied under anti-site disorder for the similar properties.

This alloy is selected for this study because it has been predicted as a HMF and already

synthesized by Alijani et al. [50] with a high TC (646 K), well above room temperature.

5.2 Details of Calculations

The electronic structure calculations for both inverse and quaternary Heusler

alloys were performed using the FPLAPW method based on DFT [51] as implemented in

WIEN2k code [52]. The XC potentials were constructed using GGA within the

parameterization of Perdew-Burke-Ernzerhof (PBE) [53]. In FPLAPW calculations, the

core states were treated fully relativistically whereas for the valence states, a scalar

relativistic approximation was used. Additionally, the valence wave function inside the

muffin-tin (MT) sphere were expanded up to lmax = 10. The Radii of MT sphere (RMT) for

various atoms were taken in the calculations, of pristine and disordered Mn2CoSi, such as

to ensure the nearly touching spheres. A 1×1×1 supercell of 16 atoms was generated to

simulate the various disordered concentrations. The k-space integration was carried out

using the modified tetrahedron method [54] in which 17 × 17 × 17 k-point mesh was used

as base for the integration resulting in 165 k-points for ordered, Mn2CoSi alloy, whilst 56

and 140 k-points, respectively, were used for its disordered concentrations of 12.5%, 75%

and 37.5%, 75% in the irreducible Brillouin zone (IBZ). The plane wave cut-off

Chapter 5

112

parameters were decided by RMTkmax = 8 (where kmax is the largest wave vector of the

basis set such that kmax controls the accuracy of the calculation) and Gmax = 12 a.u.-1 for

Fourier expansion of potential in the interstitial region. In the case of (Ni,Co)MnGa

quaternary Heusler alloy, 63 k-points in the IBZ were used to study the disordered alloys.

The RMT values for various atoms i.e. 2.1 . ., 2.3 . .Ni Co Mn Ga

MT MT MT MTR R R a u R a u= = = = , in the

case of (Ni,Co)MnGa, were taken in order to ensure the nearly touching spheres. The

energy convergence criterion was set to 10-4 Ry/cell and the charge convergence was also

monitored along with it. Further, full relaxations of internal atomic coordinates have also

been carried out prior to study the electronic and magnetic properties of present systems

in both studies.

Fig. 5.2 The primitive cell of Hg2CuTi-type Mn22CoSi inverse Heusler alloy

(left) and corresponding Brillouin Zone (BZ) and its IBZ (in red color)

on right.

The Mn2CoSi inverse Heusler alloys crystallizes in X- type structure and the

Wyckoff positions for this structure are 4a (0,0,0), 4b (½, ½, ½ ), 4c (¼, ¼, ¼ ) and 4d

(¾, ¾, ¾ ), where Mn occupies the two inequivalent 4a and 4c sites as nearest neighbors

as shown in Fig. 5.2. In our nomenclature, they are represented by MnI and MnII and we

use this terminology throughout the text. Beside this, Co and Z atoms reside at 4b and

4d, respectively.


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In order to generate various disordered structures i.e. DO3-, A2- and B2-type

disorders in Mn2CoSi inverse Heusler alloy and Mn-disorder in NiCoMnGa quaternary

Heusler alloy, a (1×1×1) supercell has been constructed. The NiCoMnGa quaternary

Heusler alloy crystallizes in Y-structure and the Wyckoff positions for this structure are

4a (0,0,0), 4b (½,½,½ ), 4c (¼,¼,¼ ) and 4d (¾,¾,¾ ), respectively, occupied by Sb, Mn,

Fe and Cr atoms. This site occupation is shown in Fig.5.4.

Fig. 5.4 The primitive cell of Y-type NiCoMnGa quaternary Heusler alloy (left)

and corresponding Brillouin Zone (BZ) and its IBZ (in red color) on

right.

5.3. Result and discussion

The results of the study of disorders in Mn2CoSi inverse Heusler alloy and

NiCoMnGa quaternary Heusler alloy have been reported and discussed in two parts as

under:

5.3.1 Mn2CoSi inverse Heusler alloy

The electronic and magnetic properties of pristine Mn2CoSi inverse Heusler alloy

and its disordered phases are discussed to investigate the half-metallicity and magnetic

properties. After that, effect of various disorders prone to such type of alloys has been

analyzed in detail. We have presented the exhaustive data resulting from this study for

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114

the comparison and cross-check with the future experimental studies to be performed on

this system.

