# Spin waves and spin-state transitions in a ruthenate high-temperature antiferromagnet

## Abstract

Ruthenium compounds serve as a platform for fundamental concepts such as spin-triplet superconductivity1, Kitaev spin liquids2,3,4,5 and solid-state analogues of the Higgs mode in particle physics6,7. However, basic questions about the electronic structure of ruthenates remain unanswered, because several key parameters (including Hund’s coupling, spin–orbit coupling and exchange interactions) are comparable in magnitude and their interplay is poorly understood, partly due to difficulties in synthesizing large single crystals for spectroscopic experiments. Here we introduce a resonant inelastic X-ray scattering (RIXS)8,9 technique capable of probing collective modes in microcrystals of 4d electron materials. We observe spin waves and spin-state transitions in the honeycomb antiferromagnet SrRu2O6 (ref. 10) and use the extracted exchange interactions and measured magnon gap to explain its high Néel temperature11,12,13,14,15,16. We expect that the RIXS method presented here will enable momentum-resolved spectroscopy of a large class of 4d transition-metal compounds.

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from$8.99 All prices are NET prices. ## Data availability The data sets generated during and/or analysed during the current study are available from the corresponding author upon reasonable request. ## References 1. 1. Maeno, Y., Kittaka, S., Nomura, T., Yonezawa, S. & Ishida, K. Evaluation of spin-triplet superconductivity in Sr2RuO4. J. Phys. Soc. Jpn 81, 011009 (2012). 2. 2. Jackeli, G. & Khaliullin, G. Mott insulators in the strong spin–orbit coupling limit: from Heisenberg to a quantum compass and Kitaev models. Phys. Rev. Lett. 102, 017205 (2009). 3. 3. Chaloupka, J., Jackeli, G. & Khaliullin, G. Kitaev–Heisenberg model on a honeycomb lattice: possible exotic phases in iridium oxides A2IrO3. Phys. Rev. Lett. 105, 027204 (2010). 4. 4. Sandilands, L. J., Tian, Y., Plumb, K. W., Kim, Y.-J. & Burch, K. S. Scattering continuum and possible fractionalized excitations in α-RuCl3. Phys. Rev. Lett. 114, 147201 (2015). 5. 5. Banerjee, A. et al. Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet. Nat. Mater. 15, 733–740 (2016). 6. 6. Jain, A. et al. Higgs mode and its decay in a two-dimensional antiferromagnet. Nat. Phys. 13, 633–637 (2017). 7. 7. Souliou, S.-M. et al. Raman scattering from Higgs mode oscillations in the two-dimensional antiferromagnet Ca2RuO4. Phys. Rev. Lett. 119, 067201 (2017). 8. 8. Kotani, A. & Shin, S. Resonant inelastic X-ray scattering spectra for electrons in solids. Rev. Mod. Phys. 73, 203–246 (2001). 9. 9. Ament, L. J. P., van Veenendaal, M., Devereaux, T. P., Hill, J. P. & van den Brink, J. Resonant inelastic X-ray scattering studies of elementary excitations. Rev. Mod. Phys. 83, 705–767 (2011). 10. 10. Hiley, C. I. et al. Ruthenium(v) oxides from low-temperature hydrothermal synthesis. Angew. Chem. Int. Ed. 53, 4423–4427 (2014). 11. 11. Tian, W. et al. High antiferromagnetic transition temperature of the honeycomb compound SrRu2O6. Phys. Rev. B 92, 100404 (2015). 12. 12. Hiley, C. I. et al. Antiferromagnetism at T > 500 K in the layered hexagonal ruthenate SrRu2O6. Phys. Rev. B 92, 104413 (2015). 13. 13. Streltsov, S., Mazin, I. I. & Foyevtsova, K. Localized itinerant electrons and unique magnetic properties of SrRu2O6. Phys. Rev. B 92, 134408 (2015). 14. 14. Singh, D. J. Electronic structure and the origin of the high ordering temperature in SrRu2O6. Phys. Rev. B 91, 214420 (2015). 15. 15. Hariki, A., Hausoel, A., Sangiovanni, G. & Kuneš, J. DFT+DMFT study on soft moment magnetism and covalent bonding in SrRu2O6. Phys. Rev. B 96, 155135 (2017). 16. 16. Okamoto, S., Ochi, M., Arita, R., Yan, J. & Trivedi, N. Localized-itinerant dichotomy and unconventional magnetism in SrRu2O6. Sci. Rep. 7, 11742 (2017). 17. 17. Braicovich, L. et al. Dispersion of magnetic excitations in the cuprate La2CuO4 and CaCuO2 compounds measured using resonant x-ray scattering. Phys. Rev. Lett. 102, 167401 (2009). 18. 18. Kim, J. et al. Magnetic excitation spectra of Sr2IrO4 probed by resonant inelastic X-ray scattering: establishing links to cuprate superconductors. Phys. Rev. Lett. 108, 177003 (2012). 19. 19. Kim, B. J. & Khaliullin, G. Resonant inelastic X-ray scattering operators for t 2g orbital systems. Phys. Rev. B 96, 085108 (2017). Download references ## Acknowledgements The authors thank I. I. Mazin and Y. L. Xie for stimulating discussions. The project was supported by the European Research Council under advanced grant no. 669550 (Com4Com). The authors thank DESY, a member of the Helmholtz Association HGF, for the provision of experimental facilities. The experiments were carried out at beamlines P01 and P09 of PETRA III at DESY. H.S. and K.U. acknowledge financial support from the JSPS Research Fellowship for Research Abroad. H.S. is partially supported by the Alexander von Humboldt Foundation. ## Author information ### Affiliations Authors ### Contributions H.S., H.G., K.U., Z.Y., M.M. and H.Y. performed the RIXS experiments. H.I., J.N. and H.T. grew SrRu2O6 single crystals and performed sample characterization. H.G., H.C.W. and H.Y. designed the beamline and IRIXS spectrometer. H.S., H.G. and K.U. performed the magnetic REXS experiment with the help of J.A.S. and S.F. H.S. analysed the experimental data. H.L., H.K., D.K., A.Y., B.J.K. and G.K. carried out the theoretical calculations and contributed to the interpretation of the experimental data. H.S. and B.K. wrote the manuscript with comments from all co-authors. B.K. initiated and supervised the project. ### Corresponding authors Correspondence to H. Suzuki or B. Keimer. ## Ethics declarations ### Competing interests The authors declare no competing interests. ## Additional information Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ## Supplementary information ### Supplementary Information Supplementary Figures 1–4, Supplementary Table 1, Supplementary Notes 1–5, Supplementary References 1–12 ## Rights and permissions Reprints and Permissions ## About this article ### Cite this article Suzuki, H., Gretarsson, H., Ishikawa, H. et al. Spin waves and spin-state transitions in a ruthenate high-temperature antiferromagnet. Nat. Mater. 18, 563–567 (2019). https://doi.org/10.1038/s41563-019-0327-2 Download citation • Received: • Accepted: • Published: • Issue Date: ## Further reading • ### Magnetic and intercalation properties of BaRu2O6 and SrRu2O6 • Thomas Marchandier • , Gwenaëlle Rousse • , Quentin Jacquet • , Artem M. 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