Classical Heisenberg Chain Research Articles

Soliton dynamics in the discrete classical Heisenberg chain. Velocity modulation and stochastic depinning

Abstract The effect of lattice discreteness on the dynamics of solitons in a classical Heisenberg chain in a periodic external field is investigated. Velocity modulation and stochastic depinning of a soliton is shown to take place.

Steepest descent approach to the domain-wall thermodynamics of a classical easy-plane ferromagnetic chain: Application to CsNiF3

We derive asymptotic low-temperature expressions for the free energy, the specific heat, and the magnetization of the classical easy-plane Heisenberg chain in a field. At low field the system forms a stable gas of spin waves and domain walls. In a temperature-broadened region about a characteristic field given by the anisotropy, the domain-wall gas becomes unstable and dissociates into spin waves. At higher fields the domain-wall gas is absent. Applying our results to CsNi${\mathrm{F}}_{3}$ we find qualitative agreement.

Non-linear modes and statistical mechanics of a classical Heisenberg chain with two anisotropies

The authors investigate the relevance of soliton modes for the statistical mechanics of a classical Heisenberg chain with two single-ion anisotropies-a model that has two continuous degrees of freedom and allows one to treat exactly the crossover between broken Heisenberg and planar symmetries. Starting from exact soliton solutions as given by Sklyanin the authors discuss the two branches of the soliton spectrum, small vibrations in the presence of solitons and the stability of solitons. They show that the statistical mechanics of this chain as obtained from the transfer integral method is reproduced exactly by the phenomenological approach using solitons and phonons. The relevance of the model for the properties of the easy-plane antiferromagnetic chain in an external magnetic field is discussed.

Coupled spin-lattice solitary waves in a compressible classical Heisenberg chain

Coupled spin-lattice solitary waves in a compressible classical Heisenberg chain

Energy fluctuations in a linear Heisenberg ferromagnet

The exchange energy fluctuations of the classical Heisenberg chain with an applied field are theoretically studied by a non-perturbative interacting-boson theory. Computer simulations are also presented at different wavevectors and found in satisfactory agreement.

On the inhomogeneous Heisenberg chain

The author derives the spin evolution equation of a classical inhomogeneous Heisenberg chain and proves its exact equivalence (in the continuum limit) to an integro-differential nonlinear Schrodinger equation whose soliton solutions have been discussed earlier. Energy transport along the chain is related to the solution of this equation. He also describes possible physical systems to which the model is applicable.

Solitary waves in a 1D isotropic Heisenberg ferromagnet

The authors present the derivation of a non-linear Schrodinger equation for the quantum isotropic Heisenberg chain using the coherent-states method combined with the Holstein-Primakoff bosons representation of the spin operator. The solution of this equation gives rise to solitary-waves excitations of the system that are similar to those discussed by Tjon and Wright (1977) for the classical Heisenberg chain. A discussion of their results as compared with others in the literature is made.

Solitary waves along the compressible Heisenberg chain

The classical compressible 1D Heisenberg chain is considered in the continuum limit to lowest non-trivial order in the derivatives. On the grounds of the equations of motion recently deduced by J. Fivez (1982), the existence of magnetic solitary waves, coupled with simultaneous travelling of deformations of the lattice, is proved. Explicit solutions are written down and discussed.

Dynamics of a generalised classical Heisenberg chain

The spin evolution and its equivalent integro-differential nonlinear Schrödinger equation are presented for a classical Heisenberg chain with an arbitrary site-dependent interaction. An extension of the AKNS-ZS formalism is given, which solves the generalised nonlinear Schrödinger equation and also enables classification of the types of interaction amenable to exact solution.

A computer simulation study of the classical isotropic Heisenberg chain with an applied field

Results are presented of an extensive study of the classical one-dimensional ferromagnetically coupled Heisenberg magnet with an applied field. The variation of the spectrum of spin density fluctuations with temperature, applied field and wavevector have been investigated. The results at low temperature and strong applied field are shown to be consistent with non-interacting spin wave theory. At higher temperatures, and weaker field, qualitatively different behaviour is observed. The modifications to the spectra are attributed to the thermally activated spin-energy density coupling leading to a hybridised mode, which couples to both spin and energy densities.

On the continuum limit of a classical compressible Heisenberg chain

The author derives the equations of motion for the classical compressible Heisenberg chain in the continuum limit to lowest non-trivial order in the derivatives. It is possible to eliminate the translations from the equation for the spins. The resulting equation does not admit of simple magnetic solitary wave solutions, in contradiction to the results of other authors.

A branching path approach to the large-N limit Heisenberg chain: the S=1/2case

For a Heisenberg linear chain of N one-half spins, a class of solutions is built and explicit expressions for the energy given in the large-N continuum limit using a branching path approach. With such a technique connections with the classical Heisenberg chain appear clearly, and 'quantum' corrections to this classical description can be derived explicitly.

