Nonlinear dynamics and collective excitations of spin-1 magnets

The Poisson brackets for macroscopic parameters are obtained and nonlinear dynamic equations of spin-1 magnets are derived. Two types of magnetic exchange Hamiltonians corresponding to two Kazimir invariants of SU(3) group are introduced. Thermodynamics of spin-1 magnets is studied and the flux densities of additive integrals of motion are found in terms of exchange energy density. The momentum of magnons is introduced and the corresponding dynamic equation is derived. The spectra of spin and quadrupole waves of magnets with various symmetry of equilibrium state with respect to time inversion are found.     

Ferroelectricity in spiral magnets

It was recently observed that the ferroelectrics showing the strongest sensitivity to an applied magnetic field are spiral magnets. We present a phenomenological theory of inhomogeneous ferroelectric magnets, which describes their thermodynamics and magnetic field behavior, e.g., dielectric susceptibility anomalies at magnetic transitions and sudden flops of electric polarization in an applied magnetic field. We show that electric polarization can also be induced at domain walls and that magnetic vortices carry electric charge.     

Nonlinear dynamics of a quasi-one-dimensional spiral structure

The nonlinear dynamics of solitons and spin waves in spiral magnets without inversion centers is investigated using the sine-Gordon model. The possibility of finding solitons in spiral structures is discussed.     

Spiral structures in helicoidal magnets

The structure and properties of two-dimensional spiral textures in helical ferromagnets are studied. The existence of novel types of periodic structures, namely, of spiral lattices, is predicted for these magnetic systems.     

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.     

NMR dynamics in disordered magnets

The excitation dynamics of site diluted magnets can be described at low energies (long length scales) by magnons, and above a crossover frequency, ω_c, (short length scales) by fractons. The density of fracton states is given by , where is the fracton dimensionality. Dilution gives rise to a characteristic length ξ∝(p−p _c)^ν, wherep _c is the critical concentration for (magnetic) percolation. The crossover frequency ω_c is proportional to ξ^-1[1+(θ/2)], where θ is the rate at which the diffusion constant decays with distance for diffusion on an equivalent network. A fractal dimensionD describes the density of magnetic sites on the infinite network, and . For percolating networks, for all dimensions ≥2. Neutron scattering structure factor measurements by Uemura and Birgeneau compare well with calculations using fracton concepts. Magnons are extended at low energies, while the fracton states are geometrically localized, with a wave function envelope proportional to exp . Here, is the fracton length scale at frequency ω. The exponentd _ϕ lies between 1 andd _min, the chemical length index (of the order of 1.6 in three dimensions). The localization of the magnetic excitations causes a spread in the NMR relaxation rates. A given nuclear moment will experience only a limited set of fracton excitations, resulting in an overall non-exponential decay of the NMR relaxation signal. When strong cross-relaxation is present, the relaxation will be exponential, but the temperature dependence will be strongly altered from the concentrated result.     

Theory of magnetic switching of ferroelectricity in spiral magnets

We propose a microscopic theory for magnetic switching of electric polarization (P) in the spin-spiral multiferroics by taking TbMnO3 and DyMnO3 as examples. We reproduce their phase diagrams under a magnetic field Hex by Monte Carlo simulation of an accurate spin model and reveal that competition among the Dzyaloshinskii-Moriya interaction, spin anisotropy, and spin exchange is controlled by the applied Hex, resulting in magnetic transitions accompanied by reorientation or vanishing of P. We also discuss the relevance of the proposed mechanisms to many other multiferroics such as LiCu2O2, MnWO4, and Ni3V2O4.     

Quantum dynamics of Gaudin magnets

Quantum dynamics of many-body systems is a fascinating and significant subject for both theory and experiment. The question of how an isolated many-body system evolves to its steady state after a sudden perturbation or quench still remains challenging. In this paper, using the Bethe ansatz wave function, we study the quantum dynamics of an inhomogeneous Gaudin magnet. We derive explicit analytical expressions for various local dynamic quantities with an arbitrary number of flipped bath spins, such as: the spin distribution function, the spin–spin correlation function, and the Loschmidt echo. We also numerically study the relaxation behavior of these dynamic properties, gaining considerable insight into coherence and entanglement between the central spin and the bath. In particular, we find that the spin–spin correlations relax to their steady value via a nearly logarithmic scaling, whereas the Loschmidt echo shows an exponential relaxation to its steady value. Our results advance the understanding of relaxation dynamics and quantum correlations of long-range interacting models of the Gaudin type.     

Ultrafast spin dynamics in multisublattice magnets

We propose a general theoretical framework for ultrafast laser-induced spin dynamics in multisublattice magnets. We distinguish relaxation of relativistic and exchange origin and show that when the former dominates, nonequivalent sublattices have distinct dynamics despite their strong exchange coupling. Even more interesting, in the exchange dominated regime sublattices can show highly counterintuitive transitions between parallel and antiparallel alignment. This allows us to explain recent experiments with antiferromagnetically coupled sublattices, and predict that such transitions are possible with ferromagnetic coupling as well. In addition, we predict that exchange relaxation enhances the demagnetization speed of both sublattices only when they are antiferromagnetically coupled.     

