Commensurate structural modulation in the charge- and orbitally ordered phase of the quadruple perovskite (NaMn3) Mn4 O12

By means of synchrotron x-ray and electron diffraction, we studied the structural changes at the charge order transition ${T}_{\text{CO}}=176$ K in the mixed-valence quadruple perovskite $({\mathrm{NaMn}}_{3}){\mathrm{Mn}}_{4}{\mathrm{O}}_{12}$. Below ${T}_{\text{CO}}$ we find satellite peaks indicating a commensurate structural modulation with the same propagation vector $\mathbf{q}=(1/2,0,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}1/2)$ of the CE magnetic structure that orders at low temperatures, similarly to the case of simple perovskites such as ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_{3}$. In the present case, the modulated structure, together with the observation of a large entropy change at ${T}_{\text{CO}}$, gives evidence of a rare case of full ${\mathrm{Mn}}^{3+}/{\mathrm{Mn}}^{4+}$ charge and orbital order, consistent with the Goodenough-Kanamori model.