Spin-charge conversion in multiterminal Aharonov-Casher ring coupled to   precessing ferromagnets: A charge conserving Floquet-nonequilibrium Green   function approach
  We derive a non-perturbative solution to the Floquet-nonequilibrium Green function (Floquet-NEGF) describing open quantum systems periodically driven by an external field of arbitrary strength of frequency. By adopting the reduced-zone scheme, we obtain expressions rendering conserved charge currents for any given maximum number of photons, distinguishable from other existed Floquet-NEGF-based expressions where, less feasible, infinite number of photons needed to be taken into account to ensure the conservation. To justify our derived formalism and to investigate spin-charge conversions by spin-orbit coupling (SOC), we consider the spin-driven setups as reciprocal to the electric-driven setups in S. Souma et. al., Phys. Rev. B 70, 195346 (2004) and Phys. Rev. Lett. 94, 106602 (2005). In our setups, pure spin currents are driven by the magnetization dynamics of a precessing ferromagnetic (FM) island and then are pumped into the adjacent two- or four-terminal mesoscopic Aharonov-Casher (AC) ring of Rashba SOC where spin-charge conversions take place. Our spin-driven results show reciprocal features that excellently agree with the findings in the electric-driven setups mentioned above. We propose two types of symmetry operations, under which the AC ring Hamiltonian is invariant, to argue the relations of the pumped/converted currents in the leads within the same or between different pumping configurations. The symmetry arguments are independent of the ring width and the number of open channels in the leads, terminals, and precessing FM islands, In particular, net pure in-plane spin currents and pure spin currents can be generated in the leads for certain setups of two terminals and two precessing FM islands with the current magnitude and polarization direction tunable by the pumping configuration, gate voltage covering the two-terminal AC ring in between the FM islands. 
Son-Hsien Chen, Chien-Liang Chen, Farzad Mahfouzi, and Ching-Ray Chang
cond-mat.mes-hall