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Description of a dissipative quantum spin dynamics with a Landau-Lifshitz/Gilbert like damping and complete derivation of the classical Landau-Lifshitz equation

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Abstract

The classical Landau-Lifshitz equation has been derived from quantum mechanics. Starting point is the assumption of a non-Hermitian Hamilton operator to take the energy dissipation into account. The corresponding quantum mechanical spin dynamics along with the time dependent Schrödinger, Liouville and Heisenberg equation has been described and the similarities and differences between classical and quantum mechanical spin dynamics have been discussed. Furthermore, a time dependent Schrödinger equation corresponding to the classical Landau-Lifshitz-Gilbert equation and two ways to include temperature into the quantum mechanical spin dynamics have been proposed.

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References

  1. V.V. Kruglyak, S.O. Demokritov, D. Grundler, J. Phys. D 43, 264001 (2010)

    Article  ADS  Google Scholar 

  2. R. Wieser, E.Y. Vedmedenko, R. Wiesendanger, Phys. Rev. Lett. 101, 177202 (2008)

    Article  ADS  Google Scholar 

  3. R. Wieser, E.Y. Vedmedenko, R. Wiesendanger, Phys. Rev. Lett. 106, 067204 (2011)

    Article  ADS  Google Scholar 

  4. A.H. MacDonald, M. Tsoi, Phil. Trans. R. Soc. A 369, 3098 (2011)

    Article  ADS  Google Scholar 

  5. V.M.T.S. Barthem, C.V. Colin, H. Mayaffre, M. Julien, D. Givord, Nat. Commun. 4, 2892 (2013)

    Article  ADS  Google Scholar 

  6. S.S.P. Parkin, M. Hayashi, L. Thomas, Science 320, 190 (2008)

    Article  ADS  Google Scholar 

  7. C. Schieback, M. Kläui, U. Nowak, U. Rüdiger, P. Nielaba, Eur. Phys. J. B 59, 429 (2007)

    Article  ADS  MATH  Google Scholar 

  8. D.C. Ralph, M.D. Stiles, J. Magn. Magn. Mater. 320, 1190 (2008)

    Article  ADS  Google Scholar 

  9. R. Wieser, E.Y. Vedmedenko, P. Weinberger, R. Wiesendanger, Phys. Rev. B 82, 144430 (2010)

    Article  ADS  Google Scholar 

  10. P. Gambardella, Nat. Mater. 5, 431 (2006)

    Article  ADS  Google Scholar 

  11. C.F. Hirjibehedin, C.P. Lutz, A.J. Heinrich, Science 312, 102 (2006)

    Article  Google Scholar 

  12. M. Menzel, Y. Mokrousov, R. Wieser, J.E. Bickel, E. Vedmedenko, S. Blügel, S. Heinze, K. von Bergmann, A. Kubetzka, R. Wiesendanger, Phys. Rev. Lett. 108, 197204 (2012)

    Article  ADS  Google Scholar 

  13. T.L. Gilbert, IEEE Trans. Mag. 40, 3443 (2004)

    Article  ADS  Google Scholar 

  14. J.D. Jackson, Classical Electrodynamics (John Wiley & Son, New York, 1999)

  15. W.F. Brown, Micromagnetics (Wiley, New York, 1963)

  16. F. Bloch, Phys. Rev. 70, 460 (1946)

    Article  ADS  Google Scholar 

  17. D. A. Garanin, Physica A 172, 470 (1991)

    Article  ADS  Google Scholar 

  18. D. A. Garanin, Phys. Rev. B 55, 3050 (1997)

    Article  ADS  Google Scholar 

  19. R.F.L. Evans, D. Hinzke, U. Atxitia, U. Nowak, R.W. Chantrell, O. Chubykalo-Fesenko, Phys. Rev. B 85, 014433 (2012)

    Article  ADS  Google Scholar 

  20. Y. Ishimori, Prog. Theor. Phys. 72, 33 (1984)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  21. H.C. Fogedby, Theoretical Aspects of Mainly Low Dimensional Magnetic Systems (Springer-Verlag, Berlin, Heidelberg, 1980)

  22. B. Guo, S. Ding, Landau-Lifshitz Equations (World Scientific, Singapore, 2008)

  23. M. Lakshmanan, Phil. Trans. R. Soc. A 369, 1280 (2011)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. A. Sakuma, arXiv:cond-mat/0602075v2 (2006)

  25. R. Wieser, Phys. Rev. B 84, 054411 (2011)

    Article  ADS  Google Scholar 

  26. M. Fähnle, D. Steiauf, J. Seib, J. Phys. D 41, 164014 (2008)

    Article  ADS  Google Scholar 

  27. V. Weisskopf, E. Wigner, Z. Phys. 65, 18 (1930)

    Article  ADS  MATH  Google Scholar 

  28. R.L. Liboff, M.A. Porter, Physica D 195, 398 (2004)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  29. R. Kosik, Ph.D. thesis, TU Wien, 2004

  30. N. Gisin, Helv. Phys. Acta 54, 457 (1981)

    Google Scholar 

  31. R. Wieser, Phys. Rev. Lett. 110, 147201 (2013)

    Article  ADS  Google Scholar 

  32. H.F. Hofmann, S. Takeuchi, Phys. Rev. A 69, 042108 (2004)

    Article  ADS  Google Scholar 

  33. E.Y. Vedmedenko, N. Mikuszeit, ChemPhysChem 9, 1222 (2008)

    Article  Google Scholar 

  34. D.L. Landau, Phys. Z. Sowjetunion 2, 46 (1932)

    Google Scholar 

  35. R. Kikuchi, J. Appl. Phys. 27, 1352 (1956)

    Article  ADS  Google Scholar 

  36. D. Altwein, Ph.D. thesis, University of Hamburg, 2015

  37. R. Wieser, Domain wall dynamics in quasi one-dimensional nanostructures (Südwestdeutscher Verlag für Hochschulschriften, Saarbrücken, 2014)

  38. D.A. Garanin, Adv. Chem. Phys. 147, 213 (2011)

    Article  Google Scholar 

  39. P. Krammer, Ph.D. thesis, Universität Wien, 2009

  40. A. Einstein, B. Podolsky, N. Rosen, Phys. Rev. 47, 777 (1935)

    Article  ADS  MATH  Google Scholar 

  41. C.E. Shannon, The Bell System Technical Journal 27, 379, 623 (1948)

    Article  MathSciNet  Google Scholar 

  42. V.L. Pokrovsky, N.A. Sinitsyn, Phys. Rev. B 67, 144303 (2003)

    Article  ADS  Google Scholar 

  43. J.L. García-Palacios, F.J. Lázaro, Phys. Rev. B 58, 14937 (1998)

    Article  ADS  Google Scholar 

  44. U. Nowak, in Annual Reviews of Computational Physics IX, edited by D. Stauffer (World Scientific, Singapore, 2001), p. 105

  45. K. Blum, Density Matrix Theory and Applications (Plenum Press, New York, London, 1996)

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  1. Institut für Nanostruktur- und Festkörperphysik, Universität Hamburg, Jungiusstrasse 11, 20355, Hamburg, Germany

    Robert Wieser

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  1. Robert Wieser
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Correspondence to Robert Wieser.

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Wieser, R. Description of a dissipative quantum spin dynamics with a Landau-Lifshitz/Gilbert like damping and complete derivation of the classical Landau-Lifshitz equation. Eur. Phys. J. B 88, 77 (2015). https://doi.org/10.1140/epjb/e2015-50832-0

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  • DOI: https://doi.org/10.1140/epjb/e2015-50832-0

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