Anisotropic Magnetoresistance Effect: General Expression of AMR Ratio and Intuitive Explanation for Sign of AMR Ratio

TL;DR

This paper derives a comprehensive formula for the anisotropic magnetoresistance (AMR) ratio in ferromagnets using a two-current model, providing insights into the sign of AMR and matching experimental data for Ni and half-metallic ferromagnets.

Contribution

It presents a general expression for the AMR ratio based on a two-current model and offers an intuitive explanation for the sign of the AMR ratio, linking it to s-d scattering processes.

Findings

Derived a general AMR ratio expression for ferromagnets.

Analyzed AMR ratios of Ni and half-metallic ferromagnets, matching experiments.

Provided an intuitive explanation for the sign of the AMR ratio.

Abstract

We derive the general expression of the anisotropic magnetoresistance (AMR) ratio of ferromagnets for a relative angle between the magnetization direction and the current direction. We here use the two-current model for a system consisting of a spin-polarized conduction state (s) and localized d states (d) with spin-orbit interaction. Using the expression, we analyze the AMR ratios of Ni and a half-metallic ferromagnet. These results correspond well to the respective experimental results. In addition, we give an intuitive explanation about a relation between the sign of the AMR ratio and the s-d scattering process.