Pure Spin Currents and the Associated Electrical Voltage

We present a generalized Landauer-Büttiker transport theory for multiterminal spin transport in the presence of spin-orbit interaction. Using this theory we point out that there exists equilibrium spin currents and nonequilibrium pure spin currents, without any magnetic element in the system. Quantitative results are presented for a $Y$-shaped conductor. It is shown that pure spin currents cause a voltage drop and, hence, can be measured.

Figure 1

$Y$-shaped three terminal junction with applied voltages $V_1$, $V_2$, and $V_3$ as depicted. The third terminal (labeled 3) is a voltage probe (nonmagnetic or ferromagnetic) which draws no charge current. However, the polarization of incoming and outgoing electrons are opposite to each other, causing a pure spin current.

Figure 2

Pure spin current flowing through a nonmagnetic voltage probe and the corresponding voltage (right panel) versus quantization axis. Disorder potential strength is shown in the inset. Calculations were performed on a device width $d=20a$ (see Fig. 1), $k_{F}a=1$, dimensionless spin-orbit parameter $\lambda /a^2=0.05$.

Figure 3

Pure spin current flowing through the ferromagnetic voltage probe versus quantization axis (left panel); right panel shows the corresponding voltage. Disorder potential strength is shown in the inset. Ferromagnet is modeled as exchange split with exchange splitting ($\Delta$) given as $\Delta /E_F=0.5$. Other parameters are the same as for Fig. 2.