  Angular momentum transport in magnetic multilayered structures plays a
central role in spintronic physics and devices. The angular momentum currents
or spin currents are carried by either quasi-particles such as electrons and
magnons, or by macroscopic order parameters such as local magnetization of
ferromagnets. Based on the generic interface exchange interaction, we develop a
microscopic theory that describes interfacial spin conductance for various
interfaces among non-magnetic metals, ferromagnetic and antiferromagnetic
insulators. Spin conductance and its temperature dependence are obtained for
different spin batteries including spin pumping, temperature gradient and spin
Hall effect. As an application of our theory, we calculate the spin current in
a trilayer made of a ferromagnetic insulator, an antiferromagnetic insulator
and a non-magnetic heavy metal. The calculated results on the temperature
dependence of spin conductance quantitatively agree with the existing
experiments.
