Dynamical two-point correlation functions in a high-temperature Heisenberg paramagnet

The dynamical two-point correlation functions of the high-temperature Heisenberg paramagnet as described by nonlinear integral equations generated by moment expansions developed by Reiter are investigated. In particular, equations for the magnetic dipole correlation functions and magnetic quadrupole correlation functions are obtained and solved in a lowest-order self-consistent approximation. These correlation functions are directly measurable in electromagnetic, neutron-scattering, and acoustic experiments in dense magnetic insulators. From the solution for the dipole correlation functions, theoretical values for the spin-diffusion coefficient and the exchange-narrowed dipolar linewidth are obtained which are within 12% and 22%, respectively, of the measured values for RbMn${\mathrm{F}}_3$.