Predicted rectification and negative differential spin Seebeck effect at magnetic interfaces

We study the nonequilibrium Seebeck spin transport across metal-magnetic insulator interfaces. The conjugate-converted thermal-spin transport is assisted by the exchange interaction at the interface, between conduction electrons in the metal lead and localized spins in the insulating magnet lead. We predict the rectification and negative differential spin Seebeck effect and resolve their microscopic mechanism, as a consequence of the strongly fluctuated electronic density of states in the metal lead. The rectification of spin Peltier effect is also discussed. The phenomena predicted here are relevant for designing efficient spin/magnon diode and transistor, which could play crucial roles in controlling energy and information in functional devices.

Figure 1

Schematic illustration of different setups of the metal-insulating magnetic interfaces.

Figure 2

Rectification and negative differential spin Seebeck effect in macroscopic magnetic interface. Spin Seebeck current $I_S$ as a function of the temperature bias $\Delta T$ with $T_{L,R}=T_0\pm \Delta T/2$, for varying $T_0$ and Lorentzian peak positions: $T_0=100$ K, ${\varepsilon }_0=20$ meV; $T_0=150$ K, ${\varepsilon }_0=35$ meV; $T_0=200$ K, ${\varepsilon }_0=50$ meV. We set $S_0=16$, which is comparable with the experimental ones in typical magnetic insulators, cf. Refs. 21, 30, and 31. ${\mu }_0=0$ and the Ohmic spectrum $F_R\left(\omega \right)=\alpha \frac{\omega }{{\omega }_c}{e}^{-\omega /{\omega }_c}$ is adopted, with $\alpha =10$, ${\omega }_c=50$ meV. Other choices of $F_R\left(\omega \right)$ will not change the results qualitatively.

Figure 3

Rectification and negative differential spin Seebeck effect in nanoscale magnetic interface. (a) Magnon spin current $I_S$ as a function of the normalized temperature bias $\Delta T/\left(2T_0\right)$ with $T_{L,R}=T_0\pm \Delta T/2$, for varying ${\varepsilon }_{\uparrow ,\downarrow }$: (i) ${\varepsilon }_{\downarrow }=50$ meV, ${\varepsilon }_{\uparrow }=10$ meV; (ii) ${\varepsilon }_{\downarrow }=50$ meV, ${\varepsilon }_{\uparrow }=0$; (iii) ${\varepsilon }_{\downarrow }=50$ meV, ${\varepsilon }_{\uparrow }=-25$ meV; (iv) ${\varepsilon }_{\downarrow }=-25$ meV, ${\varepsilon }_{\uparrow }=-75$ meV. (b) Magnonic spin Seebeck current as a function of the temperature bias: for $T_R=150$ K, ${\varepsilon }_{\downarrow }=50$ meV, ${\varepsilon }_{\uparrow }=30$ meV; For $T_R=200$ K, ${\varepsilon }_{\downarrow }=60$ meV, ${\varepsilon }_{\uparrow }=40$ meV; For $T_R=250$ K, ${\varepsilon }_{\downarrow }=70$ meV, ${\varepsilon }_{\uparrow }=50$ meV. We set ${\Gamma }_J=2.5$ meV and $S_0=16$, which is comparable with the experimental ones in typical magnetic insulators; cf. Refs. 21, 30, and 31.