First-principles study of new quaternary Heusler compounds without 3d transition metal elements: ZrRhHfZ (ZÂ =Â Al, Ga, In)

Plane-wave pseudo-potential methods based on density functional theory are employed to investigate the electronic structures, and the magnetic and half-metallic properties of the newly designed quaternary Heusler compounds ZrRhHfZ (Z = Al, Ga, In) without 3d transition metal elements. The calculated results show that ZrRhHfZ (Z = Al, Ga, In) compounds are half-metallic, with 100% spin polarization around the Fermi level. The structural stability of these compounds has been tested from the aspects of their cohesion energy and formation. The spin-flip/half-metallic gaps of ZrRhHfZ (Z = Al, Ga, In) compounds are quite large, with values of 0.2548 eV, 0.3483 eV, and 0.2866 eV, respectively. These compounds show Slater-Pauling behavior, and the total spin magnetic moment per unit cell (Mt) scales with the total number of valence electrons (Zt) following the rule: Mt = Zt − 18. The magnetization of ZrRhHfZ (Z = Al, Ga, In) compounds mainly comes from the 4d electrons of the Zr atoms and the 5d electrons of the Hf atoms. Furthermore, the effects of uniform strain and tetragonal deformation on the half metallicity has been investigated in detail, which is important for practical application. Finally, we reveal that the half-metallicity can be maintained when the Coulomb interactions are considered.