Suppression of Thermal Conductivity via Singlet-Dominated Scattering in TmFeO$_3$

We measured the thermal conductivity of the rare-earth orthoferrites, $R$FeO$_3$, where $R$ = Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb from 3 K to 300 K and see an anomalous strong suppression for TmFeO$_3$ over most of the temperature range. Using a Debye thermal transport model, we demonstrate that this suppression is due to resonant scattering between phonons and the Tm$^{3+}$ $4f$ singlet crystal field levels. The implications of these results are discussed in context of thermal conductivity studies in quantum magnets.