Floquet no-go theorem and engineering topological magnons

Topological magnonics opens avenues for robust, reconfigurable, and scalable magnon-based spintronic devices. In this paper, we propose a Floquet no-go theorem for magnetically ordered systems, which identifies forbidden auxiliary hoppings induced by circularly polarized laser light. Based on this theorem and perturbation theory, we establish a set of rules for engineering topological magnons from massless Dirac magnons. We demonstrate the realization of topological magnons in both non-Bravais lattice ferromagnets and Bravais lattice antiferromagnets, along with calculations of their magnon band topological properties and thermal Hall conductivities. We discuss potential material candidates for experimental realization of our results. Our research establishes a systematic framework for engineering topological magnons in magnetically ordered systems, thereby expanding the search scope for topological magnon materials.