Spin motive force and generation of pure spin current in ferromagnetic ring under time modulation and Rashba spin orbit coupling

We studied the spin motive force induced in a 1D ferromagnetic ring with presence of Rashba spin orbit coupling. The domain wall (DW) is assumed to precess periodically between Bloch-like and Neel-like DW (Fig. 1) at frequency ω. In strong exchange coupling limit (adiabatic approximation), we showed that the induced spin motive force between any two points separated by an angle Δφ on the ring is simply given by V=V₀ω sin(Δφ/2)cos(ωt+ Δφ/2), where is the precession frequency, and V₀=2mRα/e being dependent on material and geometric parameters, i.e. Rashba coupling α and ring radius R. In strong Rashba system, the SMF is significantly large comparing with the conventional SMF due to time-varying chiral magnetization, in the absence of Rashba SOC. Since the induced spin motive force is opposite for spin up and spin down, it would be possible to generate a pure spin current circulating around the ring, which can be extracted via attached leads. Due to the sin(Δφ/2) factor, the maximum spin current is obtained by placing the leads diametrically opposite to one another. Therefore, the set-up can achieve a spin current battery function.