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  direction, the magnetization M lies in the (001) plane, and the current I flows in the , , or  direction. When the I direction is denoted by i, we obtain the AMR ratio as AMRi(φi) = Ci 0 + Ci 2 cos 2φi+Ci 4 cos 4φi . . . = Σ j=0,2,4,. Ci j cos jφi, with i = , , and , φ = φ = φ, and φ = φ'. The quantity φ (φ') is the relative angle between M and the  () direction, and Ci j is a coefficient composed of a spin-orbit coupling constant, an exchange field, the crystal field, and resistivities. We elucidate the origin of Ci j cos jφi and the features of Ci j . In addition, we obtain the relation C 4 = -C 4 , which was experimentally observed for Ni, under a certain condition. We also qualitatively explain the experimental results of C 2 , C 4 , C 2 , and C 4 at 293 K for Ni.
|Publication status||Published - 2019 Mar 4|
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