  Motivated by cold atom and ultra-fast pump-probe experiments we study the
melting of long-range antiferromagnetic order of a perfect N\'eel state in a
periodically driven repulsive Hubbard model. The dynamics is calculated for a
Bethe lattice in infinite dimensions with non-equilibrium dynamical mean-field
theory. In the absence of driving melting proceeds differently depending on the
quench of the interactions to hopping ratio $U/J_0$ from the atomic limit. For
$U \gg J_0$ decay occurs due to mobile charge-excitations transferring energy
to the spin sector, while for $J_0 \gtrsim U$ it is governed by the dynamics of
residual quasi-particles. Here we explore the rich effects strong periodic
driving has on this relaxation process spanning three frequency $\omega$
regimes: (i) high-frequency $\omega \gg U,J_0$, (ii) resonant $l\omega = U >
J_0$ with integer $l$, and (iii) in-gap $U > \omega > J_0$ away from resonance.
In case (i) we can quickly switch the decay from quasi-particle to
charge-excitation mechanism through the suppression of $J_0$. For (ii) the
interaction can be engineered, even allowing an effective $U=0$ regime to be
reached, giving the reverse switch from a charge-excitation to quasi-particle
decay mechanism. For (iii) the exchange interaction can be controlled with
little effect on the decay. By combining these regimes we show how periodic
driving could be a potential pathway for controlling magnetism in
antiferromagnetic materials. Finally, our numerical results demonstrate the
accuracy and applicability of matrix product state techniques to the
Hamiltonian DMFT impurity problem subjected to strong periodic driving.
