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Moiré magnetic exchange interactions in twisted magnets

Nature Computational Science volume 3, pages 314–320 (2023)Cite this article

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A preprint version of the article is available at arXiv.

Abstract

In addition to moiré superlattices, twisting can also generate moiré magnetic exchange interactions (MMEIs) in van der Waals magnets. However, owing to the extreme complexity and twist-angle-dependent sensitivity, all existing models fail to fully capture MMEIs and thus cannot provide an understanding of MMEI-induced physics. Here, we develop a microscopic moiré spin Hamiltonian that enables the effective description of MMEIs via a sliding-mapping approach in twisted magnets, as demonstrated in twisted bilayer CrI3. We show that the emergence of MMEIs can create a magnetic skyrmion bubble with non-conserved helicity, a ‘moiré-type skyrmion bubble’. This represents a unique spin texture solely generated by MMEIs and ready to be detected under the current experimental conditions. Importantly, the size and population of skyrmion bubbles can be finely controlled by twist angle, a key step for skyrmion-based information storage. Furthermore, we reveal that MMEIs can be effectively manipulated by substrate-induced interfacial Dzyaloshinskii–Moriya interactions, modulating the twist-angle-dependent magnetic phase diagram, which solves outstanding disagreements between theories and experiments.

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Fig. 1: MMEI-induced moiré-type SkBs at θ ~ 1.41°.
Fig. 2: θ- and substrate-controlled moiré-type SkBs.

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Data availability

The raw data for the first-principles calculations and atomic spin simulations have been deposited in the Zenodo32. Source Data for Figs. 1, 2 and Extended Data Fig. 1 are available with this Paper. Those data are generated by the code developed for this study.

Code availability

The code used in the current study is available at Zenodo33.

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Acknowledgements

The authors acknowledge the support from National Key Research and Development Program of China (Grant No. 2022YFA1402400), National Natural Science Foundation of China (Grant No. 12088101) and NSAF Grant U2230402. All the calculations were performed at Tianhe2-JK at CSRC.

Author information

Authors and Affiliations

  1. Beijing Computational Science Research Center, Beijing, China

    Baishun Yang, Yang Li, Haiqing Lin & Bing Huang

  2. Shenzhen JL Computational Science and Applied Research Institute, Shenzhen, China

    Baishun Yang

  3. Key Laboratory of Computational Physical Sciences (Ministry of Education), Institute of Computational Physical Sciences, State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai, China

    Hongjun Xiang

  4. School of Physics, Zhejiang University, Hangzhou, China

    Haiqing Lin

  5. Department of Physics, Beijing Normal University, Beijing, China

    Haiqing Lin & Bing Huang

Authors
  1. Baishun Yang
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Contributions

B.H. supervised and led the project. B.Y. and B.H. directed the project. B.Y., Y.L. and B.H. prepared the manuscript. All authors discussed the results and contributed to the manuscript.

Corresponding author

Correspondence to Bing Huang.

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The authors declare no competing interests.

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Nature Computational Science thanks Jiadong Zhou and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Jie Pan, in collaboration with the Nature Computational Science team.

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Extended data

Extended Data Fig. 1 Generating MMEIs via Sliding-mapping Approach.

a, Moiré superlattice of the tBL-CrI3. Surrounded insets show the regions with local AA, AB, AB’ and BA stackings, where Cr in the top and bottom layers are colored as the gold and blue, respectively. Dashed-yellow line indicates the unit cell of moiré superlattice. Blue frame represents the local site in Extended Data Fig. 1c. b, Schematic diagram of the relative position of the interlayer Cr atoms with the sliding vector r. c, Examples of one-to-one correspondence between Jinter(r) in tBL-CrI3 to \({{{\mathcal{J}}}}_{inter}\left( r \right)\) in BL-CrI3 via sliding. Color mapping of d, interlayer exchange interaction \({{{\mathcal{J}}}}_{inter}\), e, intralayer nearest-neighboring exchange interaction \({{{\mathcal{J}}}}_{intra}^{1{{{\mathrm{N}}}}}\), f, intralayer next-nearest-neighboring exchange interaction \({{{\mathcal{J}}}}_{intra}^{2{{{\mathrm{N}}}}}\), g, interlayer DM vector Dinter, and h, intralayer DM vector \({{{\mathcal{D}}}}_{intra}^{1{{{\mathrm{N}}}}}\) between two Cr atoms as a function of sliding vector r. Here, all the magnetic parameters are in the unit of meV.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–13, Table 1 and Sections 1 and 2.

Reporting Summary

Source data

Source Data Fig. 1

Statistical source data for Fig. 1.

Source Data Fig. 2

Statistical source data for Fig. 2.

Source Data Extended Data Fig. 1

Statistical source data for Extended Data Fig. 1.

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Yang, B., Li, Y., Xiang, H. et al. Moiré magnetic exchange interactions in twisted magnets. Nat Comput Sci 3, 314–320 (2023). https://doi.org/10.1038/s43588-023-00430-5

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