Local and Global Reciprocity in Orbital-Charge-Coupled Transport

TL;DR

This paper investigates the reciprocal relations between orbital and charge currents in thin films, highlighting the importance of proper orbital current definitions and revealing local nonreciprocity effects supported by first-principles calculations.

Contribution

It introduces a proper orbital current definition, establishes global reciprocity, and uncovers local nonreciprocity effects in orbital-charge transport in thin films.

Findings

Global orbital-charge response is reciprocal.

Local responses can show significant nonreciprocity.

Surface contributions lead to local nonreciprocity in thin films.

Abstract

The coupled transport of charge and orbital angular momentum (OAM) lies at the core of orbitronics. Here, we examine the reciprocal relation in orbital-charge-coupled transport in thin films, treating bulk and surface contributions on equal footing. We argue that the conventional definition of orbital current is ill-defiled, as it violates reciprocity due to the nonconservation of OAM. This issue is resolved by adopting the so-called \emph{proper} orbital current, which is directly linked to orbital accumulation. We establish the reciprocal relation for the \emph{global} (spatially integrated) response between orbital and charge currents, while showing that their \emph{local} (spatially resolved) responses can differ significantly. In particular, we find large surface contributions that may lead to nonreciprocity when currents are measured locally. These findings are supported by first-principles calculations on W(110) and Pt(111) thin films. In W(110), orbital-charge interconversion is strongly nonreciprocal at the layer level, despite exact reciprocity in the integrated response. Interestingly, spin-charge interconversion in W(110) remains nearly reciprocal even locally. In contrast, Pt(111) exhibits local nonreciprocity for both orbital-charge and spin-charge conversions, which we attribute to strong spin-orbit coupling. We propose that such local distinctions can be exploited to experimentally differentiate spin and orbital currents.