Spin dynamics simulations of the magnetic dynamics of RbMnF${}_3$ and direct comparison with experiment

Spin-dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of the classical Heisenberg antiferromagnet in simple cubic lattices with linear sizes $L\le 60$. This system is widely recognized as an appropriate model for the magnetic properties of RbMnF${}_3$. Time-evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a new algorithm implemented by Krech {\it etal}, which is based on fourth-order Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor was calculated from the space- and time-displaced spin-spin correlation function. The crossover from hydrodynamic to critical behavior of the dispersion curve and spin-wave half-width was studied as the temperature was increased towards the critical temperature. The dynamic critical exponent was estimated to be $z=(1.43\pm 0.03)$, which is slightly lower than the dynamic scaling prediction, but in good agreement with a recent experimental value. Direct, quantitative comparisons of both the dispersion curve and the lineshapes obtained from our simulations with very recent experimental results for RbMnF${}_3$ are presented.