Abstract
This chapter is devoted to the study of linear and nonlinear processes and techniques for the excitation of magnons. In the presentation of the linear excitation process we employ three different quantum approaches that are commonly used and show that they are all consistent. The last one serves to show that the magnons excited by microwave radiation are in quantum coherent states. The theory is used to interpret experimental measurements. A quantum approach is also used to study the parametric excitation of magnons by three different techniques, parallel pumping, perpendicular pumping in the first-order and in the second-order Suhl processes. The four-magnon interaction is discussed in the third section and shown to have three important effects: saturation of the parametric magnon population; coherence of the parametric magnon states; and nonlinear dynamics. The last section is devoted to study the nonlinear dynamics of parametric magnons that manifests in self-oscillations in the magnon populations and chaotic behavior.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Zagury, N., Rezende, S.M.: Theory of macroscopic excitations of magnons. Phys. Rev. B. 4, 201 (1971)
Huebl, H., Zollitsch, C.W., Lotze, J., Hocke, F., Greifenstein, M., Marx, A., Gross, R., Goennenwein, S.T.B.: High cooperativity in coupled microwave resonator ferrimagnetic insulator hybrids. Phys. Rev. Lett. 111, 127003 (2013)
Tabuchi, Y., Ishino, S., Noguchi, A., Ishikawa, T., Yamazaki, R., Usami, K., Nakamura, Y.: Coherent coupling between a ferromagnetic magnon and a superconducting qubit. Science. 349, 405 (2015)
Lachance-Quirion, D., Tabuchi, Y., Ishino, S., Noguchi, A., Ishikawa, T., Yamazaki, R., Nakamura, Y.: Resolving quanta of collective spin excitations in a millimeter-sized ferromagnet. Sci. Adv. 3(1603150), e1603150 (2017)
Koch, J., Yu, T.M., Gambetta, J., Houck, A.A., Schuster, D.I., Majer, J., Blais, A., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A. 76, 042319 (2007)
Bloembergen, N., Damon, R.W.: Relaxation effects in ferromagnetic resonance. Phys. Rev. 85, 699 (1952)
Damon, R.W.: Relaxation effects in the ferromagnetic resonance. Rev. Mod. Phys. 25, 239 (1953)
Bloembergen, N., Wang, S.: Relaxation effects in para-and ferromagnetic resonance. Phys. Rev. 93, 72 (1954)
Suhl, H.: The theory of ferromagnetic resonance at high signal powers. J. Phys. Chem. Solids. 1, 209 (1957)
Morgenthaler, F.R.: Survey of ferromagnetic resonance in small ferrimagnetic ellipsoids. J. Appl. Phys. 31, 95 S (1960)
Schlömann, E., Green, J.J., Milano, U.: Recent developments in ferromagnetic resonance at high power levels. J. Appl. Phys. 31, 386 S (1960)
Kasuya, T., Le Craw, R.C.: Relaxation mechanisms in ferromagnetic resonance. Phys. Rev. Lett. 6, 223 (1961)
de Aguiar, F.M., Rezende, S.M.: Observation of subharmonic routes to chaos in parallel-pumped spin waves in yttrium iron garnet. Phys. Rev. Lett. 56, 1070 (1986)
Damon, R.W.: Ferromagnetic resonance at high power. In: Rado, G.T., Suhl, H. (eds.) Magnetism, vol. I, p. 551. Academic, New York (1963)
Azevedo, A., Rezende, S.M.: Controlling chaos in spin-wave instabilities. Phys. Rev. Lett. 66, 1342 (1991)
Kurebayashi, H., Dzyapko, O., Demidov, V.E., Fang, D., Ferguson, A.J., Demokritov, S.O.: Controlled enhancement of spin-current emission by three-magnon splitting. Nat. Mat. 10, 660 (2011)
Cunha, R.O., Holanda, J., Vilela-Leão, L.H., Azevedo, A., RodrÃguez-Suárez, R.L., Rezende, S.M.: Nonlinear dynamics of three-magnon process driven by ferromagnetic resonance in yttrium iron garnet. Appl. Phys. Lett. 106, 192403 (2015)
Zakharov, V.E., L’vov, V.S., Starobinets, S.S.: Spin-wave turbulence beyond the parametric excitation threshold. Usp. Fiz. Nauk. 114, 609 (1974). [Sov. Phys. Usp. 17, 896 (1975)]
de Araújo, C.B.: Quantum-statistical theory of the nonlinear excitation of magnons in parallel pumping experiments. Phys. Rev. B. 10, 3961 (1974)
