Orbital fluctuations in the RVO₃ perovskites

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The properties of Mott insulators with orbital degrees of freedom are described by spin-orbital superexchange models, which provide a theoretical framework for understanding their magnetic and optical properties. We introduce such a model derived for (xy)¹(yz/zx)¹ configuration of V³⁺ ions in the RVO₃ perovskites, R=Lu,Yb,,La, and demonstrate that {yz,zx} orbital fluctuations along the c axis are responsible for the huge magnetic and optical anisotropies observed in the almost perfectly cubic compound LaVO₃. We argue that the GdFeO₃ distortion and the large difference in entropy of C-AF and G-AF phases is responsible for the second magnetic transition observed at Tₙ₂ in YVO₃. Next we address the variation of orbital and magnetic transition temperature, T OO and Tₙ₁, in the RVO₃ perovskites, after extending the spin-orbital model by the crystal-field and the orbital interactions which arise from the GdFeO₃ and Jahn-Teller distortions of the VO₆ octahedra. We further find that the orthorhombic distortion which increases from LaVO₃ to LuVO₃ plays a crucial role by controlling the orbital fluctuations, and via the modified orbital correlations influences the onset of both magnetic and orbital order.