Fig. 5.5 Calculated total energy versus the lattice constants of Mn2CoSi in the

L21- and X-type structures. The zero of the energy corresponds to the

global equilibrium lattice constant. The solid/dotted line represents the

polynomial fit semi empirical Murnaghan equation of state [55]. Emin

corresponds to the global minimum value of energy.

5.3.1.1 Structural properties

The equilibrium lattice constants of ordered Mn2CoSi Heusler alloy were

estimated for both X-type and L21-type configurations by fitting the semi empirical

Murnaghan equation of state [55] as shown in Fig. 5.5. It is observed that this alloy is

more stable in X-type configuration and the corresponding optimized lattice constant is

found to be 5.63 Å which is in a close agreement with 5.65 Å, as calculated by Xing et al.

[48].


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Table-5.1: The calculated lattice constants (in Å), formation energy/atom (in eV), with

respect to the pristine phase, of various disordered phases of Mn2CoSi inverse Heusler

alloy.

The simulations of various disorders were executed as suggested by Gercsi et al.

[40] for Co2Fe-based Heusler alloys. The mixing of the position of Mn atoms by Co

atoms results in the DO3-type disorder. The B2-type disorder was modeled by swapping

the position of Si atoms by Co atoms. The A2-type disorder was realized by the

replacement of Mn atoms by Si atoms. These disorders were simulated using a Mn2CoSi

supercell composed of 16 atoms (eight Mn atoms, four Co atoms and four Si atoms).

Therefore the smallest amounts of disorders that can be introduced were 12.5% for A2 or

DO3-type and 25% for B2-type disorder in 1×1×1 cell of Mn2CoSi inverse Heusler alloy.

The binary mixing is the most common form of atomic disorder, in which the elements

on two different sublattices intermix. Depending upon different sublattices to be mixed,

the can be characterized as DO3, A2, or B2. Fig 5.6 shows all these disorders along with

the X-type structure. The lattice constants of the disordered structures, having X-type

Disorder type Total disorder (%) Lattice constant Formation energy

DO3 12.5

25

37.5

5.63

5.63

5.62

0.22

0.45

0.68

A2 12.5

25

37.5

5.60

5.58

5.66

0.07

0.15

0.23

B2 25

50

75

5.62

5.63

5.65

0.31

0.58

0.85

Chapter 5

116

configuration as base structure, were also calculated using the same approach (listed in

Table-5.1).

Fig. 5.6 Ball model illustration of Mn2CoSi inverse Heusler alloy with (a)

ordered X-type structure, (b) DO3-type disorder, (c) A2-type

disorder and (d) B2-type disorder.

5.3.1.2 Density of states (DOS)

As it is shown by Orgassa et al. [46] that even small amount of disorder can

destroy the HM nature of Heusler alloys, hence we have also restricted ourselves to

minimum disorder that can be introduced using the supercell approach as discussed

above. We first present our results on the stoichiometric Mn2CoSi parent alloy, followed

by the disordered compositions. The density of states (DOS) plots for pristine and

disordered (12.5% and 25% of DO3- and A2-type and 25% and 50% of B2-type)


117

Mn2CoSi Heusler alloys are shown in Fig. 5.7(a-d). Fig. 5.7(a) shows the spin resolved

total DOS of the Mn2CoSi phase with X-type structure.

Fig. 5.7 Total DOS of pristine and disordered Mn2CoSi inverse Heusler alloy.

EF corresponds to Fermi level (EF).

The majority spin channel (MAC) is strongly metallic, while the minority spin

channel (MIC) shows a semiconducting behavior with a gap around the EF. The bottom

of the MIC conduction band (CB) is 0.29 eV and the top of the MIC valence band (VB)

is -0.30 eV, with the minority-spin band gap (Eg↓) and HM gap or spin-flip gap (Esf) as

0.58 and 0.29 eV, respectively, in Mn2CoSi. These values are in good agreement with the

previous calculated values [48] of Eg↓ (0.53 eV) and Esf (0.18 eV). The gap in the

minority DOS around EF reflects the half-metallicity of this compound. The lowest

energy of the dispersed unoccupied d band in the MIC formed by both Mn and Co are

about ~0.3 eV above EF, detailed explanation regarding this can be found elsewhere [49].

The total DOS in the MAC have three peaks in which two peaks at the lower energies can

Chapter 5

118

be traced to the eg−t2g splitting in the cubic crystal field and third peak at the higher

energy, which spreads around EF, is composed mostly of Mn-d states. However, in MIC

the two main peaks can be observed; one below EF mainly due to Co-d states and the

other above EF is of an antibonding nature mainly arising from the MnII atom.

