Abstract
Quantum materials governed by emergent topological fermions have become a cornerstone of physics. Dirac fermions in graphene form the basis for moiré quantum matter and Dirac fermions in magnetic topological insulators enabled the discovery of the quantum anomalous Hall (QAH) effect1,2,3. By contrast, there are few materials whose electromagnetic response is dominated by emergent Weyl fermions4,5,6. Nearly all known Weyl materials are overwhelmingly metallic and are largely governed by irrelevant, conventional electrons. Here we theoretically predict and experimentally observe a semimetallic Weyl ferromagnet in van der Waals (Cr,Bi)2Te3. In transport, we find a record bulk anomalous Hall angle of greater than 0.5 along with non-metallic conductivity, a regime that is strongly distinct from conventional ferromagnets. Together with symmetry analysis, our data suggest a semimetallic Fermi surface composed of two Weyl points, with a giant separation of more than 75% of the linear dimension of the bulk Brillouin zone, and no other electronic states. Using state-of-the-art crystal-synthesis techniques, we widely tune the electronic structure, allowing us to annihilate the Weyl state and visualize a unique topological phase diagram exhibiting broad Chern insulating, Weyl semimetallic and magnetic semiconducting regions. Our observation of a semimetallic Weyl ferromagnet offers an avenue towards new correlated states and nonlinear phenomena, as well as zero-magnetic-field Weyl spintronic and optical devices.
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All data relevant to the conclusions of this study are available from Zenodo53.
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Acknowledgements
I.B. acknowledges discussions on transport measurements with M. T. Birch and discussions about BaF2 substrates with M. Nakamura. I.B. acknowledges M. Hirschmann for insights on the theory. I.B. and R.Y. acknowledge film synthesis by T. Ueda. We acknowledge K. Manna for transport data on Co2MnGa, C. Zhang for transport data on TaAs and Y. Wang, S.-Y. Yang and M. Ali for anomalous Hall scaling data on reference materials. I.B. acknowledges discussions on Weyl physics with L. Tai, M. Mogi, H. Isobe, T. A. Cochran, D. S. Sanchez, Q. Ma, S.-Y. Xu, J. Checkelsky and K. Yasuda. We are grateful to all members of the RIKEN Center for Emergent Matter Science (CEMS) for discussions. This work was supported by the Japan Society for the Promotion of Science (JSPS), KAKENHI grant 23H05431 (Y. Tokura), 24K17020 (Y.S.), 24H01607 (M.H.), 22H04958 (M. Kawasaki), 24H00197 (N.N.), 24H02231 (N.N.) and 23H01861 (M. Kawamura); and by the Japan Science and Technology Agency (JST) FOREST JPMJFR2238 (M.H.). N.N. was also supported by the RIKEN TRIP Initiative. C.-K.C. was supported by JST Presto grant JPMJPR2357 and partially supported by JST as part of Adopting Sustainable Partnerships for Innovative Research Ecosystem (ASPIRE) grant JPMJAP2318. This work was further supported by the RIKEN TRIP Initiative (Many-Body Electron Systems). Work at Nanyang Technological University was supported by the National Research Foundation, Singapore, under its Fellowship Award (NRF-NRFF13-2021-0010); the Agency for Science, Technology and Research (A*STAR) under its Manufacturing, Trade and Connectivity (MTC) Individual Research Grant (IRG) (grant M23M6c0100); a Singapore Ministry of Education (MOE) Academic Research Fund Tier 3 grant (MOE-MOET32023-0003); a Singapore Ministry of Education (MOE) AcRF Tier 2 grant (MOE-T2EP50222-0014); and the Nanyang Assistant Professorship grant (NTU-SUG).
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Y.To. and N.N. supervised the project. I.B. conceived the research. R.W. and I.B. synthesized thin films and fabricated devices with help from Y.S. and S.N. and under the guidance of R.Y., M.Kawam., A.T., K.S.T., M.Kawas. and Y.To. Y.Z., S.S. and Y.J. performed first-principles calculations under the supervision of G.C. Y.K., Y.O., I.B. and X.-X.Z. acquired and analysed Terahertz spectra under the guidance of Y.Ta., N.N. and Y.To. R.W. and I.B. performed transport measurements with help from Y.S., Y.F. and M.H. C.-K.C. performed the numerical calculations with I.B. and Y.S. I.B. wrote the theory under the guidance of C.-K.C., N.N. and Y.To. I.B. wrote the manuscript, with contributions from all authors.
