  Dynamically driven interacting quantum many-body systems have the potential
to exhibit properties that defy the laws of equilibrium statistical mechanics.
A widely studied model is the impulsively driven antiferromagnetic Mott
insulator, which is predicted to realize exotic transient phenomena including
dynamical phase transitions into thermally forbidden states and highly
non-thermal magnon distributions. However such far-from-equilibrium regimes,
where conventional time-dependent Ginzburg-Landau descriptions fail, are
experimentally challenging to prepare and to probe especially in solid state
systems. Here we use a combination of time-resolved second harmonic optical
polarimetry and coherent magnon spectroscopy to interrogate $n$-type
photo-doping induced ultrafast magnetic order parameter dynamics in the Mott
insulator Sr$_2$IrO$_4$. We uncover an unusual far-from-equilibrium critical
regime in which the divergences of the magnetic correlation length and
relaxation time are decoupled. This violation of conventional thermal critical
behavior arises from the interplay of photo-doping and non-thermal magnon
population induced demagnetization effects. Our findings, embodied in a
non-equilibrium "phase diagram", provide a blueprint for engineering the
out-of-equilibrium properties of quantum matter, with potential applications to
terahertz spintronics technologies.
