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, $P_{\rm DOS}$, and $\Delta \rho/\rho$ for nearly half-metallic ferromagnets. We find that $P_\rho$ and $P_{\rm DOS}$ increase with increasing $|\Delta \rho/\rho|$ from 0 to a maximum value. In addition, we roughly estimate $P_\rho$ and $P_{\rm DOS}$ for a Co$_2$FeGa$_{0.5}$Ge$_{0.5}$ Heusler alloy by substituting its experimentally observed $\Delta \rho/\rho$ into the respective expressions.