Role of electronegativity on the bulk modulus magnetic moment and band gap of co2mnal based heusler alloys

Journal of Science: Advanced Materials and Devices (2019) 158e162 Contents lists available at ScienceDirect Journal of Science: Advanced Materials and Devices journal homepage: www.elsevier.com/locate/jsamd Original Article Role of electronegativity on the bulk modulus, magnetic moment and band gap of Co2MnAl 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 a b s t r a c t Article history: Received January 2019 Received in revised form February 2019 Accepted February 2019 Available online 10 February 2019 In this paper, we have presented the comparative study of mechanical, electrical and magnetic properties of Co2MnAl1ÀxZx Heusler alloy with Z ¼ 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 Co2MnAl1ÀxZx with Z ¼ Ga, Ge follow the Vegard's law while Co2MnAl1ÀxSix does not follow the same trend Among all composition Co2MnAl.25Si.75 alloy is found to be more compressible Electronic density distribution depicts the ionic nature of Co2MnAl1ÀxZx alloy systems The Co2MnAl1ÀxZx with Z ¼ Si, Ge possess larger magnetic moment and band gap with respect to Co2MnAl1ÀxGax system 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/) Keywords: Heusler alloy Lattice parameter Bulk modulus (BM) Magnetic moment Band gap 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 wyckoffpositions 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 positioned 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, helimagnetism, antiferromagnetism, Pauli paramagnetism or heavy fermionic behaviour [5] Therefore, understanding of electrical, * 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 mechanical and magnetic behaviors of these alloys is very important for application point of view It is well established that mechanical 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 temperature 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, disordered phase like A2, B2 or DO3 of 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 Co2MnAl1ÀxZx (where Z ¼ Si, Ge and Ga) Heusler alloy using density https://doi.org/10.1016/j.jsamd.2019.02.001 2468-2179/© 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/) A.-S Om Kumar et al / Journal of Science: Advanced Materials and Devices (2019) 158e162 159 functional theory based method to search the materials of potential application Calculation method The numerical investigations were accomplished by using the Density Functional Theory (DFT) based WIEN2k code [10] The exchange 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 cutoff 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   super cells were made for Co2MnAl1ÀxZx (where Z ¼ Ge, Si, Ga except x ¼ 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 a ¼ 5.749 Å as we reported previously [12] Results and discussion Fig Calculated total energy as the function of volume of Co2MnGa/Al Heusler alloy In order to evaluate the mechanical properties of Co2MnAl1ÀxZx (where Z ¼ Si, Ge and Ga and x ¼ 0.0, 0.25, 0.75, and 1.0 compositions) 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 in Fig We found the equilibrium lattice parameters (a0) and the bulk modulus (B) from the Birch Murnaghan equation as given by [13] ETot Vị ẳ E0 ỵ VB * B0 ðB0 À 1Þ " V0 V B  #  V ỵ V (1) where E0, B and B0 refer 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: Fig Crystal structure of Co2MnGa Heusler alloy B ¼ ÀV vP v2 E ¼V vV vV (2) where P and V are the pressure and volume of the system, respectively It can be seen from Fig (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, Co2MnAl1ÀxSix follow 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 Co2MnAl1ÀxZx (where Z ¼ Si, Ge and Ga) alloys have been shown in Fig (b) It is clear that all Ge, Si and Ga substituted composition upshot bigger modulus relative to parent Co2MnAl alloy except only Co2MnAl.25Si.75 composition Interestingly, all Co2MnAl1ÀxZx (where Z ¼ 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 Co2MnAl.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: Co2MnAl1ÀxSix > Co2MnAl1ÀxGax > Co2MnAl1ÀxGex Above variation in bulk modulus after the addition of 25% Si, Ge and Ga substitution 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 interaction 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% substitution of Ge, Si or Ga in parent alloys [16] Among all 160 A.-S Om Kumar et al / Journal of Science: Advanced Materials and Devices (2019) 158e162 Fig (a) Lattice constant (b) Bulk modulus in Co2MnAl1ÀxZx (where Z ¼ Si, Ge and Ga) alloys 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 a) 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 density distribution curve Here only curve for Co2MnAl and Co2MnAl.25Ge.75 alloys have been shown in Fig 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 Co2MnAl1ÀxZx (Z ¼ Si, Ge and Ga) alloys have been depicted in Fig (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: mtotal ¼ Ztotal-24 where Ztotal is the total number of valence electrons The total number of electrons Ztotal is given by the sum of the number of spin-up (N[) and spindown (N[) electrons (Ztotal ẳ N[ỵNY) and the total moment mtotal is given by the difference of the number of spin-up and spin-down electrons (mtotal ¼ N[ÀNY) [17] It is found that total moment follow the Slater-Pauling rule for Ge as well but shows a little deviation for Co2MnAl.75Ge.25 1% and Co2MnAl.25Si.75 almost 9% However, in case of Ga replacement, particularly 25% composition of Ga, major deviation occurred For more details, Fig (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.75 alloy 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 much fluctuation in total as well as in partial moments It is obvious from Fig (a) that for Co2MnAl.75Ga.25 composition total moments decreases while total moment increases for 75% and 100% Ga substituted alloys On other hand, Co, Mn and Ga moment contributions were least rather Al for Co2MnAl.75Ga.25 composition In case of Co2MnAl.25Ga.75, total and partial moments follow the reverse trend Firstly, it is anticipated that large fluctuation 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 in Fig (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 distances 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 Partial magnetic moment of Al, (b) magnetic moment of Ga, Ge, Si, (c) Band gap plot of Co2MnAl1ÀxZx (Z ¼ Si, Ge, Ga) Heusler alloys A.-S Om Kumar et al / Journal of Science: Advanced Materials and Devices (2019) 158e162 161 Fig Electron density plot for (a) Co2MnAl and (b) Co2MnAl.25Ge.75 alloy Fig Total magnetic moment, (b) partial magnetic moment of Co, (c) partial magnetic moment of Mn in Co2MnAlZx (Z ¼ Si, Ge, Ga) Heusler alloys 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.25 and minimum Co2MnAl.25Ga.75 composition [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 Co2MnAl1ÀxZx (Z ¼ 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 Conclusion In brief, we performed the comparative study of mechanical, electrical and magnetic properties of Co2MnAl1ÀxZx Heusler alloys (Z ¼ 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 density distribution depicts the ionic nature of Co2MnAlÀxZx alloy systems The alloys with Z ¼ Ga, Ge follow the Vegard's law while Co2MnAl1ÀxSix does 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 Z ¼ Si and Ge They possess larger magnetic moment and band gap with respect to Co2MnAl1ÀxGax system 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 Kharagpur and MHRD, India for providing the necessary facilities and financial support, respectively References [1] F Heusler, Über manganbronze und über die synthese magnetisierbarer legierungen aus unmagnetischen metallen, Angew Chem 17 (9) (1904) 260e264 [2] S.O Kumar, V Shukla, S.K Srivastava, Ferromagnetic behavior of Si substituted Co2MnAl.25Si.75 full Heusler alloy, Mater Lett 225 (2018) 134e137 [3] F Casper, T Graf, S Chadov, B Balke, C Felser, Half-Heusler compounds: novel materials for energy and spintronic applications, Semicond Sci 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arises... electrons Ztotal is given by the sum of the number of spin-up (N[) and spindown (N[) electrons (Ztotal ẳ N[ỵNY) and the total moment mtotal is given by the difference of the number of spin-up and. .. for the alloys with Z ¼ Si and Ge They possess larger magnetic moment and band gap with respect to Co2MnAl1 ÀxGax system This finding is attributed to the EN difference, degree of delocalization of