Kondo ferromagnets beyond the strong coupling limit

In this talk we consider the spin wave theory of Kondo lattice ferromagnets and examine two important aspects: (i) going beyond the strong coupling (or double-exchange) limit and (ii) introducing the effect of spin-orbit coupling. In particular the latter has recently come into focus in the context of itinerant magnets. We employ a recently introduced strong coupling spin wave expansion of the Kondo lattice model, which is essentially a double expansion in 1/S and in t/J, where J is the Kondo coupling. We show that corrections to the spin wave dispersion beyond strong coupling map to the dispersion of a Heisenberg ferromagnet with exchange interactions beyond nearest neighbors. We furthermore show that topological magnon bands can emerge at the level of linear spin wave theory in Kondo ferromagnets with Kane-Mele spin-orbit coupling in one and two dimensions. We provide a direct correspondence between previous Heisenberg models that host topological magnon bands, in which a next-nearest neighbor Dzyaloshinskii–Moriya term opens a gap at the Dirac points.