Damping of Magnetoelastic Waves
Keywords:magnetoelastic interaction, dissipative function, dispersion law, uniaxial ferromagnet, relaxation
A general method for constructing a model of the dissipative function describing the relaxation processes induced by the damping of coupled magnetoacoustic waves in magnetically ordered materials has been developed. The obtained model is based on the symmetry of the magnet and describes both exchange and relativistic interactions in the crystal. The model accounts for the contributions of both the magnetic and elastic subsystems to the dissipation, as well asthe relaxation associated with the magnetoelastic interaction. The dispersion law for coupled magnetoelastic waves is calculated in the case of a uniaxial ferromagnet of the “easy axis” type. It is shown that the contribution of the magnetoelastic interaction to dissipative processes can play a significant role in the case of magnetoacoustic resonance.
C. Kittel. Interaction of spin waves and ultrasonic waves in ferromagnetic crystals. Phys. Rev. 110, 836 (1958). https://doi.org/10.1103/PhysRev.110.836
A.I. Akhiezer, V.G. Bar'yakhtar, S.V. Peletminskii. Coupled magnetoelastic waves in ferromagnetic media and ferroacoustic resonance. JETP 8, 157 (1959).
A.I. Akhiezer, V.G. Bar'yakhtar, S.V. Peletminskii. Spin Waves (North Holland, 1968).
V.G. Bar'yakhtar, E.A. Turov. Magnetoelastic excitations. In Spin Waves and Magnetic Excitations. Edited by A.S. Borovik-Romanov, S.K. Sinha (North Holland, 1988), Pt. 2, p. 333. https://doi.org/10.1016/B978-0-444-87078-0.50012-9
V.G. Bar'yakhtar, A.G. Danilevich. Magnetoelastic waves in ferromagnets in the vicinity of lattice structural phase transitions. Ukr. J. Phys. 63, 836 (2018). https://doi.org/10.15407/ujpe63.9.836
V.G. Bar'yakhtar, A.G. Danilevich, V.A. L'vov. Coupled magnetoelastic waves in ferromagnetic shape-memory alloys. Phys. Rev. B 84, 134304 (2011). https://doi.org/10.1103/PhysRevB.84.134304
A.G. Danilevich. The influence of magnetoelastic interaction on the first transverse sound in a ferromagnet of cubic symmetry in a vicinity of the martensitic transformation. Ukr. J. Phys. 59, 1007 (2014). https://doi.org/10.15407/ujpe59.10.1007
B.N. Sahu, R. Prabhu, N. Venkataramani, Sh. Prasad, R. Krishnan, A. Nabialek, O.M. Chumak, R. Zuberek. Magnetostriction studies in nano-crystalline zinc ferrite thin films by strain modulated ferromagnetic resonance. J. Magn. Magn. Mater. 460, 203 (2018). https://doi.org/10.1016/j.jmmm.2018.04.012
K. Dey, S. Sauerland, J. Werner, Y. Skourski, M. Abdel-Hafiez, R. Bag, S. Singh, R. Klingeler. Magnetic phase diagram and magnetoelastic coupling of NiTiO3. Phys. Rev. B 101, 195122 (2020). https://doi.org/10.1103/PhysRevB.101.195122
A. Mazzamurro, Ya. Dusch, Ph. Pernod, O. Bou Matar, A. Addad, A. Talbi, N. Tiercelin. Giant magnetoelastic coupling in a Love acoustic waveguide based on TbCo/FeCo nanostructured film on ST-cut quartz. Phys. Rev. Appl. 13, 044001 (2020). https://doi.org/10.1103/PhysRevApplied.13.044001
Sh. Tateno, Yu. Nozaki. Highly nonreciprocal spin waves excited by magnetoelastic coupling in a Ni/Si bilayer. Phys. Rev. Appl. 13, 034074 (2020). https://doi.org/10.1103/PhysRevApplied.13.034074
R. Verba, I. Lisenkov, I. Krivorotov, V. Tiberkevich, A. Slavin. Nonreciprocal surface acoustic waves in multilayers with magnetoelastic and interfacial Dzyaloshinskii-Moriya interactions. Phys. Rev. Appl. 9, 064014 (2018). https://doi.org/10.1103/PhysRevApplied.9.064014
V.V. Kruglyak, S.O. Demokritov, D. Grundler. Magnonics. J. Phys. D 43, 264001 (2010). https://doi.org/10.1088/0022-3727/43/26/264001
A.M. Pogorilyi, S.M. Ryabchenko, O.I. Tovstolytkin. Spintronics. Main phenomena. Development trends. Ukr. Fiz. Zh. Oglyad. 6, 37 (2010) (in Ukrainian).
