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 AMRiðiÞ ¼ Ci 0 þ Ci 2 cos 2i þ Ci 4 cos 4i . . . ¼ Ci j cos ji, with i = , , and , ϕ = ϕ = ϕ, and ϕ = ϕA. The quantity ϕ (ϕA) is the P j¼0;2;4;... 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 ji and the features of Ci j. In addition, we obtain the relation C½ 4 100 ¼ C½ 4 110, which was experimentally observed for Ni, under a certain condition. We also qualitatively explain the experimental results of C½ 2 100, C½ 4 100, C½ 2 110, and C½ 4 110 at 293 K for Ni.
ASJC Scopus subject areas
- Physics and Astronomy(all)