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 firstprinciples 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 mu t of the ZrTiCrZ alloys are -1 mu(B) / f.u. for Z = Al, Ga and In, while 0 mu(B) / f.u. for Z = Si, Ge and Sn, both linearly scaled with the total number of valence electrons Z(t) by Slater-Pauling rule mu(t) = Z(t) - 18. The elastic constants C-11, C-12 and C-44 of the single crystal and the related elastic moduli G, B, E, v and A of the polycrystalline aggregates are also calculated and used to study the mechanical stability of these alloys. Although the Curie temperatures T-C 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.