Electronic structure, Mechanical and Thermodynamic properties of CoYSb (Y= Cr, Mo, W) half-Heusler compounds as potential spintronic materials

We used Density Functional Theory (DFT) calculations to investigate the structural, electronic, magnetic, mechanical and thermodynamic properties of CoYSb (Y = Cr, Mo and W) compounds. These are XYZ type half-Heusler alloys, which also exist in the face centred cubic MgAgAs-type structure and conform to F ¯43 m space group. We computed these properties in three dif-ferent atomic arrangements known as Type-I, Type-II and Type-III phases. In all these phases, the alloys were found to be in the ferromagnetic state. Furthermore, the calculated electronic band structure and the total electronic density of states indicated a metallic behaviour in CoWSb, nearly half-metallic in CoMoSb and half-metallic in CoCrSb, with a minority-spin band gap of 0.81 eV. Furthermore, the calculated mechanical properties predicted an anisotropic behaviour of these alloys in their stable phase. Finally, due to its high Debye temperature value, CoCrSb shows stronger covalent bonding than CoMoSb and CoWSb, respectively. investigated the structural,electronic, magnetic, 27 mechanical and thermodynamics properties of a series of half-Heusler com- 28 pounds, CoYSb (Y=Cr, Mo, W). We identify the most stable phases and 29 investigate the impact of the lattice parameter on the magnetic properties for 30 each stable phase of HH CoYSb (Y=Cr, Mo, W). To shed some light on the 31 metallic behaviour, electronic transport, mechanical stability and strength of 32 chemical bonding between their atoms, we have computed and analyzed the 33 electronic spin bands and spin density of states (DOS), the response to shear 34 deformation and unidirectional compression and the Debye temperature 35 the ﬁtted of show that the Type-I the


Introduction
1 Ternary half-Heusler (HH) compounds involving Co-atom have recently 2 attracted attention due to their high curie temperature and structural simi-3 larity with binary semiconductors with zinc-blende (ZB) structure that makes 4 them potential candidates in optoelectronic and spintronic applications such 5 as quantum sensors, resistors and computers devices [1]- [4], topological insu-6 lators [5]- [6], and thermoelectric devices [7], [14]. The wide range of usage of 7 HH in applications is due to its excellent electrical, mechanical and electronic 8 properties as well as thermal stability. 9 The crystal structure, C1 b , of any HH alloy is similar to the structure, 10 L2 1 , of a full-Heusler alloy (X 2 YZ) but missing one X atom. The absence of 11 inversion symmetry due to an empty X site and the low coordination number 12 of the d-band metals in the HH alloys are believed to be essential for these 13 materials novel electronic and magnetic properties. Some research groups 14 have reported three possible distinct atomic arrangements, called Type-I, 15 Type-II, and Type-III phases, due to this missing X atom in the HH alloy and has a spin-minority gap.

26
In this paper, we have investigated the structural,electronic, magnetic, 27 mechanical and thermodynamics properties of a series of half-Heusler com-    Type-II and (c) Type-III. In Table 1  [b] [c] ( Fig.1 and Table 2). Also, the lattice constants are smaller in this phase and bulk moduli more significant than in other structural phases. However, large

65
The calculated total and partial magnetic moments for all phases are 66 listed in Table 3. It is seen that for CoCrSb, irrespective of the structural 67 phase, the major contribution to the total magnetic moment comes from 68 the Y (Cr) atom. Whereas, for the other two materials, i.e. CoYSb (Y = the magnetic moment come from the Y atom. As shown in Table 3    [a] [a]   (2) The calculated elastic constants values for the stable Type-I structures 146 of CoYSb (Y=Cr, Mo, and W) satisfy the above stability criteria. Hence, 147 these compounds are mechanically stable, as shown from our results in Table   148 5. were calculated by using the following equations: spectively. The higher the value B, the more its resistance to deformation 158 due to pressure. CoWSb resistance to pressure is stronger than that of Co-

159
MoSb and CoCrSb alloy, respectively, as shown in Table 5. The value of 160 shear modulus G shows the resistance of a material to deformation by shear 161 stress. The higher the value G, the higher its resistance to shear stress.

162
Hence, CoCrSb>CoMoSb>CoWsb. The Young's modulus E characterizes 163 the material's stiffness, and the higher the value E, the stiffer is the material.

164
Therefore, as shown in Table 5, CoCrSb is stiffer than CoMoSb, and CoWSb 165 is the least stiffer. Also, the unidirectional elastic constant C 11 is much higher 166 than C 44 indicating that these compounds present weaker resistance to pure 167 shear deformation compared to resistance to unidirectional compression. We also deduced the cubic Shear anisotropy factor [40] for these com-  It can be seen from Fig. 6 the trend of the specific heat towards the

168
Where (v l ) is the compressional velocity and (v s ) the shear sound velocity.

202
The average sound velocity (v m ) is expressed in terms of compressional and 203 shear sound velocities, as stated below.
The Debye temperature θ D is thus expressed as  These alloys conform to F43m space group in the three possible atomic ar-218 rangements -the so called Type-I, Type-II and Type-III structural phases. 219 We determined and reported the stable atomic positions of these alloys. The