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Fluctuation Theory

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Transport Phenomena in Strongly Correlated Fermi Liquids

Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 251))

Abstract

Here, we discuss the phenomenological dynamical spin susceptibility \(\chi _{{ \mathbf{q} }}^{s}({\omega })\) in nearly AF metals. We use the unit \(c=\hbar =k_\mathrm{B}=1\) hereafter. This is the most important physical quantity in such metals since it is the origin of various non-Fermi liquid behaviors in HTSCs. The functional form of \(\chi _{{ \mathbf{q} }}^{s}({\omega })\) is given by [1–5].

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Notes

  1. 1.

    I calculated the \(1/T_1T\) of Cu nuclei for \(n=0.85\) using the FLEX approximation. I used Eq. (2.12) in Ref. [4] by correcting misprints, assuming that \(A_{\perp }=B= 3.3\times 10^{-7}\) eV. The obtained \(1/T_1T\) under \(\mathbf{H}\perp {\hat{c}}\) is 1–2 (m/s) at \({\sim }200\) K, which is consistent with experiments.

References

  1. T. Moriya, Y. Takahashi, K. Ueda, J. Phys. Soc. Jpn. 59, 2905 (1990)

    Article  ADS  Google Scholar 

  2. K. Ueda, T. Moriya, Y. Takahashi, J. Phys. Chem. Solids 53, 1515 (1992)

    Article  ADS  Google Scholar 

  3. P. Monthoux, D. Pines, Phys. Rev. B 47, 6069 (1993)

    Article  ADS  Google Scholar 

  4. A.J. Millis, H. Monien, D. Pines, Phys. Rev. B 42, 167 (1990)

    Article  ADS  Google Scholar 

  5. B.P. Stojkovic, D. Pines, Phys. Rev. B 55, 8576 (1997)

    Article  ADS  Google Scholar 

  6. V. Barzykin, D. Pines, Phys. Rev. B 52, 13585 (1995)

    Article  ADS  Google Scholar 

  7. E.M. Motoyama, G. Yu, I.M. Vishik, O.P. Vajk, P.K. Mang, M. Greven, Nature 445, 186 (2007)

    Article  ADS  Google Scholar 

  8. T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism (Springer, Berlin, 1985)

    Book  Google Scholar 

  9. N.E. Bickers, S.R. White, Phys. Rev. B 43, 8044 (1991)

    Article  ADS  Google Scholar 

  10. T. Dahm, L. Tewordt, Phys. Rev. B 52, 1297 (1995)

    Article  ADS  Google Scholar 

  11. T. Takimoto, T. Moriya, J. Phys. Soc. Jpn. 67, 3570 (1994)

    Article  ADS  Google Scholar 

  12. S. Koikegami, S. Fujimoto, K. Yamada, J. Phys. Soc. Jpn. 66, 1438 (1997)

    Article  ADS  Google Scholar 

  13. H. Kontani, K. Ueda, Phys. Rev. Lett. 80, 5619 (1998)

    Article  ADS  Google Scholar 

  14. S. Wermbter, Phys. Rev. B 55, R10149 (1997)

    Article  ADS  Google Scholar 

  15. D. Manske, I. Eremin, K.H. Bennemann, Phys. Rev. B 67, 134520 (2003)

    Article  ADS  Google Scholar 

  16. H. Kontani, M. Ohno, Phys. Rev. B 74, 014406 (2006)

    Article  ADS  Google Scholar 

  17. H. Kontani, M. Ohno, J. Magn. Magn. Mater. 310, 483 (2007)

    Article  ADS  Google Scholar 

  18. J. Yu, S. Massidda, A.J. Freeman, D.D. Koelling, Phys. Lett. A 122, 203 (2012)

    Article  ADS  Google Scholar 

  19. S. Massidda, N. Hamada, J. Yu, A.J. Freeman, Phys. C 157, 571 (1989)

    Article  ADS  Google Scholar 

  20. A.J. Freeman, J. Yu, Phys. B 150, 50 (1988)

    Google Scholar 

  21. J.-H. Xu, T.J. Watson-Yang, J. Yu, A.J. Freeman, Phys. Lett. A 120, 489 (1987)

    Article  ADS  Google Scholar 

  22. J.C. Campuzano, G. Jennings, M. Faiz, L. Beaulaigue, B.W. Veal, J.Z. Liu, A.P. Paulikas, K. Vandervoort, H. Claus, R.S. List, A.J. Arko, R.J. Bartlett, Phys. Rev. Lett. 64, 2308 (1990)