Fig. 5.8 Calculated partial DOS of pristine and three possible disordered phases

Mn2CoSi inverse Heusler alloy.

Next, we have analyzed the DOS of DO3-, A2- and B2-type disorders in Mn2CoSi

inverse Heusler alloy separately and the comparison with the DOS of pristine Mn2CoSi is

illustrated in the consecutive sections.

(i) DO3-type disorder: The swapping of one/two Mn atoms by Co atoms

introduces the DO3-type disorder of 12.5%/25%. The DOS for these disordered Heusler

phases are shown in Fig. 5.7(b). For both concentrations of disorders, the HM nature

sustains within the systems and an increase in Eg↓ and Esf have been observed. For the


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detailed analysis of the DOS, we have exposed the partial DOS of the atoms in Fig. 5.8

(b).

Fig. 5.9 Minority-spin gap (Eg↓) and HM gap (Esf) as a function of disorder

percentage for DO3-type and A2-type phases of Mn2CoSi inverse

Heusler alloy. The squares with solid line/dashed line (red color)

represents Eg↓ for DO3-/A2-type phase of Mn2CoSi and the spheres with

solid line/dotted line (red color) represents Esf for for DO3-/A2-type

phase of Mn2CoSi.

The partial DOS of ordered Mn2CoSi is also shown (Fig. 5.8 (a).) for comparison.

There is a strong covalent hybridization between the d states of MnI, Co, and MnII, which

leads to the formation of the bonding and antibonding bands separated by the gap. This

gap basically arises from covalent hybridization like in semi-Heusler alloys [11]. Fig. 5.8

(a) reflects that predominant states around EF in MAC are mainly consisting of MnI-d,

similar to Mn2CoSi. Nevertheless, a slight decrease is observed in the DOS at EF which is

due to the swapping of Mn atoms by Co atoms. The CB in MIC is blue shifted by ~ 0.1

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120

eV. Similar shifting in the case of VB is also observed, however this shifting is not so

pronounced as in CB, which results in net increase of Eg↓ and Esf to 0.72 eV and 0.33 eV,

respectively (Fig. 5.9). The shoulder which appears in the vicinity of bottom of CB in

MIC is mainly related to the 3d states of extra Co atom. These newly appeared and

disturbed states are rather localized. A further increase in disorder to 25% and above (not

shown here) results in increase of half-metallicity due to the strong expansion of the band

gap width, as shown in Fig. 5.9.

(ii) A2-type disorder: The A2-type disorder can be simulated by swapping of Mn

sites by Si atoms in Mn2CoSi. Fig. 5.7 (c) shows a disorder of 12.5% in the ordered

Mn2CoSi alloy. The band gap in the MIC is still present (Fig. 5.7 (c)) in spite of this

disorder. However, both Eg↓ and Esf get reduced in this case (Fig. 5.9). Analysis of the

partial DOS of the atoms of Mn2CoSi containing A2-type disorder (Fig. 5.8 (c)) reveals

that the states around EF in MAC are here also mainly consist of MnI-d but the further

decrease is observed in the DOS at EF, with the peak shifting towards the higher energy

region. This is again due to the swapping of Mn atoms by Si atoms. In MIC, the band

gaps shrink due to broadening of electronic states in both VB and CB near EF. This is

basically owed to the hybridization of extra Si-p states with the 3d states of TM as the

hybridization between p-states with different energies and d states is crucial to the width

of the energy gap in the MIC [49].

(iii) B2-type disorder: The introduction of 25% B2-type disorder by swapping

the position of Co atoms for Si atoms results in the appearance of new electronic states,

in the form a sharp peak, at EF in MIC which results in destruction of half-metallicity

(Fig. 5.7 (d)). This new peak at EF is solely attributed to the substituted Co atoms (Fig.

5.8 (d)) which replace the Si in ordered state. The peak in DOS at EF in MAC, as in

previous cases, shifts further towards the higher energy.

We have also calculated the formation energies for each type of disorder with

respect to the ordered phase, and are shown in Table-5.1. The 12.5% of A2-type disorder

has the lowest formation energy ~0.07 eV/atom. The DO3-type disorder has almost 3

times more energy (0.22 eV/atom) for the 12.5% of disorder, whereas more than 4 times


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higher formation energies (0.31 eV/atom) were found for 25% of B2-type disorder. In

each type of disorder, the formation energy increases with amount of disorder.

