Detection of Current-Induced Spins by Ferromagnetic Contacts

Detection of current-induced spin accumulation via ferromagnetic contacts is discussed. Onsager’s relations forbid that in a two-probe configuration, spins excited by currents in time-reversal symmetric systems can be detected by switching the magnetization of a ferromangetic detector contact. Nevertheless, current-induced spins can be transferred as a torque to a contact magnetization and can affect the charge currents in many-terminal configurations. We demonstrate the general concepts by solving the microscopic transport equations for the diffuse Rashba system with magnetic contacts.

Figure 1

Current-Voltage configuration for (a) two-probe and (b) four-probe setup.

Figure 2

The potential drop in units of $J_p\delta D^2{L}_s/4D{\nu }_R$ as a function of the magnetization direction for $\Gamma (1-\delta D^2/4)=5$ and $\xi =0.2$ (a), $\xi =1$ (b), and $\xi =5$ (c). The $y$-axis is the azimuthal angle $\theta$, and $x$-axis is the polar angle $\varphi$ of $\mathbf{m}$.

Figure 3

Components of the spin transfer torque, scaled by a factor $J_p\lambda L_s$, plotted for the set of parameters $\xi =1$, $\zeta =5$ and (a) $\Gamma =1$, (b) $\Gamma =5$, and (c) $\Gamma =25$. The $y$-axis is the azimuthal angle $\theta$, and $x$-axis is the polar angle $\varphi$ of $\mathbf{m}$.