# Theoretical Study on Four-fold Symmetric Anisotropic Magnetoresistance Effect in Cubic Single-crystal Ferromagnetic Model

## TL;DR

This paper provides a theoretical explanation for the four-fold symmetric component of anisotropic magnetoresistance in cubic ferromagnetic metals, attributing it to spin--orbit interaction effects on impurity 3d levels.

## Contribution

It introduces a model based on the Anderson impurity framework with a four-fold symmetric crystal field to explain the four-fold AMR component.

## Key findings

- The four-fold AMR component arises from fourth-order spin--orbit interaction effects.
- Impurity 3d level splitting due to SOI is key to the four-fold symmetry.
- Analytical and numerical results show parameter dependencies of the AMR component.

## Abstract

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.