Table-5.2: The calculated atom-resolved spin magnetic moment (in µB) along with the

spin polarization (P) of pristine and disordered Mn2CoSi inverse Heusler alloys.

aRef: 48, bRef: 49

These formation energies are large enough that it may be possible to remove DO3-

and B2-type disorders completely and partially A2-type disorder of 25% and above, by

annealing [56]. But 12.5% of A2-type disorder with significantly lower formation energy

can not be removed easily by annealing. Nonetheless, as the half-metallicity is quite

robust in the presence of this disorder, therefore, this need not be a barrier to device

fabrication.

It is observed experimentally that 10% to 14% of Mn sites are occupied by Co in

Co-based full-Heusler alloy [41, 57] and up to 10% of disorder was measured in semi-

Heusler alloys [44, 58]. Therefore, it is very reasonable to study inverse Heusler alloys up

to 25% of various disorders in order to have realistic predictions of its various physical

properties. It is also very important to note here that it is hard to distinguish between

some disorder types with regular XRD method in Heusler alloys [36]. In the case of DO3-

Disorder type

Total disorder

(%)

MnI MnII Co Si P

Nil 0 -0.91 -1.10a

-0.96b

3.13 3.26a

3.12b

0.88 0.80a

0.82b

0.00 0.04a

0.02b

1.00 1.00 1.00

DO3

2.5 25

37.5

-0.58 -0.55 -0.58

2.74 2.82 2.89

0.99 1.01 1.06

0.00 -0.01 -0.02

1.00 1.00 1.00

A2

12.5 25

37.5

-0.34 -0.19 -0.02

2.58 2.59 2.62

0.66 0.41 -0.13

0.00 0.00 0.00

1.00 1.00 0.97

B2

25 50 75

-0.65 0.41 1.42

2.59 2.32 2.13

1.31 1.58 1.68

0.00 -0.02 -0.04

0.31 0.20 0.13

Chapter 5

122

and A2-type disorders, 100% spin polarization (Table 5.2) exists up to 25 % disorder and

also of a very high degree beyond this. The inclusion of B2-type disorder degrades the

spin polarization very sharply as only 31% spin polarization is observed for 25% disorder

of this kind. The effects of various disorders on the atom-resolved magnetic moments for

all compositions are summarized in Table 5.2. For the all disordered phases, the predicted

total magnetic moments show the strong dependence on both the disorder and the change

in chemical composition.

5.3.1.3 Magnetic properties

The total spin magnetic moment for Mn2CoSi is found to be 3.00 µB which is in

accordance with the Slater-Pauling rule [12] for half-metals and matches with the results

of previous studies on this alloy [29-30]. The major contribution to the total spin

magnetic moment is comes from MnII atom which carries the largest moment (~3 µB) and

Co atom carries a positive moment of 0.88 µB. The magnetic moments of MnII and Co

atoms in Mn2CoSi alloy are similar to its L21-type counterpart [12]. The point which

catches the attention is the magnetic moment of MnI atom. It aligns antiparallel to the

MnII. The ferromagnetic and antiferromagnetic moment alignments, in inverse Heusler

alloys, result from a competition between two physical mechanisms i.e the intra-atomic

exchange splitting of the magnetic atom d states and the interatomic covalent interaction

of d states [59-60]. The magnetic energy applies equally to the ferromagnetic and

antiferromagnetic alignments, whilst the covalency mechanism benefits only the

antiferromagnetic alignment. The two Mn atoms in Mn2CoSi inverse Heusler alloy are

nearest neighbors therefore a strong direct interaction between these two makes the

covalency mechanism to be dominant. This leads to the antiferromagnetic alignment

between the magnetic moment of MnI and MnII atoms [49]. More details related to the

magnetic properties of inverse Heusler alloys can be found in Chapter 4 and reference

therein.

The inclusion of DO3-type disorder in Mn2CoSi inverse Heusler alloy leads to the

increase in the total spin magnetic moment, as shown in Fig. 5.10 (a). This is due to rise

in the total valence electrons by the addition of extra Co atoms. The magnetic moment at

MnI decreases from ~ -0.91 µB to ~ -0.58 µB, whereas an increase the moment (from 0.88


123

µB to ~ -0.91 µB) at Co site is observed with this disorder (Table 5.2). Similarly, the

moment at MnII site also decreases. Si atom carries a negligible moment throughout all

disorder concentrations.