Balucani, U., Barocchi, F., Tognetti, V.: Green’s-function theory of a damped Boson system (Application to an interacting Magnon system). Phys. Rev. A. 5, 442 (1972)
ter Haar, D.: Theory and applications of the density matrix. Rep. Prog. Phys. 24, 304 (1961)
Hartwick, T.S., Peressini, E.R., Weiss, M.T.: Subsidiary resonance in YIG. J. Appl. Phys. 32, 223 S (1961)
Wang, S., Thomas, G., Hsu, T.-l.: Standing-spin-wave modulation of the reflected microwave power in YIG. J. Appl. Phys. 39, 2719 (1968)
L’vov, V.S., Musher, S.L., Starobinets, S.S.: Theory of magnetization self-oscillations on parametric excitation of spin waves. Zh. Eksp. Teor. Fiz. 64, 1074 (1973) [Sov. Phys.-JETP 37, 546 (1973)]
Ozhogin, V.I., Yakubovskii, A.Y.: Parametric pairs in antiferromagnet with easy plane anisotropy. Z. Eksp. Teor. Fiz. 67, 287 (1974). [Sov. Phys. JETP 40, 144 (1975)]
Nakamura, K., Ohta, S., Kawasaki, K.: Chaotic states of ferromagnets in strong parallel pumping fields. J. Phys. C: D. 15, L143 (1982)
Gibson, G., Jeffries, C.: Observation of period doubling and chaos in spin-wave instabilities in yttrium iron garnet. Phys. Rev. A. 29, 811 (1984)
Bryant, P., Jeffries, C., Nakamura, K.: Spin-wave nonlinear dynamics in an yttrium iron garnet sphere. Phys. Rev. Lett. 60, 1185 (1988)
Rezende, S.M., de Aguiar, F.M.: Spin-wave instabilities, auto-oscillations, and chaos in yttrium-iron-garnet. Proc. IEEE. 78, 893 (1990)
Rezende, S.M., Azevedo, A.: Self-oscillations in spin-wave instabilities. Phys. Rev. B. 45(10), 387 (1992)
Suhl, H., Zhang, X.Y.: Theory of auto-oscillations in high-power ferromagnetic resonance. Phys. Rev. B. 38, 4893 (1988)
Rezende, S.M., Azevedo, A., de Aguiar, F.M.: Spin-wave instabilities, auto-oscillations, chaos, and control of chaos in YIG spheres. In: Cottam, M.G. (ed.) Linear and Nonlinear Spin Waves in Magnetic Films and Superlattices. World Scientific, Singapore (1994)
de Aguiar, F.M., Azevedo, A., Rezende, S.M.: Characterization of strange attractors in spin-wave chaos. Phys. Rev. B. 39(9), 448 (1989)
Further Reading
Akhiezer, A.I., Bar’yakhtar, V.G., Peletminskii, S.V.: Spin Waves. North-Holland, Amsterdam (1968)
Cohen-Tannoudji, C., Diu, B., Laloë, F.: Quantum Mechanics. Wiley, New York (1977)
Cottam, M.G. (ed.): Linear and nonlinear spin waves in magnetic films and superlattices. World Scientific, Singapore (1994)
Gurevich, A.G., Melkov, G.A.: Magnetization Oscillations and Waves. CRC, Boca Raton (1994)
Kabos, P., Stalmachov, V.S.: Magnetostatic Waves and Their Applications. Chapman and Hall, London (1994)
Keffer, F.: Spin Waves. In: Flugge, S. (ed.) Handbuch der Physik, vol. XVIII/B. Springer, Berlin (1966)
Lax, B., Button, K.J.: Microwave Ferrites and Ferrimagnetics. McGraw-Hill, New York (1962)
L’vov, V.S.: Turbulence Under Parametric Excitation, Applications to Magnets. Springer, Berlin (1994)
Nussenzweig, H.M.: Topics in Quantum Optics. Gordon and Breach, New York (1973)
Pozar, D.M.: Microwave Engineering, 4th edn. Wiley, New York (2012)
Sparks, M.: Ferromagnetic Relaxation. McGraw-Hill, New York (1964)
Stancil, D.D., Prabhakar, A.: Spin Waves: Theory and Applications. Springer Science, New York (2009)
White, R.M.: Quantum Theory of Magnetism, 3rd edn. Springer, Berlin (2007)
Wigen, P.E. (ed.): Nonlinear phenomena and chaos in magnetic materials. World Scientific, Singapore (1994)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Rezende, S.M. (2020). Magnon Excitation and Nonlinear Dynamics. In: Fundamentals of Magnonics. Lecture Notes in Physics, vol 969. Springer, Cham. https://doi.org/10.1007/978-3-030-41317-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-41317-0_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-41316-3
Online ISBN: 978-3-030-41317-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)