  We reveal the crucial effect of strong spin-charge coupling on high-harmonic
generation (HHG) in Mott insulators. In a system with antiferromagnetic
correlations, the HHG signal is drastically enhanced with decreasing
temperature, even though the gap increases and the production of charge
carriers is suppressed. This anomalous behavior, which has also been observed
in recent HHG experiments on Ca$_2$RuO$_4$, originates from a cooperative
effect between the spin-charge coupling and the thermal ensemble, and the
strongly temperature-dependent coherence between charge carriers. We argue that
the peculiar temperature dependence of HHG is a generic feature of Mott
insulators, which can be controlled via the Coulomb interaction and
dimensionality of the system. Our results demonstrate that correlations between
different degrees of freedom, which are a characteristic feature of strongly
correlated solids, have significant and nontrivial effects on nonlinear optical
responses.
