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Measurement of Orthogonal Spin orbit Field Current along the [010] Crystallographic Direction in GaMnAs Film
We investigated orthogonal spin-orbit-induced (SOI) fields generated by a current along the 010 crystallographic direction in a ferromagnetic semiconductor GaMnAs film with 4-fold in-plane magnetic anisotropy. To perforem this study, we fabricated a Hall device aligned with the 010 direction, and carried out magnetoresistance (MR) measurements to monitor the magnetization reversal process in the film. Field scans of MR measured with opposite current polarities (Fig. 1(a)) clearly show shifts in opposite direction, indicating the presence of current-direction-dependent effective magnetic fields. The observed hysteresis shift is caused by the simultaneous presence of Dresselhaus and Rashba SOI fields that are perpendicular to each other when the current is oriented along the 010 direction. In order to quantify the two SOI fields, we performed angle-dependent MR measurements with two opposite current polarities (Fig. 1(b)). The splitting in transition angles between the two polarities increases with decreasing magnetic field. The equation relating this splitting and the applied external field was developed based on magnetic free energy that includes the effect of the two orthogonal SOI fields. Based on this formulation, we were able to obtain the magnitudes of the Rashba and Dresselhaus SOI fields from the magnetization transition angles as 0.568 and 1.632 Oe, respectively, at current density of 4.80×105 A/cm2 (2mA).
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