Solitons in the anisotropic Heisenberg chain in the Holstein-Primakoff representation

Škrinjar, M. J.; Kapor, D.; Stojanović, S.

doi:10.1088/0022-3719/20/15/010

Cited by 21 publications

(9 citation statements)

References 6 publications

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“…13 ' There are some relations between the inverse of the spin magnitude e(= S~ ' ) and the characteristic soliton length Ao-The nonlinear modified terms in the equation of motion of coherent amplitude are strongly constrained by the above relations. Kapor et afj 12 ! thought that it is impossible to establish a direct relation between e and Ao-They have not found any new method to avoid .the inconsistence of the two-.parameter theory of solitons in magnetic systems.…”

Section: Discussionmentioning

confidence: 99%

“…( 14). In the previous works,t 12,13 ' 21 ' ipl ' was neglected. In fact, ipi ' can result in tremendous difference in the structure of succeeding equations.…”

Section: Solitary Excitationsmentioning

confidence: 99%

“…The other coherent-state treatments adopted a severely truncated Holstein-Primakoff expansion for 5*, further approximated the Hamiltonian in boson operators and got solitons in the system.' [10][11][12] ^ In Glauber's coherent-state representation, HUANG et alS 13 1 made the semiclassical approximations and found solitons in the system.…”

Section: Introductionmentioning

confidence: 99%

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Solitary Excitations in Antiferrornagnets AFeBr ₃

Liu¹,

Zhou²,

Pu³

1995

Commun. Theor. Phys.

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Introducing the Holstein-Primakoff transformation, the coherent-state ansatz and the timedependent variation principle, we obtain two partial differential equations of motion. Employing the method of multiple scales, we reduce these equations into the envelope function equations and force the amplitude function to satisfy a nonlinear Schrodinger equation. Using the inverse-scattering transformation, we obtain the single-, two-and N-soliton solutions and discuss the gap soliton in antiferromagnets AFeBr3.

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Section: Discussionmentioning

confidence: 99%

“…( 14). In the previous works,t 12,13 ' 21 ' ipl ' was neglected. In fact, ipi ' can result in tremendous difference in the structure of succeeding equations.…”

Section: Solitary Excitationsmentioning

confidence: 99%

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Solitary Excitations in Antiferrornagnets AFeBr ₃

Liu¹,

Zhou²,

Pu³

1995

Commun. Theor. Phys.

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“…The HP transformation for spin operator is widely used in spin-wave theory. Most of the works made so far on the nonlinear excitations in the Heisenberg magnets in the HP representation are based on the semiclassical approximation and the long wavelength approximation' [10][11][12][13][14] '. The two approximations have been thought to be independent of each other.…”

Section: ^ = 2 C(^s-f{p) {1 + Tanh [Q °{X -Xo ~Vot)]} 'mentioning

confidence: 99%

Soliton Excitations in the Compressible Heisenberg Spin Chain: A General Approach

Huang

Shi

Dai

et al. 1992

Commun. Theor. Phys.

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A genera] approach is given for the nonlinear excitations in the compressible Heisenberg ferromagnetic chain in coherent-state representation. It is shown that the relative ratio of e to 6 is very important for determining the nonlinear modified terms of the equations of motion, e. = 1\/S (S is the spin length) and 6 = a/Xo (a is the lattice constant and Xo is the characteristic wavelength of the excitations) are two small dimensionless parameters used in the semiclassical approximation and in the long wavelength approximation, respectively. In the case of 6 -O(e), the reduced equations of motion are solved exactly and spin soliton and elastic kink solutions are obtained. The other cases of the relation between 6 and e are also discussed and the solitary wave solutions are aho given. The result obtained by Ferrer, as a special case, has been included in our approach.

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“…In the spin-coherentstate representation [15], one can work directly with spin operators, make no approximations to a Hamiltonian and obtain an exact non-linear equation of motion for the spincoherent amplitude [ 161. The other coherent-state treatments use a severely truncated operator expansion for S' [17][18][19][20][21] or an approximate Hamiltonian which is biquadratic in boson operators [22]. Working in Glauber's coherent-state representation and making the semiclassical approximation and the long-wavelength approximation, one then finds solitary-wave profiles of the system, which is the so-called semiclassical treatment.…”

Section: Introductionmentioning

confidence: 99%

Soliton-like magnon localization and the two-magnon bound state in a Heisenberg ferromagnetic chain

Huang

Shi

Dai

et al. 1990

J. Phys.: Condens. Matter

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An inhomogeneous Heisenberg spin Hamiltonian with single-ion anisotropy is used to investigate the non-linear excitations in a ferromagnetic chain. By means of the Holstein-Primakoff transformation and Glauber's coherent-state representation, the equation of motion for the annihilation operator a(j) is reduced to a non-linear Schrodinger-like equation with variable coefficients. Its non-linear modified terms are strongly restricted by the relation between the continuum approximation ( eta =a/ lambda 0, where eta is the 'degree' of the long wavelength, a is the lattice constant and lambda 0 the characteristic wavelength of the excitation) and the semiclassical approximation ( in =1/ square root S, where in is the degree of truncation of the operator expansion and S is the spin length). When assuming that eta =O( in ) and after retaining the terms to O( in 4), the motion of the coherent amplitude for the homogeneous case satisfies the non-linear Schrodinger equation. The single-soliton and two-soliton bound-state solutions are given. The results show that the magnon localization and two-magnon bound state are possible in the chain. Other relations between eta and in ( eta =O( in 1/2), eta =O( in 3/2 and eta =O( in 2)) are also discussed.

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Solitons in the anisotropic Heisenberg chain in the Holstein-Primakoff representation

Cited by 21 publications

References 6 publications

Solitary Excitations in Antiferrornagnets AFeBr ₃

Solitary Excitations in Antiferrornagnets AFeBr ₃

Soliton Excitations in the Compressible Heisenberg Spin Chain: A General Approach

Soliton-like magnon localization and the two-magnon bound state in a Heisenberg ferromagnetic chain

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Solitons in the anisotropic Heisenberg chain in the Holstein-Primakoff representation

Cited by 21 publications

References 6 publications

Solitary Excitations in Antiferrornagnets AFeBr 3

Solitary Excitations in Antiferrornagnets AFeBr 3

Soliton Excitations in the Compressible Heisenberg Spin Chain: A General Approach

Soliton-like magnon localization and the two-magnon bound state in a Heisenberg ferromagnetic chain

Contact Info

Product

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About

Solitary Excitations in Antiferrornagnets AFeBr ₃

Solitary Excitations in Antiferrornagnets AFeBr ₃