    Article  ADS  Google Scholar 

  23. N.P. Armitage, D.H. Lu, C. Kim, A. Damascelli, K.M. Shen, F. Ronning, D.L. Feng, P. Bogdanov, Z.-X. Shen, Phys. Rev. Lett. 87, 147003 (2001)

    Article  ADS  Google Scholar 

  24. N.P. Armitage, F. Ronning, D.H. Lu, C. Kim, A. Damascelli, K.M. Shen, D.L. Feng, H. Eisaki, Z.-X. Shen, P.K. Mang, N. Kaneko, M. Greven, Y. Onose, Y. Taguchi, Y. Tokura, Phys. Rev. Lett. 88, 257001 (2002)

    Article  ADS  Google Scholar 

  25. A. Ino, C. Kim, M. Nakamura, T. Yoshida, T. Mizokawa, A. Fujimori, Z.-X. Shen, T. Kakeshita, H. Eisaki, S. Uchida, Phys. Rev. B 65, 094504 (2002)

    Article  ADS  Google Scholar 

  26. T. Tanamoto, H. Kohno, H. Fukuyama, J. Phys. Soc. Jpn. 61, 1886 (1992)

    Article  ADS  Google Scholar 

  27. H. Kontani, K. Kanki, K. Ueda, Phys. Rev. B 59, 14723 (1999)

    Article  ADS  Google Scholar 

  28. M. Lindroos, S. Sahrakorpi, V. Arpiainen, R.S. Markiewicz, A. Bansil, J. Phys. Chem. Solids 67, 244 (2006)

    Article  ADS  Google Scholar 

  29. G. Baym, L.P. Kadanoff, Phys. Rev. 124, 287 (1961)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. G. Baym, Phys. Rev. 127, 1391 (1962)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. H. Kino, H. Kontani, J. Phys. Soc. Jpn. 67, 3691 (1998)

