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Magnetic fluctuations and itinerant ferromagnetism in two-dimensional systems with Van Hove singularities

Abstract

A criterion for ferromagnetism in two-dimensional systems with the Fermi level near Van Hove singularities (VHSs) is analyzed. In the quasistatic approximation applied to a spin-fermion model, it is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction I between the electronic and spin degrees of freedom is sufficiently large (I > I c). The critical interaction I c is much greater than its value determined from the Stoner criterion; hence, the latter criterion is not an adequate criterion for ferromagnetism in the presence of Van Hove singularities in the electronic spectrum. By combining the quasistatic approximation with the method of equations of motion, the electronic self-energy is obtained in the first order in the inverse number of spin components.

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References

  1. J. Bednorz and K. F. Muller, Z. Phys. B 64, 189 (1986).

    Article  Google Scholar 

  2. I. I. Mazin and D. J. Singh, Phys. Rev. Lett. 79, 773 (1997).

    Article  ADS  Google Scholar 

  3. N. Kikugawa and Y. Maeno, Phys. Rev. B 70, 134520 (2004).

    Article  ADS  Google Scholar 

  4. F. Nakamura, T. Goko, M. Ito, et al., Phys. Rev. B 65, 220402 (2002).

    Article  ADS  Google Scholar 

  5. K. K. Murata and S. Doniach, Phys. Rev. Lett. 29, 285 (1972).

    Article  ADS  Google Scholar 

  6. I. E. Dzyaloshinskii and P. S. Kondratenko, Zh. Éksp. Teor. Fiz. 70, 1987 (1976) [Sov. Phys. JETP 43, 1036 (1976)].

    Google Scholar 

  7. T. Moriya, J. Phys. Soc. Jpn. 40, 933 (1976).

    Article  ADS  Google Scholar 

  8. J. A. Hertz, Phys. Rev. B 14, 1165 (1976).

    Article  ADS  Google Scholar 

  9. A. J. Millis, Phys. Rev. B 48, 7183 (1993).

    Article  ADS  Google Scholar 

  10. D. Belitz, T. Kirkpatrick, and T. Vojta, Phys. Rev. B 55, 9452 (1997); A. V. Chubukov, C. Pepin, and J. Rech, Phys. Rev. Lett. 92, 147003 (2004), cond-mat/0605306.

    Article  ADS  Google Scholar 

  11. F. Onufrieva, P. Pfeuty, and M. Kiselev, Phys. Rev. Lett. 82, 2370 (1999); F. Onufrieva and P. Pfeuty, Phys. Rev. B 61, 799 (2000).

    Article  ADS  Google Scholar 

  12. J. A. Hertz and M. A. Klenin, Phys. Rev. B 10, 1084 (1974).

    Article  ADS  Google Scholar 

  13. J. Schmalian, D. Pines, and B. Stojcovic, Phys. Rev. B 60, 667 (1999); É. Z. Kuchinskiĭ and M. V. Sadovskiĭ, Zh. Éksp. Teor. Fiz. 115, 1765 (1999) [JETP 88, 968 (1999)]; M. V. Sadovskiĭ, Usp. Fiz. Nauk 171, 539 (2001) [Phys. Usp. 44, 515 (2001)].

    Article  ADS  Google Scholar 

  14. A. A. Katanin, Phys. Rev. B 72, 035111 (2005).

    Article  ADS  Google Scholar 

  15. A. A. Katanin and A. P. Kampf, Phys. Rev. B 68, 195101 (2003).

    Article  ADS  Google Scholar 

  16. H. Tasaki, Phys. Rev. Lett. 69, 1608 (1992); A. Mielke and H. Tasaki, Commun. Math. Phys. 158, 341 (1993).

    MATH  Article  ADS  MathSciNet  Google Scholar 

  17. S. V. Vonsovskiĭ, M. I. Katsnel’son, and A. V. Trefilov, Fiz. Met. Metalloved. 76(3), 3 (1993) [Phys. Met. Metallogr. 76, 247 (1993)]; Fiz. Met. Metalloved. 76 (4), 3 (1993) [Phys. Met. Metallogr. 76, 343 (1993)].

    Google Scholar 

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

    Article  ADS  Google Scholar 

  19. A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer, New York, 1994).

    Google Scholar 

  20. N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966); T. Koma and H. Tasaki, Phys. Rev. Lett. 68, 3248 (1992).

    Article  ADS  Google Scholar 

  21. F. Guinea, Nucl. Phys. B 642, 407 (2002).

    Google Scholar 

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

    Article  Google Scholar 

  23. A. A. Katanin, A. P. Kampf, and V. Yu. Irkhin, Phys. Rev. B 71, 085105 (2005).

    Article  ADS  Google Scholar 

  24. R. Hlubina, Phys. Rev. B 59, 184 516 (1998).

    Google Scholar 

  25. C. Honerkamp and M. Salmhofer, Phys. Rev. B 64, 184516 (2001).

    Article  ADS  Google Scholar 

  26. S. Ma, Modern Theory of Critical Phenomena (Benjamin, Reading, Mass., 1976; Mir, Moscow, 1980).

    Book  Google Scholar 

  27. A. A. Katanin and V. Yu. Irkhin, cond-mat/0602657.

  28. S. L. Adler, Phys. Rev. B 137, 1022 (1965).

    Article  ADS  Google Scholar 

  29. V. G. Bar’yakhtar, V. I. Krivoruchko, and D. A. Yablonskiĭ, Green Functions in Theory of Magnetism (Naukova Dumka, Kiev, 1984) [in Russian].

    Google Scholar 

  30. J. Kanamori, Prog. Theor. Phys. 30, 275 (1963).

    MATH  Article  ADS  Google Scholar 

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Correspondence to A. A. Katanin.

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Original Russian Text © P.A. Igoshev, A.A. Katanin, V.Yu. Irkhin, 2007, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 132, No. 5, pp. 1187–1202.

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Igoshev, P.A., Katanin, A.A. & Irkhin, V.Y. Magnetic fluctuations and itinerant ferromagnetism in two-dimensional systems with Van Hove singularities. J. Exp. Theor. Phys. 105, 1043–1056 (2007). https://doi.org/10.1134/S1063776107110167

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  • DOI: https://doi.org/10.1134/S1063776107110167

PACS numbers

  • 71.10.Fd
  • 71.10.Hf
  • 75.10.Lp