Abstract
Soliton states in a semi-infinite ferromagnetic film with partially pinned spins at its boundary are found and analyzed within the focusing nonlinear Schrödinger equation (NLSE). It is shown that solitons are divided into two classes. The first class includes magnetization oscillations with discrete frequencies localized near the film edge. The second class contains moving particle-like objects whose cores are strongly deformed at the film boundary; these objects are elastically reflected from this boundary, thus recovering the shape of solitons typical for a unbounded sample. A series of conservation laws for a wave field is obtained that ensures the localization of soliton oscillations near the boundary of the sample and the elastic reflection of moving solitons from this boundary. It is shown that a change in the phase of the internal precession of a soliton during reflection depends on the character of spin pinning at the edge of the sample.
Similar content being viewed by others
REFERENCES
B. A. Kalinikos, N. G. Kovshikov, and A. N. Slavin, JETP Lett. 38, 413 (1983).
B. A. Kalinikos, N. G. Kovshikov, and A. N. Slavin, Sov. Phys. JETP 67, 89 (1988).
V. A. Kalinikos, N. G. Kovshikov, and A. N. Slavin, Phys. Rev. B. 42, 8658 (1990).
A. B. Borisov and V. V. Kiselev, Quasi-One-Dimensional Magnetic Solitons (Fizmatlit, Moscow, 2014) [in Russian].
A. K. Zvezdin and A. F. Popkov, Sov. Phys. JETP 57, 350 (1983).
R. E. de Wames and T. Wolfram, J. Appl. Phys. 41, 987 (1970).
V. V. Kiselev, A. P. Tankeev, and A. V. Kobelev, Physics of Metals and Metallography 82 (5), 458 (1996).
B. A. Kalinikos, Izv. Vyssh. Uchebn. Zaved., Fiz. 25, 42 (1981).
G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).
V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method (Nauka, Moscow, 1980; Springer, Berlin, 1984).
L. D. Faddeev and L. A. Takhtadzhyan, Hamiltonian Approach in the Theory of Solitons, Classics in Mathematics (Nauka, Moscow, 1986; Springer, Berlin, 1987).
N. Akhmediev and A. Ankiewicz, Solitons: Non-linear Pulses and Beams (Fizmatlit, Moscow, 2003; Springer, New York, 1997).
Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, New York, 2003).
N. N. Rosanov, Dissipative Optical Solitons: From Micro- to Nano- and Atto- (Fizmatlit, Moscow, 2011) [in Russian].
H. C. Yuen and B. M. Lake, Adv. Appl. Mech. 22, 67 (1982).
P. N. Bibikov and V. O. Tarasov, Sov. J. Theor. Math. Phys. 79, 570 (1989).
V. O. Tarasov, Inverse Probl. 7, 435 (1991).
I. T. Khabibullin, Sov. J. Theor. Math. Phys. 86, 28 (1991).
A. S. Fokas, Phys. D (Amsterdam, Neth.) 35, 167 (1989).
E. K. Sklyanin, Funkts. Anal. Pril. 21, 86 (1987).
G. V. Dreiden, A. V. Porubov, A. M. Samsonov, and I. V. Semenova, Tech. Phys. 46, 505 (2001).
A. B. Migdal, Qualitative Methods in Quantum Theory (Nauka, Moscow, 1979; Benjamin, Reading, 1977).
A. M. Kosevich, E. A. Ivanov, and A. S. Kovalev, Nonlinear Magnetization Waves. Dynamic and Topological Solitons (Naukova Dumka, Kiev, 1983) [in Russian].
A. M. Kosevich, B. A. Ivanov, and A. S. Kovalev, Phys. Rep. 194, 117 (1990).
V. V. Kiselev and A. P. Tankeyev, J. Phys.: Condens. Matter 8, 10219 (1996).
Funding
This work was carried out within the state assignment of the Ministry of Science and Higher Education of the Russian Federation (project “Quant,” no. AAAAA18-118020190095-4).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
Additional information
Translated by I. Nikitin
Rights and permissions
About this article
Cite this article
Kiselev, V.V., Raskovalov, A.A. Interaction of Solitons with the Boundary of a Ferromagnetic Plate. J. Exp. Theor. Phys. 135, 676–689 (2022). https://doi.org/10.1134/S1063776122110085
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776122110085