Anisotropic magnetoresistance (AMR) is generally characterized by the variation of resistance under the rotation of magnetic field. When the magnetic field is much stronger than an anisotropic field, the resistance is proportional to cos $^{2}\alpha $ , where $\alpha $ is an angle between current and the magnetic field. However, when the magnetic-field strength ( $H$ ) is comparable with the anisotropic field ( $H_{a}$ ), the angle-dependent AMR depends on the competition between $H$ and $H_{a}$ . In this article, we report our numerical calculation about angle-dependent AMR under weak magnetic field for different kinds of magnetic anisotropy energy. As to uniaxial anisotropy field, when current is parallel to the anisotropic field, the angle for the extreme resistance ( $\varphi _{e}$ ) in the angle-dependent AMR curve is fixed no matter how weak the magnetic field is. While when the easy axis deviates from current at an angle ( $\varepsilon$ ), the $\varphi _{e}$ shifts under a weak magnetic field by an angle that is relevant to $\varepsilon $ . The magnetic-field-dependent $\varphi _{e}$ can also be observed for fourfold anisotropy and the combination of uniaxial and fourfold anisotropy. This work provides a possible route for analyzing the magnetic anisotropic field via the AMR measurement.

中文翻译：

---

各向异性场与磁场竞争下的角度相关各向异性磁阻

各向异性磁阻（AMR）的一般特征是在磁场旋转下电阻会发生变化。当磁场远强于各向异性场时，电阻与 cos 成正比 $^{2}\alpha $ ，哪里 $\alpha $ 是电流和磁场之间的夹角。然而，当磁场强度（ $H$ ) 与各向异性场 ( $H_{a}$ )，角度相关的 AMR 取决于之间的竞争 $H$ 和 $H_{a}$ . 在本文中，我们报告了在弱磁场下不同类型磁各向异性能量的角度相关 AMR 的数值计算。对于单轴各向异性场，当电流平行于各向异性场时，极电阻的角度为（ $\varphi _{e}$ ) 在与角度相关的 AMR 曲线中是固定的，无论磁场有多弱。而当易轴以一定角度偏离电流时（ $\varepsilon$ ）， 这 $\varphi _{e}$ 在弱磁场下移动的角度与 $\varepsilon $ . 磁场相关 $\varphi _{e}$ 也可以观察到四重各向异性以及单轴和四重各向异性的组合。这项工作为通过 AMR 测量分析磁各向异性场提供了可能的途径。