Supercurrent-induced spin-orbit torques

We theoretically investigate the supercurrent-induced magnetization dynamics of a two-dimensional lattice of ferromagnetically ordered spins placed on a conventional superconductor with broken spatial inversion symmetry and strong spin-orbit coupling. We develop a phenomenological description of the coupled dynamics of the superconducting condensate and the spin system and demonstrate that supercurrents produce a reactive spin-orbit torque on the magnetization. By performing a microscopic self-consistent calculation, we show that the spin-orbit torque originates from a spin polarization of the Cooper pairs due to current-induced spin-triplet correlations. Interestingly, we find that there exists an intrinsic limitation for the maximum achievable spin-orbit torque, which is determined by the coupling strength between the condensate and the spin system. In proximitized hole-doped semiconductors, the maximum achievable spin-orbit torque field is estimated to be on the order of $0.16$ mT, which is comparable to the critical field for current-induced magnetization switching in ferromagnetic semiconductors.