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. 2025 Feb 25;16:1959. doi: 10.1038/s41467-025-57235-5

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© The Author(s) 2025

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 2 — a Spontaneous magnetic circular dichroism (MCD) as a function of moiré lattice filling factor $ν$ and out-of-plane electric field $E$ at 1.6 K. The dashed lines (from Fig. 1c) separate the layer-hybridized and layer-polarized regions. b Magnetic-field dependence of MCD of the hot spot in (a) at representative temperatures. Clear magnetic hysteresis is observed at low temperatures. Inset: temperature dependence of the spontaneous MCD. c Same as (a) under magnetic field $B = 0.5$ T. The dashed lines are a guide to the eye of the boundary of the region with enhanced magnetic susceptibility. d Calculated electronic density of states (DOS) as a function of $ν$ and $E$ showing the evolution of the van Hove singularity (vHS) with $E$ . All results are for 2.7° twisted WSe₂.