Incommensurate magnetic modulation in K-rich cryptomelane, K$_x$Mn$_8$O$_{16}$ ($x\approx1.45$)

Abstract

Cryptomelane is a hollandite-like material consisting of K$^+$ cations in an $\alpha$-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$\rightarrow$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 $\alpha$-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.