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Effect of Phonons on the Magnetic Characteristics of Metals at Finite Temperatures

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Abstract

We consider the electron-phonon interaction in the framework of dynamic spin-fluctuation theory and obtain an expression for the self-energy part that depends explicitly on the spin fluctuations and lattice vibrations. We illustrate the theoretical results with the example of iron. We show that the effect of phonons on temperature dependence of the magnetic characteristics of metals is appreciable but not as large as in the static single-site approximation of the spin-fluctuation theory and spin dynamics using classical Hamiltonians.

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References

  1. T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism, Springer, Heidelberg (1985).

    Book  Google Scholar 

  2. Y. Kakehashi, Modern Theory of Magnetism in Metals and Alloys, Springer, Berlin (2012).

    Google Scholar 

  3. N. B. Melnikov and B. I. Reser, Dynamic Spin-Fluctuation Theory of Metallic Magnetism, Springer, Berlin (2018).

    Book  Google Scholar 

  4. G. V. Paradezhenko, N. B. Melnikov, and B. I. Reser, “Debye-Waller factor in neutron scattering by ferromagnetic metals,” Theor. Math. Phys., 195, 572–583 (2018).

    Article  MathSciNet  Google Scholar 

  5. D. J. Kim, New Perspectives in Magnetism of Metals, Kluwer, New York (1999).

    Book  Google Scholar 

  6. V. I. Grebennikov, “Influence of thermal oscillations of atoms on the electronic properties of transition metals,” Phys. Metals Metallogr., 64, 59–69.

  7. E. A. Turov and V. I. Grebennikov, “Magnetism and transport phenomena of transition metals in spin fluctuation theory of itinerant electrons,” Phys. B, 149, 150–155 (1988).

    Article  Google Scholar 

  8. J. Yin, M. Eisenbach, D. M. Nicholson, and A. Rusanu, “Effect of lattice vibrations on magnetic phase transition in bcc iron,” Phys. Rev. B, 86, 214423 (2012).

  9. B. Alling, F. Körmann, B. Grabowski, A. Glensk, I. A. Abrikosov, and J. Neugebauer, “Strong impact of lattice vibrations on electronic and magnetic properties of paramagnetic Fe revealed by disordered local moments molecular dynamics,” Phys. Rev. B, 93, 224411 (2016).

    Google Scholar 

  10. A. V. Ruban and O. E. Peil, “Impact of thermal atomic displacements on the Curie temperature of 3d transition metals,” Phys. Rev. B, 97, 174426 (2018).

    Google Scholar 

  11. B. L. Gyorffy, A. J. Pindor, J. Staunton, G. M. Stocks, and H. Winter, “A first-principles theory of ferromagnetic phase transitions in metals,” J. Phys. F: Met. Phys., 15, 1337–1386 (1985).

    Article  ADS  Google Scholar 

  12. B. T. Willis, “Lattice vibrations and the accurate determination of structure factors for the elastic scattering of X-rays and neutrons,” Acta Cryst. A, 25, 277–300 (1969).

    Article  Google Scholar 

  13. L. P. Pathak, J. Prakash, V. P. Singh, and M. P. Hemkar, “Debye-Waller factors of α-iron and sodium: II.Willis’s anharmonic theory,” Aust. J. Phys., 28, 707–713 (1975).

    Article  ADS  Google Scholar 

  14. W. L. McMillan, “Transition temperature of strong-coupled superconductors,” Phys. Rev., 167, 331–344 (1967).

    Article  ADS  Google Scholar 

  15. J. J. Hopfield, “Angular momentum and transition-metal superconductivity,” Phys. Rev., 186, 443–451 (1969).

    Article  ADS  Google Scholar 

  16. D. A. Papaconstantopoulos, L. L. Boyer, B. M. Klein, A. R. Williams, V. L. Morruzzi, and J. F. Janak, “Calculations of the superconducting properties of 32 metals with Z ≤ 49,” Phys. Rev. B, 15, 4221–4226 (1977).

