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

## TL;DR

This paper introduces a linear-response-based DFT+U method to accurately investigate and tune the half-metallic electronic structures of Co-based full Heusler alloys, revealing key orbital contributions and stability factors.

## Contribution

The study develops and applies a linear-response DFT+U approach to Co-based Heusler alloys, providing insights into their electronic structures and methods to tune their half-metallicity.

## Key findings

- The LR-based DFT+U method yields reasonable correlation parameters for Y sites.
- The Co site correlation can lead to unphysical ground states if overestimated.
- The half-metallic gap in Co2MnSi originates from specific Co orbitals and hybridizations.

## Abstract

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.