Electronic Structure and Half-Metallicity in the Zr₂RuZ (Z = Ga, In, Tl, Ge, Sn, and Pb) Heusler Alloys

The electronic structures, magnetic properties and half-metallicity in $Zr_2RuZ$ (Z = Ga, In, Tl, Ge, Sn, and Pb) alloys with $AlCu_2Mn-$ and $CuHg_2Ti$-type structures were investigated using first-principles density functional theory (DFT) calculations. The calculations showed that $Zr_2RuIn$, $Zr_2RuTl$, $Zr_2RuSn$, and $Zr_2RuPb$ compounds with $CuHg_2Ti$-type structures were half-metallic ferromagnets with half-metallic band gaps of 0.18, 0.24, 0.22, and 0.27 eV, respectively. The half-metallicity originated from d-d and covalent hybridizations between the transition metals Zr and Ru. The total magnetic moments of the $Zr_2RuZ$ (Z = In, Tl, Sn, and Pb) compounds with $CuHg_2Ti$-type structures were integer values of $1{\mu}B$ and $2{\mu}B$, which is in agreement with Slater-Pauling rule ($M_{tot}=Z_{tot}-18$). Among these compounds, $Zr_2RuIn$ and $Zr_2RuTl$ were half-metals over relatively wide regions of the lattice constants, indicating that these two new Heusler alloys are ideal candidates for use in spintronic devices.