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Magnetic moment of electrons in systems with spin-orbit coupling
by Ivan A. Ado, M. Titov, Rembert A. Duine, Arne Brataas
Submission summary
| Authors (as registered SciPost users): | Ivan A. Ado |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2503.10956v3 (pdf) |
| Date submitted: | Dec. 18, 2025, 7:25 p.m. |
| Submitted by: | Ivan A. Ado |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
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List of changes
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Strengths
The authors point out that there are differences between what they call a "naive" magnetic moment and their final result, given in Eq. (15)
Weaknesses
One point still needs attention from the authors:
they define the Bohr magneton with a 1/c , which is usually not done. This then makes several terms in their Hamiltonian (7) to have 1/c^3 order, but others have 1/c^2 order.
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Requested changes
The definition of the Bohr magneton is unusual - the authors should check this, as it affects what order in 1/c terms in the transformed Hamiltonian have.
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