  The critical behaviour of laser-induced changes in magnetic ordering is
studied experimentally in two-dimensional zigzag antiferromagnets $XY$-like
NiPS$_3$ and Ising-like FePS$_3$. To examine laser-induced dynamics in flakes
of these compounds, we employ time-resolved exchange linear dichroism effect
sensitive to zigzag magnetic ordering and independent of the orientation of the
antiferromagnetic vector. In both compounds laser excitation in the vicinity of
the absorption edge induces partial quenching of the antiferromagnetic ordering
manifested by exchange linear dichroism reduction. The amplitude of the effect
varies with temperature as the derivative of the antiferromagnetic vector and
exhibits a critical behaviour with the exponents corresponding to $XY$- and
Ising-models for NiPS$_3$ and FePS$_3$, respectively. Critical slowing down of
the demagnetization in the vicinity of N\'eel temperature is found, however,
only in FePS$_3$. In contrast, the increase of the demagnetization time near
the ordering temperature in NiPS$_3$ is minor. We show that the difference in
the demagnetization times correlates well with the spin specific heat in both
compounds. Beyond the range of slowing down, the demagnetization times in
NiPS$_3$ and FePS$_3$ are comparable, about 5 - 10 ps, and are longer than
those reported earlier for CoPS$_3$ and considerably shorter than for MnPS$_3$.
This points to the importance of the unquenched angular momentum of
transition-metal ions in laser-induced demagnetization process.