    Article  ADS  Google Scholar 

  17. A. L. Kuzemsky, A. Holas, and N. M. Plakida, “Self-consistent theory of the electron-phonon interaction in transition metals and their compounds,” Phys. B+C, 122, 168–182 (1983).

    Article  ADS  Google Scholar 

  18. W. John, “Elektron-Phonon-Wechselwirkung,” in: Ergebnisse in der Elektronentheorie der Metalle (P. Ziesche and G. Lehmann, eds.), Springer, Berlin (1983), pp. 375–401.

    Chapter  Google Scholar 

  19. B. I. Reser and N. B. Melnikov, “Problem of temperature dependence in the dynamic spin-fluctuation theory for strong ferromagnets,” J. Phys.: Condens. Matter, 20, 285205 (2008).

    Google Scholar 

  20. G. V. Paradezhenko, N. B. Melnikov, and B. I. Reser, “Method of continuation in a parameter for a nonlinear system of scalar and functional equations,” J. Comput. Math. Math. Phys. (to appear).

  21. N. B. Melnikov, B. I. Reser, and V. I. Grebennikov, “Extended dynamic spin-fluctuation theory of metallic magnetism,” J. Phys.: Condens. Matter, 23, 276003 (2011).

    ADS  Google Scholar 

  22. J. Crangle and G. M. Goodman, “The magnetization of pure iron and nickel,” Proc. Roy. Soc. London Ser. A, 321, 477–491 (1971).

    Article  ADS  Google Scholar 

  23. V. L. Moruzzi, J. F. Janak, and A. R. Williams, Calculated Electronic Properties of Metals, Pergamon, New York (1978).

    Google Scholar 

  24. B. I. Reser, “Calculation of the magnetic properties of Fe, Co, and Ni with account taken of the real band structure and spin fluctuations,” J. Phys.: Condens. Matter, 11, 4871–4885 (1999).

    ADS  Google Scholar 

  25. N. B. Melnikov, G. V. Paradezhenko, and B. I. Reser, “Spin-density correlations and magnetic neutron scattering in ferromagnetic metals,” Theor. Math. Phys., 191, 602–619 (2017).

    Article  MathSciNet  Google Scholar 

  26. V. J. Minkiewicz, G. Shirane, and R. Nathans, “Phonon dispersion relation for iron,” Phys. Rev., 162, 528–531 (1967).

    Article  ADS  Google Scholar 

  27. K.-H. Hellwege and J. L. Olsen, eds., Metals: Phonon States. Electron States and Fermi Surfaces. Phonon States of Elements. Electron States and Fermi Surfaces of Alloys (Landolt-Börnstein. Num. Data Funct. Relat. in Sci. Tech. New Ser., Vol. 13A), Springer, Berlin (1981).

  28. C. W. Haworth, “Measurement of the Debye-Waller temperature factor for silver and α-iron,” Philos. Mag., 5, 1229–1234 (1960).

    Article  ADS  Google Scholar 

  29. P. Debrunner and R. Morrison, “Mössbauer scattering of 14.4-keV gamma rays from Fe as a function of temperature,” Rev. Modern Phys., 36, 463 (1964).

    Article  Google Scholar 

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Acknowledgments

The authors are grateful to the referee for the useful comments.

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Correspondence to N. B. Melnikov, G. V. Paradezhenko or B. I. Reser.

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Conflicts of interest. The authors declare no conflicts of interest.

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This research was performed within the state assignment of the Ministry of Science and Education of Russia (Theme “Electron” No. AAAA-A18-118020190098-5) and was supported in part by a program of the Ural Branch of Russian Academy of Sciences (Project No. 18-2-2-11).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 201, No. 1, pp. 137–148, October, 2019.

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Melnikov, N.B., Paradezhenko, G.V. & Reser, B.I. Effect of Phonons on the Magnetic Characteristics of Metals at Finite Temperatures. Theor Math Phys 201, 1531–1540 (2019). https://doi.org/10.1134/S0040577919100106

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  • DOI: https://doi.org/10.1134/S0040577919100106

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