Magnetic moment of electrons in systems with spin-orbit coupling, by Ivan A. Ado, Mikhail Titov, Rembert A. Duine, Arne Brataas

SciPost Physics Home Authoring Refereeing Submit a manuscript About Magnetic moment of electrons in systems with spin-orbit coupling Ivan A. Ado, Mikhail Titov, Rembert A. Duine, Arne Brataas SciPost Phys. 20, 104 (2026) · published 9 April 2026 doi: 10.21468/SciPostPhys.20.4.104 pdf BiBTeX RIS Submissions/Reports Abstract Magnetic effects originating from spin-orbit coupling (SOC) have been attracting major attention. However, SOC contributions to the electron magnetic moment operator are conventionally disregarded. In this work, we analyze relativistic contributions to the latter operator, including those of the SOC-type: in vacuum, for the semiconductor 8 band Kane model, and for an arbitrary system with two spectral branches. In this endeavor, we introduce a notion of relativistic corrections to the operation $\partial/\partial B$, where $B$ is an external magnetic field. We highlight the difference between the magnetic moment and $-\partial H/\partial B$, where $H$ is the system Hamiltonian. We suggest to call this difference the abnormal magnetic moment. We demonstrate that the conventional decomposition of the total magnetic moment into the spin and orbital parts becomes ambiguous when relativistic corrections are taken into account. The latter also jeopardize the ''modern theory of orbital magnetization'' in its standard formulation. We derive a linear response Kubo formula for the kinetic magnetoelectric effect projected to individual branches of a two branch system. This allows us, in particular, to identify a source of this effect that stems from noncommutation of the position and $\partial/\partial B$ operators' components. This is an analog of the contribution to the Hall conductivity from noncommuting components of the position operator. We comment on the relation between such contributions and the Berry curvature theory. We also report several additional observations related to the electron magnetic moment operator in systems with SOC and other relativistic corrections. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.4.104TI - Magnetic moment of electrons in systems with spin-orbit couplingPY - 2026/04/09UR - https://scipost.org/SciPostPhys.20.4.104JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 4SP - 104A1 - Ado, Ivan A.AU - Titov, MikhailAU - Duine, Rembert A.AU - Brataas, ArneAB - Magnetic effects originating from spin-orbit coupling (SOC) have been attracting major attention. However, SOC contributions to the electron magnetic moment operator are conventionally disregarded. In this work, we analyze relativistic contributions to the latter operator, including those of the SOC-type: in vacuum, for the semiconductor 8 band Kane model, and for an arbitrary system with two spectral branches. In this endeavor, we introduce a notion of relativistic corrections to the operation $\partial/\partial B$, where $B$ is an external magnetic field. We highlight the difference between the magnetic moment and $-\partial H/\partial B$, where $H$ is the system Hamiltonian. We suggest to call this difference the abnormal magnetic moment. We demonstrate that the conventional decomposition of the total magnetic moment into the spin and orbital parts becomes ambiguous when relativistic corrections are taken into account. The latter also jeopardize the ''modern theory of orbital magnetization'' in its standard formulation. We derive a linear response Kubo formula for the kinetic magnetoelectric effect projected to individual branches of a two branch system. This allows us, in particular, to identify a source of this effect that stems from noncommutation of the position and $\partial/\partial B$ operators' components. This is an analog of the contribution to the Hall conductivity from noncommuting components of the position operator. We comment on the relation between such contributions and the Berry curvature theory. We also report several additional observations related to the electron magnetic moment operator in systems with SOC and other relativistic corrections.ER - × @Article{10.21468/SciPostPhys.20.4.104, title={{Magnetic moment of electrons in systems with spin-orbit coupling}}, author={Ivan A. Ado and Mikhail Titov and Rembert A. Duine and Arne Brataas}, journal={SciPost Phys.}, volume={20}, pages={104}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.4.104}, url={https://scipost.org/10.21468/SciPostPhys.20.4.104},} Ontology / Topics See full Ontology or Topics database. Spin-orbit coupling Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 Ivan A. Ado, 1 Mikhail Titov, 2 3 Rembert A. Duine, 4 Arne Brataas 1 Radboud Universiteit Nijmegen / Radboud University Nijmegen [RUN] 2 Universiteit Utrecht / University of Utrecht [UU] 3 Technische Universiteit Eindhoven / Eindhoven University of Technology [TU/e] 4 Norges Teknisk-Naturvitenskapelige Universitet / Norwegian University of Science and Technology [NTNU] Funders for the research work leading to this publication European Research Council [ERC] HORIZON EUROPE Marie Sklodowska-Curie Actions Norges Forskningsråd / The Research Council of Norway