On the critical dynamics of isotropic ferromagnets below the curie point

The transport coefficients for isotropic Heisenberg ferromagnets are evaluated by mode-mode coupling theory forT≦ T _c. Near the critical point the results agree with dynamical scaling. In the hydrodynamic critical regime the longitudinal width depends crucially on the analytic form of the static longitudinal susceptibility. In the region where the ξ/q term dominates the width of the longitudinal peak is proportional to \(q^2 \xi ^{ - 1/2} \) , whereq and ξ are respectively the wave number and critical correlation length. When the Ornstein Zernike term dominates the width is \(q\xi ^{ - 3/2} \) . The damping of the transverse modes is \(q^4 \xi ^{3/2} (a + b\log (1/q\xi ))\) . If one accounts for the critical exponentn the above expressions are to be multiplied by \(\xi ^{\eta /2} \) . These frequency independent transport coefficients are valid in the neighborhood of the resonances. For larger frequencies the frequency dependent forms are evaluated.     

Mode coupling theory for the critical dynamics of dipolar ferromagnets

The critical dynamics of ferromagnets has been studied by various experimental methods sampling different regions in wave vector space. Nevertheless there seemed to be a list of contradictions between these experiments. Within a mode coupling theory including both short range exchange and long range dipolar interaction we are able to resolve the seemingly contradictory situation.     

Dipolar interaction and critical dynamics of uniaxial ferromagnets above the Curie point

Dependence of the critical fluctuation energy on the dipolar interaction, anisotropy and temperature is determined.     

On the width of the critical regime in amorphous ferromagnets

Amorphous ferromagnets exhibit an unusually large temperature range of deviations from the Curie-Weiss behavior in the paramagnetic regime. The question is discussed whether this may be interpreted as an extended critical behavior or as a non-critical phenomenon for which scaling ideas are not valid. Comparison is made with other disordered ferromagnets.     

On the critical dynamics of spin-glasses

The dynamic scaling of the spin-glass model, proposed by Edwards and Anderson, is studied. The dynamic critical exponents are calculated at the freezing point and at the tricritical point. The coupling of the order parameter with propagating excitations is considered.     

Critical dynamics of dipolar ferromagnets

The dynamical scaling functions for ferromagnets with dipolar interactions are computed by mode coupling theory above the critical temperature T_c. On the basis of this theory we explain apparently conflicting features of neutron scattering experiments on EuO, EuS and Fe. The position of the crossover from isotropic to dipolar critical dynamics is determined and further experiments are proposed.     

Domain wall dynamics in ferromagnets

The main results of studying the linear and nonlinear dynamics of a domain wall in ferromagnets are presented beginning with the first publications. The experimental data obtained on polycrystals, single crystals, and films differing in terms of their anisotropy, as well as on magnetic nanostructures, are compared with theoretical results obtained by various methods.     

Critical dynamics in isotropic ferromagnets

Modern high resolution inelastic neutron scattering methods make very long wavelength fluctuations accessible to dynamical investigation. The new results on Fe and EuO show that: (a) the $\text{q}{}^{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ power law is well borne out at T = T_c; (b) strong zero-wavenumber relaxation due to spin non-conserving forces can make the predicted hydrodynamic spin diffusion at T >T_c unobservable; (c) this zero-wavenumber relaxation is the only appreciable deviation from the $\text{z =}\text{5}\text{2}$ exchange scaling behaviour; (d) there is no evidence for the predicted cross-over to dipolar dynamics a finite q's.     

On the investigation of magnetic critical phenomena in ferromagnets by μSR and PAC

On the basis of current theoretical views on the critical phenomena in isotropic Heisenberg ferromagnets the power temperature behavior Λ=c(τ)λ₀τ^-w has been derived for the muon spin relaxation rate Λ as π-T _c ⁻¹ (T-T _c ) → 0⁺. It is shown that the crossover from an exchange critical regime to a dipolar one is accompanied not only with the change in the critical exponentw in the above law, but also with the reduction of the coefficientc(π). A comparison with the temperature behaviour of the inverse nuclear relaxation timet _R ⁻¹ measured in the PAC experiment is carried out.     

