Quantification of spin-orbit effective fields in (Ga,Mn)(As,P) ferromagnetic semiconductor films by second harmonic Hall voltage measurements

We investigate spin-orbit torque (SOT) effective fields in a (Ga,Mn)(As,P) ferromagnetic semiconductor (FMS) film with perpendicular magnetic anisotropy using second harmonic Hall voltage measurements. Both the first harmonic (${\mathrm{V}}_{1\ensuremath{\omega}}$) and second harmonic (${\mathrm{V}}_{2\ensuremath{\omega}}$) Hall voltage signals are recorded simultaneously as the external field is swept near the film plane along two current directions: [110] and $[1\overline{1}0]$ crystallographic directions. The ${\mathrm{V}}_{2\ensuremath{\omega}}$ signal displays distinct field-dependent characteristics, which are influenced by thermal effects, mainly the anomalous Nernst effect. In order to obtain accurate values of the SOT effective fields, thermal contributions are accounted for by careful analysis of the ${\mathrm{V}}_{2\ensuremath{\omega}}$ signal. The effective fields, ${\mathrm{H}}_{\mathrm{DLT}}$ (corresponding to dampinglike torque) and ${\mathrm{H}}_{\mathrm{FLT}}$ (corresponding to fieldlike torque), are found to be significantly larger for the $[1\overline{1}0]$ current direction compared to the [110] direction. This observation agrees with the relative strengths of net spin-orbit fields arising from the Rashba and Dresselhaus effects in (Ga,Mn)(As,P) film under tensile strain. Additionally, ${\mathrm{H}}_{\mathrm{DLT}}$ is consistently stronger than ${\mathrm{H}}_{\mathrm{FLT}}$ for both current directions, confirming the dominant role of the dampinglike torque in SOT magnetization switching experiments in FMS films.