Incommensurate atomic and magnetic modulations in the spin-frustrated β−NaMnO2 triangular lattice

The layered $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{NaMn}{\mathrm{O}}_{2}$, a promising Na-ion energy-storage material, has been investigated for its triangular lattice capability to promote complex magnetic configurations that may release symmetry restrictions for the coexistence of ferroelectric and magnetic orders. The complexity of the neutron powder diffraction patterns underlines that the routinely adopted commensurate structural models are inadequate. Instead, a single-phase superspace symmetry description is necessary, demonstrating that the material crystallizes in a compositionally modulated $\mathbf{q}=(0.077(1)$, 0, 0) structure. Here $\mathrm{M}{\mathrm{n}}^{3+}$ Jahn-Teller distorted $\mathrm{Mn}{\mathrm{O}}_{6}$ octahedra form corrugated layer stacking sequences of the $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{NaMn}{\mathrm{O}}_{2}$ type, which are interrupted by flat sheets of the \ensuremath{\alpha}-like oxygen topology. Spontaneous long-range collinear antiferromagnetic order, defined by the propagation vector $\mathbf{k}=(1/2,1/2,1/2)$, appears below ${T}_{\mathrm{N}1}=200\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Moreover, a second transition into a spatially modulated proper-screw magnetic state (k \ifmmode\pm\else\textpm\fi{} q) is established at ${T}_{\mathrm{N}2}=95\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, with an antiferromagnetic order parameter resembling that of a two-dimensional (2D) system. The evolution of $^{23}\mathrm{Na}$ NMR spin-lattice relaxation identifies a magnetically inhomogeneous state in the intermediate $T$ region $({T}_{\mathrm{N}2}<T<{T}_{\mathrm{N}1})$, while its strong suppression below ${T}_{\mathrm{N}2}$ indicates that a spin gap opens in the excitation spectrum. High-resolution neutron inelastic scattering confirms that the magnetic dynamics are indeed gapped (\ensuremath{\Delta} \ensuremath{\sim} 5 meV) in the low-temperature magnetic phase, while simulations on the basis of the single-mode approximation suggest that Mn spins residing on adjacent antiferromagnetic chains, establish sizable 2D correlations. Our analysis points out that novel structural degrees of freedom promote cooperative magnetism and emerging dielectric properties in this nonperovskite type of manganite.