Anisotropic Magnetoresistance Effect: General Expression of AMR Ratio and Intuitive Explanation for Sign of AMR Ratio

We derive the general expression of the anisotropic magnetoresistance (AMR) ratio of ferromagnets for a relative angle between the magnetization direction and the current direction. We here use the two-current model for a system consisting of a spin-polarized conduction state (s) and localized d states (d) with spin-orbit interaction. Using the expression, we analyze the AMR ratios of Ni and a half-metallic ferromagnet. These results correspond well to the respective experimental results. In addition, we give an intuitive explanation about a relation between the sign of the AMR ratio and the s-d scattering process. Introduction The anisotropic magnetoresistance (AMR) effect, in which the electrical resistivity depends on a relative angle θ between the magnetization (Mex) direction and the electric current (I) direction, has been studied extensively both experimentally [1-5] and theoretically [1,6]. The AMR ratio is often defined by ( ) ( ) ρ θ ρ θ ρ ρ ρ ⊥