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.     

Critical dynamics of magnets

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 of 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.     

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.     

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.     

Nonasymptotic critical behaviour of uniaxial systems with strong dipolar interaction

Within a field-theoretic renormalization group approach general relations between specific heat, susceptibility and order parameter for uniaxial dipolar ferromagnets or ferroelectrics are derived. An advantage of these relations is that no explicit solution of the flow equation for the temperature dependence of the effective four-point coupling is needed. In this way the crossover from critical behaviour to mean field behaviour can be studied. The theory is applied to LiTbF₄ and TSCC.     

Pressure dependence of diffusion in simple glasses and supercooled liquids

Using molecular dynamics simulation, we have calculated the pressure dependence of the diffusion coefficient in a binary Lennard-Jones glass. We observe four temperature regimes. The apparent activation volume drops from high values in the hot liquid to a plateau value. Near the critical temperature of the mode coupling theory it rises steeply, but in the glassy state we find again small values, similar to the ones in the liquid. The peak of the activation volume at the critical temperature is in agreement with the prediction of mode coupling theory.     

Vanishing magnetic interactions in ferromagnetic thin films

We have used element-specific hysteresis measurements, based on the x-ray magnetic circular dichroism technique, to investigate magnetic trilayer structures composed of Fe and Ni layers. Within a critical regime we have discovered a class of structures in which the exchange interaction, the mechanism responsible for the macroscopic magnetism, can become vanishingly small. The experimental observations are supported by first principles theory and are explained as arising from a cancellation of several competing magnetic interactions. Hence, we have discovered a system with a novel exchange interaction between magnetic layers in direct contact that replaces the conventional exchange interaction in ferromagnets.     

Crossover Critical Behavior in the Three-Dimensional Ising Model

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussed.     

Electron correlations and the minority-spin band gap in half-metallic Heusler alloys

Electron-electron correlations affect the band gap of half-metallic ferromagnets by introducing nonquasiparticle states just above the Fermi level. In contrast with the spin-orbit coupling, a large asymmetric nonquasiparticle spectral weight is present in the minority-spin channel, leading to a peculiar finite-temperature spin depolarization effects. Using recently developed first-principle dynamical mean-field theory, we investigate these effects for the half-metallic ferrimagnetic Heusler compound FeMnSb. We discuss depolarization effects in terms of strength of local Coulomb interaction U and temperature in FeMnSb. We propose Ni(1-x)Fe(x)MnSb alloys as a perspective materials to be used in spin-valve structures and for experimental search of nonquasiparticle states in half-metallic materials.     

耦合作用下有机铁磁链的临界行为

利用平均场，我们研究了一个具有链间耦合作用的有机铁磁模型，并给出了该模型的全相图。计算表明，链间耦合强烈影响其基态的磁序。当链间耦合达到某临界值时，高自旋基态消失，整个系统由铁磁相转变为近藤单态（Kondo-singlet）相。     

Structural phase transitions in crystals with coupled softening modes

Structural phase transitions in crystals with more than one softening phonon mode are investigated in mean field theory. It is found that, for negative coupling energies between two modes, the critical temperature of each mode increases. For large coupling, both modes become soft at the same temperature and the phase transition becomes of first order. For positive coupling energies, the critical temperatures rapidly go to zero but not for the same value of coupling. A phase diagram is given and a possible application to alkali-TCNQ salts is discussed.     

Invar and covar behavior of ferromagnets with allowance for magnetophonon interaction: A thermodynamic simulation

Based on the Landau theory of second-order phase transitions with allowance for interaction between the magnetic subsystem and crystal lattice (magnetophonon interaction, MPI), a consistent thermodynamic model of the invar and covar behavior of ferromagnets with MPI is constructed. Model calculations carried out at real temperatures show that the invar (covar) behavior of ferromagnets results from an optimal relationship between the thermodynamic parameters of the ferromagnetic phase. It is demonstrated that MPI is a fundamentally important factor responsible for the invar and covar effects. With the thermodynamic parameters obeying a certain relationship, the invar behavior of ferromagnets is predicted in a much wider temperature range than in known invars.     

