  Ruthenium compounds play prominent roles in materials research ranging from
oxide electronics to catalysis, and serve as a platform for fundamental
concepts such as spin-triplet superconductivity, Kitaev spin-liquids, and
solid-state analogues of the Higgs mode in particle physics. However, basic
questions about the electronic structure of ruthenates remain unanswered,
because several key parameters (including the Hund's-rule, spin-orbit, and
exchange interactions) are comparable in magnitude, and their interplay is
poorly understood - partly due to difficulties in synthesizing sizable single
crystals for spectroscopic experiments. Here we introduce a resonant inelastic
x-ray scattering (RIXS) technique capable of probing collective modes in
microcrystals of $4d$-electron materials. We present a comprehensive set of
data on spin waves and spin-state transitions in the honeycomb antiferromagnet
SrRu$_{2}$O$_{6}$, which possesses an unusually high N\'eel temperature. The
new RIXS method provides fresh insight into the unconventional magnetism of
SrRu$_{2}$O$_{6}$, and enables momentum-resolved spectroscopy of a large class
of $4d$ transition-metal compounds.
