Theoretical Study on Four-fold Symmetric Anisotropic Magnetoresistance Effect in Cubic Single-crystal Ferromagnetic Model

In this study, we present a theoretical interpretation of the experimental results that the anisotropic magnetoresistance (AMR) effect has a four-fold symmetric component, $c_4$, in cubic ferromagnetic metals. The theoretical model that we employ is based on the Anderson impurity model that includes a four-fold symmetric crystalline electric field, and we assume that the impurities have 3d electron orbitals and spin–orbit interaction (SOI). We describe the DC conductivity on the basis of the Kubo formula, and we investigate $c_4$ by analyzing the magnetization direction dependence of the resultant AMR ratio. Analytical and numerical calculations are performed; the analytical calculation reveals that $c_4$ arises from the fourth-order contribution of the SOI, and the numerical calculation provides the parameter dependencies of $c_4$ in our model. From the calculation results, we observe that the splitting of impurity 3d levels due to SOI is responsible for the existence of $c_4$ in cubic ferromagnetic metals.