  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.
