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The pyrochlore ruthenate In$_2$Ru$_2$O$_7$ displays a subtle competitionbetween spin-orbital entanglement and molecular orbital formation. At roomtemperature, a spin-orbit-entangled singlet state was identified. Withdecreasing temperature, In$_2$Ru$_2$O$_7$ undergoes multiple structuraltransitions and eventually forms a nonmagnetic ground state with semi-isolatedRu$_2$O units on the pyrochlore lattice. The dominant hopping through theRu-O-Ru linkage leads to molecular orbital formation within the Ru$_2$O units.This molecular orbital formation is unique in that it involves the O$^{2-}$anions, unlike the transition-metal dimers observed in systems withedge-sharing octahedra. We argue that the covalent character of In-O bondsplays a pivotal role in the structural transitions and molecular orbitalformation and such bonding character of "$A$-site" ions is an importantingredient for electronic phase competition in complex transition metal oxides.

Formation of orbital molecules on a pyrochlore lattice induced by A-O bond covalency