Magnonics pp 39-56 | Cite as

Magnon Coherent States and Condensates

Chapter
Part of the Topics in Applied Physics book series (TAP, volume 125)

Abstract

It is known that spin waves that have quanta called magnons can be excited in magnetic materials by means of several processes. Most spin-wave phenomena involve a large number of magnons and can be well described by the semi-classical Landau–Lifshitz equation. Perhaps this is one reason for the coherent magnon states, defined in analogy to the coherent photon states that are widely used in quantum optics, to be not well known by the magnetism community. In this paper, we review the concept of coherent magnon states and show that they are the quantum states generated in a linear microwave driving process. We also address the recently observed Bose–Einstein condensation of magnons in magnetic films under strong microwave driving. Using a microscopic theoretical model that relies on the cooperative mechanisms made possible by magnon interactions, we explain quantitatively the spontaneous generation of quantum coherence and magnetic dynamic order observed above a critical microwave power level.

Keywords

Coherent State Microwave Power Spin Wave Einstein Condensation Driving Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The author thanks the Brazilian agencies CNPq, FINEP, CAPES, and FACEPE for supporting this work.

References

  1. 1.
    J.C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996) CrossRefGoogle Scholar
  2. 2.
    J.C. Slonczewski, J. Magn. Magn. Mater. 195, L261 (1999) CrossRefGoogle Scholar
  3. 3.
    L. Berger, Phys. Rev. B 54, 9353 (1996) CrossRefGoogle Scholar
  4. 4.
    S.I. Kiselev, J.C. Sankey, I.N. Krivorotov, N.C. Emley, R.J. Schoelkopf, R.A. Buhrman, D.C. Ralph, Nature (London) 425, 308 (2003) CrossRefGoogle Scholar
  5. 5.
    S. Kaka, M.R. Pufall, W.H. Rippard, T.J. Silva, S.E. Russek, J.A. Katine, Nature (London) 437, 389 (2005) CrossRefGoogle Scholar
  6. 6.
    S.M. Rezende, F.M. de Aguiar, A. Azevedo, Phys. Rev. Lett. 94, 037202 (2005) CrossRefGoogle Scholar
  7. 7.
    S.M. Rezende, F.M. de Aguiar, A. Azevedo, Phys. Rev. B 73, 094402 (2006) CrossRefGoogle Scholar
  8. 8.
    A. Slavin, P. Kabos, IEEE Trans. Magn. 41, 1264 (2005) CrossRefGoogle Scholar
  9. 9.
    Y. Tserkovnyak, A. Brataas, G.E. Bauer, Phys. Rev. Lett. 88, 117601 (2002) CrossRefGoogle Scholar
  10. 10.
    Y. Tserkovnyak, A. Brataas, G.E. Bauer, Phys. Rev. B 66, 224403 (2002) CrossRefGoogle Scholar
  11. 11.
    A. Brataas, Y. Tserkovnyak, G.E.W. Bauer, B.I. Halperin, Phys. Rev. B 66, 060404(R) (2002) CrossRefGoogle Scholar
  12. 12.
    A. Azevedo, L.H. Vilela Leão, R.L. Rodriguez-Suarez, A.B. Oliveira, S.M. Rezende, J. Appl. Phys. 97, 10C715 (2005) CrossRefGoogle Scholar
  13. 13.
    E. Saitoh, M. Ueda, H. Miyajima, G. Tatara, Appl. Phys. Lett. 88, 182509 (2006) CrossRefGoogle Scholar
  14. 14.
