  When irradiated via high frequency circularly polarized light, the
stroboscopic dynamics in a Heisenberg spin system on a honeycomb lattice
develops a next nearest neighbor (NNN) Dzyaloshinskii-Moriya (DM) type
term\cite{owerre}, making it a magnonic Floquet topological insulator. We
investigate the entanglement generation and its evolution on such systems -
particularly an irradiated ferromagnetic XXZ spin-$\frac{1}{2}$ model in a
honeycomb lattice as the system parameters are optically tuned. In the high
frequency limit, we compute the lowest quasi-energy state entanglement in terms
of the concurrence between nearest neighbor (NN) and NNN pair of spins and
witness the entanglement transitions occurring there. For the easy axis
scenario, the unirradiated system forms a product state but entanglement grows
between the NNN spin pairs beyond some cut-off DM strength. Contrarily in easy
planar case, NN and NNN spins remain already entangled in the unirradiated
limit. It then goes through an entanglement transition which causes decrease
(increase) of the NN (NNN) concurrences down to zero (up to some higher value)
at some critical finite DM interaction strength. For a high frequency of
irradiation and a suitably chosen anisotropy parameter, we can vary the field
strength to witness sudden death and revival of entanglement in the Floquet
system. Both exact diagonalization and modified Lanczos techniques are used to
obtain the results upto 24 site lattice. We also calculate the thermal
entanglement and obtain estimates for the threshold temperatures below which
non-zero concurrence can be expected in the system.
