Magnetoelastic Waves in Ferromagnets in the Vicinity of Lattice Structural Phase Transitions
Keywords:
-Abstract
The dispersion laws for coupled magnetoelastic waves in ferromagnets with uniaxial or cubic symmetry have been calculated. The features of obtained dispersion laws in the vicinity of spin-reorientation phase transitions are analyzed. The interaction between elastic and spin waves is shown to depend on the direction of the ferromagnet magnetic moment. The influence of the magnetoelastic interaction on the dispersion law of quasispin waves in the degenerate ground state of a uniaxial “easy plane” ferromagnet is studied. The results of calculations show that the magnetoelastic interaction eliminates the degeneration and leads to the appearance of a magnetoacoustic gap in the ferromagnet spectrum. The behavior of the spectra of coupled magnetoelastic waves in the vicinity of lattice phase transitions, namely, in the vicinity of martensitic phase transformations in materials with the shape memory effect, is analyzed. The obtained results are used to interpret experimental data obtained for the Ni–Mn–Ga alloy. The phenomenon of a drastic decrease of the elastic moduli for this alloy, when approaching the martensitic phase transition point is explained theoretically. It is shown that the inhomogeneous magnetostriction is the main factor affecting the elastic characteristics of the material concerned. A model dissipative function describing the relaxation processes associated with a damping of coupled magnetoelastic waves in ferromagnets with cubic or uniaxial symmetry is developed. It takes the symmetry of a ferromagnet into account and describes both the exchange and relativistic interactions in the crystal.
References
C. Kittel. Interaction of spin waves and ultrasonic waves in ferromagnetic crystals. Phys. Rev. 110, 836 (1958).
A.I. Akhiezer, V.G. Bar’iakhtar, S.V. Peletminskii. Coupled magnetoelastic waves in ferromagnetic media and ferroacoustic resonance. J. Exper. Theor. Phys. 35, 228 (1959).
A.I. Akhiezer, V.G. Bar’yakhtar, and 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.
E.A. Turov, V.G. Shavrov. Broken symmetry and magnetoacoustic effects in ferro- and antiferromagnetics. Sov. Phys. Usp. 26, 593 (1983).
V.A. Chernenko, V.V. Kokorin. Ni2MnGa as a new ferromagnetic ordered shape memory alloy. In Proceedings of the International Conference on Martensitic Transformations 1992, Monterey, California, USA (Monterey Institute for Advanced Studies, 1993), p. 1205
V.A. Chernenko, J. Pons, C. Segu´ı, E. Cesari. Premartensitic phenomena and other phase transformations in Ni–Mn–Ga alloys studied by dynamical mechanical analysis and electron diffraction. Acta Materialia 50, 53 (2002).
L. Dai, J. Cullen, M. Wuttig. Intermartensitic transformation in a Ni–Mn–Ga alloy. J. Appl. Phys. 95, 6957 (2004).
O. Heczko, H. Seiner, P. Sedl´ak, J. Kopeˇcek, M. Landa. Anomalous lattice softening of Ni2MnGa austenite due to magnetoelastic coupling. J. Appl. Phys. 111, 07A929 (2012).
В.Г. Барьяхтар, Д.А. Яблонский. О магнитоупругой щели в спектре спиновых волн. Физ. Мет. и Металловед 43, 645 (1977).
V.V. Kokorin, M. Wuttig. Magnetostriction in ferromagnetic shape memory alloys, J. Magn. Magn. Mater. 234, 25 (2001).
J. Worgull, E. Petti, J. Trivisonno, Behavior of the elastic properties near an intermediate phase transition in Ni2MnGa spectrum. Phys. Rev. B 54, 15695 (1996).
V.A. Chernenko, V. A. L’vov. Thermodynamics of martensitic transformations affected by hydrostatic pressure. Phil. Mag. 73, 999 (1996).
R.C. O’Handley, S.M. Allen. Shape-memory alloys, magnetically activated ferromagnetic shape-memory materials. In Encyclopedia of Smart Materials. Edited by M. Schwartz (Wiley, 2002).
P. Entel, V.D. Buchelnikov, M.E. Gruner, A. Hucht, V.V. Khovailo, S. Nayak, A.T. Zayak. Shape memory alloys: A summary of recent achievements. Mater. Sci. Forum 583, 21 (2008).
V.A. Chernenko, V.A. L’vov. Magnetoelastic nature of ferromagnetic shape memory effect. Mater. Sci. Forum 583, 1 (2008).