    S.O. Demokritov, V.E. Demidov, O. Dzyapko, G.A. Melkov, A.A. Serga, B. Hillebrands, A.N. Slavin, Nature 443, 430 (2006) CrossRefGoogle Scholar
  15. 15.
    V.E. Demidov, O. Dzyapko, S.O. Demokritov, G.A. Melkov, A.N. Slavin, Phys. Rev. Lett. 99, 037205 (2007) CrossRefGoogle Scholar
  16. 16.
    V.E. Demidov, O. Dzyapko, S.O. Demokritov, G.A. Melkov, A.N. Slavin, Phys. Rev. Lett. 100, 047205 (2008) CrossRefGoogle Scholar
  17. 17.
    V.E. Demidov, O. Dzyapko, M. Buchmeier, T. Stockhoff, G. Schmitz, G.A. Melkov, S.O. Demokritov, Phys. Rev. Lett. 101, 257201 (2008) CrossRefGoogle Scholar
  18. 18.
    O. Dzyapko, V.E. Demidov, M. Buchmeier, T. Stockhoff, G. Schmitz, G.A. Melkov, S.O. Demokritov, Phys. Rev. B 80, 060401(R) (2009) CrossRefGoogle Scholar
  19. 19.
    S.M. Rezende, Phys. Rev. B 79, 174411 (2009) CrossRefGoogle Scholar
  20. 20.
    Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, K. Kawai, K. Ando, K. Takanashi, S. Maekawa, E. Saitoh, Nature (London) 464, 262 (2010) CrossRefGoogle Scholar
  21. 21.
    Z. Wang, Y. Sun, M. Wu, V. Tiberkevich, A. Slavin, Phys. Rev. Lett. 107, 146602 (2011) CrossRefGoogle Scholar
  22. 22.
    E. Padrón-Hernández, A. Azevedo, S.M. Rezende, Phys. Rev. Lett. 107, 197203 (2011) CrossRefGoogle Scholar
  23. 23.
    E. Padrón-Hernández, A. Azevedo, S.M. Rezende, Appl. Phys. Lett. 99, 192511 (2011) CrossRefGoogle Scholar
  24. 24.
    V.V. Kruglyak, S.O. Demokritov, D. Grundler, J. Phys. D, Appl. Phys. 43, 264001 (2010) CrossRefGoogle Scholar
  25. 25.
    A.A. Serga, A.V. Chumak, B. Hillebrands, J. Phys. D, Appl. Phys. 43, 264002 (2010) CrossRefGoogle Scholar
  26. 26.
    F. Bloch, Z. Phys. 61, 206 (1930) CrossRefGoogle Scholar
  27. 27.
    G. Heller, H.A. Kramers, Proc. R. Acad. Sci. (Amsterdam) 37, 378 (1934) Google Scholar
  28. 28.
    L. Landau, E. Lifshitz, Phys. Z. Sowjetunion 8, 153 (1935) Google Scholar
  29. 29.
    T. Holstein, H. Primakoff, Phys. Rev. 58, 1098 (1940) CrossRefGoogle Scholar
  30. 30.
    J. Smit, H.P.J. Wijn, Ferrites (Wiley, New York, 1959) Google Scholar
  31. 31.
    B. Lax, K.J. Button, Microwave Ferrites and Ferrimagnetics (McGraw-Hill Books, New York, 1962) Google Scholar
  32. 32.
    N. Bloembergen, R.W. Damon, Phys. Rev. 85, 699 (1952) CrossRefGoogle Scholar
  33. 33.
    N. Bloembergen, S. Wang, Phys. Rev. 93, 72 (1954) CrossRefGoogle Scholar
  34. 34.
    H. Suhl, J. Phys. Chem. Solids 1, 209 (1957) CrossRefGoogle Scholar
  35. 35.
    F.R. Morgenthaler, J. Appl. Phys. 31, 1647 (1960) CrossRefGoogle Scholar
  36. 36.
    E. Schloemann, J.J. Green, U. Milano, J. Appl. Phys. 31, 386S (1960) CrossRefGoogle Scholar
  37. 37.
    J.R. Eshbach, J. Appl. Phys. 34, 1298 (1963) CrossRefGoogle Scholar
  38. 38.
    W. Strauss, J. Appl. Phys. 36, 118 (1965) CrossRefGoogle Scholar
  39. 39.
    S.M. Rezende, F.R. Morgenthaler, Appl. Phys. Lett. 10, 184 (1967) CrossRefGoogle Scholar
  40. 40.
    S.M. Rezende, F.R. Morgenthaler, J. Appl. Phys. 40, 524 (1969) CrossRefGoogle Scholar
