Determination of current-induced spin-orbit effective magnetic field in GaMnAs ferromagnetic semiconductor

We report a method for accurate determination of the strength of the current-induced spin-orbit (SO) field in ferromagnetic GaMnAs films. The SO-field manifests itself in the form of a hysteresis between planar Hall resistances (PHR) measured with positive and negative currents as an applied magnetic field is rotated in the sample plane at constant field strength. The width of the hysteresis, which is related to the strength of the SO-field, is observed to change significantly for different values of the rotating external field strength. Since the SO field occurring at a given current is an intrinsic property of the crystal, such a field dependence of the hysteresis indicates that the width of the hysteresis measured with a single field strength is insufficient for determining the SO field. However, using a model based on magnetic free energy that includes the effects of magnetic anisotropy and the SO-field as developed in the present paper, we show that the SO field for a given current density can be acc...