Prediction of half-metallic gap formation and Fermi level position in Co-based Heusler alloy epitaxial thin films through anisotropic magnetoresistance effect

We have investigated the temperature $(T)$ dependence of the anisotropic magnetoresistance (AMR) effect of ${\mathrm{Co}}_{2}{\mathrm{FeGa}}_{0.5}{\mathrm{Ge}}_{0.5}$ (CFGG) epitaxial thin films having different compositions and atomic orders to examine the relation between AMR and the half-metallic electronic structure based on a developed theoretical model. The $T$ dependence of the resistance change (\ensuremath{\Delta}\ensuremath{\rho}) of the AMR normalized at 10 K is minimal in the CFGG films having a standard composition and high atomic order. In contrast, the films having a large atomic disorder due to the Co-rich composition exhibit a large reduction of \ensuremath{\Delta}\ensuremath{\rho} with $T$. Our theoretical model of AMR well explains this behavior; namely, the half-metallic ferromagnets having the Fermi level $({E}_{\mathrm{F}})$ around the center of the half-metallic gap are predicted to show a small $T$ dependence of \ensuremath{\Delta}\ensuremath{\rho} because of no/few localized $d\ensuremath{\downarrow}$ states at ${E}_{\mathrm{F}}$. On the contrary, a large change of \ensuremath{\Delta}\ensuremath{\rho} with $T$ is expected for the half-metallic materials having ${E}_{\mathrm{F}}$ close to gap edges or large in-gap states because of the contribution of thermally excited s-d scattering involving the $d\ensuremath{\downarrow}$ states. Moreover, we have also investigated the variation of \ensuremath{\Delta}\ensuremath{\rho} with $T$ for the thin films of various half-metallic Co-based Heusler alloys and found the behavior that agrees with our theoretical prediction. The present study proves that the formation of a half-metallic gap and the position of ${E}_{\mathrm{F}}$ in a half-metallic material are readily predictable from the $T$ dependence of \ensuremath{\Delta}\ensuremath{\rho} of the AMR effect, which can be a facile way for efficient screening of half-metallic materials.