  41. 41.
    M.G. Cottam (ed.), Linear and Nonlinear Spin Waves in Magnetic Films and Superlattices (World Scientific, Singapore, 1994) Google Scholar
  42. 42.
    P. Kabos, V.S. Stalmachov, Magnetostatic Waves and Their Applications (Chapman and Hall, London, 1994) CrossRefGoogle Scholar
  43. 43.
    A.G. Gurevich, G.A. Melkov, Magnetization Oscillations and Waves (CRC Press, Boca Raton, 1996) Google Scholar
  44. 44.
    D.D. Stancil, A. Prabhakar, Spin Waves – Theory and Applications (Springer, New York, 2009) Google Scholar
  45. 45.
    A.I. Akhiezer, V.G. Bar’yakhtar, S.V. Peletminskii, Spin Waves (North-Holland, Amsterdam, 1968) Google Scholar
  46. 46.
    R.M. White, Quantum Theory of Magnetism, 3rd edn. (Springer, Berlin, 2007) CrossRefGoogle Scholar
  47. 47.
    S.M. Rezende, N. Zagury, Phys. Lett. A 29, 47 (1969) CrossRefGoogle Scholar
  48. 48.
    N. Zagury, S.M. Rezende, Phys. Rev. B 4, 201 (1971) CrossRefGoogle Scholar
  49. 49.
    R.J. Glauber, Phys. Rev. 131, 2766 (1963) CrossRefGoogle Scholar
  50. 50.
    S.M. Rezende, F.M. de Aguiar, Proc. IEEE 78, 893 (1990) CrossRefGoogle Scholar
  51. 51.
    V.E. Zakharov, V.S. L’vov, S.S. Starobinets, Usp. Fiz. Nauk 114, 609 (1974) CrossRefGoogle Scholar
  52. 52.
    V.E. Zakharov, V.S. L’vov, S.S. Starobinets, Sov. Phys. Usp. 17, 896 (1975) CrossRefGoogle Scholar
  53. 53.
    L. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Clarendon, Oxford, 2003) Google Scholar
  54. 54.
    A.J. Leggett, Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems (Oxford University Press, Oxford, 2006) CrossRefGoogle Scholar
  55. 55.
    G.A. Melkov, V.L. Safonov, A.Y. Taranenko, S.V. Sholom, J. Magn. Magn. Mater. 132, 180 (1994) CrossRefGoogle Scholar
  56. 56.
    C.B. de Araújo, Phys. Rev. B 10, 3961 (1974) CrossRefGoogle Scholar
  57. 57.
    C.B. de Araújo, S.M. Rezende, Phys. Rev. B 9, 3074 (1974) CrossRefGoogle Scholar
  58. 58.
    H. Haken, Rev. Mod. Phys. 47, 67 (1975) CrossRefGoogle Scholar
  59. 59.
    P. Meystre, M. Sargent III, Elements of Quantum Optics (Springer, Berlin, 1992) Google Scholar
  60. 60.
    S.M. Rezende, Phys. Rev. B 81, 020414(R) (2010) CrossRefGoogle Scholar
  61. 61.
    A.N. Slavin, B.A. Kalinikos, N.G. Kovshikov, in Nonlinear Phenomena and Chaos in Magnetic Materials, ed. by P.E. Wigen (World Scientific, Singapore, 1994). Chap. 9 Google Scholar
  62. 62.
    A.K. Zvezdin, A.F. Popkov, Zh. Èksp. Teor. Fiz. 84, 606 (1983) Google Scholar
  63. 63.
    A.K. Zvezdin, A.F. Popkov, Sov. Phys. JETP 57, 350 (1983) Google Scholar
  64. 64.
    V.I. Karpman, Nonlinear Waves in Dispersive Media (Pergamon, New York, 1973) Google Scholar
  65. 65.
    B.A. Malomed, O. Dzyapko, V.E. Demidov, S.O. Demokritov, Phys. Rev. B 81, 024418 (2010) CrossRefGoogle Scholar
  66. 66.
    D. Snoke, Nature (London) 443, 403 (2006) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidade Federal de PernambucoRecifeBrazil

Personalised recommendations