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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) andtwo-dimensional (2D) spin systems, respectively, in zero external field. Bothcompounds are Heisenberg antiferromagnets with a small uniaxial anisotropyresulting from dipolar spin-spin interactions, which leads to a crossover inthe critical dynamics close to the N\'eel temperature, $T_N$. By takingadvantage of the $\mu\text{eV}$ energy resolution of the spin-echospectrometer, we have determined the dynamical critical exponents $z$ for bothlongitudinal and transverse fluctuations. In MnF$_2$, both the characteristictemperature for crossover from 3D Heisenberg to 3D Ising behavior and theexponents $z$ in both regimes are consistent with predictions from thedynamical scaling theory. The amplitude ratio of longitudinal and transversefluctuations also agrees with predictions. In Rb$_2$MnF$_4$, the criticaldynamics 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 predictedby theory and may indicate the influence of long-range dipolar interactions.

Neutron spin-echo study of the critical dynamics of spin-5/2 antiferromagnets in two and three dimensions