On soliton excitations in a one-dimensional Heisenberg ferromagnet

Abstract

Soliton excitations in a one-dimensional Heisenberg ferromagnet are studied by means of the Holstein-Primakoff representation. Writing the Hamiltonian and the equation of motion into dimensionless forms, the authors show that the relative ratio of epsilon to eta is important for the determination of the modified terms of the nonlinear Schrodinger equation; epsilon =1/ square root S (S is the spin length) is the small dimensionless parameter used in the semiclassical approximation and eta =a/ lambda 0 (a is the lattice space and lambda 0 is the characteristic wavelength of the excitations) is another small dimensionless parameter used in the long-wave approximation. The soliton solutions are given in three cases ( eta =O( epsilon ), eta =O( epsilon 32/) and eta =O( epsilon 2)) which correspond to the different physical conditions of the system. The results obtained by Pushkarov and Pushkarov (1977), de Azevedo et al. (1982), and Skrinjar et al. (1989) are included in this approach.

Soliton dynamics in two coupled ferromagnetic chains

“…There was the availability of real magnetic compounds which because of extremely small coupling between neighboring chains, could be considered as reasonable realizations of magnetically onedimensional materials. Soliton solutions for classical sine-Gordon chains [2] and Heisenberg chains with various anisotropies [3][4][5][6] were obtained and analyzed. In recent years there is a renewed interest to the topic due to their application.…”

“…Bright and dark solitons as exact solutions of the nonlinear Schrödinger (NLS) equation have been studied intensively [3,4,11,12]. Another interesting topic of research with practical importance is the propagation of solitons in coupled parallel chains [13][14][15][16][17][18][19][20].…”

Dark solitons in ferromagnetic chains with first- and second-neighbor interactions

“…Bright and dark solitons as exact solutions of the nonlinear Schrödinger (NLS) equation have been studied intensively [3,4,11]. But models describing the physical effects in solids are mainly discrete and the question arises as to how this discreteness modifies the properties of the nonlinear excitations [12,13].…”

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

“…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.…”

“…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.…”