In case of A2-type disorder, the reduction in magnetization has been observed, as

depicted in Fig. 5.10 (a). This is obviously because the extra Si atoms swapping Mn

atoms carry a negligibly small magnetic moment (Table 5.2). The magnetic moment at

MnI site, the site occupied by extra Si atoms, decreases continuously (Table 5.2). Similar

decrease in moments has been also observed at other atomic sites.

Fig. 5.10 Total spin magnetic moment versus disorder percentage of (a) DO3-

and A2-type phases and (b) B2-type phase of Mn2CoSi.

For B2-type disorder, beside a small increase in total spin magnetic moment for

25% disorder (Fig. 5.10 (b)), a steep increase beyond this disorder has been observed.

Similar increment in moments at MnI and Co sites is observed, but the moment at MnII

decrease (Table 5.2).

Chapter 5

124

5.3.1.4 Bandstructures

In this section, we have explored the bandstructures of pristine and some of the

disordered alloys. Fig. 5.11-5.14 shows the bandstructure of pristine Mn2CoSi (X-type

structure) inverse Heusler alloy and of DO3- and A2-type (for 12.5%) and B2-type (25%)

disordered alloy. It is evident that the majority band structure has overlapping VB and

CB at EF, indicating a strong metallic nature of the majority electrons. However, the

minority band structure of these alloys exhibits a band gap around EF except for B2-type

disorder.

Fig. 5.11 Spin-resolved bandstructures of X-type (pristine) Mn2CoSi inverse

Heusler alloy.

The low lying energy region between -9.5 eV to -12 eV (not shown here to focus

on regime around EF) for all cases is mainly attributed Si-s electrons. These lowest

valence bands are very low in energy and remain isolated from rest of the valence bands

by an energy gap for both majority and minority spins channels. Further, these remain

unaffected by the Co-Mn or Mn-Mn exchange interaction. Therefore, the Si-s electrons


125

have little influence on the magnetic moment and the formation of a HM band gap,

except extending the valence to a broader range. The energy region between −7.0 eV and

EF (0.0 eV) consists mainly of the d electrons of Co and Mn atoms. These dispersed

bands are due to the strong hybridization of Mn-Mn and Mn-Co d electrons, including a

contribution from Si-p in the occupied valence states.

Fig. 5.12 Spin-resolved bandstructure of DO3-type Mn2CoSi Heusler alloy.

The bandstructures of all disordered phases of Mn2CoSi inverse Heusler alloy

(Fig. 5.12-5.14) have almost similar characteristics and can be understood in the way,

explained above for pristine system. The dense bandstructures for disordered system is

basically due to the more no of atoms involving in the disordered calculations. The

minority bandstructures of disordered alloys, except for B2-type disordered, also have

band formation like in the case of pristine Mn2CoSi. But the major point which we have

observed is that the formation of direct (along Γ-Γ direction) minority band gap in

disordered alloys in contrast to the indirect band gap (along Γ-Χ direction) for pristine

case. The minority bandstructure of B2-type disordered is metallic due to the overlapping

of VB and CB.

Chapter 5

126

Fig. 5.13 Spin-resolved bandstructure of A2-type Mn2CoSi Heusler alloy.

Fig. 5.14 Spin-resolved bandstructure of B2-type Mn2CoSi Heusler alloy.


127

5.3.2 NiCoMnGa quaternary Heusler alloy

In second part part, we have now discussed the effect of atomic Mn- disorder on

the electronic and magnetic properties of ordered (Ni,Co)MnGa quaternary Heusler alloy.

The important results of this study are presented for further experimental/theoretical

studies.

5.3.2.1 Structural properties

The quaternary HAs can be distinguished from the conventional ternary L21- and

C1b-type Heusler alloys in terms of site occupancy of constituent atoms as shown in

Table 5.3.

