Angle-Dependent Anisotropic Magnetoresistance Under the Competition Between Anisotropic Field and Magnetic Field

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.