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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.