Voltage-controllable spin polarization of current: Model of three-terminal spin device

In order to enhance spin injection from ferromagnetic metals into nonmagnetic semiconductors, we propose a three-terminal spin device composed of a ferromagnetic metal lead coupling with two semiconductor leads via a quantum dot. By modulating the voltage at one of the leads, a pure spin current, or a fully spin-polarized current, can be obtained in one of the semiconductor leads. The intrinsic physics is that the quasi-Fermi energy in the quantum dot is spin splitted when a current flows from the ferromagnetic lead into the quantum dot. The proposed device should be realizable using present technology for efficient spin injection into the so-called spin field effect transistor or a nanowire device.

Figure 1

Schematic of a three-terminal device, a FM and two SC leads coupled with a quantum dot. $V_0$, $V_1$, and $V_2$ denote the adjustable voltages of lead FM, SC1, and SC2, respectively. In lead SC2 two equal but opposite spin-resolved currents flowing between the QD and the lead are schematically shown.

Figure 2

The spin-polarized currents in leads SC1 (a) and SC2 (b) plotted against the voltage $V_2$. A, B, ${\mathrm{A}}^{\prime }$, and ${\mathrm{B}}^{\prime }$ represent the crossed points between the horizontal dot line and the current curves. C and ${\mathrm{C}}^{\prime }$ denote the positions for pure spin current. In the inset the occupation number of QD $n_{\uparrow (\downarrow )}$ are plotted against $V_2$. Other parameters used in the calculation are ${\Gamma }_{\mathrm{FM}}^{\uparrow }={\Gamma }_{\mathrm{SC}}=0.1$, ${\Gamma }_{\mathrm{FM}}^{\downarrow }=0.05$, ${\epsilon }_0=0$, $U=1$, and $k_{B}T=0.1$. The ratio of ${\Gamma }_{\mathrm{FM}}^{\uparrow }∕{\Gamma }_{\mathrm{FM}}^{\downarrow }$ depends mainly on that of spin-resolved density of states of electron at the Fermi energy of the FM lead, which is about $2.4$ for metal iron (Ref. 23) (spin up is assumed to be the majority spin).

Figure 3

(a) The voltage $V_2$ versus the site energy of the QD ${\epsilon }_0$ for maintaining a pure spin current in the lead SC2; (b) the corresponding spin-up and spin-down currents $I_{\mathrm{SC}2}^{\uparrow (\downarrow )}$ plotted as a function of ${\epsilon }_0$.