  We report comprehensive inelastic neutron scattering measurements of the
magnetic excitations in the 2D spin-5/2 Heisenberg antiferromagnet Rb2MnF4 as a
function of temperature from deep in the Neel ordered phase up to paramagnetic,
0.13 < kBT/4JS < 1.4. Well defined spin-waves are found for wave-vectors larger
than the inverse correlation length $\eta^{-1}$ for temperatures up to near the
Curie-Weiss temperature, $\Theta_{CW}$. For wave-vectors smaller than
$\eta^{-1}$, relaxational dynamics occurs. The observed renormalization of
spin-wave energies, and evolution of excitation line-shapes, with increasing
temperature are quantitatively compared with finite-temperature spin-wave
theory, and computer simulations for classical spins. Random phase
approximation calculations provide a good description of the low-temperature
renormalisation of spin-waves. In contrast, lifetime broadening calculated
using the first Born approximation shows, at best, modest agreement around the
zone boundary at low temperatures. Classical dynamics simulations using an
appropriate quantum-classical correspondence were found to provide a good
description of the intermediate- and high-temperature regimes over all
wave-vector and energy scales, and the crossover from quantum to classical
dynamics observed around $\Theta_{CW}/S$, where the spin S=5/2. A
characterisation of the data over the whole wave-vector/energy/temperature
parameter space is given. In this, $T^2$ behaviour is found to dominate the
wave-vector and temperature dependence of the line widths over a large
parameter range, and no evidence of hydrodynamic behaviour or dynamical scaling
behaviour found within the accuracy of the data sets.
