Role of electronegativity on the bulk modulus, magnetic moment and band gap of Co2MnAl based Heusler alloys

Keeping it mind, we aimed to study substitution effect of Ga, Ge and Si on mechanical, electrical and magnetic properties of Co 2 MnAl 1x Z x (where Z ¼ Si, Ge and Ga) Heusler alloy usi[r]

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Original Article

Role of electronegativity on the bulk modulus, magnetic moment and

band gap of Co

2

MnAl based Heusler alloys

Author-Shiv Om Kumar

, Vineeta Shukla

, Sanjeev Kumar Srivastava

Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

a r t i c l e i n f o

Article history: Received January 2019 Received in revised form February 2019 Accepted February 2019 Available online 10 February 2019 Keywords:

Heusler alloy Lattice parameter Bulk modulus (BM) Magnetic moment Band gap

a b s t r a c t

In this paper, we have presented the comparative study of mechanical, electrical and magnetic properties of Co2MnAl1xZxHeusler alloy with Z¼ Si, Ge and Ga and x ¼ 0, 0.25, 0.75 and using electronegativity

(EN) model We employed density functional theory for numerical calculations It is found that Co2

M-nAl1xZxwith Z¼ Ga, Ge follow the Vegard's law while Co2MnAl1xSixdoes not follow the same trend

Among all composition Co2MnAl.25Si.75alloy is found to be more compressible Electronic density

dis-tribution depicts the ionic nature of Co2MnAl1xZxalloy systems The Co2MnAl1xZxwith Z¼ Si, Ge

possess larger magnetic moment and band gap with respect to Co2MnAl1xGaxsystem which results

from the EN difference, degree of delocalization of valence electron, atomic size and atomic number, respectively

© 2019 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

1 Introduction

In last few years, Heusler alloys have become the promising material due to major applications in spintronics and memory shape devices[1] In this system, the full Heusler compounds are characterized by the formula X2YZ that crystallize in the L21

structure while half Heusler alloys are referred as XYZ which crystallize in the cb1 structure [2,3] There are four

wyckoff-positions which is given by P (0, 0, 0), Q (0.25, 0.25, 0.25), R (0.5, 0.5, 0.5) and S (0.75, 0.75, 0.75) Here X and Y elements are posi-tioned in P, Q and R sites while main group element Z takes always place in S sites[4]

The electronic structure of these Heusler alloys are obtained to range from metallic to semiconductor relying on their composition Infact, full Heusler alloys are popular due to half-metallic nature means these alloys possess 100% spin polarization at the Fermi level In similar way, the full Heusler alloy shows many attractive magnetic phenomena like localized and itinerant magnetism, hel-imagnetism, antiferromagnetism, Pauli paramagnetism or heavy fermionic behaviour [5] Therefore, understanding of electrical,

mechanical and magnetic behaviors of these alloys is very impor-tant for application point of view It is well established that me-chanical properties are defined in term of bulk modulus of compound The bulk modulus (B) is an parameter of materials that defines the ability of a solid, within elastic region, to resist compression deformation In microscopic framework, valence electrons play an important role in the compression process and attractive interaction between atom and valence electrons results from the electronegativity (EN) of atoms which are not only affect mechanical properties but also influence electrical and magnetic properties of materials[6] Hence, magnetic moments and band gap are also considerably influenced by the delocalization degree of valence electrons Among the Heusler materials, Cobalt-based Heusler alloys are very popular because of their high Curie tem-perature that make them favorable for various applications, e.g tunneling magnetoresistance (TMR) Upto date, many Cobalt-based full Heusler alloys have been investigated as half metallic materials which is advantageous for spintronic devices In addition, disor-dered phase like A2, B2or DO3of Heusler alloys[7e9]also have a

great inﬂuence on their physical properties Disorder can be found due to replacement of element in the parent alloys or the presence of defects which lead the structural, mechanical and electrical properties of Heusler alloys

Keeping it mind, we aimed to study substitution effect of Ga, Ge and Si on mechanical, electrical and magnetic properties of Co2MnAl1xZx(where Z¼ Si, Ge and Ga) Heusler alloy using density

* Corresponding author ** Corresponding author

E-mail addresses:shivomiit@gmail.com(A.-S Om Kumar),vineeta@phy.iitkgp ernet.in(V Shukla),sanjeev@phy.iitkgp.ernet.in(S.K Srivastava)

Peer review under responsibility of Vietnam National University, Hanoi

Contents lists available atScienceDirect

Journal of Science: Advanced Materials and Devices

https://doi.org/10.1016/j.jsamd.2019.02.001

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functional theory based method to search the materials of potential application

