A theoretical study predicts that nonlinear orbital magnetization can exceed the corresponding spin response in materials with topological band features, regardless of spin-orbit-coupling strength. The result is based on a two-dimensional massive Dirac model and first-principles calculations for strained bilayer graphene and monolayer 1T’ MoS2 and MoTe2. The examples represent negligible, moderate and strong spin-orbit coupling. The document is version 1 of an arXiv preprint dated 28 Aug 2026.
A field-sensitive calculation
The study’s central question is how nonlinear current-induced orbital magnetization can be formulated microscopically and which quantum-geometric terms govern it. To address that question, the authors expand all field-dressed wave-packet quantities in powers of the electric field and retain first-order terms.
That expansion gives a field correction to the Bloch-electron orbital magnetic moment. In the supplied formulation, the correction is a sum of a term involving the anomalous orbital polarizability tensor F and a term involving the Berry-connection polarizability-related position shift G and band velocity v. The study refers to these contributions as anomalous orbital polarizability, or AOP, and Berry-connection polarizability, or BCP.
The authors then obtain the nonlinear response tensor by substituting the field-corrected moment and the nonequilibrium carrier distribution into the magnetization expression.
Symmetry narrows the response
Among 14 non-gyrotropic point groups that prohibit linear current-induced orbital magnetization, 12 are reported to allow the nonlinear form, where it would be the leading-order contribution.
In the two-dimensional massive Dirac model, time-reversal and mirror symmetries leave only one out-of-plane response coefficient. The response is pi-periodic, meaning it repeats after a half-turn, and it vanishes when the electric field points parallel or perpendicular to the mirror line.
Two geometric contributions compete
As the chemical potential changes, AOP and BCP contributions are concentrated near the band edges, have comparable magnitudes and generally oppose one another. AOP dominates near the band edge, while BCP becomes larger at higher chemical potential.
The material calculations
In strained bilayer graphene, used for the negligible spin-orbit-coupling case, the predicted nonlinear current-induced orbital magnetization magnitude reaches about 2.5 × 10^4 µB per volt squared. The calculated spin response is negligible.
Monolayer 1T’ MoS2 shows a different pattern. Its orbital response is non-monotonic with chemical potential, changes sign, and reaches a maximum magnitude of about 2.3 × 10^2 µB per volt squared. Its nonlinear spin response is two orders of magnitude smaller.
Monolayer 1T’ MoTe2 supplies the strong spin-orbit-coupling example. The calculation is semimetallic at low energy, but the orbital response remains more than two orders of magnitude above the spin response. At the intrinsic Fermi level, the response reaches about 2 × 10^2 µB per volt squared.
A prediction awaiting measurement
At an electric field of 10^5 V/m, the calculations predict nonlinear orbital magnetization in the two-dimensional monolayers of up to about 2 × 10^-6 µB per square nanometre. The comparison in the analysis places this against previously reported linear-response values of about 10^-7 to 10^-6 µB per square nanometre.
Those values are predictions from a theoretical calculation, and the supplied analysis reports no uncertainty interval or experimental validation. The evidence covers one illustrative model and three material examples, so it does not establish that the same orbital-over-spin balance will hold in other systems. The quantitative results also depend on chemical potential, temperature, relaxation time, field strength and material parameters. For the MoS2 and MoTe2 calculations, the stated temperature is 50 K and the relaxation time is 50 fs.
Whether the predicted magnetization can be measured in the listed materials remains open. So does the robustness of the AOP-versus-BCP and orbital-versus-spin comparisons when temperature, relaxation time, disorder, strain, field strength or chemical potential changes.
Paper data and sources
Original title: Quantum Geometric Origin of Nonlinear Current Induced Orbital Magnetization
Authors: Xue-Jin Zhang, Yue-Xin Huang, Wei Du et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text