Definition and transport theory of orbital currents

Clarify the definition of orbital currents and orbital transport in solids, including the appropriate theoretical description of these quantities.

Background

The paper identifies foundational theoretical issues in orbitronics that remain unresolved independently of the domain-wall experiments. In particular, the meaning of an orbital current and the mechanisms governing its transport are not yet settled, which limits the interpretation and comparison of orbital Hall measurements and orbital-torque experiments.

This problem is distinct from the paper’s experimentally investigated question of whether orbital currents can drive domain walls in ferrimagnetic heterostructures; the authors present it as a broader unresolved issue in the field.

References

Open questions in the field concern the definition of orbital currents and orbital transport{37--39}, as well as the interplay of alternative effects generating local accumulation of orbital momenta{40,41}.

— Challenges in orbital current-driven domain wall motion in light metal/ferrimagnet heterostructures  (2609.04811 - Kang et al., 4 Sep 2026) in Section I, Introduction

Open questions in the field concern the definition of orbital currents and orbital transport{37--39}, as well as the interplay of alternative effects generating local accumulation of orbital momenta{40,41}.

— Challenges in orbital current-driven domain wall motion in light metal/ferrimagnet heterostructures  (2609.04811 - Kang et al., 4 Sep 2026) in Section I, Introduction

The construction of a conserved orbital current analogous to the proper spin current remains an open problem and lies beyond the scope of this work.

— Theory of extrinsic contributions to the full orbital current  (2609.28628 - Cullen et al., 23 Sep 2026) in Section 1, Introduction

The microscopic conversion mechanisms remain incompletely understood for both itinerant and local OAM. On-site spin-orbit coupling of the form \alpha\bm L\cdot\bm s provides a natural local conversion channel, while the transmission and conservation of Bloch OAM across interfaces remain open problems.

— Theory of extrinsic contributions to the full orbital current  (2609.28628 - Cullen et al., 23 Sep 2026) in Section 4, Discussion