Easy-plane Ferromagnetic Chain Research Articles

Localized states beyond the asymptotic parametrically driven amplitude equation

We study theoretically a family of localized states which asymptotically connect a uniform oscillatory state in the magnetization of an easy-plane ferromagnetic spin chain when an oscillatory magnetic field is applied and in a parametrically driven damped pendula chain. The conventional approach to these systems, the parametrically driven damped nonlinear Schrödinger equation, does not account for these states. Adding higher order terms to this model we were able to obtain these localized structures.

Solitons in a one-dimensional ferromagnetic chain under the influence of single-ion anisotropy

Cnoidal wave solutions and soliton solutions in a one-dimensional ferromagnetic chain with anisotropy exchange interaction and single-ion anisotropy are obtained through travelling wave solution method and the influence of single-ion anisotropy on cnoidal waves and solitons is discussed. The results indicate that single-ion anisotropy makes the cnoidal waves and solitons easy to excite in an easy-plane ferromagnetic chain but difficult in an easy-axis one, and makes them more stable in the easy-axis ferromagnetic chain but less stable in the easy-plane one. The influence of single-ion anisotropy on soliton excitations in a one-dimensional isotropic ferromagnet is also discussed.

Static properties of CsNiF 3: numerical results, experimental data and soliton bearing models

The static properties of the S=1 easy-plane ferromagnetic chain system CsNiF 3 have been calculated by the numerical Quantum Transfer Matrix method (QTM). An analysis of the relevant experimental data shows that the generally accepted spin Hamiltonian accurately describes the individual chains for J / k B=25 K, D / k B=7.7 K, g=2.1. Deviations between theory and experiment are found at temperatures extending up to several kelvin above the three-dimensional ordering temperature, that are attributed to the coupling between the chains. The QTM results are compared with various analytical results, yielding support for the description of solitary excitations in CsNiF 3 by the classical sine-Gordon model, extended to include spin fluctuations out of the easy plane and quantum effects.

Static properties ofCsNiF3: Comparison of numerical results, experimental data, and predictions from soliton-bearing models

The numerical quantum transfer-matrix method has been applied to the s=1 easy-plane ferromagnetic chain system ${\mathrm{CsNiF}}_{3}$. A detailed analysis of experimental data on the static properties reveals that the generally accepted spin Hamiltonian for this compound gives an accurate description of the individual chains for J/${\mathit{k}}_{\mathit{B}}$=25 K and D/${\mathit{k}}_{\mathit{B}}$=7.7 K. At temperatures up to several degrees Kelvin above the three-dimensional ordering temperature, deviations between theory and experiment are found that are attributed to the coupling between the chains. A comparison of the quantum-transfer-matrix-method results with various analytical results supports the description of solitary excitations in ${\mathrm{CsNiF}}_{3}$ by the classical sine-Gordon model, extended to include spin fluctuations out of the easy plane and quantum effects.

Non-linear effects in the easy-plane one-dimensional antiferromagnet in a staggered field

We present a theoretical analysis of soliton excitations in an easy-plane classical one-dimensional antiferromagnet in the presence of a staggered magnetic field transverse to the chain direction. The out-of-plane soliton solution is found to have an instability similar to the one found before by Magyari-Thomas-Kumar for the easy-plane ferromagnetic chain in an external magnetic field.

Two-spin-wave spectra of easy-plane ferromagnetic chains

The easy-plane ferromagnetic chain in an applied magnetic field is known to map onto a sine-Gordon field theory, in the classical continuum limit. The sine-Gordon field theory supports breather excitations which, when quantised, are identifiable as a hierarchy of bound states of several small-amplitude excitations. For increasing values of the interaction parameter, the highest members of the hierarchy become unstable to the emission of a soliton/anti-soliton pair. For a critical value of the interaction parameter, even the ground state of the quantised sine-Gordon theory becomes unstable. For the quantum spin system, the excitations corresponding to the two lowest members of the hierarchy of breathers are the single-spin-wave and the two-spin-wave bound states. The authors examine the two-spin-wave bound-state excitations of the quantum spin system directly, using a large-S approach. Although the method does rely on large S, they recover previously derived results valid for arbitrary S, such as the exact two-spin-wave bound states for the isotropic Heisenberg ferromagnet and the expansion in the anisotropy about this result. In the limit of large anisotropy the two-spin-wave bound state becomes unstable, in a manner suggestive of the instability of the quantum-sine-Gordon field theory.

Classical aspects of quantum spin chains.

