Dynamic Scaling Theory for Anisotropic Magnetic Systems

Abstract

A theory of dynamic critical phenomena in anisotropic magnetic systems by Wegner and the author is reviewed and compared with recent neutron scattering experiments, especially on the uniaxial antiferromagnets MnF2 and FeF2. Particular emphasis is placed on the spin-relaxation rates as functions of the anisotropy in ferromagnets and antiferromagnets in the paramagnetic critical state. Within a generalized dynamic scaling and mode-mode approach the anisotropy parameters are treated as additional ``critical'' variables. The theory applies to the entire critical state of weakly anisotropic systems and is not restricted to a small region around the critical point. Anisotropy is interpreted as introducing a second length into the critical behavior of the system. In this case the spin-relaxation rates cannot be characterized by a single set of critical exponents for all ranges of variables even in the critical state. Instead, simple corresponding-state relations are found, in which the analytical structure of the scaling functions is related to the basic symmetry and conservation-law properties of the system. It is shown that the anisotropy parameter, and in mode-mode approximation also the isotropic material parameters, enters only the amplitudes and reduced temperature and momentum variables in those relations. Quantitative results for the spin-relaxation rates are given for the uniaxial antiferromagnets MnF2 and FeF2 and, in the isotropic limit of the theory, for the ferromagnets Fe and Ni, and the antiferromagnet RbMnF3. Recent neutron scattering results on MnF2 and FeF2 by Schulhof et al. are in good agreement with the predictions of the theory.