Classical Ferromagnetic Heisenberg Chain in a Magnetic Field

The dynamics of classical ferromagnetic Heisenberg chains in a magnetic field is investigated. Contrary to previous theories, in the longitudinal spectral shapes temperature is found to play a crucial role through a dynamical spin-energy coupling whose effect is competitive with the field. Thermal disorder ultimately causes a nearly isotropic situation, leading to a new interpretation of the features of recent computer experiments.

Interacting boson approach to the static properties of classical ferromagnetic chains in applied field

An interacting spin wave theory is presented for describing the temperature behaviour of the thermodynamical quantities of classical ferromagnetic Heisenberg chains in an applied field. An explicit expression for the Green function of the longitudinal magnetisation fluctuation is given and longitudinal susceptibility correlation length and magnetisation are evaluated. The inadequacy of a naive Hartree-Fock renormalisation and the determinant role of the thermal activated spin-energy coupling are shown.

Low-temperature spin dynamics of a classical compressible Heisenberg chain

The dynamic spin correlation function of a classical compressible Heisenberg chain is investigated in the low temperature limit. Anharmonic processes, arising from the nonlinearity of the spin equations of motion and from the coupling of the spins to translational degrees of freedom, are taken into account to lowest order. Two-magnon processes and magnon-phonon processes contribute to the spectra. They can give rise to additional resonances but mostly their weight is very small. The main influence of the spin-phonon coupling lies in a change of the width and position of the spin-wave resonance. Comparison is made with previous work.

Energy fluctuations in a classical Heisenberg chain

The dynamic structure factor of the energy density fluctuations in the classical Heisenberg chain is studied theoretically. Using exact expressions for the first six frequency moments and the knowledge of the exact $T=0$ result, simple approximations are used to calculate the spectrum. We show rigorously that the time-dependent correlation function is different for ferro-and antiferromagnetic coupling if $T\ensuremath{\ne}0$.

Low-temperature study of the static and dynamical magnetic properties of the random one-dimensional antiferromagnet(CD3)4NMncCu1−cCl3

In a recent paper we reported a neutron scattering study of the random one-dimensional (1D) Heisenberg antiferromagnetic (CD/sub 3/)/sub 4/NMn/sub c/Cu/sub 1-x/Cl/sub 3/, with c = 0.93 and 0.85. The main emphasis was on the static properties. In the present publication we present the results and analyses of extended quasielastic and inelastic neutron scattering experiments at temperatures down to 0.3 K. The low-temperature behavior of the inverse correlation length k and staggered susceptibility x(Q = r) of the c = 0.93 specimen indicates that the exchange J/sub CuhyphenCu/ between pairs of Cu/sup + +/ ions is ferromagnetic. Well-defined spin-wave-like excitations are observed for wave vectors larger than a critical wave vector q/sub cr/. The low-temperature measurements indicate that q/sub cr/ is governed by the percolation limit k/sub c/ of k itself, indicating that the observed excitations are associated with the pure Mn/sup + +/ segments. We have carried out spin-wave perturbation calculations and computer simulations of the spin-dynamical properties of the dilute classical Heisenberg chain at T = 0. These two calculations are in good agreement with each other. No Ising resonances, associated with states at chain ends, were found in these calculations. These resonances occur in similar systems inmore » higher dimensions but are shown not to occur in 1D because of the singular nature of the density of states at the band edges. For q>q/sub cr/, the observed inelastic scattering response is quantitatively accounted for by means of the perturbation calculations. For qapprox.q/sub cr/ the experimentally measured line shapes are in qualitative agreement with the computer simulations.« less

Nonlinear Effects in the Dynamic Structure Factor of the Classical Antiferromagnetic Heisenberg Chain in an External Field at Low Temperatures

Is is found that nonlinear effects give rise to anomalies in the spectrum of the antiferromagnetic Heisenberg chain in an external field, even at low temperatures. Divergences in the two-magnon density of states are responsible for additional resonances, besides the usual spin-wave peak, in the dynamic structure factor.

Computer simulation of the approach to equilibrium in the classical Heisenberg chain

Computer studies of the approach to equilibrium in the classical 3-component Heisenberg chain, starting from a configuration with a large staggered magnetization (i. e., far from equilibrium) are reported. The equal time transverse and reduced longitudinal correlations g⊥(ℓ, t) and g∥(ℓ, t), respectively, were monitored for times long enough to show the approach to equilibrium. Results for g⊥ confirm predictions by Nelson and Fisher of wave-like behavior with a propagation speed equal to twice the zero-temperature spin wave velocity. The equilibration of g∥ was found to be slower and diffusive in nature. The fitted diffusivity appears to be comparable to the value of the spin diffusivity for the corresponding equilibrium problem.

Solitons in quantum Heisenberg chain

Using the coherent states method combined with the Schwinger coupled boson representation of the spin operators (1965) it is shown that solitons can propagate in the continuum limit of the quantum ferromagnetic Heisenberg chain. These solitons are solutions of a nonlinear Schrodinger equation similar to that discussed by Lakshmanan (1977) for the classical Heisenberg chain. Several characteristics of the soliton, like its momentum, energy, and the number of bosonic excitations involved in the soliton formation, are calculated.