Abstract
Structural fluctuation in ${\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$, which is proposed to exhibit a spin-orbital entangled state, has been studied by diffuse x-ray scattering, x-ray fluorescence holography, and inelastic x-ray scattering. Two kinds of spatial fluctuations are observed: temperature-independent and temperature-dependent ones. The former is related to Cu/Sb arrangement. The short-range chemical correlation in ${\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$ is honeycomblike, whereas the correlation length is as short as the diameter of the honeycomb unit. The temperature variation of ferro- and antiferro-orbital correlations is extracted from Huang scattering intensity distributions. Both of these correlations increase with decreasing temperature down to 60 K, which corresponds to the energy of magnetic interaction of ${\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$. A wide distribution of the characteristic time scale of the orbital motion is proposed from the spatial fluctuation of the ionic arrangement in ${\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$.
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