Solitons in one-dimensional Heisenberg ferromagnetic chain with linear magnetic field
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摘要: 研究了在线性磁场作用下，一维铁磁链的两种孤子激发.分别通过导出了两个不同的修正的非线性薛定谔方程，可以得到各自所激发的孤子解.两种孤子激发均结果表明，在增加了线性磁场后，孤子的外形与有效质量并没有受到它的影响，但孤子的运动模式却改变了从一般的匀速运动变成了匀变速运动.而且在线性磁场作用下孤子的能量出现了定域分布，随位置的不同而不同.由此发现，引入线性磁场的普遍意义在于使得一维铁磁链中的孤子激发和移动可受到更好的控制，又不破坏孤子的稳定性.Abstract: Two kinds of soliton excitations in 1D ferromagnetic chain with linear magnetic field are considered. The results, two soliton solutions derived from two different modified NLS equations, all show that linear term of magnetic field has no influence on the shape and effective mass of each soliton, but changes the motional mode from uniformly motion to uniformly variable motion. Moreover, the energy of soliton appears the localized distribution after introducing the linear magnetic field. To introduce the linear magnetic can makes the excitation and motion of soliton more controllable without any bad damage in 1D ferromagnetic chain.
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[2] Pushkarov D I, Pushkarov K I. Solitons in One‐Dimensional Ferromagnetic Systems[J]. Physica Status Solidi, 1977, 81(81):703-707.
[3] Mikeska H J, Osano K. Dynamics of the soliton instability in the easy-plane ferromagnetic chain[J]. Zeitschrift Für Physik B Condensed Matter, 1983, 52(2):111-116.
[4] Balakrishnan R, Bishop A R. Nonlinear excitations on a quantum ferromagnetic chain[J]. Physical Review Letters, 1985, 55(5):537-540.
[5] Kawasaki T. Dynamics of Solitons in an Easy-Plane Ferromagnetic Chain : A Discrete Lattice Model : Condensed Matter and Statistical Physics[J]. Progress of Theoretical Physics, 1986, 75(3):534-549.
[6] Daniel M, Amuda R. Nonlinear dynamics of weak ferromagnetic spin chains[J]. Journal of Physics A General Physics, 1998, 28(19):5529-5537.
[7] Kumar P, Samalam V K. Solitons in an easy-plane ferromagnetic chain[J]. Journal of Applied Physics, 1982, 53(3):1856-1857.
[8] Kavitha L, Sathishkumar P, Saravanan M, et al. Soliton switching in an anisotropic Heisenberg ferromagnetic spin chain with octupole–dipole interaction[J]. Physica Scripta, 2011, 83(5):434-440.
[9] Tang B, Li D J, Tang Y. Quantum breathers in Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction[J]. Chaos, 2014, 24(2):023113-023113.
[10] Primatarowa M T, Kamburova R S. Dark solitons in ferromagnetic chains with first- and second-neighbor interactions[J]. Central European Journal of Physics, 2012, 10(5):1102-1108.
[11] Huang G, Jia Z. Self-induced gap solitons in Heisenberg ferromagnetic chains[J]. Physical review B, 1995, 51(1):613-616.
[12] Wang P. Conservation laws and solitons for a generalized inhomogeneous fifth-order nonlinear Schr?dinger equation from the inhomogeneous Heisenberg ferromagnetic spin system[J]. European Physical Journal D, 2014, 68(7):1-8.
[13] Dmitriev D V, Krivnov V Y. Magnetic solitons in a frustrated ferromagnetic spin chain[J]. Physical Review B, 2010, 81(5): 054408.
[14] Chen H, Chen Y. Effect of the Aharonov-Bohm flux to the soliton in a one-dimensional ferromagnetic ring[J]. Acta Physica Sinica, 1996, 45(8):1249-1254.
[15] Li D J, Tang Y. Interactions Between the Time-Varying Electromagnetic Field and the Quantum Solitary Wave in a Ferromagnetic Chain[J]. Modern Physics Letters B, 2012, 26(24):204-204.
[16] Li Z D, Li L, Liang J Q. Soliton Collision in a Ferromagnetic Spin Chain Driven by a Magnetic Field[J]. Chinese Physics Letters, 2004, 21(3):443-44.
[17] Kavitha L, Saravanan M, Gopi D. Propagation of an electromagnetic soliton in an anisotropic biquadratic ferromagnetic medium[J]. Chinese Physics B, 2013, 22(3):030512.
[18] Veerakumar V, Daniel M. Electromagnetic soliton damping in a ferromagnetic medium[J]. Physical Review E Statistical Physics Plasmas Fluids & Related Interdisciplinary Topics, 1998, 57(1):1197-1200.
[19] Mohn P. Magnetism in the Solid State: An Introduction[M]. Berlin Heidelberg: Springer-Verlag, 2006: 63-67.
[20] T. D. Holstein, Primakoff H. Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet[J]. Physical Review, 1940, 58(12):1098-1113.
[21] Glauber R J. Coherent and Incoherent States of the Radiation Field[J]. Physical Review, 1963, 131(6):2766-2788.
[22] Chen H H, Liu C S. Solitons in Nonuniform Media[J]. Physical Review Letters, 1976, 37(37):693-697.
[23] Serkin V N, Akira H, Belyaeva T L. Nonautonomous solitons in external potentials.[J]. Physical Review Letters, 2007, 98(7):074102.
