  The spin-charge coupled dynamics in a thin, magnetized metallic system are
investigated. The effective driving force acting on the charge carriers is
generated by a dynamical magnetic texture, which can be induced, e.g., by a
magnetic material in contact with a normal-metal system. We consider a general
inversion-asymmetric substrate/normal-metal/magnet structure, which, by
specifying the precise nature of each layer, can mimick various experimentally
employed setups. Inversion symmetry breaking gives rise to an effective Rashba
spin-orbit interaction. We derive general spin-charge kinetic equations which
show that such spin-orbit interaction, together with anisotropic Elliott-Yafet
spin relaxation, yields significant corrections to the magnetization-induced
dynamics. In particular, we present a consistent treatment of the spin density
and spin current contributions to the equations of motion, inter alia
identifying a novel term in the effective force which appears due to a spin
current polarized parallel to the magnetization. This "inverse spin filter"
contribution depends markedly on the parameter which describes the anisotropy
in spin relaxation. To further highlight the physical meaning of the different
contributions, the spin pumping configuration of typical experimental setups is
analyzed in detail. In the two-dimensional limit the build-up of a DC voltage
is dominated by the spin galvanic (inverse Edelstein) effect. A measuring
scheme that could isolate this contribution is discussed.
