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We study the topological phase transitions induced in spin-orbit coupledmaterials with buckling like silicene, germanene, stanene, etc, by circularlypolarised light, beyond the high frequency regime, and unearth many newtopological phases. These phases are characterised by the spin-resolvedtopological invariants, $C_0^\uparrow$, $C_0^\downarrow$, $C_\pi^\uparrow$ and$C_\pi^\downarrow$, which specify the spin-resolved edge states traversing thegaps at zero quasi-energy and the Floquet zone boundaries respectively. We showthat for each phase boundary, and independently for each spin sector, the gapclosure in the Brillouin zone occurs at a high symmetry point.

Bulk-edge correspondence and new topological phases in periodically driven spin-orbit coupled materials in the low frequency limit