On the reciprocal relation between the direct and inverse orbital Hall effects

The reciprocal relation is a fundamental manifestation of the fluctuation-dissipation theorem for near-equilibrium transport phenomena. In orbitronics, the orbital Hall effect plays a pivotal role as it can be used to generate orbital currents. Its reciprocal counterpart, the inverse orbital Hall effect refers to a generation of charge current by gradient of orbital-dependent chemical potential, namely “orbital voltage”, which can serve as a mechanism to electrically detect orbital currents in orbitronic devices. In recent years, the orbital-to-charge conversion has been experimentally detected [1-5]. However, the theoretical description of the reciprocity between the direct and inverse orbital Hall effects is far from trivial because orbital currents are ill-defined and the orbital angular momentum is not conserved. We show that the reciprocal relation between charge and orbital transport can be rigorously established by adopting the definition of “proper” current proposed by Shi et al. [6], in which the non-conserving effect is considered. Based on the implementation in our first-principles codes, we present a detailed analysis of the direct and inverse orbital Hall effects in Pt(111) and W(110) thin films, prototypical systems used in experiments. We demonstrate that the reciprocal relation is exactly satisfied for the “total” responses. However, we find interesting features in “local” responses, especially near the surface, where the direct and inverse effects can significantly deviate from each other. We find its origin in the orbital Rashba coupling at the surface, in which the angular momentum transfer between the lattice and orbital degrees of freedom is strongly pronounced. We believe this explains the large inverse orbital Rashba-Edelstein effect measured in a recent THz spectroscopy experiment [1]. We discuss further implications of our finding and its relevance in various experimental setups.

[1] T. Seifert, D. Go et al. Nat. Nanotechnol. 18, 1132 (2023)

[2] P. Wang et al. npj Quantum Mater. 8, 28 (2023).

[3] Y. Xu et al. arXiv:2208.01866 (2022).

[4] A. E. Hamdi et al. Nat. Phys. (2023). https://doi.org/10.1038/s41567-023-02121-4

[5] H. Hayashi and K. Ando, arXiv:2304.05266 (2023).

[6] J. Shi et al. Phys. Rev. Lett. 96, 076604 (2006).

[7] D. Go et al. Manuscript in Preparation.