  The ultrafast manipulation of magnetic order due to optical excitation is
governed by the intricate flow of energy and momentum between the electron,
lattice and spin subsystems. While various models are commonly employed to
describe these dynamics, a prominent example being the microscopic three
temperature model (M3TM), systematic, quantitative comparisons to both the
dynamics of energy flow and magnetic order are scarce. Here, we apply a M3TM to
the ultrafast magnetic order dynamics of the layered antiferromagnet
GdRh$_2$Si$_2$. The femtosecond dynamics of electronic temperature, surface
ferromagnetic order, and bulk antiferromagnetic order were explored at various
pump fluences employing time- and angle-resolved photoemission spectroscopy and
time-resolved resonant magnetic soft x-ray diffraction, respectively. After
optical excitation, both the surface ferromagnetic order and the bulk
antiferromagnetic order dynamics exhibit two-step demagnetization behaviors
with two similar timescales (<1 ps, ~10 ps), indicating a strong exchange
coupling between localized 4f and itinerant conduction electrons. Despite a
good qualitative agreement, the M3TM predicts larger demagnetization than our
experimental observation, which can be phenomenologically described by a
transient, fluence-dependent increased N\'eel temperature. Our results indicate
that effects beyond a mean-field description have to be considered for a
quantitative description of ultrafast magnetic order dynamics.
