Electronic structure of Lu$_{1-x}$La$_{x}$VO$_{3}$ single crystals using soft x-ray spectroscopy*

The rare-earth vanadates, $R$VO$_{3}$, offer a rich phase diagram of both orbital and spin ordering phenomena, stemming from their two-fold occupation of the three-fold degenerate V $t_{2g}$ orbitals. It has been discussed that, in $R$VO$_{3}$, which shows the $t_{2g}$ orbital ordering, the Jahn-Teller coupling suppression is much weaker than that in the $e_{g}$ electron systems. In order to address the orbital ordering effects, we report soft x-ray measurements of Lu$_{1-x}$La$_{x}$VO$_{3}$ single crystals, which approach both the smallest and largest rare-earth ionic sizes. X-ray absorption spectroscopy and x-ray emission spectroscopy, which reveal both the unoccupied and occupied partial density of states, are employed to observe the changes in the V 3$d$ and O 2$p$ states, across the orbital ordering transitions and $R$-site ionic radii. Also, resonant inelastic x-ray scattering is applied to probe the O 2$p$-V 3$d$* charge transfer excitations and V 3$d$-3$d$* transitions. Together, these complementary techniques provide a picture of the electronic structure of Lu$_{1-x}$La$_{x}$VO$_{3}$ to test the role of the orbital ordering during phase transitions with varying rare-earth ionic sizes.