Theoretical study on anisotropic magnetoresistance effects of I//[100], I//[110], and I//[001] for ferromagnets with a crystal field of tetragonal symmetry

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 AMRi(φi) = Ci 0 + Ci 2 cos 2φi+Ci 4 cos 4φi . . . = Σ j=0,2,4,. Ci j cos jφi, with i = [100], [110], and [001], φ[100] = φ[001] = φ, and φ[110] = φ'. The quantity φ (φ') is the relative angle between M and the [100] ([110]) 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[100] 4 = -C[110] 4 , which was experimentally observed for Ni, under a certain condition. We also qualitatively explain the experimental results of C[100] 2 , C[100] 4 , C[110] 2 , and C[110] 4 at 293 K for Ni.