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

Abstract

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 of the ZrTiCrZ alloys are −1 for Z = Al, Ga and In, while 0 for Z = Si, Ge and Sn, both linearly scaled with the total number of valence electrons by Slater–Pauling rule . The elastic constants , and of the single crystal and the related elastic moduli , , , and of the polycrystalline aggregates are also calculated and used to study the mechanical stability of these alloys. Although the Curie temperatures 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.