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We derive a non-perturbative solution to the Floquet-nonequilibrium Greenfunction (Floquet-NEGF) describing open quantum systems periodically driven byan external field of arbitrary strength of frequency. By adopting thereduced-zone scheme, we obtain expressions rendering conserved charge currentsfor any given maximum number of photons, distinguishable from other existedFloquet-NEGF-based expressions where, less feasible, infinite number of photonsneeded to be taken into account to ensure the conservation. To justify ourderived formalism and to investigate spin-charge conversions by spin-orbitcoupling (SOC), we consider the spin-driven setups as reciprocal to theelectric-driven setups in S. Souma et. al., Phys. Rev. B 70, 195346 (2004) andPhys. Rev. Lett. 94, 106602 (2005). In our setups, pure spin currents aredriven by the magnetization dynamics of a precessing ferromagnetic (FM) islandand then are pumped into the adjacent two- or four-terminal mesoscopicAharonov-Casher (AC) ring of Rashba SOC where spin-charge conversions takeplace. Our spin-driven results show reciprocal features that excellently agreewith the findings in the electric-driven setups mentioned above. We propose twotypes of symmetry operations, under which the AC ring Hamiltonian is invariant,to argue the relations of the pumped/converted currents in the leads within thesame or between different pumping configurations. The symmetry arguments areindependent of the ring width and the number of open channels in the leads,terminals, and precessing FM islands, In particular, net pure in-plane spincurrents and pure spin currents can be generated in the leads for certainsetups of two terminals and two precessing FM islands with the currentmagnitude and polarization direction tunable by the pumping configuration, gatevoltage covering the two-terminal AC ring in between the FM islands.

physical review. b, condensed matter and materials physics

Spin-charge conversion in multiterminal Aharonov-Casher ring coupled to  precessing ferromagnets: A charge conserving Floquet-nonequilibrium Green  function approach