Abstract
The charge order in multiferroic LuFe${}_{2}$O${}_{4}$ has been investigated with resonant x-ray diffraction at the Fe K edge in the combined charge ordered and magnetic phase. The energy dependence of the charge order reflection ($\frac{1}{3}\frac{1}{3}\frac{7}{2}$) has been analyzed in detail to investigate the charge disproportionation between the iron sites as a function of temperature. It is found that the charge disproportionation is constant within $0.02e$ across the N\'eel temperature ${T}_{N}$. The charge order reflection exhibits a decrease in intensity with increasing temperature which is attributed to an increase in the probability of electron hopping. We confirm the increase in polarization at ${T}_{N}$ is not of static origin but rather dynamic. Our observations are consistent with antiferromagnetically aligned magnetic moments inhibiting the double exchange mechanism and reducing the probability of electrons hopping between Fe${}^{2+}$ and Fe${}^{3+}$ in the magnetic phase.
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