Critical dynamics of magnets

Abstract

We review our current understanding of the critical dynamics of magnets above and below the transition temperature with focus on the effects due to the dipole-dipole interaction present in all real magnets. Significant progress in our understanding of real ferromagnets in the vicinity of the critical point has been made in the last decade through improved experimental techniques and theoretical advances in taking into account realistic spin-spin interactions. We start our review with a discussion of the theoretical results for the critical dynamics based on recent renormalization group, mode coupling and spin-wave theories. A detailed comparison is made ot~ the theory with experimental results obtained by different measuring techniques, such as neutron scattering, hyperfine interaction, muon spin resonance, electron spin resonance, and magnetic relaxation, in various materials. Furthermore we discuss the effects of dipolar interaction on the critical dynamics of three-dimensional isotropic antiferromagnets and uniaxial ferromagnets. Special attention is also paid to a discussion of the consequences of dipolar anisotropies on the existence of magnetic order and the spin-wave spectrum in two-dimensional ferromagnets and antiferromagnets. We close our review with a formulation of critical dynamics in terms of nonlinear Langevin equations.

Renormalization Group: Applications in Statistical Physics

“…, and through comparison with the definition of the susceptibility in (20) arrive at the fluctuation-response theorem C(q) = k B T χ(q), valid in thermal equilibrium.…”

“…4,5]. In addition to purely relaxational kinetics, we shall also address the critical dynamics of isotropic ferromagnets [20], as well as generic scale invariance and non-equilibrium phase transitions in driven diffusive systems [21].…”

“…Since the mode-coupling vertex does not contribute genuinely new IR singularities, dynamic scaling functions for isotropic ferromagnets and related models can be computed to exquisit precision by means of the mode-coupling approximation, which essentially amounts to a self-consistent one-loop theory for the propagators, ignoring vertex corrections [20].…”

“…Often, however, the Langevin description of critical dynamics needs to take into account reversible systematic forces contributing to F[S ] in (96). The Langevin dynamics of isotropic ferromagnets provides a prominent example [20], [9,Chap. 6].…”

“…The Ornstein-Zernicke function (20) satisfies the scaling law (23) with the mean-field values ν = 1 2 and η = 0. Notice that the set of mean-field critical exponents obeys (26) only in d = 4 dimensions.…”