  This theoretical work is devoted to investigating laser-irradiated Floquet
topological magnon insulators on a two-dimensional checkerboard ferromagnet and
corresponding topological phase transitions. It is shown that the checkerboard
Floquet topological magnon insulator is able to be transformed from a
topological magnon insulator into another one possessing various Berry
curvatures and Chern numbers by changing the light intensity. Especially, we
also show that both Tamm-like and topologically protected Floquet magnon edge
states can exist when a nontrivial gap opens. In addition, our results display
that the sign of the Floquet thermal Hall conductivity is also tunable via
varying the light intensity of the laser field.
