The original concept of topological insulators (TIs) and Floquet TIs is rooted in electronic systems. For example, graphene with strong spin-orbit coupling (SOC) is a TI with topologically protected chiral edge modes. Whereas in the absence of SOC, graphene irradiated by circularly polarized electric field can be turned to a Floquet topological insulator. In the first part of this talk, I will introduce the concept of topological magnon insulator in honeycomb ferromagnet CrI3 and kagome antiferromagnets. I will also discuss recent material realization of topological magnons in CrI3 by inelastic neutron scattering. In the second part of this talk, I will introduce the concept of Floquet topological magnon insulators as an alternative way to induce topological magnons in irradiated quantum magnets.
Furthermore, I will discuss the potential practical applications of Floquet topological magnons to ultrafast spintronics.