Critical and paramagnetic spin fluctuations in Heisenberg magnets

The frequency- and wave-vector-dependent spin response function is calculated for a Heisenberg ferromagnet using the mode-coupling theory. Results are presented for the critical and paramagnetic regions. The work is motivated largely by recent, high-resolution neutron spectroscopy studies of EuO and EuS. In view of this, the Heisenberg model used incorporates nearest- and next-nearest-exchange interactions between spins on a face-centered-cubic lattice. The coupled-mode theory is shown to be successful in describing the measurements. Additional features are predicted as possible subjects of future experimental work. We present a review of various derivations of mode-coupling equations and demonstrate the equivalence of some prescriptions. The question of incorporating an external magnetic field in the theory is addressed, and we conclude that readily attainable fields have a minimal effect on the spin dynamics.