T.L. Gilbert. A Lagrangian formulation of the gyromagnetic equation of the magnetization fields. Phys. Rev. 100, 1243 (1955).
L.D. Landau, E.M. Lifshits. On the theory of the dispersion of magnetic permeability in ferromagnetic bodies, Phys. Zs. Sowjet. 8, 153 (1935), reprinted in Ukr. J. Phys., 53, Special Issue, 14 (2008).
V.G. Bar'yakhtar. Phenomenological description of relaxation processes in magnetic materials. JETP 60, 863 (1984).
V.G. Bar'yakhtar, A.G. Danilevich. Spin wave damping under spin orientation phase transitions. Fiz. Nizk. Temp. 32, 1010 (2006) (in Russian). https://doi.org/10.1063/1.2219498
V.G. Bar'yakhtar, A.G. Danilevich. Dissipative function of magnetic media. Fiz. Nizk. Temp. 36, 385 (2010) (in Russian). https://doi.org/10.1063/1.3421029
V.G. Bar'yakhtar, B.A. Ivanov, V.N. Krivoruchko, A.G. Danilevich. Modern Problems of Magnetization Dynamics: From the Basics to Ultrafast Relaxation (Khimdzhest, 2013) (in Russian).
L.D. Landau, E.M. Lifshitz. Theory of Elasticity (Butterworth-Heinemann, 1986) [ISBN: 978-0-7506-2633-0].
L.D. Landau, E.M. Lifshitz. L.P. Pitaevskii. Electrodynamics of Continuous Media (Butterworth-Heinemann, 1984) [ISBN: 978-0-7506-2634-7]. https://doi.org/10.1016/B978-0-08-030275-1.50007-2
V.G. Bar'yakhtar, B.A. Ivanov, T.K. Sobolyeva, A.L. Sukstanskii. Theory of dynamical-soliton relaxation in ferromagnets. Zh. Eksp. Teor. Fiz. 91, 1454 (1986) (in Russian).
V.G. Bar'yakhtar, B.A. Ivanov, A.L. Sukstanskii, E.Yu. Melikhov. Soliton relaxation in magnets. Phys. Rev. B 56, 619 (1997). https://doi.org/10.1103/PhysRevB.56.619
V.G. Bar'yakhtar, B.A. Ivanov, K.A. Safaryan. On the phenomenological description of the damping of the domain walls in ferrite-garnets. Solid State Commun. 72, 1117 (1989). https://doi.org/10.1016/0038-1098(89)90257-3
E.G. Galkina, B.A. Ivanov, V.A. Stephanovich. Phenomenological theory of Bloch point relaxation. J. Magn. Magn. Mater. 118, 373 (1993). https://doi.org/10.1016/0304-8853(93)90441-4
V.G. Bar'yakhtar, V.M. Loktev, S.M. Ryabchenko. Rotational invariance and magnetoflexural oscillations of ferromagnetic plates and rods. JETP 61, 1040 (1985).
A.G. Danilevich. Spin wave damping stimulated by exchange interaction at spin-orientation phase transitions in hexagonal ferromagnets. Ukr. J. Phys. 51, 668 (2006).
How to Cite
License to Publish the Paper
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.