Topological phases of electrons induced by electron-magnon interactions

Topological phases of electrons such as topological insulators and quantum Hall states typically require strong spin-orbit coupling or magnetic fields. In this study, we consider an electron system coupled to a spin system, where electrons interact with magnons, i.e., quasiparticles of spin waves. We show that the interaction between electrons and magnons transfers the effect of symmetry breaking in the spin system to the electron system, whereby a nontrivial topological phase can be induced in the electron system that is otherwise topologically trivial. Through this ``topology transfer'' mechanism, we demonstrate the realization of various topological phases, including quantum Hall and quantum spin Hall insulators, in simple ferromagnetic spin systems, without requiring strong spin-orbit coupling or an external magnetic field for electron systems.