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The thermal conductivity $\kappa$ of the Kondo insulator SmB$_6$ was measuredat low temperature, down to 70 mK, in magnetic fields up to 15 T, on singlecrystals grown using both the floating-zone and the flux methods. The residuallinear term $\kappa_0/T$ at $T \to 0$ is found to be zero in all samples, forall magnetic fields, in agreement with previous studies. There is therefore noclear evidence of fermionic heat carriers. In contrast to some prior data, weobserve a large enhancement of $\kappa(T)$ with increasing field. The effect offield is anisotropic, depending on the relative orientation of field and heatcurrent (parallel or perpendicular), and with respect to the cubic crystalstructure. We interpret our data in terms of heat transport predominantly byphonons, which are scattered by magnetic impurities.

Field-dependent heat transport in the Kondo insulator SmB6 : phonons scattered by magnetic impurities