Linear-response-based DFT+U method for exploring half-metallic Co-based full Heusler alloys

The density functional theory (DFT)+U method based on the linear response (LR) theory was applied to investigate the electronic structures of Co-based ternary full Heusler alloy Co$_2Y$Si for exploring half-metallic (HM) ferromagnets with a wide HM gap. The LR-based DFT+U calculations tend to obtain a reasonable correlation parameter for $Y$ site, while the correlation of Co site misleads to the unphysical ground state due to the overestimated parameter value that arises from the delocalized electronic structure of Co. Furthermore, we found that the HM gap of Co$_2$MnSi originates from Co $e_u$ orbital in the conduction state and Co-Mn hybridizing $t_{2g}$ orbital in the valence state around the Fermi energy. This means that the HM gap is a tunable property by selecting the $Y$ element and/or mixing several elements into the $Y$ site through $t_{2g}$ atomic-orbital coupling. Our LR-based DFT+U method was extended to other ternary Co$_2Y$Si and quaternary Co$_2$($Y$,Mn)Si. We found that Co$_2$(Ti$_{0.25}$,Mn$_{0.75}$)Si and Co$_2$(Fe$_{0.25}$,Mn$_{0.75}$)Si show HM nature, with the Fermi energy being at almost the center of the minority band gap, which leads to high thermal stability.