We suggest a new variational approach for quantum spin chains, based on the stochastic behavior of the quantization axes, which describes a chain in terms of a classical and a quantum contribution to the free energy. For an easy-plane ferromagnetic chain with the external field in the plane it reveals that the nonlinear excitations are predominantly described by the classical degrees of freedom. Hence it offers a fundamental basis for the description of the elementary excitations of such systems in terms of classical solitons and quantum spin waves, as suggested by various experiments.

Quantum fluctuations in Sine-Gordon like magnetic chains: Corrections to soliton energies

The effect of quantum fluctuations on solitons in the easy-plane ferromagnetic chain is considered within the semiclassical approximation. In accordance with the low temperature ideal gas picture we treat the solitons as a Boltzmann gas and impose quantisation on the spin wave spectrum. We present a method which allows to calculate quantum corrections in a systematic perturbation expansion in 1/S, whereS is the spin length. We use this method to obtain the soliton energy to second order at zero temperature. Our results indicate that the semiclassical approach reasonably describes quantum effects on soliton properties.

QUANTUM EFFECTS ON SOLITON PROPERTIES IN FERROMAGNETIC SPIN CHAINS

Quantum effects on soliton-like excitations are investigated for the easy-plane ferromagnetic chain and for the anisotropic xy-chain. Our results for the soliton energy to order 1/S2 and for the soliton contribution to the specific heat indicate that the semiclassical approach reasonably describes quantum effects on solitons properties (in particular the strong reduction of the specific heat) for realistic spin chains.

Nonlinear excitations in a realistic ferromagnetic chain: thermodynamics and correlation functions

For the classical easy-plane ferromagnetic chain in an external magnetic field the authors calculate numerically the contributions of nonlinear, soliton-like excitations to the free energy and to static and dynamical correlation functions, using a phenomenological, low-temperature approach, which takes into account the full spectrum of soliton-like excitations for the realistic magnetic chain. Deviations from the sine-Gordon model are found and discussed quantitatively for the soliton density, for the width and shape of the dynamical structure factor and for the form factor of the out-of-plane correlation function. Results are given for various values of the ratio of the Zeeman energy to single-ion anisotropy energy, covering in particular the Magyari-Thomas instability against motion and showing a smooth behaviour of the properties of the system across this instability.

Shape correction, shape mode control, and stability of solitons in the discrete easy-plane ferromagnet

The authors present a new one-parameter ansatz modifying the continuum soliton shape which allows control of the amplitude of the bound shape mode oscillation moving with the soliton along the discrete easy-plane ferromagnetic chain. The shape mode is usually excited, when as in previous simulations the start configuration of the single soliton is known only approximately. They are now able to choose the shape correction parameter in their ansatz such that the excitation of the shape mode is suppressed completely. Thus, well defined discrete solitons can be generated, an important precondition for studying soliton-soliton collisions. They analyse the frequency of the shape mode of the static in-plane soliton as a function of the magnetic field using an approximation related to their shape correction ansatz, from which they conjecture the range of existence of stable solitons and the corresponding shape modes coincide. They also obtain the generalised symmetry of the shape mode eigenfunction for moving solitons. Next they describe two series of static solitary solutions which contain large angles (greater than pi /2) between adjacent spins. Some members of these series are pairwise connected by a continuous crossover. Finally they introduce an approximation which yields qualitatively new results for the high-field limit of existence of stable moving solitons, extending the previously known range, and also discuss the relation of the static soliton branching point to linear stability analysis results.

Bound states and correlation functions in the easy-plane Heisenberg ferromagnetic chain

The two-magnon excitation spectrum of the quantum spin-one easy-plane Heisenberg ferromagnetic chain is discussed. The spin-spin correlation functions are calculated within a systematic perturbation theory in terms of the anisotropy, and contributions from the two-magnon bound states are discussed. The results are compared with the predictions for non-interacting spin waves.

Quantum specific heat of the easy-plane ferromagnetic chain: Application to CsNiF3 and (C6H

Quantum effects in the easy-plane ferromagnetic chain are considered in the semiclassical approximation. It is shown that the soliton part of the specific heat is reduced significantly by the inclusion of quantum effects. The results are compared with the data for CsNi${\mathrm{F}}_{3}$ and (${\mathrm{C}}_{6}$${\mathrm{H}}_{11}$N${\mathrm{H}}_{3}$) Cu${\mathrm{Br}}_{3}$.

