Spin-lattice coupling and thermal transport in multiferroic CuCrO$_{2}$*

The co-existence and interplay of ferroelectricity and magnetism in multiferroic materials is of both fundamental and technological importance. We report extensive neutron and x-ray scattering measurements of lattice dynamics in CuCrO$_{2\, }$(7 $\le $T$\le $ 530 K) across the concomitant magnetic and ferroelectric transition (T$_{N}$ \textasciitilde 24 K). These experiments are complemented by first-principles simulations of the phonons. Our phonon dispersions and density of states measurements reveal very anisotropic vibrations of Cu atoms that are also supported by additional atomic displacement parameters from neutron diffraction. Little overall change in phonon frequencies is observed across T$_{N}$. We find that spin fluctuations persist up to $\sim $300 K, far above T$_{N}$. Furthermore, modeling of the thermal conductivity indicates that these spin fluctuations above T$_{N}$ constitute a strong source of phonon scattering, significantly suppressing thermal transport. We compare our results on CuCrO$_{2}$ with another geometrically frustrated multiferroic, YMnO$_{3}$.