## Abstract

Using the electron scattering theory, we obtain analytic expressions for anisotropic magnetoresistance (AMR) ratios for ferromagnets with a crystal field of tetragonal symmetry. Here, a tetragonal distortion exists in the [001] direction, the magnetization M lies in the (001) plane, and the current I flows in the [100], [010], or [001] direction. When the I direction is denoted by i, we obtain the AMR ratio as AMR^{i}ð_{i}Þ ¼ C^{i} _{0} þ C^{i} _{2} cos 2_{i} þ C^{i} _{4} cos 4_{i} . . . ¼ C^{i} _{j} cos j_{i}, with i = [100], [110], and [001], ϕ_{[100]} = ϕ_{[001]} = ϕ, and ϕ_{[110]} = ϕA. The quantity ϕ (ϕA) is the ^{P} j¼0;2;4;... relative angle between M and the [100] ([110]) direction, and C^{i} _{j} is a coefficient composed of a spin–orbit coupling constant, an exchange field, the crystal field, and resistivities. We elucidate the origin of C^{i} _{j} cos j_{i} and the features of C^{i} _{j}. In addition, we obtain the relation C^{½} _{4} ^{100} ¼ C^{½} _{4} ^{110}, which was experimentally observed for Ni, under a certain condition. We also qualitatively explain the experimental results of C^{½} _{2} ^{100}, C^{½} _{4} ^{100}, C^{½} _{2} ^{110}, and C^{½} _{4} ^{110} at 293 K for Ni.

Original language | English |
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Article number | 034706 |

Journal | Journal of the Physical Society of Japan |

Volume | 88 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2019 |