Elastic properties of magnetic materials

This review discusses the theoretical aspects of magnetoelastic coupling with emphasis on the magnetic perturbation of elastic properties. The basic theory of magnetostriction is set out with application to ferromagnets, ferrimagnets and antiferromagnets, and is followed by a discussion of the physical origin of the magnetoelastic coupling coefficients in both localized and itinerant magnetic systems. Magnetic contributions to elastic compliance are then discussed and sound velocity anomalies near magnetic phase transitions investigated, including the cooperative Jahn-Teller limit for which the acoustic mode itself drives a structural transition even when magnetic ordering does not occur. The review concludes with discussion of magnetoelastic (or mixed magnon-phonon) waves in low temperature magnetically ordered phases and with a study of local striction phenomena in magnetically dilute materials. The latter leads to a recognition of internal rearrangement modes which may also be present in concentrated magnetic systems, and which may or may not couple significantly to bulk homogenous strain.     

Molecular-orbital model of heat-induced effective exchange coupling in magnetic multilayers

Heat-induced effective exchange coupling between two ferromagnets across a semiconductor spacer layer is described by the interaction of localized, weakly bound electron states which are situated at the two interfaces. These states overlap across the spacer layer and form large molecular orbitals. The energies of these orbitals depend on the spin configuration of the electrons and therefore determine the exchange coupling. Thermal repopulation of the levels yields a positive temperature coefficient of the coupling. The results are found to well reproduce the experimental observations.     

The magnetic phase transition in amorphous ferromagnets and in spin glasses

The magnetic phase transition in materials with exchange disorder (amorphous ferromagnets, spin glasses) is discussed. In the critical temperature range the behavior of amorphous ferromagnetic transition metal-metalloid glasses is found to be similar to the one derived for a three-dimensional homogeneous Heisenberg ferromagnet. The most prominent difference between disordered and homogeneous materials is manifested in a large temperature range of deviations from the mean field behavior beyond the critical region, as observed experimentally for the temperature dependence of the linear susceptibility of amorphous ferromagnets and of the nonlinear susceptibility of spin glasses. A molecular field theory with correlations in space and time is developed, which relates the deviations from the mean field behavior to the interplay between the temperature dependent thermal correlations in the spin system and the spatial fluctuations of the material. Application to dynamical processes (kinetic critical slowing down) is discussed.     

Continuous Replica Symmetry Breaking in Critical Phenomena in Disordered Ferromagnets

The replica symmetry breaking (RSB) in critical phenomena in disordered ferromagnets is studied. We modified the assumption of Dotsenko et al. about the local minimum solutions of the Hamiltonian with random temperature. It is shown explicitly that the continuous RSB is generated in the renormalization group (RG). The physical regime of the coupling constants are investigated through the RG equations.     

Universal amplitude ratios of critical sound attenuation

The universal amplitude ratios for ultrasonic attenuation above and below the critical point are determined for uniaxial magnets, the gas liquid critical point, binary mixtures and related universality classes. For uniaxial ferromagnets also the scaling functions are computed. The theory is based on time dependent Ginzburg-Landau models and the ?=4?d-expansion. Depending on the universality class the universal amplitude ratio assumes values in the range 1/15 to 15. In systems with continuous internal symmetry Goldstone mode singularities are found.     

Dual symmetries and universality of the critical behavior of a disordered ising ferromagnet

The critical behavior of a d-dimensional random Ising ferromagnet described in the critical region by the Ginzburg-Landau model with a random temperature has been considered. The critical temperature dependences of thermodynamic quantities, the equation of state, and the spin correlation function at the Curie point have been calculated by the renormalization group method. The most profound questions of the theory of impurity ferromagnets are the problem of universality and the role of the Griffiths singularities.     

Mean field theory with correlations in space and time for the ferromagnetic phase transition

A mean field theory with correlations in space and time is proposed which implicitly takes into account the effect of thermal spin fluctuations. The theory describes the kinetic critical slowing down of the relaxation of the magnetization near the ferromagnetic phase transition in crystalline and amorphous ferromagnets. Furthermore, it provides an explanation for the large temperature range of apparent “critical” behaviour as observed experimentally for the paramagnetic susceptibility of amorphous ferromagnets.     

On the dynamics of Heisenberg magnets with lattice anisotropy near the phase transition

The kinetic theory (mode-mode coupling theory) is applied to lattice anisotropic Heisenberg ferromagnets and anti-ferromagnets in the paramagnetic region near the phase transition. The distinction of a hydrodynamic and a critical region is refined by introducing regimes of essentially lower-dimensional (1-d or 2-d) behavior and three-dimensional behavior of the magnet. In the regime of 3-d behavior the scaling function of the line-width of the dynamic spin correlation function is discussed extensively.