Prediction of Giant Spin Motive Force due to Rashba Spin-Orbit Coupling

Magnetization dynamics in a ferromagnet can induce a spin-dependent electric field through a spin motive force. Spin current generated by the spin-dependent electric field can in turn modify the magnetization dynamics through spin-transfer torque. While this feedback effect is usually weak and thus ignored, we predict that in Rashba spin-orbit coupling systems with a large Rashba parameter ${\alpha }_{\mathrm{R}}$, the coupling generates the spin-dependent electric field [$\pm ({\alpha }_{\mathrm{R}}{m}_e/e\hslash )(\widehat{\mathbf{z}}\times \partial \mathbf{m}/\partial t)$], which can be large enough to modify the magnetization dynamics significantly. This effect should be relevant for device applications based on ultrathin magnetic layers with strong Rashba spin-orbit coupling.

Figure 1

Voltage produced by a precessing DW in a nanowire. For simplicity, the DW motion along the nanowire is assumed to be suppressed by a notch in the nanowire. (a) Schematic structure of DW. DW is assumed to precess and change its structure periodically between the Bloch DW ($\psi =0$ or $\pi$) and the Néel DW ($\psi =\pi /2$ or $3\pi /2$) with $\omega =d\psi /dt=2\pi \times 100\mathrm{MHz}$. (b) Voltage between the two ends of the nanowire due to ${\mathbf{E}}_{\pm }$. This voltage does not depend on time $t$ in this particular case since the $t$ dependences of $\mathbf{m}$, $\partial \mathbf{m}/\partial t$, and $\partial \mathbf{m}/\partial x_i$ mutually cancel in Eq. (3). The voltage magnitude is comparable to the value reported in Ref. 8. (c) Voltage due to ${\mathbf{E}}_{\pm }^{\mathrm{RSOC}}$, which oscillates with $t$. Here ${\alpha }_{\mathrm{R}}={10}^{-10}\mathrm{eV}·\mathrm{m}$ [12], $P=1$, and the DW width of 20 nm are assumed.

Figure 2

Measurement scheme of the RSOC effect on the SMF for a uniformly magnetized layer with the perpendicular magnetic anisotropy.