Spin polarization ratios of resistivity and density of states estimated from anisotropic magnetoresistance ratio for nearly half-metallic ferromagnets

We derive a simple relational expression between the spin polarization ratio of resistivity, $P_{\rho }$, and the anisotropic magnetoresistance ratio $\Delta \rho/\rho$, and that between the spin polarization ratio of the density of states at the Fermi energy, $P_{\mathrm{D}\mathrm{O}\mathrm{S}}$, and $\mathrm{\Delta }\rho \mathrm{/}\rho$ for nearly half-metallic ferromagnets. We find that $P_{\rho }$ and $P_{\mathrm{D}\mathrm{O}\mathrm{S}}$ increase with increasing $\mathrm{\mid }\mathrm{\Delta }\rho \mathrm{/}\rho \mathrm{\mid }$ from 0 to a maximum value. In addition, we roughly estimate $P_{\rho }$ and $P_{\mathrm{D}\mathrm{O}\mathrm{S}}$ for a Co${}_2$FeGa${}_{0.5}$Ge${}_{0.5}$ Heusler alloy by substituting its experimentally observed $\mathrm{\Delta }\rho \mathrm{/}\rho$ into the respective expressions.