Incommensurate magnetic modulation in K-rich cryptomelane, K${}_x$Mn${}_8$O${}_{16}$ ($x\approx 1.45$)

Abstract

Cryptomelane is a hollandite-like material consisting of K${}^{+}$ cations in an $\hat{I}\pm$-MnO${}_2$ tunnel-like crystallographic motif. A sample with stoichiometry K${}_{1.448(3)}$Mn${}_8$O${}_{16}$ has been synthesised and its magnetic properties investigated using variable-temperature magnetic susceptibility, heat capacity, and neutron powder diffraction. Three distinct transitions at $T_1=184$\,K, $T_2=54.5$\,K, and $T_3=24$\,K are observed. At $T_1$ there is a subtle tetragonal$\to$monoclinic transition associated with Mn${}^{3+}$/Mn${}^{4+}$ ordering, and a set of non-magnetic superstructure peaks emerge; these could not be indexed definitively and are indicative of an ordering that is incommensurate with the unit cell. Magnetic Bragg peaks emerge below $T_2=54.5$\,K, and their positions indicate an incommensurate modulated magnetic structure. The model consistent with the data is a dual-${\vec{k}}_{\mathrm{mag}}$ structure with a ferromagnetic $|{\vec{k}}_{\mathrm{mag}}|=0$ component and an incommensurate ${\vec{k}}_{\mathrm{mag}}$ parallel to the $\hat{I}\pm$-MnO${}_2$ tunnels [$|{\vec{k}}_{\mathrm{mag}}|=0.36902(15)$], with the latter most likely to be helical. The period of oscillation of the helical component is in line with predictions based on a Heisenberg spin Hamiltonian [Mandal \textit{et al}. Phys. Rev. B 90, 104420 (2014)]. Below $T_3=24$\,K, there is a magnetic transition, which gives rise to a different set of magnetic Bragg peaks indicative of a highly complex magnetic structure.

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