Solitons in the continuous Heisenberg spin chain

Tjon, J.A.; Wright, Jon

doi:10.1103/physrevb.15.3470

Cited by 275 publications

(153 citation statements)

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“…In particular, it explains the existence of ferromagnetism and antiferromagnetism at temperatures below the Curie temperature. The magnetic soliton [10], which describes localized magnetization, is an important excitation in the Heisenberg spin chain [11,12,13,14]. The Haldane gap [15] of antiferromagnets has been reported in integer Heisenberg spin chain.…”

mentioning

confidence: 99%

Magnetic soliton and soliton collisions of spinor Bose-Einstein condensates in an optical lattice

Li¹,

He²,

Li³

et al. 2005

Phys. Rev. A

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confidence: 99%

Magnetic soliton and soliton collisions of spinor Bose-Einstein condensates in an optical lattice

Li¹,

He²,

Li³

et al. 2005

Phys. Rev. A

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“…Several explicit solutions of these are known [10,11]. We note that Bloch walls form a certain class of exact solutions [9,11]of the nonlinear classical equations , namely non linear spin waves.…”

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confidence: 99%

“…If we write n the spin deviation from the saturated ferromagnet ( S z = N/2 − n) in terms of the density d as n = d N , the spectrum can be written as ω BW = Before presenting our calculations, we also note that the bound states of Bethe for s = 1/2 have been identified recently with solitonic excitations [9] of the non linear classical, i.e. large s, Landau Lifschitz equationṡ S(x) = S(x) × ∂ 2 /∂x 2 S(x).…”

mentioning

confidence: 99%

Bloch Walls and Macroscopic String States in Bethe's Solution of the Heisenberg Ferromagnetic Linear Chain

Dhar

Shastry

2000

Phys. Rev. Lett.

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We present a calculation of the lowest excited states of the Heisenberg ferromagnet in 1-d for any wave vector. These turn out to be string solutions of Bethe's equations with a macroscopic number of particles in them. These are identified as generalized quantum Bloch wall states, and a simple physical picture provided for the same. . In addition to providing the celebrated Ansatz named after him, Bethe asked if Bloch's magnons are the "most elementary" excitations in 1-d. He came to the conclusion that they were not, and instead found that the bound states of spin reversals were. After the original paper of Bethe, the ferromagnet has received [2-4] comparatively less attention than its antipode, namely the antiferromagnet [5,6]. One source of revival of interest in the ferromagnet is in connection with stochastic dynamical systems, albeit with a complex Aharonov Bohm magnetic flux [7,8]. Another notable recent exception is a work by Sutherland [4], who shows that the excited states of the ferromagnet contain a singlet state at momentum π, with an excitation energy (EE) that is very low, of O(1/N ), where N is the length of the ring.At the semiclassical level, domain wall arguments [12] lead one to expect in dimensions d ( with volume = N d ) the Bloch wall excitations to be of O(N d−2 ) , and hence to be amongst contenders for the lowest EE in d = 1. Such "large deviation" excitations carry spin as well as momentum as we show below. These configurations of spins will be discussed within the context of Bethe's Ansatz (BA) for the s = 1/2 ferromagnet presently.In this work we ask ( and answer) the following question: For a given value of the total momentum or total spin of the Bethe ferromagnet, what is the lowest excited state? The nontriviality of the question arises from the fact that within the famous Bethe formula for the boundstate of n magnons, ω Bethe (q) = J

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“…All numerical experiments utilize the soliton solution to the LLE published by Tjon and Wright [26]. The soliton is defined, for the anisotropic LLE (D = I ), by…”

Section: Numerical Verificationmentioning

confidence: 99%

Geometric space–time integration of ferromagnetic materials

Frank¹

2004

Applied Numerical Mathematics

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The Landau-Lifshitz equation (LLE) governing the flow of magnetic spin in a ferromagnetic material is a PDE with a noncanonical Hamiltonian structure. In this paper we derive a number of new formulations of the LLE as a partial differential equation on a multisymplectic structure. Using this form we show that the standard central spatial discretization of the LLE gives a semi-discrete multisymplectic PDE, and suggest an efficient symplectic splitting method for time integration. Furthermore we introduce a new space-time box scheme discretization which satisfies a discrete local conservation law for energy flow, implicit in the LLE, and made transparent by the multisymplectic framework. Hamiltonian structure of the Landau-Lifshitz equationThis paper addresses the Landau-Lifshitz equation (LLE) as a nonlinear wave equation supporting solitons and stable magnetic vortices, as considered, e.g., in [5,19,23]. The LLE governs the flow of magnetic spin in a ferromagnetic material. At a pointwhere is the Laplacian operator in3 ) models anisotropy in the material, and Ω is an external magnetic field.In applications in micromagnetics, the LLE may additionally include a nonlocal term, a spin magnitude-preserving Gilbert damping term, as well as a coupling terms to a dynamic external field governed by Maxwell's equations, see [6].

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Solitons in the continuous Heisenberg spin chain

Cited by 275 publications

References 2 publications

Magnetic soliton and soliton collisions of spinor Bose-Einstein condensates in an optical lattice

Magnetic soliton and soliton collisions of spinor Bose-Einstein condensates in an optical lattice

Bloch Walls and Macroscopic String States in Bethe's Solution of the Heisenberg Ferromagnetic Linear Chain

Geometric space–time integration of ferromagnetic materials

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