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Fingerprints of spin-orbital entanglement in transition metal oxides

The concept of spin-orbital entanglement on superexchange bonds in transition metal oxides is introduced and explained on several examples. It is shown that spin-orbital entanglement in superexchange models destabilizes the long-range (spin and orbital) order and may lead either to a disordered spin-liquid state or to novel phases at low temperature which arise from strongly frustrated interactions. Such novel ground states cannot be described within the conventionally used mean field theory which separates spin and orbital degrees of freedom. Even in cases where the ground states are disentangled, spin-orbital entanglement occurs in excited states and may become crucial for a correct description of physical properties at finite temperature. As an important example of this behaviour we present spin-orbital entanglement in the $R$VO$_3$ perovskites, with $R$=La,Pr,...,Yb,Lu, where such finite temperature properties of these compounds can be understood only using entangled states: ($i$) thermal evolution of the optical spectral weights, ($ii$) the dependence of transition temperatures for the onset of orbital and magnetic order on the ionic radius in the phase diagram of the $R$VO$_3$ perovskites, and ($iii$) dimerization observed in the magnon spectra for the $C$-type antiferromagnetic phase of YVO$_3$. Finally, it is shown that joint spin-orbital excitations in an ordered phase with coexisting antiferromagnetic and alternating orbital order introduces topological constraints for the hole propagation and will thus radically modify transport properties in doped Mott insulators where hole motion implies simultaneous spin and orbital excitations.