Twofold and Fourfold Symmetric Anisotropic Magnetoresistance Effect in a Model with Crystal Field

We theoretically study the twofold and fourfold symmetric anisotropic magnetoresistance (AMR) effects of ferromagnets. We here use the two-current model for a system consisting of a conduction state and localized d states. The localized d states are obtained from a Hamiltonian with a spin-orbit interaction, an exchange field, and a crystal field. From the model, we first derive general expressions for the coefficient of the twofold symmetric term (C-2) and that of the fourfold symmetric term (C-4) in the AMR ratio. In the case of a strong ferromagnet, the dominant term in C-2 is proportional to the difference in the partial densities of states (PDOSs) at the Fermi energy (EF) between the de and d. states, and that in C-4 is proportional to the difference in the PDOSs at EF among the de states. Using the dominant terms, we next analyze the experimental results for Fe4N, in which vertical bar C-2 vertical bar and vertical bar C-4 vertical bar increase with decreasing temperature. The experimental results can be reproduced by assuming that the tetragonal distortion increases with decreasing temperature.