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The structural, electronic, magnetic and mechanical properties of quaternary Heusler alloys ZrTiCrZ (Z  =  Al, Ga, In, Si, Ge, Sn): a first-principles study

The structural, electronic, magnetic and mechanical properties of the quaternary Heusler alloys ZrTiCrZ (Z  =  Al, Ga, In, Si, Ge, Sn) have been investigated firstly by using the first-principles calculations. The preferred configurations of the ZrTiCrZ alloys are all Y-type (I). At their equilibrium lattice constants, the ZrTiCrZ alloys are half-metallic (HM) ferrimagnets for Z  =  Al, Ga and In, while spin-gapless semiconductor (SGS) antiferromagnets (AFM) for Z  =  Si, Ge and Sn. The total magnetic moments μt of the ZrTiCrZ alloys are  −1 μB/f.u. for Z  =  Al, Ga and In, while 0 μB/f.u. for Z  =  Si, Ge and Sn, both linearly scaled with the total number of valence electrons Zt by Slater–Pauling rule μt=Zt−18. The elastic constants C11, C12 and C44 of the single crystal and the related elastic moduli G, B, E, υ and A of the polycrystalline aggregates are also calculated and used to study the mechanical stability of these alloys. Although the Curie temperatures TC of the ZrTiCrZ alloys are overestimated by using the mean field approximation (MFA), they can be better estimated by including the exchange interactions. Finally, the HM stabilities as well as the total and atomic magnetic moments of the ZrTiCrZ alloys (Z  =  Al, Ga, In) under either hydrostatic strain or tetragonal strain are also discussed.