In two-dimensional (2D) insulating magnets, the thermal Hall effect of magnons is believed to be a consequence of topological magnon insulator with separated magnon bands and a well-defined Chern number. Due to broken time-reversal symmetry the thermal Hall effect vanishes in Dirac magnons. In this paper, we show that periodically driven semi-Dirac magnon in 2D insulating honeycomb ferromagnet results in a photoinduced Dirac magnon at the topological phase transition between a photoinduced topological and trivial magnon insulator. Remarkably, the photoinduced Dirac magnon and the photoinduced trivial magnon insulator possess a nonzero Berry curvature and exhibit a finite thermal Hall effect. These intriguing properties of periodically driven 2D insulating magnets originate from the bosonic nature of magnons. Hence, they are not expected to exist in 2D electronic Floquet systems.
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