2 Calculation method

The numerical investigations were accomplished by using the Density Functional Theory (DFT) based WIEN2k code[10] The ex-change correlation potential was characterized by the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) function[11] The plane wave basis set with an energy cut-off of 300 eV is used for all cases The energy threshold between the core and the valence states and k points were set to 6.0 Rydberg (Ry) and 1000, respectively The primitive cell was taken for Co2MnAl, Co2MnGa, Co2MnGe and Co2MnSi while 1 super

cells were made for Co2MnAl1xZx(where Z¼ Ge, Si, Ga except

x¼ 0) alloy systems In case of Co2MnGa alloy Co, Mn and Ga take

place at wyckoff coordinates Mn (0, 0, 0), Co1(0.75, 0.75, 0.75), Co2

(0.25, 0.25, 0.25) and Ga (0.5, 0.5, 0.5), respectively, as shown in Fig All compounds were optimized by using Hellmann-Feynman forces on atoms We used lattice parameter a¼ 5.749 Å as we re-ported previously[12]

3 Results and discussion

In order to evaluate the mechanical properties of Co2MnAl1xZx

(where Z¼ Si, Ge and Ga and x ¼ 0.0, 0.25, 0.75, and 1.0 compo-sitions) Heusler alloys, the volume optimization was performed by minimizing the total energy for a number of volumes of Ga, Si and Ge substituted alloys as shown inFig

We found the equilibrium lattice parameters (a0) and the bulk

modulus (B) from the Birch Murnaghan equation as given by[13]

ETotVị ẳ E0ỵ VB B0B0 1ị*

" V0

V B

ỵ

1V0 V

1#

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where E0, B and B0refer to equilibrium energy, bulk modulus and its

ﬁrst derivative at equilibrium volume V0, respectively Generally,

the bulk modulus B is deﬁned by the following equation:

B¼ VvVvP¼ Vv2E

vV2 (2)

where P and V are the pressure and volume of the system, respectively

It can be seen fromFig (a) that with increasing Ge and Ga content, the lattice constant increases linearly This higher value of the lattice parameter is a result of greater atomic radius of Ge and Ga atoms in compare to Al atom However, Co2MnAl1xSixfollow

the opposite trend that is usual for Heusler alloys

In any system bulk modulus (B) represents the hardness of compounds Thus, bulk modulus variation for Co2MnAl1xZx

(where Z¼ Si, Ge and Ga) alloys have been shown inFig 3(b) It is clear that all Ge, Si and Ga substituted composition upshot bigger modulus relative to parent Co2MnAl alloy except only Co2

M-nAl.25Si.75 composition Interestingly, all Co2MnAl1xZx (where

Z¼ Si, Ge and Ga) alloys follow the same trend Initially on addition of 25% of Ge, Si or Ga in place of Al site (for example Co2

M-nAl.75Ge.25 composition), bulk modulus increases However, bulk

modulus decreases for 75% substitution of Ge, Si or Ga and again increases for pure Co2MnSi, Co2MnGa and Co2MnGe alloys Such

kind of variation occurs according to the following order: Co2MnAl1xSix> Co2MnAl1xGax> Co2MnAl1xGex Above

varia-tion in bulk modulus after the addivaria-tion of 25% Si, Ge and Ga sub-stitution might be the result of valence electrons difference (excluding core electrons), taking part in the compression process or EN difference Al (1.61 eV1/2), Ga (1.81 eV1/2), Si (1.90 eV1/2) and Ge (2.01 eV1/2) which controls the attractive and repulsive inter-action between atom and valence electrons[14,15]

Since EN value of Ga, Ge and Si are larger than that of Al atom, the average binding force of chemical bonds in the alloys increases when alloying Co2MnAl with Ga, Si and Ge, respectively It is

noteworthy that bulk modulus of alloys is expected to increase with increasing of these p-element content in Co2MnAl alloy according

to simple chemical bonding formulation based on tight-binding model In contrast, substitution of 75% Ge, Si or Ga in Co2MnAl

alloy, B decreases that might be the result of increasing number of p-p and p-d bonds, which make them more rigid than 25% sub-stitution of Ge, Si or Ga in parent alloys [16] Among all Fig Crystal structure of Co2MnGa Heusler alloy

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compositions, Co2MnAl.25Si.75 is found to be more compressible

There may be two reasons: either sharp changes in B upon doping of Si might be related to local Al magnetic moment contribution (Fig 4a) or signiﬁcant contraction of the lattice occurs on Si doping due to less variation in atomic number of Si and Al elements

Another important parameter is electron density distribution Basically, electronic charge density is useful entity for studying the nature of bond character in any materials Moreover, it provides information on the charge transfer, bonding nature (e.g the ionic, metallic and covalent bonding) in alloys As we predicted earlier that atomic number, EN etc plays an important role in above mentioned properties For this purpose, we studied the electronic charge den-sity distribution curve Here only curve for Co2MnAl and Co2

M-nAl.25Ge.75alloys have been shown inFig 5(a and b) The electronic

charges are mainly distributed in the vicinity of atoms, and decreases away from the core region The formation of well-deﬁned spherically symmetric peaks centered on Co, Mn, Ge/Al atoms occurs due to the difference of electron density The interstitial region between the Co, Mn and Ge/Al atom has no electrons at all which shows CoGe/Al and MnGe/Al bonds has a similar character with the ionic bond This character is accompanied by a transfer of charge from the Co and Mn atoms to Ge or Co to Al atom because of different EN of elements except Mn to Al which possess almost same EN[8]

