Spin dynamics in two-dimensional quantum Heisenberg antiferromagnets

We demonstrate that the self-consistent theory of Blume and Hubbard, a variant of the mode-mode coupling theory, works well for a wide range of temperature to describe the spin dynamics of the two-dimensional Heisenberg model. At low temperatures, the relaxation function is shown to satisfy a dynamical scaling relation consistent with the nonlinear a model analysis and the Monte Carlo simulations. The theory is also applied to calculate the spin-lattice relaxation time T-1. The inverse, 1/T-1, is shown to decrease rapidly and then to turn to increase gradually as temperature increases in agreement with the Monte Carlo simulation. When the hyperfine interaction has a large intersite coupling, the contribution of the diffusion mode is found to become very large with increasing temperatures. We discuss the necessity of introducing a cutoff in the long wave-length for the diffusion mode for comparison with the experiments on La2CuO4.