Table 5.3: Possible structures of ternary and quaternary Heusler alloys

Formula Prototype Example Occupancy sequence structure Space group

XX'YZ LiMgPdSn NiCoMnGa Ni-Co-Mn-Ga Y 43F m (216)

X2YZ Cu2MnAl Ni2MnGa Ni-Mn-Ni-Ga L21 3Fm m (225)

X*2YZ Hg2CuTi Mn2NiGa Mn-Mn-Ni-Ga X 43F m (216)

XYZ MgAgAs NiMnGa Ni-Mn-(void)-Ga C1b 43F m (216)

In order to simulate the ground state properties of present disordered Ni1-

xCoMn1+xGa (x = 0.25, 0.50, 0.75) Heusler alloys, the exact lattice constants for these in

stable configuration were to be found initially. As the present alloys are the intermediate

ones between ferromagnetic-(Ni,Co)MnGa (x= 0) and ferrimagnetic-Mn2CoGa Heusler

alloys, therefore systematic structural optimization of these alloys have been performed

in the neighborhood of experimental lattice parameters of ordered (Ni,Co)MnGa Heusler

alloy in both, ferromagnetic and ferrimagnetic configuration. The ferrimagnetic

configuration has been realized by flipping the spin of one of Mn-atoms whereas for

ferromagnetic configuration, the spins of both Mn-atoms have been kept same. Our

calculations predict the stability of ferrimagnetic ground state over the ferromagnetic

state for all the intermediate alloys.

Chapter 5

128

In Fig. 5.15, we demonstrate the optimization curve for Ni0.75CoMn1.25Ga alloy.

The ferrimagnetic state is found stable over ferromagnetic state by an energy, ∆E = -

113.21 meV.

Fig. 5.15 Total energy (E*) versus lattice parameter of Ni0.75CoMn1.25Ga

quaternary Heusler alloy. The solid lines show a polynomial fit for

determining the equilibrium lattice constant. The actual equilibrium

energy is Eequi = (E*×10-3 -644809) eV.

Further, the value of ∆E increases with increase in amount of Mn-disorder in

(Ni,Co)MnGa (as listed in Table 5.4) such that the observation is in accordance with

ferrimagnetic nature of end compound, Mn2CoGa [49]. Ni0.25CoMn1.75Ga is most stable

in ferrimagnetic configuration among present alloys with ∆E = - 2770.35 meV. The

optimized lattice parameters are summarized in Table 5.4. The lattice parameter of

(Ni,Co)MnGa alloy is in good agreement with the corresponding experiment value [50].

Moreover, it exhibits a linear increase with increase in Mn-disorder. To proceed further,

all the calculations have been executed at optimized lattice parameters.


129

5.3.2.2 Density of states (DOS)

In Fig 5.16, we mainly focus on total DOS of the disordered systems. The

explanation for ordered systems (Ni,Co)MnGa and Mn2CoGa) can be found elsewhere

[49, 50]. The generic total DOS of all alloys manifest the strong metallic character of

majority spin channel (MAC), whereas for minority spin channel (MIC), almost a clear

dip at EF is evident for HM ferromagnetism of these alloys.

Table 5.4: Optimized lattice parameters (a), spin polarized DOS at EF (n↑, n↓), spin

polarization (P) and energy difference between ferromagnetic and ferrimagnetic states

(∆E = EFiM – EFM) of present Ni1-xCoMn1+xGa (x = 0, 0.25, 0.50, 0.75) Heusler alloys.

x a (Å) m (µB) n↑ (eV) n↓ (eV) P ∆E (meV)

0

0.25

0.50

0.75

5.79

5.80a

5.80

5.81

5.82

4.95

5.07a

4.25

3.50

2.75

0.95

-

6.14

8.67

10.64

0.01

-

0.35

0.04

0.04

0.98

-

0.89

0.99

0.99

12.50

-113.21

-194.54

-2770.35

The ordered (Ni,Co)MnGa Heusler alloys is a true HMF with a band gap in MIC.

The replacement of one Ni atom with Mn in (1×1×1) conventional cell of (Ni,Co)MnGa

creates a disorder of 25% and resulting alloy formed is Ni0.75CoMn1.25Ga, with two

inequivalent Mn-atoms (MnI and MnII). Now, the EF cuts the bottom of minority CB

( C

botE ) such that a pseudogap appears in MIC which reduces the spin polarization to 83%

(Table-5.4). On increasing Mn-disorder further, C

botE is blueshifted which raises the spin

polarization again to 99%. Almost complete spin polarization makes the disordered alloys

Chapter 5

130

Ni1-xCoMn1+xGa (x = 0.50, 0.75) as HM ferrimagets. On comparing the total DOS of all

systems, it is found that increase in Mn-disorder creates more states in CB of MAC which

eventually decrease the magnetization in the alloys.

Fig. 5.16 Calculated total DOS of Ni1-xCoMn1+xGa (x= 0, 0.25, 0.50, 0.75)

Heusler alloys. EF corresponds to Fermi level.

