Orbital state and metal-insulator transition in ${\mathrm{Ca}}_{2-x}{\mathrm{Sr}}_x{\mathrm{RuO}}_4$ $(x=0.0\mathrm{}$ and 0.09) studied by x-ray absorption spectroscopy

The nature of metal-insulator (MI) transition in a $t_{2g}$-electron system ${\mathrm{Ca}}_{2-x}{\mathrm{Sr}}_x{\mathrm{RuO}}_4$ has been investigated using O $1s$ x-ray absorption spectroscopy (XAS). The O $1s$ XAS data strongly depend on temperature and demonstrate that the hysteresis of the MI transition is accompanied by the hysteresis of the orbital change. An unrestricted Hartree-Fock analysis indicates that the amount of $yz/zx$ hole is discontinuously reduced at the MI transition. In the insulating phase, the amount of $4d$ $yz/zx$ hole gradually decreases on heating, suggesting that partial orbital fluctuation increases with temperature.