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A system composed of a conducting planar strip with Rashba spin-orbitcoupling (RSOC), magnetically coupled to a layer of localized magnetic moments,at equilibrium, is studied within a microscopic Hamiltonian with numericaltechniques at zero temperature in the clean limit. In particular, transportproperties for the cases of ferromagnetic (FM) and antiferromagnetic (AFM)coupled layers are computed in linear response on strips of varying width. Somebehaviors observed for these properties are consistent with the ones observedfor the corresponding Rashba helical currents. The case of uncoupled Rashbastrips is also studied for comparison. In the case of Rashba strips coupled toan AFM localized order, results for the longitudinal dc conductivity, for smallstrip widths, suggest the proximity to a metal-insulator transition. Moreinteresting, in the proximity of this transition, and in general atintermediate values of the RSOC, it is observed a large spin-Hall conductivitythat is two orders of magnitude larger than the one for the FM order for thesame values of the RSOC and strip widths. There are clearly two differentregimes for small and for large RSOC, which is also present in the behavior ofRashba helical currents. Different contributions to the optical and thespin-Hall conductivities, according to a new classification of inter- orintra-band origin proposed for planar strips in the clean limit, or coming fromthe hopping or spin-orbit terms of the Hamiltonian, are examined. Finally, theeffects of different orientation of the coupled magnetic moments will be alsostudied.

Longitudinal optical and spin-Hall conductivities of Rashba conducting strips coupled to ferro- and antiferromagnetic layers