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.
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