The actual shape of DOS in these disordered alloys is decided by various TM-d states

present. Therefore, to have the more insight in qualitative features of DOS, d-DOS for all

TMs of present disordered systems are presented in Fig. 5.17. In all cases, the d-electrons

of TM atoms primarily contribute to the formation of bonding states of MAC, whereas

the bonding states of MIC predominantly consist of d-electrons of Ni, MnII and Co atoms

only. The minority antibonding states are totally dominated by d-electrons of MnI atom.

In (Ni,Co)MnGa, the majority antibonding states are almost absent. This is quite obvious

from the electronic distribution in the d-subshell of all the TM atoms. In all TM atoms,

the majority orbitals are full and therefore, no space is available for further electrons.

On the other hand, few minority orbitals are vacant in Ni which generates the

DOS in minority antibonding region. This vacancy further increases with increase in Mn-

disorder which augments this DOS. On exploring p-DOS of Ga (not shown here to focus


131

mainly in the vicinity of EF), it is found that these are mainly dominating from -6.0 eV to

-2.0 eV and take part effectively in the hybridization with TM-d states to determine the

occupancy of p-d orbitals.

Fig. 5.17 Calculated d-DOS of each TM in Ni1-xCoMn1+xGa (x= 0, 0.25, 0.50,

0.75) Heusler alloys.

Firstly, in all these systems, Ni-d or Co-d states are hybridized covalently with

Mn-d to form bonding and antibonding hybrids which are separated by a gap in MIC. Ga

atom is not responsible for formation of band gap in MIC but the position of EF depends

upon how Ga-p states interact with hybrids of TM-d states.

5.3.2.3 Magnetic properties

Fig. 5.18 indicates the effect of increasing x in Ni1-xCoMn1+xGa on total magnetic

moment. For ordered (Ni,Co)MnGa alloy, the magnetic moment (4.95 µB) is closer to

experimental observation [50] as listed in Table-5.4 which confirms the accuracy of

present calculations.

Chapter 5

132

The magnetic moment at the Ni, Co, MnI and Ga sites remain almost constant

with increment of x. In present alloys, Ni atom is nearest neighbor to Co and Mn atoms.

Therefore, the magnetic moment at Ni site is of induced character by the neighboring

magnetic atoms and its value remains almost constant (~ 0.57 µB) in all cases. For

disordered systems, MnII enters at the site of Ni and align itself antiferromagnetically

with the MnI atom which results in the reduction of total magnetic moment.

Fig. 5.18 Total and atom-resolved magnetic moments versus amount of Mn-

disorder in NiCoMnGa quaternary Heusler alloy.

We have found that even 25 % replacement of Ni with MnII, changes magnetic

ordering of resulting alloy from ferromagnetic to ferrimagnetic. Moreover, this

replacement also modifies the Y-type structure of parent (Ni,Co)MnGa and start showing

transition towards X-type structure. The antiferromagnetic alignment of the MnII atom

with MnI can be understood in terms of exchange interaction mechanism.

It is well established that there are mainly two magnetic processes i.e. exchange

splitting of d-states of magnetic atoms and the interatomic covalent interaction of d-states

[59] which dominant in Heusler alloys. More precisely, it is the competition between

these two processes which decides the ferromagnetic or antiferromagnetic alignment of


133

atomic magnetic moments in these alloys. In our cases, the strong direct-interaction

between MnI and MnII d-states (covalent) leads to the antiferromagnetic alignment of

their atomic magnetic moments. This interaction is favorable as both Mn atoms are

nearest neighbor. We observe that MnII d-states plays an important role in reconstructing

the bands near EF after hybridization with d-states of Co and MnI, thus we can claim that

the magnetic interaction of d-states of MnII with d-states Co and MnI governs the net

magnetic moment. In contrast to this, due to its non-magnetic nature, Ni does not

contribute much to the exchange interaction and takes a stable value of magnetic moment

in all cases.

5.3.2.4 Bandstructures

The bandstructure for ordered NiCoMnGa and disordered Ni0.25CoMn1.75Ga

quaternary Heusler alloys are shown in Fig. 5.19 and Fig. 5.20, respectively. The absence

of electronic states at EF in minority bandstructure is clearly visible in the case of

NiCoMnGa quaternary Heusler alloy.

Fig. 5.19 Spin-resolved bandstructures of NiCoMnGa quaternary Heusler alloy.

Chapter 5

134

The bandstructures of ordered and disordered alloys (shown in Fig 5.19 and 5.20)

are presented here to understand the interaction of various atoms in the vicinity of EF.

