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When spin-orbit-entangled $d$-electrons reside on a honeycomb lattice, richquantum states are anticipated to emerge, as exemplified by the $d^5$ Kitaevmaterials. Distinct yet equally intriguing physics may be realized with a$d$-electron count other than $d^5$. We found that the layered ruthenateAg$_3$LiRu$_2$O$_6$ with $d^4$ Ru$^{4+}$ ions at ambient pressure forms ahoneycomb lattice of spin-orbit-entangled singlets, which is a playground forfrustrated excitonic magnetism. Under pressure, the singlet state does notdevelop the expected excitonic magnetism but experiences two successivetransitions to other nonmagnetic phases, first to an intermediate phase withmoderate distortion of honeycomb lattice, and eventually to a high-pressurephase with very short Ru-Ru dimer bonds. While the strong dimerization in thehigh-pressure phase originates from a molecular orbital formation as in thesister compound Li$_2$RuO$_3$, the intermediate phase represents aspin-orbit-coupled $J$-dimer state which is stabilized by the admixture ofupper-lying $J_{\rm eff} = 1$-derived states. We argue that the $J$-dimer stateis induced by a pseudo-Jahn-Teller effect associated with the low-lyingspin-orbital excited states and is unique to spin-orbit-entangled $d^4$systems. The discovery of competing singlet phases demonstrates richspin-orbital physics of $d^4$ honeycomb compounds and paves the way forrealization of unconventional magnetism.

Competing spin-orbital singlet states in the 4$d^4$ honeycomb ruthenate Ag$_3$LiRu$_2$O$_6$