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Scale-invariant magnetic anisotropy in RuCl3 at high magnetic fields


In RuCl3, inelastic neutron scattering and Raman spectroscopy reveal a continuum of non-spin-wave excitations that persists to high temperature, suggesting the presence of a spin liquid state on a honeycomb lattice. In the context of the Kitaev model, finite magnetic fields introduce interactions between the elementary excitations, and thus the effects of high magnetic fields that are comparable to the spin-exchange energy scale must be explored. Here, we report measurements of the magnetotropic coefficient—the thermodynamic coefficient associated with magnetic anisotropy—over a wide range of magnetic fields and temperatures. We find that magnetic field and temperature compete to determine the magnetic response in a way that is independent of the large intrinsic exchange-interaction energy. This emergent scale-invariant magnetic anisotropy provides evidence for a high degree of exchange frustration that favours the formation of a spin liquid state in RuCl3.

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Fig. 1: The anisotropic AFM phase boundary.
Fig. 2: Saturation of the magnetic anisotropy above Bc.
Fig. 3: Temperature–magnetic field scaling of the magnetotropic coefficient.
Fig. 4: Angle dependence of the magnetotropic coefficient.

Data availability

All data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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We thank M. Baenitz, A. Bangura, R. Coldea, G. Jackeli, S. Kivelson, S. Nagler, R. Valenti, C. Varma, S. Winter and J. Zaanen for insightful discussions. Samples were grown at the Max Planck Institute for Chemical Physics of Solids. The d.c.-field measurements were made at the National High Magnetic Field Laboratory (NHMFL) in Tallahassee, FL. The pulsed-field measurements were made in the Pulsed Field Facility of the NHMFL in Los Alamos, NM. All work at the NHMFL is supported through the National Science Foundation Cooperative Agreement nos. DMR-1157490 and DMR-1644779, the US Department of Energy and the State of Florida. R.D.M. acknowledges support from LANL LDRD-DR 20160085 Topology and Strong Correlations. M.C. acknowledges support from the Department of Energy ‘Science of 100 tesla’ BES programme for high-field experiments. X-ray data acquisition and analysis was performed at Cornell University. Research conducted at the Cornell High Energy Synchrotron Source (CHESS) is supported by the National Science Foundation under award no. DMR-1332208. B.J.R. acknowledges support from the Institute for Quantum Matter, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under award no. DE-SC0019331. Y.L. acknowledges support from the US Department of Energy through the LANL/LDRD programme and the G.T. Seaborg institute. J.C.P. is supported by a Gabilan Stanford Graduate Fellowship and an NSF Graduate Research Fellowship (grant no. DGE-114747). P.J.W.M. acknowledges funding from the Swiss National Science Foundation through project no. PP00P2-176789.

Author information




K.A.M., R.D.M., B.J.R. and A.S. conceived the experiment. M.S. grew the samples. J.P.C.R., B.J.R. and D.A.S. performed X-ray characterization. K.A.M., R.D.M., M.D.B., Y.L., J.C.P., D.G., M.C., F.F.B., J.B.B. and A.S. performed the measurements. K.A.M., R.D.M, M.J.L., P.J.W.M., B.J.R. and A.S. analysed data and performed simulations. K.A.M., R.D.M., G.S.B., B.J.R. and A.S. wrote the manuscript with contributions from all authors.

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Correspondence to K. A. Modic.

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Nature Physics thanks Arnab Banerjee, Martin Klanjsek and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary text, Figs. 1–15 and references.

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Modic, K.A., McDonald, R.D., Ruff, J.P.C. et al. Scale-invariant magnetic anisotropy in RuCl3 at high magnetic fields. Nat. Phys. 17, 240–244 (2021).

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