Critical slowing of quantum atomic deuterium/hydrogen with features of multiferroicity in the geometrically frustrated system Co2(OD)3Cl/Co2(OH)3Cl

Abstract

An extensive study of hydroxyl salts $\mathrm{C}{\mathrm{o}}_{2}{(\mathrm{OD})}_{3}\mathrm{Cl}/\mathrm{C}{\mathrm{o}}_{2}{(\mathrm{OH})}_{3}\mathrm{Cl}$ utilizing muon-spin-relaxation (\ensuremath{\mu}SR), nuclear magnetic resonance (NMR), and Raman spectroscopy, supplemented by dielectric constant and magnetic susceptibility measurements, has revealed a unique multiferroic system with deuterium-order-type ferroelectricity and geometrically frustrated magnetism. Through the temperature-dependent dynamics of the nuclear fields probed by \ensuremath{\mu}SR, the deuterium atoms in $\mathrm{C}{\mathrm{o}}_{2}{(\mathrm{OD})}_{3}\mathrm{Cl}$ were found to be rapidly fluctuating in the paraelectric phase. Upon cooling, they showed a critical slowing down toward the ferroelectric transition at ${T}_{c}\phantom{\rule{4pt}{0ex}}={T}_{\ensuremath{\varepsilon}}=230\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, below which eight new Raman-active phonon bands appeared as a result of symmetry breaking due to deuterium ordering. Meanwhile, the hydrogen atoms in $\mathrm{C}{\mathrm{o}}_{2}{(\mathrm{OH})}_{3}\mathrm{Cl}$ became quasistatic at a reduced temperature near 210 K, wherein only one new Raman band appeared with a broad dielectric anomaly, suggesting incomplete ordering. Furthermore, the \ensuremath{\mu}SR, NMR, Raman spectroscopy, and the magnetic susceptibility all suggested an increase in magnetic couplings below $\ensuremath{\sim}250\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ in both $\mathrm{C}{\mathrm{o}}_{2}{(\mathrm{OD})}_{3}\mathrm{Cl}$ and $\mathrm{C}{\mathrm{o}}_{2}{(\mathrm{OH})}_{3}\mathrm{Cl}$, demonstrating a multiferroic feature for $\mathrm{C}{\mathrm{o}}_{2}{(\mathrm{OD})}_{3}\mathrm{Cl}$. This work presents a new and unique multiferroic system with an exceptional high ${T}_{\mathrm{c}}$. It also demonstrates that conventional \ensuremath{\mu}SR can be an effective tool for studying ferroelectrics.