Quantum critical behavior of clean itinerant ferromagnets

We consider the quantum ferromagnetic transition at zero temperature in clean itinerant electron systems. We find that the Landau-Ginzburg-Wilson order parameter field theory breaks down since the electron-electron interaction leads to singular coupling constants in the Landau- Ginzburg-Wilson functional. These couplings generate an effective long-range interaction between the spin or order parameter fluctuations of the form 1 <r ² d?1, with d the spatial dimension. This leads to unusual scaling behavior at the quantum critical point in 1 < d ≤ 3, which we determine exactly. We also discuss the quantum-to-classical crossover at small but finite temperatures, which is characterized by the appearance of multiple temperature scales. A comparison with recent results on disordered itinerant ferromagnets is given.     

Glassy properties of the Kawasaki dynamics of two-dimensional ferromagnets

We study numerically the Kawasaki dynamics of the 2D Ising model. At large time we recover the coarsening growth as l(c)(t) proportional t(1/3). At shorter time however, the system enters a metastable glassy regime that displays an extremely slow growth and nontrivial violations of the fluctuation-dissipation theorem similar to those observed in spin glasses: this is one of the simplest systems in which such violations occur. We also consider Potts models, where a similar behavior is observed, and the model of Shore and Sethna where the domain growth is also slow, but where violations of the fluctuation-dissipation theorem are trivial. We finally comment on these violations in the context of activated coarsening, and on similarities and differences with the glass transition phenomenology.     

On the critical dynamics of disordered spin systems

The dynamic critical behaviour of spin systems with quenched impurities, and of amorphous spin systems as characterized by the additional presence of random anisotropy directions, is studied by renormalization group methods to second order in=4–d. For the Halperin-Hohenberg-Ma model with purely relaxational dynamics it is concluded that in three dimensions (d=3) the critical slowing down should be enhanced by impurities for systems with Ising type statics, whereas there is no change forXY- and Heisenberg systems. For amorphous systems, however, the critical dynamics should change also in theXY- and Heisenberg cases. Furthermore, it is concluded that additional conserved, but noncritical modes become always statically decoupled from the order parameter for systems with impurities, but not for amorphous systems. Thus, for the impure system, the energy density mode and the asymmetric models of Halperin, Hohenberg and Siggia are ruled out. But the effects of dynamic coupling remain: Especially, the relationz=d/2 for the dynamic exponent of planar and isotropic antiferromagnets is modified for impure or amorphous systems.     

On the critical dynamics of a disordered system

The dynamic critical exponent is calculated for a disordered time-dependent Ginzburg-Landau model with n isotropically coupled spin components per site. For n<4, in 3.99 dimensions, the critical slowing down is enhanced.     

On the mixed susceptibility of ferromagnets

Based on the macroscopic approach developed by the authors, the frequency and orientational dependences of the mixed susceptibility and magnetic capacity of polydomain ferromagnets caused by shear of domain boundaries are described with allowance for the interaction of ferromagnet subsystems. The effect of constant displacing electric and magnetic fields is examined. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 51–55, August, 2006.     

A general bound on the critical temperature of Ising ferromagnets

An inequality relating the spin correlation functions for a general Ising ferromagnet is found. This inequality gives an improved upper bound for the critical temperature of translationally invariant ferromagnets with pair-wise interactions.     

Nonuniversal properties in the dipolar critical region of uniaxial ferromagnets

The amplitude of the critical isotherm is expressed by microscopic magnetic parameters and the transition temperature. The agreement between calculated and experimental values is good for GdCl₃ and LiTbF₄, whereas for DyEs a discrepancy is observed.     

Logarithmic corrections for dilute uniaxial ferromagnets at the critical dimension

The leading logarithmic corrections to the critical behavior of a dilute uniaxial (Ising) ferromagnet in the disordered phase are derived using renormalization group methods. The values of the exponents in the logarithmic terms differ from those given by previous authors.