LAUSR

We present a study of the thermal Hall effect in the extended Heisenberg model with $XXZ$ anisotropy in the kagome lattice. This model has the particularity that, in the classical case, and for a broad region in parameter space, an external magnetic field induces a chiral symmetry breaking: the ground state is a doubly degenerate $q=0$ order with either positive or negative net chirality. Here, we focus on the effect of this chiral phase transition in the thermal Hall conductivity using linear-spin-waves theory. We explore the topology and calculate the Chern numbers of the magnonic bands, obtaining a variety of topological phase transitions. We also compute the magnonic effect to the critical temperature associated with the chiral phase transition (${T}_{c}^{SW}$). Our main result is that, the thermal Hall conductivity, which is null for $Tg{T}_{c}^{SW}$, becomes nonzero as a consequence of the spontaneous chiral symmetry breaking at low temperatures. Therefore, we present a simple model where it is possible to ``switch'' on/off the thermal transport properties introducing a magnetic field and heating or cooling the system.