Orbital Liquid in Three-Dimensional Mott Insulator: ${\mathrm{LaTiO}}_3$

We present a theory of spin and orbital states in Mott insulator ${\mathrm{LaTiO}}_3$. The spin-orbital superexchange interaction between $d^1\left(t_{2g}\right)$ ions in cubic crystal suffers from a pathological degeneracy of orbital states at the classical level. Quantum effects remove this degeneracy and result in the formation of the coherent ground state, in which the orbital moment of $t_{2g}$ level is fully quenched. We find a finite gap for orbital excitations. Such a disordered state of local degrees of freedom on unfrustrated, simple cubic lattice is highly unusual. Orbital liquid state naturally explains observed anomalies of ${\mathrm{LaTiO}}_3$.