  Insulating quantum magnets lie at the forefront both of fundamental research
into quantum matter and of technological exploitation in the increasingly
applied field of spintronics. In this context, the magnetic thermal transport
is a particularly sensitive probe of the elementary spin and exotic topological
excitations in unconventional magnetic insulators. However, magnetic
contributions to heat conduction are invariably intertwined with lattice
contributions, and thus the issue of spin-phonon coupling in determining the
spin and thermal transport properties becomes more important with emergent
topological magnetic system. Here we report the observation of an anomalously
strong enhancement of the thermal conductivity, occurring at all relevant
temperatures, in the layered honeycomb material CrCl$_3$ in the presence of an
applied magnetic field. Away from the magnetically ordered phase at low
temperatures and small fields, there is no coherent spin contribution to the
heat conduction, and hence the effect must be caused by a strong suppression of
the phonon thermal conductivity due to magnetic fluctuations, which are in turn
suppressed by the field. We build an empirical model for the thermal
conductivity of CrCl$_3$ within a formalism assuming an independently
determined number of spin-flip processes and an efficiency of the phonon
scattering events they mediate. By extracting the intrinsic phonon thermal
conductivity we obtain a quantitative description at all fields and
temperatures and demonstrate that the scattering efficiency is entirely
independent of the field. In this way we use CrCl$_3$ as a model system to
understand the interactions between spin and phonon excitations in the context
of thermal transport. We anticipate that the completely general framework we
introduce will have broad implications for the interpretation of transport
phenomena in magnetic quantum materials.
