Temperature dependence of angular momentum transport across interfaces

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 quasiparticles 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 nonmagnetic metals, ferromagnetic insulators, 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 nonmagnetic heavy metal. The calculated results on the temperature dependence of spin conductance quantitatively agree with the existing experiments.

Figure 1

The spin Seebeck signal enhancement factor ${\eta }_{\mathrm{th}}$ as a function of temperature for various spin conductance of the NM layer from $G_{\mathrm{N}}=1,2,5,10,\infty \left({10}^{18}{\mathrm{m}}^{-2}\right)$, calculated by using Eq. (28). The parameters are $a_{\mathrm{F}}=1.39$ nm, $a_{\mathrm{A}}=0.42$ nm, $T_C=560$ K, $T_N=160$ K ($t_{\mathrm{NiO}}=0.6$ nm), $g_e\left(E_F\right)=3n_e/2E_F$ with $n_e=5\times {10}^{22}{\mathrm{cm}}^{-3}$, and $E_F=5$ eV. $J_{\mathrm{YIG}/\mathrm{Pt}}=$ 0.07 eV and $J_{\mathrm{NiO}/\mathrm{Pt}}=0.13$ eV are the $sd$ constants at the interface. (a) The enhancement factor for a number of spin conductance of the NM layer. (b) Comparison of the experimental points [14] with the theoretical curve for $G_{\mathrm{N}}=6.7\times {10}^{18}{\mathrm{m}}^{-2}$.