Pressure-temperature phase diagram for orbital and spin states in $R$VO$_{3}(R$=Y,Tb)

Perovskite-type vanadium oxides $R$VO$_{3}$ ($R$=Y, La-Lu) show various physical properties coupled with the orbital and spin states. Orbitally ordered states of V 3$d^{2}$ in YVO$_{3}$ have been systematically investigated by X-ray scattering technique under high-pressure and low-temperature (HP-LT). The pressure-temperature phase diagram for the orbital state was clearly determined from the crystal parameters, i.e. the lattice constants and the reflection conditions. It indicates that the $C$-type orbital ordering ($C$-OO) is stabilized as compared with the $G$-type orbital ordering ($G$-OO) by applying hydrostatic pressure. Based on the result, we succeeded in controlling the ground state of 3$d$-orbital in TbVO$_{3}$ from $G$-OO to $C$-OO by applying pressure. The spin state coupled with the orbital was also studied by neutron scattering under HP-LT. It elucidated that the magnetic ground state changed from the $C$-type spin ordering to the $G$-type one. This result indicates the strong coupling between orbital and spin states.