Discrete breathers in anisotropic ferromagnetic spin chains

Speight, J.M.; Sutcliffe, Paul

doi:10.1088/0305-4470/34/49/307

Cited by 8 publications

(9 citation statements)

References 16 publications

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“…With the appearance of publications on discrete breathers, the one-dimensional Heisenberg antiferromagnetic chain was re-considered by Lai, Kiselev and Sievers [232,233], who numerically found site-centered and bond-centered discrete breathers and studied stability and mobility properties of these solutions. A rigorous proof of existence of such stationary discrete breathers has been performed by Zolotaryuk et al [410], and Speight and Sutcliffe [372]. Several experiments aimed to detect discrete breathers in layered antiferromagnetic crystals have been performed.…”

Section: The Case Of Xy Isotropic Exchange Interactionmentioning

confidence: 99%

Discrete breathers — Advances in theory and applications

Flach¹,

Gorbach²

2008

Physics Reports

940

830

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Section: The Case Of Xy Isotropic Exchange Interactionmentioning

confidence: 99%

Discrete breathers — Advances in theory and applications

Flach¹,

Gorbach²

2008

Physics Reports

940

830

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“…It was used to prove breather existence rigorously for easy-axis ferromagnets. 18,19 Also, Zolotaryuk and co-workers 18 have used this approach to find numerically a new type of breather solution in easy-plane ferromagnets which have no continuum analog. These solutions consist of a core of spins precessing around the hard ͑single-ion anisotropy͒ axis and tails of spins precessing in the easy plane.…”

Section: ͒mentioning

confidence: 99%

Discrete breathers in classical ferromagnetic lattices with easy-plane anisotropy

Khalack

Zolotaryuk

Christiansen

2003

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Discrete breathers ͑nonlinear localized modes͒ have been shown to exist in various nonlinear Hamiltonian lattice systems. This paper is devoted to the investigation of a classical d-dimensional ferromagnetic lattice with easy plane anisotropy. Its dynamics is described via the Heisenberg model. Discrete breathers exist in such a model and represent excitations with locally tilted magnetization. They possess energy thresholds and have no analogs in the continuum limit. We are going to review the previous results on such solutions and also to report new results. Among the new results we show the existence of a big variety of these breather solutions, depending on the respective orientation of the tilted spins. Floquet stability analysis has been used to classify the stable solutions depending on their spatial structure, their frequency, and other system parameters, such as exchange interaction and local ͑single-ion͒ anisotropy. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1573611͔The problem of energy localization in spatially distributed systems in condensed matter and biology is an important topic of modern physics. A lot of attention in the last several decades has been devoted to the phenomenon of localization due to spatial disorder. In particular, it is a well-known fact that lattice vibrations can localize themselves on impurities "creating so-called impurity localized modes…. In this paper we deal with the relatively new concept of intrinsic localized modes "discrete breathers…. These objects are spatially localized time-periodic lattice vibrations and their existence in translationally invariant "homogeneous… lattices has been proven rigorously. This remarkable phenomenon occurs in nonlinear lattices "lattices, governed by nonlinear equations of motion… and is based on the fact that the spectrum of the linear waves of the system under investigation is bounded and all possible resonances with the linear spectrum can be avoided. In this paper we are going to report on discrete breathers in classical ferromagnetic lattices with the easy-plane anisotropy. We are going to focus on the new type of solutions which have no continuum "soliton… analogs. Discrete breathers here have interesting spatial structure, consisting of a core of several spins, precessing around the hard axis and of tails, consisting of spins precessing with small amplitudes in the easy plane. These solutions possess energy thresholds so that their energy is separated from the energy of the ferromagnetic ground state by a gap. We also study linear stability of these excitations and how it depends on the spatial structure of the breather.

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“…Although the system of differential equations ( 4)-( 6) is in general nonintegrable, it admits a few classes of exact solutions [29]. In this connection, the above type of spin evolutions are known to admit intrinsic localized modes (ILM), essentially through numerical analysis [8,9,10,30,31]. Consequently, it will be of interest to look for exact solutions of ILM type by making appropriate ansatzes.…”

Section: The Heisenberg Anisotropic Spin Chain: Model and Equation Of...mentioning

confidence: 99%

“…In this connection ILMs have been explored in anisotropic spin chains starting from the anticontinuum limit to the nonzero exchange constant case analytically and numerically by several authors [8,9,10,30,31] and the existence of ILMs under specific interactions has been established. However, to our knowledge, no exact ILM solutions for the spin chains have been reported in the literature.…”

Section: Introductionmentioning

confidence: 99%