Time-Dependent Spin Correlations in Heisenberg Linear Chains

We have used the self-consistent theory of Blume and Hubbard1 to calculate the Fourier transform S(q, ω) of the time-dependent spin pair correlation function for the Heisenberg linear chain at finite temperatures. The spins are treated as classical unit vectors2 and the time-independent correlation functions for the linear chain with nearest-neighbor interactions are used as initial conditions for the approximate integrodifferential equations. Numerical solution of these equations yields S(q, ω) for both ferromagnetic and antiferromagnetic interactions. At low temperatures in the paramagnetic regime, ``spin-wave'' type peaks are found in the scattering function. The shape and position of these peaks as a function of temperature agrees qualitatively with the experimental results of Birgeneau et al.