Generation and measurement of nonequilibrium spin currents in two-terminal systems

Generation and measurement of nonequilibrium spin current in two probe phase coherent conductors are discussed. It is argued and shown that spin current can be generated in a two-terminal nonmagnetic system by application of electrical voltage. These spin currents can be measured via conductance in two probe configuration when the detector probe is ferromagnetic. It is shown that for a two-terminal system with one ferromagnetic probe, the conductance depends on the absolute direction of magnetization and is related to spin currents. Thus, this allows one to measure spin currents via conductance.

Figure 1

Setup for spin current generation and detection: (a) current leads are nonmagnetic and injected currents are unpolarized but outgoing current is polarized due to SO region. (b) Detector lead is magnetic, and the conductance depends on absolute direction of magnetization $(\theta ,\varphi )$ because of the spin current generated by the SO region.

Figure 2

(Color online) Spin polarization of outgoing current versus quantization axis ($\theta =90$ and $\varphi$ is varied) for nonmagnetic systems corresponding to Fig. 1a. The dimensionless SO interaction strength $\alpha =0.1$ and $E_F=1.0\mathrm{t}$ and $k_{f}l=100a$ ($l$ is mean free path) for diffusive case. The straight line with filled circles corresponds to the magnitude of polarization.

Figure 3

(Color online) Conductance and spin polarization of outgoing current as a function of quantization axis for ballistic system with ferromagnetic detector shown in Fig. 1b. Other parameters are the same as in Fig. 2.

Figure 4

(Color online) Conductance and spin polarization of outgoing current as a function of quantization axis for diffusive system with ferromagnetic detector shown in Fig. 1b. The results are for diffusive case with $k_{f}l=100a$ ($l$ is mean free path). Other parameters are the same as in Fig. 3.

Figure 5

(Color online) Torque acting on ferromagnet detector as a function of quantization axis corresponding to configuration shown in Fig. 1b.