How to control spin-Seebeck current in a metal-quantum dot-magnetic insulator junction

The control of the spin-Seebeck current is still a challenging task for the development of spin caloritronic devices. Here, we construct a spin-Seebeck device by inserting a quantum dot (QD) between the metal lead and magnetic insulator. Using the slave-particle approach and noncrossing approximation, we find that the spin-Seebeck effect increases significantly when the energy level of the QD locates near the Fermi level of the metal lead due to the enhancement of spin flipping and occurrences of quantum resonance. Since this can be easily realized by applying a gate voltage in experiments, the spin-Seebeck device proposed here can also work as a thermovoltaic transistor. Moreover, the optimal correlation strength and the energy level position of the QD are discussed to maximize the spin-Seebeck current as required for applications in controllable spin caloritronic devices.

Figure 1

Schematic of a strongly correlated quantum dot attached to the left metal lead and the right magnetic insulator with coupling ${\mathrm{\Gamma }}_k$ and $J_q$, respectively. Here, $U$ is the Coulomb correlation, and ${\varepsilon }_{\sigma }$ denotes the dot level, which can be tuned by the top gate voltage. It is assumed that $J_q$ is much smaller than ${\mathrm{\Gamma }}_k$ so that we approximate the spin current to the lowest order in $J_q$ and neglect the self-energy due to interaction with magnons.

Figure 2

Dependence of the spin-Seebeck current $I_S$ in the infinite-$U$ QD with the constant temperature difference $\mathrm{\Delta }T=50$ K on the QD level energy for various $T_L$. In the inset, the results for the noncorrelated QD are plotted for comparison.

Figure 3

Schematic of how the magnetic insulator drives a spin current in the metal lead. Three processes take place in turn: (1) A spin-down electron tunnels into the QD; (2) the spin is flipped by absorbing a magnon; (3) the spin-up electron tunnels back to the metal.

Figure 4

Two peaks of the DOS of the spin-up states: a broad peak around the QD level and a narrow one at the Fermi level. The temperature of the metal lead is set at $T_L=200$ K.

Figure 5

Diagrammatic representation of the NCA self-energies. ${\mathrm{\Sigma }}_{f\sigma }$ is the spinon self-energy. The solid line, wavy line, and dotted line represent propagators of the lead electrons, holon, and doublon, respectively. $\mathrm{\Pi }$ and $\mathrm{\Lambda }$ are the holon and the doublon self-energies, where the dashed line denotes the spinon propagator.

Figure 6

Variation of the spin-Seebeck current $I_S$ vs the QD level ${\varepsilon }_{\uparrow }$ and correlation $U$. Temperature of the metal lead $T_L$ and the temperature gradient $\mathrm{\Delta }T$ are fixed at 200 and $50\mathrm{K}$, respectively.

Figure 7

DOS of spin-up electrons for some correlations ranging from $U=0$ to 5 eV. The QD level is fixed at ${\varepsilon }_{\uparrow }=0$ eV and temperature of the metal lead is $T_L=200$ K.

Figure 8

Variation of the position of the spin current peak vs temperature of the metal lead. Results for temperatures $T_L=150$ and 60 K are presented with temperature gradient $\mathrm{\Delta }T=50$ K. The corresponding QD level is at ${\varepsilon }_{\uparrow }\approx 0.4$ and 0.8 eV, respectively. In both cases the peak is located at $U\approx 3.8$ eV, the same as it is in Fig. 6.