  We study the topological phase transitions induced in spin-orbit coupled
materials with buckling like silicene, germanene, stanene, etc, by circularly
polarised light, beyond the high frequency regime, and unearth many new
topological phases. These phases are characterised by the spin-resolved
topological invariants, $C_0^\uparrow$, $C_0^\downarrow$, $C_\pi^\uparrow$ and
$C_\pi^\downarrow$, which specify the spin-resolved edge states traversing the
gaps at zero quasi-energy and the Floquet zone boundaries respectively. We show
that for each phase boundary, and independently for each spin sector, the gap
closure in the Brillouin zone occurs at a high symmetry point.