V.G. Bar’yakhtar, A.G. Danilevich, V.A. L’vov. Magneto-elastic resonance in a crystal with lattice phase transition. Ukr. J. Phys. 56, 1068 (2011).
L.D. Landau, E.M. Lifshitz. Theory of Elasticity. (Butterworth-Heinemann, 1986).
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).
T.L. Gilbert. A Lagrangian formulation of the gyromagnetic equation of the magnetization fields. Phys. Rev. 100, 1243 (1955).
V.G. Bar’yakhtar. Phenomenological description of relaxation processes in magnetic materials. J. Exper. Theor. Phys. 60, 863 (1984).
V.G. Bar’yakhtar, A.G. Danilevich. Spin-wave damping at spin-orientation phase transitions. Low Temp. Phys. 32, 768 (2006).
V.G. Bar’yakhtar, A.G. Danilevich. Dissipation function of magnetic media. Low Temp. Phys. 36, 303 (2010).
V.A. L’vov, E.A. Gomonaj, V.A. Chernenko. A phenomenological model of ferromagnetic martensite. J. Phys.: Condens. Matter 10, 4587 (1998).
A.G. Danilevich, V.A. L’vov. Strong influence of ferromagnetic ordering and internal pressure on the elastic modulus of shape memory alloy. J. Magn. Magn. Mater. 333, 108 (2013).
P.J. Webster, K.R.A. Ziebeck, S.L. Town, M.S. Peak. Magnetic order and phase transformation in Ni2MnGa. Phil. Mag. B 49, 295 (1984).
R. Tickle, R.D. James. Magnetic and magnetomechanical properties of Ni2MnGa. J. Magn. Magn. Mater. 195, 627 (1999).
L. Dai, J. Cui, M. Wuttig. Elasticity of austenitic and martensitic Ni–Mn–Ga. Proc. SPIE 5053, 595 (2003).
V.G. Bar’yakhtar, I.M. Vitebsky, Yu.G. Pashkevich, V.L. Sobolev, V.V. Tarasenko. Striction effects and dynamics of the magnetic subsystem in spin-reorientation phase transitions. Symmetry aspects. J. Exper. Theor. Phys. 60, 587 (1984).
V.I. Ozhogin, V.L. Preobrazhenskii. Nonlinear dynamics of coupled systems near magnetic phase transitions of the “order-order” type. J. Magn. Magn. Mater. 100, 544 (1991).
N.N. Bogoliubov, D.V. Shirkov. Quantum Fields (Benjamin-Cummings, 1982).
V.G. Bar’yakhtar, A.G. Danilevich. The Higgs effect and the magnetoelastic gap in ferromagnets. Low Temp. Phys. 41, 379 (2015).
V.G.Bar’yakhtar,B.A. Ivanov,V.N.Krivoruchko,A.G.Danilevich. Modern Problems of Magnetization Dynamics: From the Basis to the Ultrafast Relaxation (Himgest, 2013) (in Russian).
V.G. Bar’yakhtar, V.M. Loktev, S.M. Ryabchenko. Rotational invariance and magnetoflexural oscillations of ferromagnetic plates and rods. J. Exper. Theor. Phys. 61, 1040 (1985)
L.D. Landau, E.M. Lifshitz, L.P. Pitaevskii. Electrodynamics of Continuous Media (Butterworth-Heinemann, 1984).
В.В. Еременко, В.Н. Криворучко, Н.М. Лавриненко, Д.А. Яблонский. Возбуждение переменным электрическим полем обменных магнитных колебаний в CsMnF3. ФТТ 30 (12), 3605 (1988).
V.G. Bar’yakhtar, V.V. Eremenko, S.A. Zvyagin, Yu.G. Pashkevich, V.V. Pishko, V.L. Sobolev, V.V. Shakhov. Line width of magnetic resonance exchange modes in a four-sublattice orthorhombic antiferromagnet. J. Exper. Theor. Phys. 73, 1046 (1991).
Yu.G. Pashkevich, V.A. Blinkin, V.P. Gnezdilov, V.V. Tsapenko, V.V. Eremenko, P. Lemmens, M. Fischer, M. Grove, G. Guntherodt, L. Degiorgi, P. Wachter, J.M. Tranquada, D.J. Buttrey. Stripe conductivity in La1.775Sr0.225NiO4. Phys. Rev. Lett. 84, 3919 (2000).
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
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. Duration.
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. Loyalty.
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.