Solitons and magnons in a one-dimensional easy-plane ferromagnet

Linear and non-linear excitations are investigated theoretically in an easy-plane ferromagnetic chain in an external symmetry-breaking field. As for non-linear modes, the ideal-gas phenomenology is applied to evaluate the thermodynamic and dynamic quantities due to stable sine-Gordon-like solitons that exist for the external field smaller than the critical value, while small-amplitude excitations are treated by the standard spin wave theory with the lowest-order 1/S quantum corrections included. The contributions to the cross sections of polarised neutron scattering from both linear and non-linear modes are evaluated. Some of the results are compared with an experiment on CsNiF3 by Kakurai and co-workers (1984) and the importance of the finite out-of-plane fluctuations that are underestimated in the sine-Gordon approximation is pointed out.

Solitons on a realistic ferromagnetic chain

The nonlinear spin dynamics of the discrete classical easy-plane ferromagnetic spin chain in an external field is investigated by computing the time evolution of nonplanar soliton configurations. Owing to the discreteness we find a soliton instability and a substantial contraction of the soliton spectrum. We discuss the important roles of quantum effects and of discreteness for the understanding of the soliton contribution to the specific heat.

ChemInform Abstract: THERMODYNAMICS AND CORRELATION FUNCTIONS OF NONLINEAR EXCITATIONS IN THE EASY‐PLANE FERROMAGNETIC CHAIN

Chemischer InformationsdienstVolume 16, Issue 25 Reviews ChemInform Abstract: THERMODYNAMICS AND CORRELATION FUNCTIONS OF NONLINEAR EXCITATIONS IN THE EASY-PLANE FERROMAGNETIC CHAIN H. FOGEDBY, H. FOGEDBYSearch for more papers by this author H. FOGEDBY, H. FOGEDBYSearch for more papers by this author First published: June 25, 1985 https://doi.org/10.1002/chin.198525383AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume16, Issue25June 25, 1985 RelatedInformation

On Static Kink Solutions for an Anisotropic Heisenberg Ferromagnetic Chain

AbstractFor the anisotropic Heisenberg chain nonlinear equations are derived, describing static kink properties. The equations are exactly solved for an easy axis respectively easy plane ferromagnetic chain. The influence of different forms of local anisotropy is discussed.

Low temperature spin wave and domain wall thermodynamics and form factors for the classical easy-plane ferromagnetic chain

Using the steepest descent approach, equivalent to the static limit of the ideal gas phenomenology, we derive low temperature expressions for the free energy and the static spin correlation functions of the classical easy-plane ferromagnetic chain in an in-plane field. At low field the system forms a stable gas spin waves and domain walls. Approaching the critical field for domain wall transition, the domain wall free energy, the longitudinal and transverse in-plane domain wall form factors increase in strength. The transverse in-plane spin wave correlation display damped oscillations and the out-of-plane spin correlations decay exponentially with a growing correlation length. Correspondingly, the out-of-plane form factor increases in intensity. We propose to look for this effect in CsNiF 3 by means of (polarized) neutrons.

Soliton dynamics on an easy-plane ferromagnetic chain

It is now generally accepted that the description of solitons in a classical easy-plane ferromagnetic chain in terms of a sine-Gordon theory is inadequate. The structural and dynamic properties of these solitons are not very clear. The authors present here results of a numerical simulation of the dynamics of a single soliton as well as collisions between a soliton-antisoliton pair. The dynamics of a single soliton appears to be consistent with variational method calculations. The energy dispersion E(u), where u is the propagation velocity, consists of three continuously connected branches. Only the first branch is sine-Gordon-like with an effective soliton mass. A soliton-antisoliton pair collision leads to a variety of final states. As a function of magnetic field B, there are four major regimes. At very low fields, the pair transmit through each other similar to a pair collision for true sine-Gordon solitons. For somewhat higher fields, the pair forms a bound state (breather mode) on collision. Further increase in magnetic field leads to reflection of the soliton-antisoliton pair. As a function of increasing collision velocity usG for an initial sine-Gordon pair, the various critical fields in general decrease. Furthermore, there are details in the final state diagram (in the usG-B plane) that correspond to resonance scattering (for breather modes) and branch transfer (in the pair collision leading to reflection). Implications of these results for quasi-one-dimensional ferromagnets such as CsNiF3 and CHAB ((C6H11NH3)CuBr3) are suggested. In particular, they suggest that non-linear elementary excitations in these chains may be breathers rather than isolated solitons.

Solitons in an easy-plane ferromagnetic chain-beyond the sine-Gordon approximation

The ideal gas phenomenology is applied to evaluate the dynamical correlation functions due to solitons in an easy-plane ferromagnetic chain in an external symmetry-breaking field. The importance of the finite out-of-plane fluctuations, which are neglected in the sine-Gordon approximation, is pointed out. The relevance of these fluctuations is discussed in connection with a recent polarised neutron scattering experiment on CsNiF3 by Kakurai et al. (1984).