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

The pyrochlore ruthenate In$_2$Ru$_2$O$_7$ displays a subtle competition between spin-orbital entanglement and molecular orbital formation. At room temperature, a spin-orbit-entangled singlet state was identified. With decreasing temperature, In$_2$Ru$_2$O$_7$ undergoes multiple structural transitions and eventually forms a nonmagnetic ground state with semi-isolated Ru$_2$O units on the pyrochlore lattice. The dominant hopping through the Ru-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 with edge-sharing octahedra. We argue that the covalent character of In-O bonds plays a pivotal role in the structural transitions and molecular orbital formation and such bonding character of "$A$-site" ions is an important ingredient for electronic phase competition in complex transition metal oxides.