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

Ruthenium compounds serve as a platform for fundamental concepts such as spin-triplet superconductivity¹, Kitaev spin liquids^2-5 and solid-state analogues of the Higgs mode in particle physics^6,7. 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 temperature^11-16. We expect that the RIXS method presented here will enable momentum-resolved spectroscopy of a large class of 4d transition-metal compounds.