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Planar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl3


The honeycomb magnet α-RuCl3 has attracted considerable interest because it is proximate to the Kitaev Hamiltonian whose excitations are Majoranas and vortices. The thermal Hall conductivity κxy of Majorana fermions is predicted to be half-quantized. Half-quantization of κxy/T (T, temperature) was recently reported, but this observation has proven difficult to reproduce. Here, we report detailed measurements of κxy on α-RuCl3 with the magnetic field B  a (zigzag axis). In our experiment, κxy/T is observed to be strongly temperature dependent between 0.5 and 10 K. We show that its temperature profile matches the distinct form expected for topological bosonic modes in a Chern-insulator-like model. Our analysis yields magnon band energies in agreement with spectroscopic experiments. At high B, the spin excitations evolve into magnon-like modes with a Chern number of ~1. The bosonic character is incompatible with half-quantization of κxy/T.

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Fig. 1: Planar thermal Hall response of α-RuCl3 with Ba.
Fig. 2: Curves of κxy/T versus T at selected values of B.
Fig. 3: Bosonic edge mode and the planar κxy.

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We acknowledge useful discussions with I. Sodemann and S. Todadri. P.C., T.G., N.Q. and N.P.O. were supported by the US Department of Energy (DE-SC0017863), by a Materials Research Science and Engineering Centers award from the US National Science Foundation (DMR 2011750) and by the Gordon and Betty Moore Foundation EPiQS initiative through grant GBMF9466 (to N.P.O.). A.B. and S.E.N. were supported by the Quantum Science Center, a National Quantum Information Science Research Center of the US Department of Energy. P.L.-K. and D.G.M. were supported by the Gordon and Betty Moore Foundation’s EPiQS initiative through grant GBMF9069.

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Authors and Affiliations



P.C. performed the measurements and analysed the data with N.P.O.; P.C., T.G. and N.P.O. conceptualized the experiment, which employs a methodology developed by them and M.H. The crystals were grown and characterized at Oak Ridge National Laboratory by P.L.-K., A.B., D.G.M. and S.E.N.; N.Q. performed the precision measurements of the experimentally relevant sample dimensions. The manuscript was written by P.C. and N.P.O. with input from all authors.

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Correspondence to N. P. Ong.

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Nature Materials thanks Joseph P. Heremans and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Image of crystal S3.

The three thermometers used for temperature measurements are labeled (TA, TB, TC) as shown.

Extended Data Fig. 2 Time trace of temperature readings in a field-step sequence.

The inset depicts the same data over a narrower time window so that the timescales for the relaxation process can be seen.

Supplementary information

Supplementary Information

Supplementary Figs. 1–12 and Discussion Sections 1–9.

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Czajka, P., Gao, T., Hirschberger, M. et al. Planar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl3. Nat. Mater. 22, 36–41 (2023).

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