[24] Scharf R, Bishop A R. Properties of the nonlinear Schr?dinger equation on a lattice.[J]. Physical Review A, 1991, 43(12):6535-6544.
[25] Cordeiro C E, Moura M A D. Solitary waves in an isotropic ferromagnetic chain[J]. Physics Letters A, 1978, 66(4):332–333.
[26] Chen H, Chen Y. Influences of the Aharonov-Bohm Flux on the Improved Soliton in a One-Dimensional Ferromagnetic Ring[J]. Communications in Theoretical Physics, 1998, 30(2):173-270.
[1] Pushkarov D I, Pushkarov K I. Solitary magnons in one-dimensional ferromagnetic chain[J]. Physics Letters A, 1977, 61(5):339-340.
[2] Pushkarov D I, Pushkarov K I. Solitons in One‐Dimensional Ferromagnetic Systems[J]. Physica Status Solidi, 1977, 81(81):703-707.
[3] Mikeska H J, Osano K. Dynamics of the soliton instability in the easy-plane ferromagnetic chain[J]. Zeitschrift Für Physik B Condensed Matter, 1983, 52(2):111-116.
[4] Balakrishnan R, Bishop A R. Nonlinear excitations on a quantum ferromagnetic chain[J]. Physical Review Letters, 1985, 55(5):537-540.
[5] Kawasaki T. Dynamics of Solitons in an Easy-Plane Ferromagnetic Chain : A Discrete Lattice Model : Condensed Matter and Statistical Physics[J]. Progress of Theoretical Physics, 1986, 75(3):534-549.
[6] Daniel M, Amuda R. Nonlinear dynamics of weak ferromagnetic spin chains[J]. Journal of Physics A General Physics, 1998, 28(19):5529-5537.
[7] Kumar P, Samalam V K. Solitons in an easy-plane ferromagnetic chain[J]. Journal of Applied Physics, 1982, 53(3):1856-1857.
[8] Kavitha L, Sathishkumar P, Saravanan M, et al. Soliton switching in an anisotropic Heisenberg ferromagnetic spin chain with octupole–dipole interaction[J]. Physica Scripta, 2011, 83(5):434-440.
[9] Tang B, Li D J, Tang Y. Quantum breathers in Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction[J]. Chaos, 2014, 24(2):023113-023113.
[10] Primatarowa M T, Kamburova R S. Dark solitons in ferromagnetic chains with first- and second-neighbor interactions[J]. Central European Journal of Physics, 2012, 10(5):1102-1108.
[11] Huang G, Jia Z. Self-induced gap solitons in Heisenberg ferromagnetic chains[J]. Physical review B, 1995, 51(1):613-616.
[12] Wang P. Conservation laws and solitons for a generalized inhomogeneous fifth-order nonlinear Schr?dinger equation from the inhomogeneous Heisenberg ferromagnetic spin system[J]. European Physical Journal D, 2014, 68(7):1-8.
[13] Dmitriev D V, Krivnov V Y. Magnetic solitons in a frustrated ferromagnetic spin chain[J]. Physical Review B, 2010, 81(5): 054408.
[14] Chen H, Chen Y. Effect of the Aharonov-Bohm flux to the soliton in a one-dimensional ferromagnetic ring[J]. Acta Physica Sinica, 1996, 45(8):1249-1254.
[15] Li D J, Tang Y. Interactions Between the Time-Varying Electromagnetic Field and the Quantum Solitary Wave in a Ferromagnetic Chain[J]. Modern Physics Letters B, 2012, 26(24):204-204.
[16] Li Z D, Li L, Liang J Q. Soliton Collision in a Ferromagnetic Spin Chain Driven by a Magnetic Field[J]. Chinese Physics Letters, 2004, 21(3):443-44.
[17] Kavitha L, Saravanan M, Gopi D. Propagation of an electromagnetic soliton in an anisotropic biquadratic ferromagnetic medium[J]. Chinese Physics B, 2013, 22(3):030512.
[18] Veerakumar V, Daniel M. Electromagnetic soliton damping in a ferromagnetic medium[J]. Physical Review E Statistical Physics Plasmas Fluids & Related Interdisciplinary Topics, 1998, 57(1):1197-1200.
[19] Mohn P. Magnetism in the Solid State: An Introduction[M]. Berlin Heidelberg: Springer-Verlag, 2006: 63-67.
[20] T. D. Holstein, Primakoff H. Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet[J]. Physical Review, 1940, 58(12):1098-1113.
[21] Glauber R J. Coherent and Incoherent States of the Radiation Field[J]. Physical Review, 1963, 131(6):2766-2788.
[22] Chen H H, Liu C S. Solitons in Nonuniform Media[J]. Physical Review Letters, 1976, 37(37):693-697.
[23] Serkin V N, Akira H, Belyaeva T L. Nonautonomous solitons in external potentials.[J]. Physical Review Letters, 2007, 98(7):074102.
[24] Scharf R, Bishop A R. Properties of the nonlinear Schr?dinger equation on a lattice.[J]. Physical Review A, 1991, 43(12):6535-6544.
[25] Cordeiro C E, Moura M A D. Solitary waves in an isotropic ferromagnetic chain[J]. Physics Letters A, 1978, 66(4):332–333.
[26] Chen H, Chen Y. Influences of the Aharonov-Bohm Flux on the Improved Soliton in a One-Dimensional Ferromagnetic Ring[J]. Communications in Theoretical Physics, 1998, 30(2):173-270. -
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