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

Abstract

A system composed of a conducting planar strip with Rashba spin-orbit coupling (RSOC), magnetically coupled to a layer of localized magnetic moments, at equilibrium, is studied within a microscopic Hamiltonian with numerical techniques at zero temperature in the clean limit. In particular, transport properties for the cases of ferromagnetic (FM) and antiferromagnetic (AFM) coupled layers are computed in linear response on strips of varying width. Some behaviors observed for these properties are consistent with the ones observed for the corresponding Rashba helical currents. The case of uncoupled Rashba strips is also studied for comparison. In the case of Rashba strips coupled to an AFM localized order, results for the longitudinal dc conductivity, for small strip widths, suggest the proximity to a metal-insulator transition. More interesting, in the proximity of this transition, and in general at intermediate values of the RSOC, it is observed a large spin-Hall conductivity that is two orders of magnitude larger than the one for the FM order for the same values of the RSOC and strip widths. There are clearly two different regimes for small and for large RSOC, which is also present in the behavior of Rashba helical currents. Different contributions to the optical and the spin-Hall conductivities, according to a new classification of inter-or intra-band origin proposed for planar strips in the clean limit, or coming from the hopping or spin-orbit terms of the Hamiltonian, are examined. Finally, the effects of different orientation of the coupled magnetic moments will be also studied.

Transport properties of Rashba conducting strips coupled to magnetic moments with spiral order

“…It is also interesting to compare the present results, where as said above, the spiral order is driven by the SO coupling in the conducting strip, to the two cases more considered in the previous literature [37] where a FM or an AFM order is fixed by a large exchange coupling |J| for all values of λ/t and J sd . By comparing the SP state with the fixed FM system, one should notice that the RHC for the later (dashed line in Fig.…”

“…3(d)) are much larger than those for the staggered SP state for λ/t 0.5, and of course much larger than the ones for the fixed FM case as originally noticed in Ref. [37].…”

“…4(a). The Drude peak for the fixed FM state [37], for W = 32, is close to the one for the SP state for small λ/t, but it is clearly larger for large λ/t, indicating the expected favouring of transport by the FM state. Fig.…”

“…4(d). It should also be noticed that σ sH for the fixed FM state is entirely due to the transitions SO x h y [37].…”

“…4(d). The values of σ sH for the fixed AFM state, W = 32, [37] were also included in Fig. 5(d) for the sake of comparison.…”