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The high-temperature relaxation function of a spin system with a quadratic contribution of fluctuations to the resonance frequency

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Abstract

We investigate the high-temperature relaxation function of a spin system with quadratic coupling of the resonance frequency to the Gaussian random process. In the general case, this function is expressed as an integral of an infinite auxiliary series. For theN-exponential Gauss Markov process, the problem is reduced to solving a system of 2N linear equations. For brevity, we analyze the effect of fluctuations on the form of the magnetic resonance line (the Fourier image of the relaxation function). For both the one- and multiexponential processes in a crystal with dynamics of a relaxation type in the continuous phase transition domain, we find a nonmonotonic dependence of the asymmetrical homogeneously widened resonance line on the rate of fluctuations.

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References

  1. A. Abragam,The Principles of Nuclear Magnetism, Clarendon, Oxford (1961).

    Google Scholar 

  2. P. W. Anderson and P. R. Weiss,Rev. Mod. Phys.,25, 269 (1953).

    Article  ADS  Google Scholar 

  3. P. W. Anderson,J. Phys. Soc. Japan,9, 316 (1954).

    Article  ADS  Google Scholar 

  4. W. B. Mims,Phys. Rev. 168, 370 (1968).

    Article  ADS  Google Scholar 

  5. V. E. Zobov and A. A. Lundin,JETP Letters,43, 536 (1986).

    ADS  Google Scholar 

  6. É. L. Nagaev,Magnets with Complicated Exchange Interactions [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  7. U. Haeberlen,High Resolution NMR in Solids: Selective Averaging, Acad. Press, New York (1976); M. Mehring,High Resolution in NMR Spectroscopy in Solids, Springer, Berlin (1976).

    Google Scholar 

  8. I. N. Kovalenko N. Yu. Kuznetsov, and V. M. Shurenkov,Models of Random Processes [in Russian], Naukova Dumka, Kiev (1983); English transl., CRC, Boca Raton, Florida (1996).

    Google Scholar 

  9. R. Kubo, M. Toda, and N. Hashitsume,Statistical physics: II, Springer, Berlin (1985).

    Google Scholar 

  10. V. A. Emelichev, O. I. Mel'nikov, V. I. Sarvanov, and R. I. Tyshkevich,Lectures on Graph Theory [in Russian]. Nauka, Moscow (1990); English transl.: O. I. Melnikov, R. I. Tyshkevich, V. A. Yemelichev, and V. I. Sarvanov, Bibliographisches Institute, Mannheim (1994).

    MATH  Google Scholar 

  11. V. E. Zobov and M. A. Popov,Theor. Math. Phys.,102, 224 (1995).

    Article  MATH  Google Scholar 

  12. G. E. Uhlenbeck and G. W. Ford,Lectures in Statistical Mechanics (Lect. Appl. Math. Proc. Summer Seminar. Boulder, Colorado, 1960, Vol. 1), Am. Math. Soc., Providence, RI (1963).

    MATH  Google Scholar 

  13. J. Luczka,J. Phys. A,21, 3063 (1988).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. L. D. Landau and E. M. Lifshitz,Course of Theoretical Physics Vol. 5,Statistical Physics: Part 1 [in Russian], Nauka, Moscow (1976); English, transl., Pergamon, Oxford (1980).

    Google Scholar 

  15. V. L. Ginzburg,Fiz. Tverd. Tela 2, 2031 (1960).

    MathSciNet  Google Scholar 

  16. R. L. Amstrong,Progr. NMR Spectroscopy,21, 151 (1989).

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Krasnoyarsk State University, Krasnoyarsk, Russia

    O. A. Indyukov & M. A. Popov

Authors
  1. O. A. Indyukov
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  2. M. A. Popov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 2, pp. 316–328, November, 1999.

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Indyukov, O.A., Popov, M.A. The high-temperature relaxation function of a spin system with a quadratic contribution of fluctuations to the resonance frequency. Theor Math Phys 121, 1524–1534 (1999). https://doi.org/10.1007/BF02557223

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  • DOI: https://doi.org/10.1007/BF02557223

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