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

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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 (C₂) and that of the fourfold symmetric term (C₄) in the AMR ratio. In the case of a strong ferromagnet, the dominant term in C₂ is proportional to the difference in the partial densities of states (PDOSs) at the Fermi energy (EF) between the dε and dγ states, and that in C₄ is proportional to the difference in the PDOSs at EF among the dε states. Using the dominant terms, we next analyze the experimental results for Fe₄N, in which |C₂| and |C₄| increase with decreasing temperature. The experimental results can be reproduced by assuming that the tetragonal distortion increases with decreasing temperature.