TY - JOUR

T1 - Theoretical study on anisotropic magnetoresistance effects of i == [100], I == [110], and I == [001] for ferromagnets with a crystal field of tetragonal symmetry

AU - Kokado, Satoshi

AU - Tsunoda, Masakiyo

N1 - Funding Information:
Acknowledgments This work has been supported by the Cooperative Research Project (H26=A04) of the RIEC, Tohoku University, and a Grant-in-Aid for Scientific Research (C) (No. 25390055) from the Japan Society for the Promotion of Science.
Publisher Copyright:
Physical ©2019 Society The Author(s) of Japan

PY - 2019

Y1 - 2019

N2 - 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 AMRiðiÞ ¼ Ci 0 þ Ci 2 cos 2i þ Ci 4 cos 4i . . . ¼ Ci j cos ji, 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 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.

AB - 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 AMRiðiÞ ¼ Ci 0 þ Ci 2 cos 2i þ Ci 4 cos 4i . . . ¼ Ci j cos ji, 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 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.

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U2 - 10.7566/JPSJ.88.034706

DO - 10.7566/JPSJ.88.034706

M3 - Article

AN - SCOPUS:85066745131

VL - 88

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 3

M1 - 034706

ER -