Abstract
Crystal and magnetic structures of the high-pressure-stabilized perovskite modification of ${\mathrm{Mn}}_{2}{\mathrm{O}}_{3}$ ($\ensuremath{\zeta}\text{\ensuremath{-}}{\mathrm{Mn}}_{2}{\mathrm{O}}_{3}$) have been studied by neutron powder diffraction combined with symmetry arguments based on the phenomenological Landau theory. This metastable phase exhibits a unique charge disproportionation phenomenon stabilizing the quadruple perovskite structure (${\mathrm{Mn}}^{2+}{\mathrm{Mn}}_{3}^{3+}){\mathrm{Mn}}_{4}^{3.25+}{\mathrm{O}}_{12}$ with an additional charge-ordering and commensurate orbital density wave localized in the B-site perovskite position. The commensurate nature of the orbital density wave is stimulated by a coupling of the orbital ordering to independent structural distortions, which improve poor bonding conditions of ${\mathrm{Mn}}^{2+}$ in the A-site perovskite position. Below ${T}_{1}\ensuremath{\sim}100$ K, an anharmonic longitudinal spin density wave arises and locks to the structural modulation associated with the orbital density. At ${T}_{2}\ensuremath{\sim}50$ K, the magnetic subsystem delocks from the structural modulation giving rise to a multi-$k$ phase-modulated ground state admixing cycloidal and helical components. The complex anharmonic and phase-modulated magnetic structures are discussed based on a phenomenological magneto-orbital coupling scheme, previously developed to explain the multi-$k$ helical ground states with modulated spin chirality observed in ${\mathrm{A}}^{2+}{\mathrm{Mn}}_{7}{\mathrm{O}}_{12}$ (${\mathrm{A}}^{2+}=\text{Ca}$, Sr, Pb, and Cd) quadruple perovskites.
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