Two-field measurements of spin-orbit-torque efficiency in crystalline (Ga,Mn)(As,P) ferromagnetic semiconductors

We investigated spin-orbit-torque (SOT) efficiency in a crystalline (Ga,Mn)(As,P) ferromagnetic film with out-of-plane anisotropy. By performing Hall resistance measurements with opposite current polarities, we identified current-induced SOT effects in magnetization transition. The SOT efficiency was then quantified by analyzing hysteresis shifts as a function of in-plane magnetic bias fields. We found that SOT efficiency depends on crystal direction along which current flows, consistent with the dependence of net spin-orbit fields (SOFs) in tensile-strained (Ga,Mn)(As,P) film. The highest efficiency (7.4 Oe/${10}^{5}\phantom{\rule{0.16em}{0ex}}\mathrm{A}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$) was observed for the $[1\overline{1}0]$ current direction, for which Dresselhaus- and Rashba-type SOFs are parallel and of the same sign in the film. Additionally, the SOT efficiency showed saturation behavior as a function of in-plane bias field, which suggests the presence of Dzyaloshinskii-Moriya interaction in the (Ga,Mn)(As,P) film due to its noncentrosymmetric crystal structure.