Heat transport by delocalized spin excitations in SmB$_6$

Measurements of thermal conductivity at low temperatures may offer insights into the low-energy landscape of excitations in the bulk of a material. Here we report thermal transport data in the canonical Kondo insulator, SmB$_6$. In zero magnetic field, we find that the heat transport below T=1 K can be entirely accounted for by phonons, consistent with an insulating state with no long-range magnetic order. With the application of a magnetic field however, new heat carriers are introduced which are neither electrons nor phonons. We discuss these results within the framework of delocalized spin excitations, supporting a gapping of the charge, but not the spin degrees of freedom in the bulk of SmB$_6$.