  Crystalline solids are generally known as excellent heat conductors,
amorphous materials or glasses as thermal insulators. It has thus come as a
surprise that certain crystal structures defy this paradigm. A prominent
example are type-I clathrates and other materials with guest-host structures.
They sustain low-energy Einstein-like modes in their phonon spectra, but are
also prone to various types of disorder and phonon-electron scattering and thus
the mechanism responsible for their ultralow thermal conductivities has
remained elusive. While recent ab initio lattice dynamics simulations show that
the Einstein-like modes enhance phonon-phonon Umklapp scattering, they
reproduce experimental data only at low temperatures. Here we show that a new
effect, an "all phononic Kondo effect", can resolve this discrepancy. This is
evidenced by our thermodynamic and transport measurements on various clathrate
single crystal series and their comparison with ab initio simulations. Our new
understanding devises design strategies to further suppress the thermal
conductivity of clathrates and other related materials classes, with relevance
for the field of thermoelectric waste heat recovery but also more generally for
phononic applications. More fundamentally, it may trigger theoretical work on
strong correlation effects in phonon systems.
