Commensurate structural modulation in the charge- and orbitally-ordered phase of the quadruple perovskite (NaMn$_3$)Mn$_4$O$_{12}$

Abstract: By means of synchrotron x-ray and electron diffraction, we studied the structural changes at the charge order transition $T_{CO}$=176 K in the mixed-valence quadruple perovskite (NaMn$3$)Mn$_4$O${12}$. Below $T_{CO}$ we find satellite peaks indicating a commensurate structural modulation with the same propagation vector q =(1/2,0,-1/2) of the CE magnetic order that appears at low temperature, similarly to the case of simple perovskites like La${0.5}$Ca${0.5}$MnO$3$. In the present case, the modulated structure together with the observation of a large entropy change at $T{CO}$ gives evidence of a rare case of full Mn$^{3+}$/Mn$^{4+}$ charge and orbital order consistent with the Goodenough-Kanamori model.