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By means of diffuse and inelastic x-ray scattering (DS,IXS), we probedirectly the charge-ordering (CO) dynamics in the Verwey system(NaMn$_3$)Mn$_4$O$_{12}$, where a peculiar quadruple perovskite structure withno oxygen disorder stabilizes a nearly full Mn$^{3+}$/Mn$^{4+}$ static chargeorder at $T_{\rm CO}$=175 K concomitant to a commensurate structural modulationwith propagation vector ${\bf q}_{\rm CO}=(\frac{1}{2},\frac{1}{2},0)$. At$T_{\rm CO}$, the IXS spectra unveil a softening of a 35.3 meV phonon at ${\bfq}_{\rm CO}$. Lattice dynamical calculations enable us to attribute this softphonon to a A$_g$ mode whose polarization matches the Jahn-Teller-likedistortion pattern of the structural modulation. This result demonstrates thatthe Jahn-Teller instability is the driving force of the CO Verwey transition in(NaMn$_3$)Mn$_4$O$_{12}$, thus elucidating a long-standing controversyregarding the mechanism of this transition observed in other mixed-valencesystems like magnetite.

Direct observation of Jahn-Teller critical dynamics at a charge-order Verwey transition