Switching of magnetization by spin–orbit torque in the (Ga,Mn)(As,P) film was studied with currents along ⟨100⟩ crystal directions and an in-plane magnetic field bias. This geometry allowed us to identify the presence of two independent spin–orbit-induced magnetic fields: the Rashba field and the Dresselhaus field. Specifically, we observe that when the in-plane bias field is along the current (I[Formula: see text]H bias ), switching is dominated by the Rashba field, while the Dresselhaus field dominates magnetization reversal when the bias field is perpendicular to the current (I ⊥ H bias ). In our experiments, the magnitudes of the Rashba and Dresselhaus fields were determined to be 2.0 and 7.5 Oe, respectively, at a current density of 8.0 × 10 5 A/cm 2 .
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Interfacial spin-orbit torque without bulk spin-orbit coupling
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We present a new implementation for computing spin–orbit couplings (SOCs) within a time-dependent density-functional theory (TD-DFT) framework in the standard spin-conserving formulation as well in the spin–flip variant (SF-TD-DFT). This approach employs the Breit–Pauli Hamiltonian and Wigner–Eckart’s theorem applied to the reduced one-particle transition density matrices, together with the spin–orbit mean-field treatment of the two-electron contributions. We use a state-interaction procedure and compute the SOC matrix elements using zero-order non-relativistic states. Benchmark calculations using several closed-shell organic molecules, diradicals, and a single-molecule magnet illustrate the efficiency of the SOC protocol. The results for organic molecules (described by standard TD-DFT) show that SOCs are insensitive to the choice of the functional or basis sets, as long as the states of the same characters are compared. In contrast, the SF-TD-DFT results for small diradicals (CH 2 , [Formula: see text], SiH 2 , and [Formula: see text]) show strong functional dependence. The spin-reversal energy barrier in a Fe(III) single-molecule magnet computed using non-collinear SF-TD-DFT (PBE0, ωPBEh/cc-pVDZ) agrees well with the experimental estimate.more » « less
