Microscopic theory of spin-orbit torque and spin memory loss from interfacial spin-orbit coupling

Despite extensive efforts it has remained elusive how the spin-relaxation and spin-precession processes influence the spin-orbit torque and spin memory loss at heavy metal (HM)-ferromagnetic insulator (FI) heterostructure. Here, we study the spin transport of the spin-orbit-coupled ferromagnets based on the SU(2) gauge field theory and reveal that the interfacial spin-orbit coupling is responsible for (i) noncollinear spin exchange, (ii) anisotropic spin relaxation, and (iii) interfacial magnetic field. We show that the noncollinear spin exchange can tune the damping- and field-like torques. The spin-loss conductance is analytically derived by considering interfacial Rashba, Dresselhaus, and strain-induced spin-orbit couplings. Our theory offers a deep understanding of the spin transport across the HM|FI interface.