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

TL;DR

This paper investigates the optical and spin-Hall conductivities of Rashba conducting strips coupled to magnetic layers, revealing a large spin-Hall response near a metal-insulator transition and analyzing contributions from various electronic processes.

Contribution

It provides a detailed microscopic analysis of transport properties in Rashba strips with magnetic coupling, highlighting regimes with enhanced spin-Hall conductivity and a new classification of conductivity contributions.

Findings

Large spin-Hall conductivity near metal-insulator transition.

Two distinct regimes for small and large Rashba spin-orbit coupling.

Different contributions to conductivities from inter/intra-band and hopping/spin-orbit processes.

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.