Incommensurate structural and magnetic modulations in potassium-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 $\alpha$-MnO${}_2$ tunnel-like crystallographic motif. Cryptomelane with stoichiometry K${}_x$Mn${}_8$O${}_{16}$ ($x\approx 1.45$) has been synthesized 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 emergence of a set of non-magnetic superstructure peaks indexable to a ${\vec{k}}_{\mathrm{struc}}\approx 0.74\overrightarrow{c^{\ast }}$ incommensurate modulation parallel to the $\alpha$-MnO${}_2$ tunnels. Our findings are consistent with a relation previously reported in titanate hollandites, that $x\approx 2|{\vec{k}}_{\mathrm{struc}}|$. 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 ${\vec{k}}_{\mathrm{mag}}\approx 0.37\overrightarrow{c^{\ast }}$, with the latter most likely to be helical. The period of oscillation of the incommensurate magnetic 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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