Reciprocity of Charge-Orbital-Spin Transport in Normal-Metal/Ferromagnet Heterostructures

TL;DR

This paper demonstrates the reciprocal relationship between orbital torque and orbital pumping in heterostructures, establishing a unified framework for orbital transport phenomena through experimental measurements.

Contribution

It provides the first direct experimental evidence of reciprocal conversion between charge, orbital, and spin angular momenta in non-magnet/ferromagnet heterostructures.

Findings

Orbital Hall effect generates orbital torques in heterostructures.

Transmission coefficients satisfy Onsager reciprocity relations.

Orbital pumping is confirmed as the reciprocal of orbital torque.

Abstract

Orbital angular momentum has recently emerged as an important carrier of angular momentum in solids, offering new pathways for spin orbitronic functionality beyond conventional spin transport. Here, we investigate the orbital Hall effect which generates orbital torques and their reciprocal process viz orbital pumping and the inverse orbital Hall effect (iOHE) in non-magnet/ferromagnet heterostructures. Using two port scattering parameter measurements on Ru/Ni, Ru/Pt/CoFeB and Co/Cu/SiO2 devices, we directly probe both orbital torque driven magnetization dynamics and orbital pumping within the same device platform. We observe that the transmission coefficients satisfy the symmetry relations required by Onsager reciprocity, demonstrating reciprocal conversion between charge, orbital and spin angular momenta. Our results establish orbital pumping as the reciprocal counterpart of orbital torque. Our experimental findings provide a unified framework for orbital transport phenomena.