Therefore, we have not shown the deep lying bands here

In NiCoMnGa, the low lying bands ~12.0 eV (not shown here) are solely

attributed to s-electrons. In MAC, the bands from ~ -4.0 eV to ~ -2.5 eV mainly of t2g

character of Mn and Ni atoms. Above this, up ~ -1.5 eV, the Co-t2g and Ni-t2g states

dominate in band formation. A less dispersive band of Mn-eg character lies from -1.5 eV

to -1.0 eV. Above ~ -1.0 eV, the Mn-t2g bands dominate which extend to CB including

EF. On the other hand, in MIC, a rather more dispersive band which extends from ~ -4.0

eV to ~ -1.5 eV, has the major contribution from Ni-t2g and Ni-eg states. A less dispersive

band, from ~ -1.5 eV to ~ -0.5 eV, has the Co-t2g character. The energy gap in MIC

around EF is a result of the covalent hybridization between lower-energy Mn-d states and

higher-energy Ni-d states which leads to the formation of bonding and antibonding states.

The two bands are visible, in MIC, above EF. One, from ~0.1 eV to ~0.9 eV is mixture of

Ni-eg and Co-eg character and the second one is exclusively of Mn-d (eg-t2g) character

which lies in the range of ~0.9 eV to ~2.0 eV.

Fig. 5.20 Spin-resolved bandstructures of Ni0.25CoMn1.75Ga Heusler alloy.


135

The bandstructure of disordered Ni0.25CoMn1.75Ga can also be explained in the

similar way. The shifting of overall band toward higher energy has been observed with

the Mn-disordered. Unlike in ordered NiCoMnGa, the VB and CB in minority of

disordered Ni0.25CoMn1.75Ga touches each other at EF. But on the same time, the numbers

of states increases at EF in majority spin which results in the increase of net spin

polarization.

5.4. Conclusions

We have focused on the study of disorder in context to the HM nature of Mn2CoSi

inverse Heusler alloy. We have adopted all-electron full-potential linearized augmented

plane wave method for this study. The all three possible disorders i.e. DO3-, A2- and B2-

type, are investigated in detail for their electronic and magnetic properties. The supercell

(1×1×1) approach allowed us to introduce a minimum of 12.5% disorder of both DO3-,

A2-type and 25% of B2-type in ordered cell. It is found that the Eg↓ for DO3-, A2-type

keeps on increasing, whilst the Esf decreases with the increase in amount of disorders.

Nonetheless, 100% spin polarization is maintained in both disorders for all

concentrations. The inclusion of B2-type disorder completely destroys the half-

metallicity. Therefore it should be avoided in experimental fabrication. The calculated

formation energy shows that the A2-type disorder is most likely to occur. However, the

100% spin polarization for this assured that it may not hinder the use of Mn2CoSi inverse

Heusler alloy in spin based device application. We believe, after going through many

experimental studies, that disorder concentration studied in this work may be sufficient

enough to provide authentic data for this alloy which can be compared with the future

experiments.

In second part of this study, a systematic analysis of transition from ferro- to ferri-

magnetic ordering in stoichiometric (Ni,Co)MnGa quaternary Heusler alloy is performed

by increasing Mn-disorder. The antiparallel alignment of magnetic moment of extra MnII

atom with respect to MnI atom originates the ferrimagnetic ordering in studied disordered

compounds. Further, total magnetic moment also decreases with increasing Mn-disorder.

A suitable band gap in minority spin channel places these disordered alloys, Ni1-

xCoMn1+xGa (x = 0.50, 0.75) in the category of HM ferrimagnets. This gap actually

Chapter 5

136

depends on how Ga-p states interact with hybrids of TM-d states. Due to very high

degree of spin polarization, these can also serve as the potential candidate for spintronic

applications. Mn-disorder in (Ni,Co)MnGa quaternary Heusler alloy represents the

intermediate stage of changeover from Y-type structure ((Ni,Co)MnGa) to X-type

structure (Mn2CoGa). Our FPLAPW calculations present exhaustive data for realistic

comparison of electronic and magnetic properties of studied disordered alloys with future

experiments as the disorders can not be ignored in experimental synthesis.


137

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Chapter 5 June 25 man - INFLIBNETshodhganga.inflibnet.ac.in/bitstream/10603/35685/34/12... · 2018-07-02 · 107 Chapter 5 5.1 Introduction The eccentric materials that are characterized