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

Abstract

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 accurately established by fitting to the experimentally observed dependence of transition angles of PHR measured with different applied field strengths. Using the known dependence of magnetic anisotropy of GaMnAs on temperature, we also show that this method applies reliably as the temperature varies.

Quantitative determination of spin–orbit-induced magnetic field in GaMnAs by field-scan planar Hall measurements

“…Specifically, the switching fields occurring during magnetization reversal are sensitive functions of the scanning field orientation, and—as will be shown—this dependence can be used to obtain the SOI values. The magnetization reversal processes are analyzed based on magnetic free energy 24 , 29 , which is given by where and are uniaxial and the cubic anisotropy coefficients, respectively. The effective SOI field and external magnetic field are expressed as and , respectively.…”

“…This trend is consistent with earlier reports in which the SOI field was obtained from the angular dependence of PHR measurements 16 , 17 , 19 , 20 . For direct comparison, we also carried out the angular dependent PHR measurements on our present GaMnAs film, at the same current densities as those used in the field scan PHR measurements, and obtained the values of the SOI fields following the analysis as developed in the Ref 24 . These values are plotted as open squares in Fig.…”

“…The red solid circles are obtained by analyzing the field scan PHR measurement at several different directions, as discussed in this paper. The black open symbols represent the SOI fields obtained by using methods developed in Ref 24 . Both methods provide consistent results, showing that the SOI field increases monotonically with increasing current density.…”

“…In that work, the SOI field was determined by considering a geometrical construction that involves the applied magnetic field and the difference in magnetization switching angles. Later, a new method was developed by considering magnetic free energy based on domain nucleation and propagation model for that occurs in magnetization reversal process observed by rotating a magnetic field 24 . However, field scan measurements are much more commonly used for studying the process of magnetization reversal, and it is therefore desirable to use such measurements to study the SOI field.…”