  We study the spin transport theoretically in heterostructures consisting of a
ferromagnetic metallic thin film sandwiched between heavy-metal and oxide
layers. The spin current in the heavy metal layer is generated via the spin
Hall effect, while the oxide layer induces at the interface with the
ferromagnetic layer a spin-orbital coupling of the Rashba type. Impact of the
spin Hall effect and Rashba spin-orbit coupling on the spin Seebeck current is
explored with a particular emphasis on nonlinear effects. Technically, we
employ the Fokker-Planck approach and contrast the analytical expressions with
full numerical micromagnetic simulations. We show that when an external
magnetic field is aligned parallel (antiparallel) to the Rashba field, the
spin-orbit coupling enhances (reduces) the spin pumping current. In turn, the
spin Hall effect and the Dzyaloshinskii-Moriya interaction are shown to
increase the spin pumping current.
