Phonon drag in thermal conductivity of antiferromagnets

We use Boltzmann equation approach to the thermal transport in low-dimensional antiferromagnets with spin-lattice coupling. We consider the limit of fast spin excitations, relevant to many compounds with $J>>\Theta_D$, where $\Theta_D$ is the Debye energy. We discuss the ``off-diagonal'' contribution to the heat current due to the drag of spin excitations on phonons. We calculate this effect for the one-dimensional spin chain materials.