Theoretical Study on Twofold and Fourfold Symmetric Anisotropic Magnetoresistance Effect

We theoretically study the twofold and fourfold symmetric anisotropic magnetoresistance (AMR) effect $[1]$. We first extend our previous model $[2]$ to a model including the crystal field effect $[1]$. Using the model, we next obtain an analytical expression of the AMR ratio, i.e., ${\rm AMR}(\phi)$=$C_0 + C_2 \cos (2 \phi) + C_4 \cos (4 \phi)$, with $C_0$=$C_2 - C_4$ $[1]$. Here, $\phi$ is the relative angle between the magnetization direction and the electric current direction and $C_2$ ($C_4$) is a coefficient of the twofold (fourfold) symmetric term. The coefficients $C_2$ and $C_4$ are expressed by a spin-orbit coupling constant, an exchange field, a crystal field, and s-s and s-d scattering resistivities. Using this expression, we analyze the experimental results for Fe$_4$N $[3]$, 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. \\ $[1]$ S. Kokado {\it et al}., J. Phys. Soc. Jpn. {\bf 84} (2015) 094710. \\ $[2]$ S. Kokado {\it et al}., J. Phys. Soc. Jpn. {\bf 81} (2012) 024705. \\ $[3]$ M. Tsunoda {\it et al}., Appl. Phys. Express {\bf 3} (2010) 113003.