6-GHz lattice response in a quantum spin-orbital liquid probed by time-resolved resonant x-ray scattering

Long-sought quantum spin liquids usually emerge in geometrically frustrated magnets. Less commonly, unfrustrated magnets can harbor a variety of quantum spin liquids if charge and/or orbital degrees of freedom are involved. Jahn-Teller distortion of ${\mathrm{Cu}}^{2+}{\mathrm{O}}_6$ octahedra is absent in hexagonal ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ suggesting a Cu $3d$ spin-orbital liquid state. Here, by means of time-resolved resonant x-ray scattering, we show that hexagonal ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ exhibits a charge-orbital dynamics which is absent in the orthorhombic phase of ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ with Jahn-Teller distortion and Cu $3d$ orbital order. The time scale of charge-orbital dynamics manifests in the coherent phonons at 6 GHz. The present work reveals a role of electron-lattice entanglement in the quantum spin-orbital liquid state.

Figure 1

(a) Schematic crystal structure of hexagonal ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$. Sb and Cu ions are indicated by blue and yellow, respectively. The space groups of hexagonal and orthorhombic phases at low temperature are $P{6}_3/mmc$ and $Cmcm$, respectively [11, 17]. The occupancy of Cu and Sb in the two metal sites of the Cu-Sb face-sharing dumbbells is 50%. In the orthorhombic phase, the Cu and Sb ions are ordered in the dumbbells and form a honeycomb structure as shown in (b) where the Cu sites are connected by O-O bonds.

Figure 2

(a) XAS spectrum in the total fluorescence yield mode and static RSXS spectrum at $\mathrm{Q}=\left(002\right)$ for hexagonal ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ near the Cu $L_3$ edge ($2p_{3/2}$) taken at 250 and 25 K. The RSXS intensities $I$(250 K) and $I$(25 K) are normalized by the intensities of XAS at $hv=923\mathrm{eV}$ at 250 and 25 K, respectively, which were simultaneously measured with RSXS. The bottom panel shows the change ratio of $\left[I\right(250\mathrm{K})-I(25\mathrm{K}\left)\right]/I\left(25\mathrm{K}\right)$. (b) Temperature dependence of RSXS at $hv=930.2\mathrm{eV}$. The intensity was normalized by the value at $T=25\mathrm{K}$.

Figure 3

(a) Photoinduced dynamics at $\mathrm{Q}=\left(002\right)$ with x ray of 930.2 eV (and 923.0 eV) for the hexagonal and orthorhombic phases after the pump pulse at 3.1 eV. (b) Fourier transform of the time-resolved resonant x-ray scattering signals.

Figure 4

Schematic picture of photoinduced charge-orbital dynamics in the hexagonal phase. In the initial state of the hexagonal phase, the spin-orbital resonant state or dynamical Jahn-Teller effects for the Cu sites have been suggested. It is believed that the orbitals are not aligned, but form randomly distributed singletlike states through the Cu-O-O-Cu couplings. The red arrows indicate the resonancelike orbital fluctuations proposed by Nasu et al. [15], which constitute one of the examples of possible orbital fluctuation mechanisms. Coherent vibration between the possible resonant states is observed, reflecting the characteristic frequency for the system.