--- _id: '10025' abstract: - lang: eng text: Ferromagnetism is most common in transition metal compounds but may also arise in low-density two-dimensional electron systems, with signatures observed in silicon, III-V semiconductor systems, and graphene moiré heterostructures. Here we show that gate-tuned van Hove singularities in rhombohedral trilayer graphene drive the spontaneous ferromagnetic polarization of the electron system into one or more spin- and valley flavors. Using capacitance measurements on graphite-gated van der Waals heterostructures, we find a cascade of density- and electronic displacement field tuned phase transitions marked by negative electronic compressibility. The transitions define the boundaries between phases where quantum oscillations have either four-fold, two-fold, or one-fold degeneracy, associated with a spin and valley degenerate normal metal, spin-polarized `half-metal', and spin and valley polarized `quarter metal', respectively. For electron doping, the salient features are well captured by a phenomenological Stoner model with a valley-anisotropic Hund's coupling, likely arising from interactions at the lattice scale. For hole filling, we observe a richer phase diagram featuring a delicate interplay of broken symmetries and transitions in the Fermi surface topology. Finally, by rotational alignment of a hexagonal boron nitride substrate to induce a moiré superlattice, we find that the superlattice perturbs the preexisting isospin order only weakly, leaving the basic phase diagram intact while catalyzing the formation of topologically nontrivial gapped states whenever itinerant half- or quarter metal states occur at half- or quarter superlattice band filling. Our results show that rhombohedral trilayer graphene is an ideal platform for well-controlled tests of many-body theory and reveal magnetism in moiré materials to be fundamentally itinerant in nature. acknowledgement: "The authors acknowledge discussions with A. Macdonald, L. Fu, F. Wang and M. Zaletel. AFY acknowledges support of the National Science Foundation under DMR1654186, and the Gordon and Betty Moore Foundation under award GBMF9471. The authors acknowledge the use of the research facilities within the California NanoSystems Institute, supported by the University of California, Santa Barbara and the University of California, Office of the President.\r\nK.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, Grant Number JPMXP0112101001 and JSPS KAKENHI, Grant Number JP20H00354. EB and TH were supported by the European Research Council (ERC) under grant HQMAT (Grant Agreement No. 817799). A.G. acknowledges support by the European Unions Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement\r\nNo. 754411.\r\n" article_processing_charge: No article_type: original author: - first_name: Haoxin full_name: Zhou, Haoxin last_name: Zhou - first_name: Tian full_name: Xie, Tian last_name: Xie - first_name: Areg full_name: Ghazaryan, Areg id: 4AF46FD6-F248-11E8-B48F-1D18A9856A87 last_name: Ghazaryan orcid: 0000-0001-9666-3543 - first_name: Tobias full_name: Holder, Tobias last_name: Holder - first_name: James R. full_name: Ehrets, James R. last_name: Ehrets - first_name: Eric M. full_name: Spanton, Eric M. last_name: Spanton - first_name: Takashi full_name: Taniguchi, Takashi last_name: Taniguchi - first_name: Kenji full_name: Watanabe, Kenji last_name: Watanabe - first_name: Erez full_name: Berg, Erez last_name: Berg - first_name: Maksym full_name: Serbyn, Maksym id: 47809E7E-F248-11E8-B48F-1D18A9856A87 last_name: Serbyn orcid: 0000-0002-2399-5827 - first_name: Andrea F. full_name: Young, Andrea F. last_name: Young citation: ama: Zhou H, Xie T, Ghazaryan A, et al. Half and quarter metals in rhombohedral trilayer graphene. Nature. 2021. doi:10.1038/s41586-021-03938-w apa: Zhou, H., Xie, T., Ghazaryan, A., Holder, T., Ehrets, J. R., Spanton, E. M., … Young, A. F. (2021). Half and quarter metals in rhombohedral trilayer graphene. Nature. Springer Nature. https://doi.org/10.1038/s41586-021-03938-w chicago: Zhou, Haoxin, Tian Xie, Areg Ghazaryan, Tobias Holder, James R. Ehrets, Eric M. Spanton, Takashi Taniguchi, et al. “Half and Quarter Metals in Rhombohedral Trilayer Graphene.” Nature. Springer Nature, 2021. https://doi.org/10.1038/s41586-021-03938-w. ieee: H. Zhou et al., “Half and quarter metals in rhombohedral trilayer graphene,” Nature. Springer Nature, 2021. ista: Zhou H, Xie T, Ghazaryan A, Holder T, Ehrets JR, Spanton EM, Taniguchi T, Watanabe K, Berg E, Serbyn M, Young AF. 2021. Half and quarter metals in rhombohedral trilayer graphene. Nature. mla: Zhou, Haoxin, et al. “Half and Quarter Metals in Rhombohedral Trilayer Graphene.” Nature, Springer Nature, 2021, doi:10.1038/s41586-021-03938-w. short: H. Zhou, T. Xie, A. Ghazaryan, T. Holder, J.R. Ehrets, E.M. Spanton, T. Taniguchi, K. Watanabe, E. Berg, M. Serbyn, A.F. Young, Nature (2021). date_created: 2021-09-19T22:01:25Z date_published: 2021-09-01T00:00:00Z date_updated: 2023-08-14T07:04:06Z day: '01' department: - _id: MaSe - _id: MiLe doi: 10.1038/s41586-021-03938-w ec_funded: 1 external_id: arxiv: - '2104.00653' isi: - '000706977400002' isi: 1 keyword: - condensed matter - mesoscale and nanoscale physics - condensed matter - strongly correlated electrons - multidisciplinary language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2104.00653 month: '09' oa: 1 oa_version: Preprint project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Nature publication_identifier: eissn: - 1476-4687 issn: - 0028-0836 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: link: - relation: erratum url: https://doi.org/10.1038/s41586-021-04181-z scopus_import: '1' status: public title: Half and quarter metals in rhombohedral trilayer graphene type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2021' ...