    Article  ADS  Google Scholar 

  32. H. Kondo, T. Moriya, J. Phys. Soc. Jpn. 67, 3695 (1998)

    Article  ADS  Google Scholar 

  33. J. Schmalian, Phys. Rev. Lett. 81, 4232 (1998)

    Article  ADS  Google Scholar 

  34. H. Kino, H. Kontani, T. Miyazaki, J. Phys. Soc. Jpn. 73, 25 (2004)

    Article  ADS  Google Scholar 

  35. H. Kino, H. Kontani, T. Miyazaki, J. Phys. Soc. Jpn. 75, 104702 (2006)

    Article  ADS  Google Scholar 

  36. S. Onari, R. Arita, K. Kuroki, H. Aoki, Phys. Rev. B 68, 024525 (2003)

    Article  ADS  Google Scholar 

  37. P. Noziéres, Theory of Interaction Fermion Systems (Benjamin, New York, 1964)

    Google Scholar 

  38. A.A. Abricosov, L.P. Gor’kov, I.E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1975)

    Google Scholar 

  39. T. Moriya, K. Ueda, Adv. Phys. 49, 555 (2000)

    Article  ADS  Google Scholar 

  40. K. Yamada, Electron Correlation in Metals (Cambridge University Press, Cambridge, 2004)

    Book  Google Scholar 

  41. R. Hlubina, T.M. Rice, Phys. Rev. B 51, 9253–9260 (1995)

    Article  ADS  Google Scholar 

  42. A. Damascelli, Z. Hussain, Z.-X. Shen, Rev. Mod. Phys. 75, 473 (2003)

    Article  ADS  Google Scholar 

  43. H. Kohno, K. Yamada, Prog. Theor. Phys. 85, 13 (1991)

    Article  ADS  Google Scholar 

  44. A. Rosch, Phys. Rev. Lett. 82, 4280 (1999)

    Article  ADS  Google Scholar 

  45. Ch. Renner, B. Revaz, J.-Y. Genoud, K. Kadowaki, Ø. Fischer, Phys. Rev. Lett. 80, 149 (1998)

    Article  ADS  Google Scholar 

  46. N. Miyakawa, P. Guptasarma, J.F. Zasadzinski, D.G. Hinks, K.E. Gray, Phys. Rev. Lett. 80, 157 (1998)

    Article  ADS  Google Scholar 

  47. R.M. Dipasupil, M. Oda, N. Momono, M. Ido, J. Phys. Soc. Jpn. 71, 1535 (2002)

    Article  ADS  Google Scholar 

  48. T. Sato, T. Yokoya, Y. Naitoh, T. Takahashi, K. Yamada, Y. Endoh, Phys. Rev. Lett. 83, 2254 (1999)

    Article  ADS  Google Scholar 

  49. M. Takigawa, A.P. Reyes, P.C. Hammel, J.D. Thompson, R.H. Heffner, Z. Fisk, K.C. Ott, Phys. Rev. B 43, 247–1991 (1991)

    Article  ADS  Google Scholar 

  50. H. Alloul, T. Ohno, P. Mendels, Phys. Rev. Lett. 63, 1700 (1989)

    Article  ADS  Google Scholar 

  51. K. Ishida, Y. Kitaoka, G-q Zheng, J. Phys. Soc. Jpn. 60, 3516 (1991)

    Article  ADS  Google Scholar 

  52. D.C. Johnston, Phys. Rev. Lett. 62, 957 (1989)

    Article  ADS  Google Scholar 

  53. M. Oda, H. Matsuki, M. Ido, Solid State Commun. 74, 1321 (1990)

    Article  ADS  Google Scholar 

  54. B. Holm, F. Aryasetiawan, Phys. Rev. B 56, 12825 (1997)

    Article  ADS  Google Scholar 

  55. B. Holm, U. von Barth, Phys. Rev. B 57, 2108 (1998)

    Article  ADS  Google Scholar 

  56. P. Garcia-Gonzalez, R.W. Godby, Phys. Rev. B 63, 075112 (2001)

    Article  ADS  Google Scholar 

  57. J. Schmalian, D. Pines, B. Stojkovi, Phys. Rev. B 60, 667 (1999)

    Article  ADS  Google Scholar 

  58. J. Schmalian, D. Pines, B. Stojkovi, Phys. Rev. Lett. 80, 3839 (1998)

    Article  ADS  Google Scholar 

  59. S. Fujimoto, J. Phys. Soc. Jpn. 71, 1230 (2002)

    Article  ADS  Google Scholar 

  60. H. Ikeda, S. Shinkai, K. Yamada, submitted to J. Phys. Soc. Jpn. (2007)

    Google Scholar 

  61. S. Shinkai, H. Ikeda, K. Yamada, J. Phys. Soc. Jpn. 74, 2592 (2005)

    Article  ADS  Google Scholar 

  62. S. Shinkai, H. Ikeda, K. Yamada, J. Phys. Soc. Jpn. 75, 104712 (2006)

    Article  ADS  Google Scholar 

  63. T. Nomura, K. Yamada, J. Phys. Soc. Jpn. 69, 3678 (2000)

    Article  ADS  Google Scholar 

  64. T. Nomura, K. Yamada, J. Phys. Soc. Jpn. 71, 1993 (2002)

    Article  ADS  Google Scholar 

  65. M. Vilk, A.-M.S. Tremblay, J. Phys. I France 7, 1309 (1997)

    Article  Google Scholar 

  66. H. Kusunose, J. Phys. Soc. Jpn. 75, 054713 (2006)

    Article  ADS  Google Scholar 

  67. T. Saso, J. Phys. Soc. Jpn. 68, 3941 (1999)

    Article  ADS  Google Scholar 

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  1. Department of Physics, Nagoya University, Furo-cho, Nagoya-shi, Aichi, 464-8602, Japan

    Hiroshi Kontani

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Kontani, H. (2013). Fluctuation Theory. In: Transport Phenomena in Strongly Correlated Fermi Liquids. Springer Tracts in Modern Physics, vol 251. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35365-9_2

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  • DOI: https://doi.org/10.1007/978-3-642-35365-9_2

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