Magnetic moment of electrons in systems with spin-orbit coupling

[2503.10956] Magnetic moment of electrons in systems with spin-orbit coupling Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Mesoscale and Nanoscale Physics arXiv:2503.10956 (cond-mat) [Submitted on 13 Mar 2025 ( v1 ), last revised 9 Apr 2026 (this version, v5)] Title: Magnetic moment of electrons in systems with spin-orbit coupling Authors: I. A. Ado , M. Titov , Rembert A. Duine , Arne Brataas View a PDF of the paper titled Magnetic moment of electrons in systems with spin-orbit coupling, by I. A. Ado and 3 other authors View PDF HTML (experimental) 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 $\partial/\partial\boldsymbol B$, where $\boldsymbol B$ is an external magnetic field. We highlight the difference between the magnetic moment and $-\partial H/\partial\boldsymbol B$, 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 $\partial/\partial\boldsymbol B$ 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. Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Cite as: arXiv:2503.10956 [cond-mat.mes-hall] (or arXiv:2503.10956v5 [cond-mat.mes-hall] for this version) https://doi.org/10.48550/arXiv.2503.10956 Focus to learn more arXiv-issued DOI via DataCite Journal reference: SciPost Phys. 20, 104 (2026) Related DOI : https://doi.org/10.21468/SciPostPhys.20.4.104 Focus to learn more DOI(s) linking to related resources Submission history From: Ivan Ado [ view email ] [v1] Thu, 13 Mar 2025 23:45:26 UTC (30 KB) [v2] Wed, 9 Apr 2025 16:25:01 UTC (29 KB) [v3] Wed, 17 Dec 2025 16:41:20 UTC (33 KB) [v4] Thu, 19 Feb 2026 16:19:53 UTC (32 KB) [v5] Thu, 9 Apr 2026 20:56:45 UTC (32 KB) Full-text links: Access Paper: View a PDF of the paper titled Magnetic moment of electrons in systems with spin-orbit coupling, by I. A. 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