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

TL;DR

This paper presents a theoretical analysis of twofold and fourfold symmetric anisotropic magnetoresistance effects in ferromagnets, deriving formulas and explaining experimental temperature-dependent behaviors in Fe4N through crystal field and distortion effects.

Contribution

It introduces a model combining conduction and localized d states to derive expressions for AMR symmetry coefficients, linking them to crystal field effects and experimental observations.

Findings

Derived general expressions for AMR symmetry coefficients.

Identified dominant terms related to density of states differences.

Reproduced experimental temperature dependence in Fe4N.

Abstract

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 ($E_{\rm F}$) between the $d\varepsilon$ and $d\gamma$ states, and that in $C_4$ is proportional to the difference in the PDOSs at $E_{\rm F}$ among the $d\varepsilon$ states. Using the dominant terms, we next analyze the experimental results for Fe$_4$N, in which $|C_2|$ and $|C_4|$ increase with decreasing temperature. The experimental results can be reproduced by assuming that the tetragonal distortion increases with decreasing temperature.