Lattice distortion in the spin-orbital entangled state in RVO3 perovskites.

We report a thorough study of Y$_{0.7}$La$_{0.3}$VO$_3$ single crystals by measuring magnetic properties, specific heat, thermal conductivity, x-ray and neutron diffraction with the motivation of revealing the lattice response to the spin-orbital entanglement in \textit{R}VO$_3$. Upon cooling from room temperature, the orbitally disordered paramagnetic state changes around T*$\sim$220\,K to spin-orbital entangled state which is then followed by a transition at T$_N$=116\,K to C-type orbital ordered (OO) and G-type antiferromagnetic ordered (AF) ground state. In the temperature interval T$_Norbital entanglement of partially filled and degenerate yz/zx orbitals. However, this distortion is incompatible with the steric octahedral site distortion intrinsic to orthorhombic perovskites. Their competition induces a second order transition from the spin-orbital entangled state to C-OO/G-AF ground state where the long range OO suppresses the spin-orbital entanglement. Our analysis suggests that the spin-orbital entangled state and G-OO are comparable in energy and compete with each other. Rare earth site disorder favors the spin-orbital entanglement rather than a cooperative Jahn-Teller distortion. The results also indicate for LaVO$_3$ a C-OO/G-AF state in T$_t$\,$\leq$\,T\,$\leq$T$_N$ and an orbital flipping transition at T$_t$.