Nonlinear dynamics of a continuum Heisenberg spin chain with an anisotropy and an external magnetic field

Liu, Wu-Ming; Yang, Shijie; Pu, Fu‐Cho; Huang, Nian-Ning

doi:10.1007/s002570050342

Cited by 5 publications

(4 citation statements)

References 44 publications

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“…The continuum spin chain in an external magnetic field is of great interest and multi-soliton solutions of Landau-Lifschitz equation for an isotropic spin chain have been reported [25]. Using Darboux transformation the nonlinear dynamics of anisotropic Heisenberg spin chain in an external magnetic field is investigated and exact soliton solutions are obtained [26]. Recently soliton interaction has been investigated [16].…”

Section: Introductionmentioning

confidence: 99%

Exact soliton solution and inelastic two-soliton collision in a spin chain driven by a time-dependent magnetic field

Liu

et al. 2003

Phys. Rev. E

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We investigate dynamics of exact N-soliton trains in spin chain driven by a time-dependent magnetic field by means of an inverse scattering transformation. The one-soliton solution indicates obviously the spin precession around the magnetic field and periodic shape-variation induced by the time varying field as well. In terms of the general soliton solutions N-soliton interaction and particularly various two-soliton collisions are analyzed. The inelastic collision by which we mean the soliton shape change before and after collision appears generally due to the time varying field. We, moreover, show that complete inelastic collisions can be achieved by adjusting spectrum and field parameters. This may lead a potential technique of shape control of soliton.

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Section: Introductionmentioning

confidence: 99%

Exact soliton solution and inelastic two-soliton collision in a spin chain driven by a time-dependent magnetic field

Liu

et al. 2003

Phys. Rev. E

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“…Regarding the motion of a continuum Heisenberg spin chain, people have paid attention towards the new effects of an external magnetic field on the nonlinear wave. The dynamical behaviors of the magnetic chain have been observationally indicated and theoretically addressed for isotropic and anisotropic spin chains with an external magnetic field depending on time [10][11][12][13][14][15]20,21]. In particular, investigation of the partial-like excitation described by the soliton solution in a spin system is of great interest, to study the peculiarities of slow neutron scattering on magnets, dynamic structures from factors, and so on [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…(1) have been studied extensively in much literature and many monographs [5][6][7][8][9]. The relevant nonlinear waves are of current interest for magnetic systems under the action of an external magnetic field [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Regarding the motion of a continuum Heisenberg spin chain, people have paid attention towards the new effects of an external magnetic field on the nonlinear wave.…”

Section: Introductionmentioning

confidence: 99%

Soliton dynamics and elastic collisions in a spin chain with an external time-dependent magnetic field

Zhang

Tian

et al. 2010

Physica A: Statistical Mechanics and its Applications

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“…It is worth to noted that the inverse scattering transformation [10,12] is a useful method to solve the L-L equation. On the other hand great efforts [13] are also devoted to construct the soliton solution by means of the Darboux transformation [14][15][16][17].…”

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confidence: 99%

Soliton dynamics of magnetization driven by a magnetic field in uniaxial anisotropic ferromagnet

Zheng¹,

Li²,

Li³

et al. 2006

Braz. J. Phys.

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We study the nonlinear magnetic excitation in an anisotropic ferromagnet with a magnetic field. In the long wave approximation, the Landau-Lifschitz equation with easy axis anisotropy is transformed into the nonlinear Schrödinger type. By means of a straightforward Darboux transformation we obtain the one-and two-soliton solutions of uniaxial anisotropic ferromagnet. From a careful analysis for the asymptotic behavior of twosoliton solution we find that the collision between two magnetic solitons is elastic. This will be very helpful to understand the significant nature of the interactions between solitons in the future.Keywords: Soliton; Darboux transformation; Soliton interactionsThe Heisenberg model of spin-spin interactions can be considered as the starting point for understanding the complex magnetic structures in solid physics. In particular, it explains the existence of ferromagnetism and antiferromagnetism at temperature below the Curie temperature. This model has attracted considerable attentions in nonlinear science and condensed-matter physics [1]. The concept of soliton in spin chain which exhibits both coherent and chaotic structures depending on the nature of the magnetic interactions [1-3] has been studied for decades. In the present time soliton in quasi one-dimensional magnetic systems is no longer a theoretical concept but can be probed by neutron inelastic scattering [4], nuclear magnetic resonance [5], and electron spin resonance [6]. The magnetic soliton [7], which describes localized magnetization, is an important excitation in the classical Heisenberg spin chain. In particular, the continuum limit for the nonlinear dynamics of magnetization in the classical ferromagnet is governed by the Landau-Lifschitz (L-L) equation [8]. This equation governs a classical nonlinear dynamically system with novel properties. In a onedimensional case, some types of L-L equation is complete integrable. The isotropic case has been studied in various aspects [9,10], and the construction of soliton solutions of L-L equation with an easy axis is also discussed [11]. It is worth to noted that the inverse scattering transformation [10,12] is a useful method to solve the L-L equation. On the other hand great efforts [13] are also devoted to construct the soliton solution by means of the Darboux transformation [14][15][16][17].In the recent years, considerable attentions have been devoted to the study of soliton interactions in nonlinear science. However, the soliton collisions in spin chain is not fully explored. In this paper, we investigate soliton interactions of uniaxial anisotropic ferromagnet with an external magnetic field. By transforming the L-L equation with an easy-axis into an equation of the nonlinear Schrődinger (NLS) type we obtain the one-and two-soliton solutions by using the Darboux transformation.In the classical limit, the dynamics of spin chain is governed by the magnetization vector M = (M x , M y , M z ). The energy function including the exchange energy, anisotropic energy and the Zeeman ene...

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Nonlinear dynamics of a continuum Heisenberg spin chain with an anisotropy and an external magnetic field

Cited by 5 publications

References 44 publications

Exact soliton solution and inelastic two-soliton collision in a spin chain driven by a time-dependent magnetic field

Exact soliton solution and inelastic two-soliton collision in a spin chain driven by a time-dependent magnetic field

Soliton dynamics and elastic collisions in a spin chain with an external time-dependent magnetic field

Soliton dynamics of magnetization driven by a magnetic field in uniaxial anisotropic ferromagnet

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