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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, $P_ρ$, and the anisotropic magnetoresistance ratio $Δρ/ρ$, and that between the spin polarization ratio of the density of states at the Fermi energy, $P_{\rm DOS}$, and $Δρ/ρ$ for nearly half-metallic ferromagnets. We find that $P_ρ$ and $P_{\rm DOS}$ increase with increasing $|Δρ/ρ|$ from 0 to a maximum value. In addition, we roughly estimate $P_ρ$ and $P_{\rm DOS}$ for a Co$_2$FeGa$_{0.5}$Ge$_{0.5}$ Heusler alloy by substituting its experimentally observed $Δρ/ρ$ into the respective expressions.