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Extended data figures and tables
Extended Data Fig. 1 Burkov–Balents proposal without a multilayer.
a, The original theoretical model considers a stack of alternating layers of topological and trivial insulators hosting two-dimensional Dirac cones (red cones) at each interface. These interface states hybridize with one another with amplitude t across the topological layer and u across the trivial layer; there is also ferromagnetism m (ref. 28). b, The resulting electronic structure shows a semimetallic Weyl phase with two Weyl points along kz (cyan and green dots). c, We circumvent the complicated multilayer structure and realize the same electronic structure as the Burkov–Balents proposal in homogeneously doped thin films of (Cr,Bi)2Te3.
Extended Data Fig. 2 Systematics on the magnetic semiconductor.
AHE of composition E, a trivial magnetic semiconductor. The film shows negligible AHE ≪ 1 e2/h for all thicknesses.
Extended Data Fig. 3 Resistivity of compositions A and B.
Measured ρxx(B) and ρyx(B) for (Cr,Bi,Sb)2Te3 and (Cr,Bi)2Te3, used to calculate the conductivity σ(B) in Fig. 1d,e.
Extended Data Fig. 4 Measured Cr composition.
Chromium content x for a series of (Cr,Bi,Sb)2Te3 films measured by ICP-MS, plotted against the nominal chromium content xnominal determined by beam flux pressure during film synthesis. We observe x ≈ 5.7 × xnominal.
Extended Data Fig. 5 Optical conductivity.
Frequency-dependent Hall conductivity in the terahertz range for a Weyl film, composition C of thickness h = 160 nm. The low-frequency ℜ[σxy] is approximately constant and consistent with dc transport (square points).
Extended Data Fig. 6 Temperature dependence and angular magnetoresistance.
a, Temperature dependence of the angular magnetoresistance at xCr = 0.13 and xIn = 0 (included in Fig. 3b, between compositions C and D). b, The change in sign of the angular magnetoresistance suggests that, as the magnetization M develops on cooling, the system shows a transition from a Chern insulator to a semimetallic Weyl phase.
Extended Data Fig. 7 Wide-range electronic structure of Cr0.25Sb1.75Te3 under Cr disorder.
The electronic structure was calculated for an Sb2Te3 supercell with one of eight Sb atoms replaced by Cr dopant atoms, under several dopant disorder configurations. The resulting on-site potentials were averaged out. The disordered electronic structure reveals a single pair of Weyl points along Γ–Z, with Weyl point separation Δkz = 48%, and no other bands at the Fermi level.
Extended Data Fig. 8 Distinguishing topological phases through ρxx(T) and σxx(T).
a, Temperature dependence of the resistivity for a Chern insulating composition, similar to composition D (blue); semimetallic Weyl composition C (purple); and magnetic semiconductor at higher indium doping, z = 0.12 (orange). The Curie temperature for the Chern insulating composition is TC ≈ 55 K, obtained from the onset of the Hall resistivity (light blue). Composition C shows a similar TC. Notably, the Weyl composition C shows a marked metallic downturn in ρxx(T) below TC, whereas the Chern insulator film shows no notable feature around TC. The metallic downturn provides an extra signature of the emergence of a semimetallic Weyl state. b, σxx(T) for the same films, obtained from the resistivity.
Extended Data Fig. 9 AHE.
Magnetization M(B) and Hall resistivity ρyx(B) for composition A. We see that ρyx(B) is approximately proportional to M(B), suggesting that the observed Hall resistivity mainly consists of an AHE54.
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This file contains Supplementary Figs. 1–6, detailing aspects of the numerical and ab initio calculations; thin-film structural characterization; and the definition of Weyl point separation
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Belopolski, I., Watanabe, R., Sato, Y. et al. Synthesis of a semimetallic Weyl ferromagnet with point Fermi surface. Nature 637, 1078–1083 (2025). https://doi.org/10.1038/s41586-024-08330-y
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DOI: https://doi.org/10.1038/s41586-024-08330-y
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