  Spin transport at metallic interfaces is an essential ingredient of various
spintronic device concepts, such as giant magnetoresistance, spin-transfer
torque, and spin pumping. Spin-orbit coupling plays an important role in many
such devices. In particular, spin current is partially absorbed at the
interface due to spin-orbit coupling. We develop a general magnetoelectronic
circuit theory and generalize the concept of the spin mixing conductance,
accounting for various mechanisms responsible for spin-flip scattering. For the
special case when exchange interactions dominate, we give a simple expression
for the spin mixing conductance in terms of the contributions responsible for
spin relaxation (i.e., spin memory loss), spin torque, and spin precession. The
spin-memory loss parameter $\delta$ is related to spin-flip transmission and
reflection probabilities. There is no straightforward relation between spin
torque and spin memory loss. We calculate the spin-flip scattering rates for
N|N, F|N, F|F interfaces using the Landauer-B\"uttiker method within the linear
muffin-tin orbital method and determine the values of $\delta$ using circuit
theory.
