Magnetoelastic Waves in Ferromagnets in the Vicinity of Lattice Structural Phase Transitions
Keywords:magnetoelastic interaction, dispersion law, ferromagnet, elastic modulus
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.
<li>C. Kittel. Interaction of spin waves and ultrasonic waves in ferromagnetic crystals. Phys. Rev. 110, 836 (1958).
<li>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).
<li>A.I. Akhiezer, V.G. Bar'yakhtar, and S.V. Peletminskii. Spin Waves (North Holland, 1968).
<li>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.
<li>E.A. Turov, V.G. Shavrov. Broken symmetry and magnetoacoustic effects in ferro- and antiferromagnetics. Sov. Phys. Usp. 26, 593 (1983).
<li>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
<li>V.A. Chernenko, J. Pons, C. Segu’?, 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).
<li>L. Dai, J. Cullen, M. Wuttig. Intermartensitic transformation in a Ni–Mn–Ga alloy. J. Appl. Phys. 95, 6957 (2004).
<li>O. Heczko, H. Seiner, P. Sedl?ak, J. Kope?cek, M. Landa. Anomalous lattice softening of Ni2MnGa austenite due to magnetoelastic coupling. J. Appl. Phys. 111, 07A929 (2012).
<li> V.G. Bar'yakhtar, D.A. Yablonskii. On the magnetoelastic gap in the spin wave spectrum. Fiz. Met. Metalloved. 43, 645 (1977) (in Russian).
<li> V.V. Kokorin, M. Wuttig. Magnetostriction in ferromagnetic shape memory alloys, J. Magn. Magn. Mater. 234, 25 (2001).
<li> 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).
<li> V.A. Chernenko, V. A. L'vov. Thermodynamics of martensitic transformations affected by hydrostatic pressure. Phil. Mag. 73, 999 (1996).
<li> 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).
<li> 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).
<li> V.A. Chernenko, V.A. L'vov. Magnetoelastic nature of ferromagnetic shape memory effect. Mater. Sci. Forum 583, 1 (2008).
<li> V.G. Bar'yakhtar, A.G. Danilevich, V.A. L'vov. Magnetoelastic resonance in a crystal with lattice phase transition. Ukr. J. Phys. 56, 1068 (2011).
<li> L.D. Landau, E.M. Lifshitz. Theory of Elasticity. (Butterworth-Heinemann, 1986).
<li> 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).
<li> T.L. Gilbert. A Lagrangian formulation of the gyromagnetic equation of the magnetization fields. Phys. Rev. 100, 1243 (1955).
<li> V.G. Bar'yakhtar. Phenomenological description of relaxation processes in magnetic materials. J. Exper. Theor. Phys. 60, 863 (1984).
<li> V.G. Bar'yakhtar, A.G. Danilevich. Spin-wave damping at spin-orientation phase transitions. Low Temp. Phys. 32, 768 (2006).
<li> V.G. Bar'yakhtar, A.G. Danilevich. Dissipation function of magnetic media. Low Temp. Phys. 36, 303 (2010).
<li> V.A. L'vov, E.A. Gomonaj, V.A. Chernenko. A phenomenological model of ferromagnetic martensite. J. Phys.: Condens. Matter 10, 4587 (1998).
<li> 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).
<li> 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).
<li> R. Tickle, R.D. James. Magnetic and magnetomechanical properties of Ni2MnGa. J. Magn. Magn. Mater. 195, 627 (1999).
<li> L. Dai, J. Cui, M. Wuttig. Elasticity of austenitic and martensitic Ni–Mn–Ga. Proc. SPIE 5053, 595 (2003).
<li> 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 phastransitions. Symmetry aspects. J. Exper. Theor. Phys. 60, 587 (1984).
<li> 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).
<li> N.N. Bogoliubov, D.V. Shirkov. Quantum Fields (Benjamin-Cummings, 1982).
<li> V.G. Bar'yakhtar, A.G. Danilevich. The Higgs effect and the magnetoelastic gap in ferromagnets. Low Temp. Phys. 41, 379 (2015).
<li> 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).
<li> 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)
<li> L.D. Landau, E.M. Lifshitz, L.P. Pitaevskii. Electrodynamics of Continuous Media (Butterworth-Heinemann, 1984).
<li> V.V. Eremenko, V.N. Krivoruchko, N.M. Lavrinenko, D.A. Yablonskii. Excitation of exchange magnetic oscillations in CsMnF3 by an alternating electric field. Fiz. Tverd. Tela 30, 3605 (1988) (in Russian).
<li> 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).
<li> 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).
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