Generation of non-equilibrium spin-motive force at the surface of a topological insulator induced by current-driven domain wall motion in the magnetic substrate

The generalized Faraday method can be used for computation of spin-motive force (SMF) within the unitary transformation approach. Meanwhile, the unitary transformation approach, which could be employed to obtain an effective collinear exchange interaction of non-collinear magnetic structures, cannot be used when the other parts of the Hamiltonian contain spin-dependent couplings. In the current study, the method of unitary transformation has been generalized to systems with spin-momentum coupling. In this way, the SMF at topological insulator surfaces has been computed analytically.