Abstract
A thermal Hall effect occurs in an increasing number of insulators and is often attributed to phonons, but the underlying mechanism is not known in most cases. Two main scenarios have been proposed: either a coupling of phonons to spins or scattering of phonons by impurities or defects, but there is no systematic evidence to support either of them. Here we present evidence for the phonon impurity scattering picture by studying the effect of adding rhodium impurities to the antiferromagnetic insulator Sr2IrO4, substituting for the spin-carrying iridium atoms. We find that adding small concentrations of rhodium impurities increases the thermal Hall conductivity, but adding enough rhodium to suppress the magnetic order eventually decreases it until it nearly vanishes. In contrast, introducing lanthanum impurities that substitute for the strontium atoms, which lie outside the IrO2 planes that are the seat of magnetism, produces a much smaller enhancement of the thermal Hall conductivity. We conclude that the thermal Hall effect in this material is caused by the scattering of phonons by impurities embedded within a magnetic environment.
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Data availability
Source data are available with this paper. All other data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.
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Acknowledgements
We thank K. Behnia, H. Guo, D. Hsieh, S. A. Kivelson and S. Sachdev for fruitful discussions. L.T. acknowledges support from the Canadian Institute for Advanced Research (CIFAR) as a Fellow and funding from the Natural Sciences and Engineering Research Council of Canada (NSERC; PIN: 123817), the Fonds de recherche du Québec – Nature et Technologies (FRQNT), the Canada Foundation for Innovation (CFI) and a Canada Research Chair. This research was undertaken thanks in part to funding from the Canada First Research Excellence Fund. A.A. acknowledges support from the NSERC-CREATE programme QSciTech and Bourse d’excellence de l’Institut quantique à l’Université de Sherbrooke.
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A.A., G.G., M.-E.B., L.C. and É.L. performed the thermal Hall conductivity measurements. A.A. prepared and characterized the samples. V.B. grew the single crystals of Sr2IrO4, Sr2Ir1−xRhxO4 and Sr2−xLaxIrO4. A.A. and L.T. wrote the paper, in consultation with all authors. L.T. supervised the project.
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Extended data
Extended Data Fig. 1 Thermal conductivities in Rh-doped Sr2IrO4.
a) Thermal conductivity of Sr2Ir1-xRhxO4 for a heat current parallel to the IrO2 planes (J // a // x) and a magnetic field of 15 T applied normal to the planes (H // c // z), plotted as κxx/T vs T, for dopings x as indicated. b) Thermal Hall conductivity for the same samples, plotted as − κxy/T vs T (κxy is negative in all samples at all temperatures).
Extended Data Fig. 2 EDX spectra of Sr2IrO4 samples.
Typical EDX spectra for Sr2IrO4 (red), La-doped Sr2IrO4 (black) and Rh-doped Sr2IrO4 (blue). From such spectra taken on samples from the same batch as our transport samples, the value of x is confirmed, within an uncertainty of at most ± 20 %.
Extended Data Fig. 3 Magnetic field dependence of κxx and κxy.
a) Thermal conductivity of Rh-doped Sr2IrO4 with x = 0.05, plotted as κxx/T vs T for different magnetic fields, as indicated. b) Thermal Hall conductivity of the same sample, plotted as – κxy/H vs T for the same magnetic fields, as indicated.
Extended Data Fig. 4 Thermal conductivities in La-doped Sr2IrO4.
a) Thermal conductivity κxx of Sr2-xLaxIrO4 for a heat current parallel to the IrO2 planes (J // a // x) and a magnetic field of 15 T applied normal to the planes (H // c // z), plotted as κxx vs T, for dopings x as indicated. b) Thermal Hall conductivity κxy for the same samples, plotted as – κxy vs T (κxy is negative in all samples at all temperatures).
Extended Data Fig. 5 Reproducibility of our two main findings.
a) Evolution of the ratio |κxy/κxx| in Sr2IrO4 with impurity concentration x, for both Rh doping (red squares) and La doping (blue circles), evaluated at T = 20 K and H = 15 T. Error bars are ± 15% (see Methods). b) Magnitude of the thermal Hall conductivity κxy in Sr2IrO4 vs x, evaluated at T = 20 K and H = 15 T, relative to its value at x = 0. We see that 3 separate samples of Rh-doped Sr2IrO4 – with x = 0.02, 0.05, 0.07 – demonstrate the main conclusion of our paper, namely that a low level of Rh impurities causes a huge enhancement of the thermal Hall angle, by a factor of at least 30 (or of the thermal Hall conductivity, by a factor of 20 or more) relative to x = 0. We also see that 3 separate samples of La-doped Sr2IrO4 – with x = 0.02, 0.04, 0.08 – demonstrate the second major conclusion of our paper, namely that La impurities cause a much smaller enhancement, by at least an order of magnitude compared to Rh doping. Having three separate samples that support each claim is a satisfactory level of reproducibility. Error bars are ± 25% (see Methods).
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Ataei, A., Grissonnanche, G., Boulanger, ME. et al. Phonon chirality from impurity scattering in the antiferromagnetic phase of Sr2IrO4. Nat. Phys. 20, 585–588 (2024). https://doi.org/10.1038/s41567-024-02384-5
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DOI: https://doi.org/10.1038/s41567-024-02384-5
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