To analysis the magnetic properties, total magnetic moment plots for Co2MnAl1xZx(Z¼ Si, Ge and Ga) alloys have been depicted

in Fig 6(a) For Si and Ge substituents, total magnetic moment shows the increasing trend while Ga does not follow any trend In general, the total moment of the half-metallic full-Heusler alloys follows the Slater-Pauling behavior:

m

the total number of valence electrons The total number of electrons Ztotalis given by the sum of the number of spin-up (N[) and

spin-down (N[) electrons (Ztotalẳ N[ỵNY) and the total moment

m

is given by the difference of the number of spin-up and spin-down electrons (

m

the Slater-Pauling rule for Ge as well but shows a little deviation for

Co2MnAl.75Ge.251% and Co2MnAl.25Si.75almost 9% However, in case

of Ga replacement, particularly 25% composition of Ga, major de-viation occurred For more details,Fig 6(b, c) shows local magnetic moment plot of Co and Mn which have major contribution in total magnetic moment Co contribution for Ge substituent varies nearly linear similar to Si but for Ga substituent it deviates for linear relation[18] For more compressible composition Co2MnAl.25Ge.75,

Co contributes least Partial moment of Co is maximum for Co2MnAl.25Ga.75alloy among all compositions On other hand, Mn

contribution does not vary much for Si and Ge substituents, but changes occur for Ga substituent that might be due to the less variation of EN values of Al and Ga Moreover, Ga substituent shows muchﬂuctuation in total as well as in partial moments It is obvious fromFig 5(a) that for Co2MnAl.75Ga.25composition total moments

decreases while total moment increases for 75% and 100% Ga substituted alloys On other hand, Co, Mn and Ga moment contri-butions were least rather Al for Co2MnAl.75Ga.25composition In

case of Co2MnAl.25Ga.75, total and partial moments follow the

reverse trend Firstly, it is anticipated that largeﬂuctuation in Ga substituent can be outcome of the same number of valence electron in Al and Ga shells Secondly, at 25% doping of Ga could not be enough for formation of number of p-d bonds that tends to reduce the Co, Mn moment In contrast 75% substitution of Ga increases Co and Mn moment offer the large expansion of the lattice caused by the p-p or p-d bonds It is found that the local moments of Si and Ge are negligibly small as inFig 4(a, b), but Ga substituent possess some partial moment The moments of Al are the negative and small values, while the Co and Mn moments are the positive values and most of the moment come from Mn This abnormal local moment of Mn arises from a small d-d wave function overlapping and hence larger exchange interaction due to the decreasing MneMn dis-tances.Fig 4(c) depicts the band gap for each composition The band gap is also inﬂuenced by the EN term Additionally, it depends on the distribution of valence electrons i.e degree of delocalization of valence electrons In all substituents EN is in order Ge> Si > Ga Fig (a) Lattice constant (b) Bulk modulus in Co2MnAl1xZx(where Z¼ Si, Ge and Ga) alloys

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Thus Ge then Si is more electronegative than Ga so that it interacts with the host atoms more strongly which offers large enough bonding-anti-bonding splitting than Ga substitution Therefore, band gap is found to be maximum for Co2MnAl.75Ge.25and

mini-mum Co2MnAl.25Ga.75composition[15] It is available in literature

that the semiconductor properties, band gap energy and lattice constant are strongly related with EN and pseudopotential radii i.e difference in the atomic size That means the variation in band gap with increasing Ge and Si content for Co2MnAl1xZx(Z¼ Si, Ge)

alloy might be the result of the competition between attractive and repulsive forces due to EN difference Thus from application point of view, EN and atomic radius play important role for making good spintronics device

4 Conclusion

In brief, we performed the comparative study of mechanical, electrical and magnetic properties of Co2MnAl1xZxHeusler alloys

(Z¼ Si, Ge and Ga and x ¼ 0, 0.25, 0.75 and 1) using the EN model and WEIN2K code for numerical calculations The electronic den-sity distribution depicts the ionic nature of Co2MnAlxZx alloy

systems The alloys with Z¼ Ga, Ge follow the Vegard's law while Co2MnAl1xSixdoes not follow the same trend The Co2MnAl.25Si.75

alloy is found to more compressible than others For the magnetic moment and the band gap, however, a similar behaviour is found for the alloys with Z¼ Si and Ge They possess larger magnetic moment and band gap with respect to Co2MnAl1xGaxsystem This

ﬁnding is attributed to the EN difference, degree of delocalization of valence electron, atomic size and atomic number, respectively They play an important role for making good spintronics devices Author contributions

The equal work was performed by Shiv Om Kumar and Vineeta Shukla in writing and reviewing the manuscript and above work was done under the supervision of Sanjeev Kumar Srivastava

Acknowledgments

Shiv Om Kumar and Vineeta Shukla are thankful to IIT Khar-agpur and MHRD, India for providing the necessary facilities and ﬁnancial support, respectively

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