  We report a neutron spin-echo study of the critical dynamics in the $S=5/2$
antiferromagnets MnF$_2$ and Rb$_2$MnF$_4$ with three-dimensional (3D) and
two-dimensional (2D) spin systems, respectively, in zero external field. Both
compounds are Heisenberg antiferromagnets with a small uniaxial anisotropy
resulting from dipolar spin-spin interactions, which leads to a crossover in
the critical dynamics close to the N\'eel temperature, $T_N$. By taking
advantage of the $\mu\text{eV}$ energy resolution of the spin-echo
spectrometer, we have determined the dynamical critical exponents $z$ for both
longitudinal and transverse fluctuations. In MnF$_2$, both the characteristic
temperature for crossover from 3D Heisenberg to 3D Ising behavior and the
exponents $z$ in both regimes are consistent with predictions from the
dynamical scaling theory. The amplitude ratio of longitudinal and transverse
fluctuations also agrees with predictions. In Rb$_2$MnF$_4$, the critical
dynamics crosses over from the expected 2D Heisenberg behavior for $T\gg T_N$
to a scaling regime with exponent $z = 1.387(4)$, which has not been predicted
by theory and may indicate the influence of long-range dipolar interactions.