Nonlinear dynamics of two harmonically excited elastic structures with impact interaction

In this paper, non-smooth dynamics of two elastic beams excited by harmonic force with impact interaction is studied through analyses, simulations, and experiments. A two degree-of-freedom vibro-impact model is improved by applying the Galerkin approach and Newton's impact law for the two cantilever beams with impact interaction. Numerical analysis is taken to investigate the vibro-impact motions of cantilever beams excited by harmonic force. The l-adding periodic motions and k=1/1, k=2/2, k=3/4, and k=4/4 type of stable periodic motions of the impacted cantilever beam are presented. Poincaré map is established and the Floquet multipliers of the periodic motions are obtained through semi-analytical method to determine the stability of the motions near the bifurcation point. Through associated experiments, typical bifurcations and chaos of the non-smooth system are examined, which are in good agreement with numerical results.     

Asymmetry of the time dynamics of breathers in the electroconvection twist structure of a nematic

Dynamics of breather defects in the periodic structures of rolls arising at electroconvection in nematic liquid crystals twisted by π/2 has been studied experimentally and theoretically. The axial components of the velocity of a hydrodynamic flow in the twist structures of nematics are opposite in the neighboring rolls. Dynamics of the breather defect is the periodic creation and annihilation of a pair of classical dislocations with the topological indices “+1” and “-1.” The annihilation occurs faster than the creation. It has been shown that the asymmetric time dynamics of the breather defect is described well by the solution of the perturbed sine-Gordon equation in the form of an interacting soliton and antisoliton.     

On the dynamics of itinerant electron magnets in the paramagnetic state

It is shown how disordered local-moment states, in a metal such as Fe, may be stabilized by constraining magnetic fields. Effective interaction parameters between moments are defined in terms of spin density functional theory. On removing the constraints the moments initially precess but then decay rapidly, the latter process leading to an energy width of S(q, ω) at large q of order $\text{(k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{C}}\text{W)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where T_C is the Curie temperature and W is the width of the d-band. T he consequences for neutron scattering experiments are discussed and the rather different case of Ni is considered.     

Linear spin dynamics of incommensurably modulated magnets

The linear spin dynamics of an incommensurably modulated Heisenberg magnet, with a single-Q structure, is studied using an analytic technique designed to calculate the transverse spin response observed in neutron scattering. Results are presented for a specialQ and also special scattering wave vectors. An approximate expression is proposed that is fully determined by the exchange and anisotropy parameters. The spin response is studied as a function ofQ and shown to be distinctly different from the case in which it is exhausted by a single collective spin oscillation.     

Simulation of the nonlinear dynamics of magnetic inhomogeneities in real magnets

The dynamics of domain walls (DW) in an infinite ferromagnet containing a flat layer with parameters of magnetic anisotropy and exchange interaction differing from the bulk values was investigated. The dependences of the minimum velocity of DW transmission through the defect region and the translational and pulsation modes of DW fluctuations on the parameters describing the inhomogeneity of magnetic anisotropy and exchange interaction were found.     

Nonlinear dynamics of longitudinal structures in the electron cloud of a coaxial electron string ion source

The results of 2.5D particle-in-cell simulation of a coaxial electron trap with an internal anode are reported. It is found that, when the circulating current reaches the value of the ultimate vacuum current, first a virtual cathode arises in the trap and then the beam compresses (distributed virtual cathode). The transient preceding the compressed state exhibits complicated nonlinear dynamics, when compressed regions alternate with regions that are in a two-flow state (phase-space bubbles or phase-space holes). Physically, phase-space holes are similar to the well-known Bernstein-Greene-Kruskal plasma structures. Three types of phasespace holes with different dynamics (oscillating holes, flying holes, and chaotic holes) are revealed. Consideration of phase-space holes as quasi-particles makes it possible to find several channels of their interaction in pair collisions. The feasibility of the coaxial trap as a source of highly charged ions is analyzed. Although the compressed beam mode provides a larger amount of accumulated electrons compared with the conventional two-flow mode, the mean kinetic energy in the presence of a virtual cathode turns out to be much lower. A way of elevating the mean kinetic energy is suggested that consists in increasing the limit vacuum current in the axial configuration with an internal electrode.     

Current-driven dynamics of skyrmion bubbles in achiral uniaxial magnets

We report dynamics of skyrmion bubbles driven by spin-transfer torque in achiral ferromagnetic nanostripes using micromagnetic simulations. In a three-dimensional uniaxial ferromagnet with a quality factor that is smaller than 1, the skyrmion bubble is forced to stay at the central nanostripe by a repulsive force from the geometry border. The coherent motion of skyrmion bubbles in the nanostripe can be realized by increasing the quality factor to ～ 3.8. Our results should propel the design for future spintronic devices such as artificial neural computing and racetrack memory based on dipole-stabilized skyrmion bubbles.