Series Expansions for High-Temperature Dynamics of Heisenberg Paramagnets

High-temperature expansions are given for the second and fourth moments of the frequency in the spin-correlation function and the frequency-dependent susceptibility. The results are applicable to loose-packed cubic Bravais lattices with general spin values and nearest-neighbor interactions. At small wave vectors, for both the ferromagnet and the antiferromagnet, the series for the reciprocal of the second moment shows the expected divergence at the critical temperature. Insufficient terms are available to yield accurate critical indices. There is good agreement between the calculation and neutron-scattering experiments on RbMn${\mathrm{F}}_3$. Paramagnon peaks are not likely to be present at temperatures of order five to ten times the critical temperature in the antiferromagnets considered, but probably do occur at favorable points in the zone for the corresponding ferromagnets.