Soliton excitations in the alternating ferromagnetic Heisenberg chain

Huang, Guoxiang; Shi, Zhu‐Pei; Dai, Xianxi; Tao, Ruibao

doi:10.1103/physrevb.43.11197

Cited by 56 publications

(23 citation statements)

References 32 publications

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“…Particularly, both in theory and experiment, the researches of nonlinear excitations in ferromagnetic and antiferromagnetic systems are quite fruitful. [5][6][7][8][9][10][11][12][13] The most remarkable discovery made in the Heisenberg ferromagnetic and antiferromagnetic chains is the existence of stationary and traveling magnetic solitary waves. These results are very important for understanding correctly nonlinear properties of one-dimensional magnetic systems.…”

Section: Introductionmentioning

confidence: 99%

Interactions Between the Time-Varying Electromagnetic Field and the Quantum Solitary Wave in a Ferromagnetic Chain

Tang

2012

Mod. Phys. Lett. B

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Starting with the Heisenberg Hamiltonian of the one-dimensional ferromagnetic chain in external fields, we have studied quantum characteristics of solitary waves and interactions between solitary waves and the time-varying electromagnetic field. It is shown that the energy and magnetic moments of the solitary wave are quantized. Utilizing these novel results, we have obtained the Bloch's equation of the two-level quantum solitary wave in a simple harmonic magnetic field.

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Section: Introductionmentioning

confidence: 99%

Interactions Between the Time-Varying Electromagnetic Field and the Quantum Solitary Wave in a Ferromagnetic Chain

Tang

2012

Mod. Phys. Lett. B

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“…[1][2][3][4] In the past decades, the nonlinear excitations (such as envelope soliton, kink and discrete breather or intrinsic localized mode) in various one-dimensional lattice chains were intensively investigated both theoretically and experimentally, and many important fruits were achieved. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] In the classical lattice theory, the nonlinear excitations occur mainly in the forms of the breather and envelope soliton, 5,6 where an internal carrier wave is modulated by the envelope which constitutes the localized soliton structure. Another most remarkable discovery made in the classical lattice theory was the existence of intrinsic localized modes.…”

Section: Introductionmentioning

confidence: 99%

Quantum solitons in the Fermi–Pasta–Ulam model

Tang

2014

Int. J. Mod. Phys. B

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In this paper, quantum solitons in the Fermi-Pasta-Ulam (FPU) model are investigated analytically. By using the canonical transform method and number-conserving approximation, we obtain the normal form of the phonon-conserving quantized Hamiltonian. In order to convert the quantized Hamiltonian into the coordinate space, we employ the inverse Fourier transform. With the help of the Hartree approximate and the semidiscrete multiple-scale method, the nonlinear Schrödinger (NLS) equation is derived. The results show that quantum solitons may exist in the FPU model. Moreover, it is found that moving quantum solitons become quantum intrinsic localized modes under certain condition. In addition, we obtain the energy level of quantum solitons, which indicates that the energy of such quantum solitons is quantized.

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“…Even though classical spin systems admit an interesting class of nonlinear spin excitations such as solitons, for quantum spin systems, semiclassical treatment turns out to be a very suitable method for studying soliton excitations because of its consistency and validity. [16][17][18][19][20][21] Soliton spin excitations and solitary wave profiles have been identified in ferromagnets under semiclassical approximation in the long wavelength and low temperature limits, in which the spins are treated as bosonic operators under the Holstein-Primakoff ͑HP͒ approximation 22 in combination with Glauber's coherent state representation. 23 All of the recent semiclassical studies 16,17 in this direction pertain to spin systems with homogeneous spin-spin exchange interactions at different levels.…”

Section: Introductionmentioning

confidence: 99%

“…Now, we consider a generalized anisotropic weak Heisenberg ferromagnetic spin system with varying bilinear, biquadratic, and octupole-dipole interactions and we study the nature of the nonlinear spin excitations and identify all possible integrable spin models so that the nonlinear spin excitations are governed by solitons. When anisotropy is present in the spin system, semiclassical treatment [16][17][18][19][20][21] makes the study of nonlinear dynamics easier. Hence, in the present paper, we study the nonlinear spin dynamics of the Heisenberg anisotropic weak ferromagnetic system with varying bilinear, biquadratic, and octupole-dipole interactions in the continuum limit under semiclassical approximation.…”

Section: Introductionmentioning

confidence: 99%

Soliton spin excitations and their perturbation in a generalized inhomogeneous Heisenberg ferromagnet

Daniel

Beula²

2008

Phys. Rev. B

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We investigate the nonlinear spin dynamics of a generalized inhomogeneous anisotropic Heisenberg ferromagnetic spin chain with bilinear and biquadratic exchange, octupole-dipole, and weak interactions in the semiclassical limit by using Glauber's coherent state method in combination with Holstein-Primakoff bosonic representation of spin operators. The dynamics is found to be governed by a generalized nonlinear Schrödinger equation in the continuum limit. We have identified several completely integrable spin models with soliton spin excitations for specific parametric choices. Finally, we carry out a multiple scale perturbation analysis to find the effect of discreteness and inhomogeneity on the soliton excitations in a more general case. The results show that the discreteness effect introduces symmetric fluctuations in the localized region of the soliton without altering its amplitude and velocity. On the other hand, the inhomogeneity introduces asymmetric fluctuations in the localized region with a decrease in the amplitude and velocity of the soliton with time. Further, the inhomogeneity reverses the velocity of the soliton after some time. different orders of the lattice parameter and integrable spin models have been identified. In Sec. IV, for the more general nonintegrable case, we carry out a multiple scale perturbation analysis to understand the effects of discreteness and inhomogeneity. The results are presented in Sec. V. II. MODEL AND DYNAMICAL EQUATIONThe Heisenberg spin Hamiltonian for an anisotropic weak ferromagnetic spin system with site-dependent bilinear, biquadratic, and octupole-dipole interactions ͑a generalized Heisenberg spin model͒ is written aswhere J 1i Ј , J 2i Ј , and J 3i Ј represent site-dependent coefficients of bilinear, biquadratic, and octupole-dipole interactions, respectively, and the constants J 4 Ј and AЈ ͑and A 1 Ј͒ correspond to weak and crystal field anisotropy interactions. D is the constant Dzyaloshinskii-Moriya ͑DM͒ vector, and the coefficients b and c introduce exchange anisotropy in the spin system. In Eq. ͑1͒, S i = ͑S i x , S i While writing Eq. ͑2͒, we have expressed the site-dependent coefficients J 1i , J 2i , and J 3i as J 1i = J 10 + J 11 f i , J 2i = J 20 + J 21 g i , and J 3i = J 30 + J 31 h i , where f i , g i , and h i are time-independent site-dependent functions related to the bilinear, biquadratic, and octupole-dipole interactions, respectively, and J 10 , J 11 , J 20 , J 21 , J 30 , and J 31 are constant coefficients. Different models of one-dimensional spin-1/2 ordered ferromagnetic chains with exchange interaction were proven to be exactly solvable with a complete description of their energy spec-

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Soliton excitations in the alternating ferromagnetic Heisenberg chain

Cited by 56 publications

References 32 publications

Interactions Between the Time-Varying Electromagnetic Field and the Quantum Solitary Wave in a Ferromagnetic Chain

Interactions Between the Time-Varying Electromagnetic Field and the Quantum Solitary Wave in a Ferromagnetic Chain

Quantum solitons in the Fermi–Pasta–Ulam model

Soliton spin excitations and their perturbation in a generalized inhomogeneous Heisenberg ferromagnet

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