Investigation of orthogonal spin–orbit fields in crystalline ferromagnetic films with four-fold in-plane magnetic anisotropy

We report an investigation of current-induced spin–orbit fields (SOFs) in a crystalline (Ga,Mn)As ferromagnetic film with four-fold in-plane anisotropy. By designing a Hall device with current channels along crystallographic 〈100〉 directions, we observe the effects of SOFs in all four magnetization transitions over the four 〈110〉 hard axes of the film. The SOF effects are observed in the form of opposite shifts of angles at which the magnetization of the film switches sign for opposite current polarities in anisotropic magnetoresistance (AMR) measurements carried out as the applied magnetic field was rotated. Note that the Dresselhaus- and Rashba-type SOFs generated by currents flowing along the 〈100〉 directions—as in the device designed for the present experiments—are orthogonal to one another and can thus be separated by appropriate analysis of AMR. The analysis of experimental results based on magnetic free energy, in which the effects of SOFs are included, reveals that the Dresselhaus-type SOF is much stronger than the Rashba-type SOF. The values of the two SOFs obtained independently with currents flowing either along the [100] or [010] channels are consistent with each other, showing the reliability of the above-mentioned approach for investigating SOFs in ferromagnetic films.