Spin-orbital liquid in Ba$_3$CuSb$_2$O$_9$ stabilized by oxygen holes

Abstract: Both the Jahn-Teller distortion of Cu$^{2+}$O$_6$ octahedra and magnetic ordering are absent in hexagonal Ba$_3$CuSb$_2$O$_9$ suggesting a Cu 3$d$ spin-orbital liquid state. Here, by means of resonant x-ray scattering and absorption experiment, we show that oxygen 2$p$ holes play crucial role in stabilizing this spin-orbital liquid state. These oxygen holes appear due to the "reaction" Sb$^{5+}$$\rightarrow$Sb$^{3+}$ $+$ two oxygen holes, with these holes being able to attach to Cu ions. The hexagonal phase with oxygen 2$p$ holes exhibits also a novel charge-orbital dynamics which is absent in the orthorhombic phase of Ba$_3$CuSb$_2$O$_9$ with Jahn-Teller distortion and Cu 3$d$ orbital order. The present work opens up a new avenue towards spin-charge-orbital entangled liquid state in transition-metal oxides with small or negative charge transfer energy.