Sw. Lovesey et E. Balcar, DYNAMICAL PROPERTIES OF CRITICAL AND PARAMAGNETIC SPIN FLUCTUATIONS IN ANISOTROPIC HEISENBERG MAGNETS, Journal of physics. Condensed matter, 7(10), 1995, pp. 2147-2164
Decay rates for long-wavelength spin fluctuations in the standard x-y
model, and a second model described by the sum of the full Heisenberg
exchange interaction and a single-site anisotropy, are calculated on t
he basis of a coupled mode theory in which the isothermal susceptibili
ties are consistent with corresponding spherical models (in consequenc
e, quantum fluctuations are absent). Results for the decay rates are p
rovided for two- and three-dimensional lattices, and ferromagnetic and
antiferromagnetic exchange interactions. Their dependence on the wave
vector, q, and the inverse correlation lengths are derived from integ
ral equations that admit homogeneous functions as solutions. The decay
rates may thus be expressed as q(d/2) R(1)(q/kappa(0)) and q((d+2)/2)
R(2)(q/kappa, q/kappa(0)) where R(1) and R(2) are, respectively, scal
ing functions for the x-y and ferromagnetic single-site anisotropy mod
els, d is the spatial dimension, and kappa (kappa(0)) is the out of pl
ane (in plane) inverse correlation length. Analytical and numerical va
lues of the scaling functions are presented for the limits of main phy
sical interest.