Skip to main content
SpringerLink
Log in

Thermodynamics of the frustrated J1-J2 Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We use the spin-rotation-invariant Green’s function method as well as the high-temperature expansion to discuss the thermodynamic properties of the frustrated spin-S J 1-J 2 Heisenberg magnet on the body-centered cubic lattice. We consider ferromagnetic nearest-neighbor bonds J 1< 0 and antiferromagnetic next-nearest-neighbor bonds J 2 ≥ 0 and arbitrary spin S. We find that the transition point \hbox{$J_2^c$} J 2 c between the ferromagnetic ground state and the antiferromagnetic one is nearly independent of the spin S, i.e., it is very close to the classical transition point \hbox{$J_2^{c,{\rm clas}}= \frac{2}{3}|J_1|$} J 2 c, clas = 2 3 | J 1 | . At finite temperatures we focus on the parameter regime \hbox{$J_2<J_2^c$} J 2 < J 2 c with a ferromagnetic ground-state. We calculate the Curie temperature T C (S, J 2) and derive an empirical formula describing the influence of the frustration parameter J 2 and spin S on T C . We find that the Curie temperature monotonically decreases with increasing frustration J 2, where very close to \hbox{$J_2^{c,{\rm clas}}$} J 2 c, clas the T C (J 2)-curve exhibits a fast decay which is well described by a logarithmic term \hbox{$1/\textrm{log}(\frac{2}{3}|J_1|-J_{2})$} 1 / log ( 2 3 | J 1 | − J 2 ) . To characterize the magnetic ordering below and above T C , we calculate the spin-spin correlation functions ⟨ S 0 S R ⟩, the spontaneous magnetization, the uniform static susceptibility χ 0 as well as the correlation length ξ. Moreover, we discuss the specific heat C V and the temperature dependence of the excitation spectrum. As approaching the transition point \hbox{$J_2^c$} J 2 c some unusual features were found, such as negative spin-spin correlations at temperatures above T C even though the ground state is ferromagnetic or an increase of the spin stiffness with growing temperature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H.P. Bader, R. Schilling, Phys. Rev. B 19, 3556 (1979)

    Article  ADS  Google Scholar 

  2. T. Hamada, J. Kane, S. Nakagawa, Y. Natsume, J. Phys. Soc. Jpn 57, 1891 (1988)

    Article  ADS  Google Scholar 

  3. T. Hamada, J. Kane, S. Nakagawa, Y. Natsume, J. Phys. Soc. Jpn 58, 3869 (1989)

    Article  ADS  Google Scholar 

  4. N. Shannon, T. Momoi, P. Sindzingre, Phys. Rev. Lett. 96, 027213 (2006)

    Article  ADS  Google Scholar 

  5. D.V. Dmitriev, V.Ya. Krivnov, J. Richter, Phys. Rev. B 75, 014424 (2007)

    Article  ADS  Google Scholar 

  6. J. Richter, R. Darradi, J. Schulenburg, D.J.J. Farnell, H. Rosner, Phys. Rev. B 81, 174429 (2010)

    Article  ADS  Google Scholar 

  7. R. Shindou, S. Yunoki, T. Momoi, Phys. Rev. B 84, 134414 (2011)

    Article  ADS  Google Scholar 

  8. V. Dmitriev, V.Ya. Krivnov, Phys. Rev. B 73, 024402 (2006)

    Article  ADS  Google Scholar 

  9. A. Nersesyan, A.O. Gogolin, F.H.L. Essler, Phys. Rev. Lett. 81, 910 (1998)

    Article  ADS  Google Scholar 

  10. C. Cabra, A. Honecker, P. Pujol, Eur. Phys. J. B 13, 55 (2000)

    Article  ADS  Google Scholar 

  11. W. Selke, Z. Phys. B 27, 81 (1977)

    Article  ADS  Google Scholar 

  12. H.T. Lu, Y.J. Wang, S. Qin, T. Xiang, Phys. Rev. B 74, 134425 (2006)

    Article  ADS  Google Scholar 

  13. J. Sirker, Phys. Rev. B 81, 014419 (2010)

    Article  ADS  Google Scholar 

  14. M. Härtel, J. Richter, D. Ihle, S.-L. Drechsler, Phys. Rev. B 78, 174412 (2008)

    Article  ADS  Google Scholar 

  15. M. Härtel, J. Richter, D. Ihle, S.-L. Drechsler, Phys. Rev. B 81, 174421 (2010)

    Article  ADS  Google Scholar 

  16. D.V. Dmitriev, V.Y. Krivnov, Phys. Rev. B 82, 054407 (2010)

    Article  ADS  Google Scholar 

  17. D.V. Dmitriev, V.Y. Krivnov, Eur. Phys. J. B 82, 123 (2011)

    Article  ADS  Google Scholar 

  18. M. Härtel, J. Richter, D. Ihle, J. Schnack, S.-L. Drechsler, Phys. Rev. B 84, 104411 (2011)

    Article  ADS  Google Scholar 

  19. J. Sirker, V.Y. Krivnov, D.V. Dmitriev, A. Herzog, O. Janson, S. Nishimoto, S.-L. Drechsler, J. Richter, Phys. Rev. B 84, 144403 (2011)

    Article  ADS  Google Scholar 

  20. R. Schmidt, J. Schulenburg, J. Richter, D.D. Betts, Phys. Rev. B 66, 224406 (2002)

    Article  ADS  Google Scholar 

  21. J. Oitmaa, W. Zheng, Phys. Rev. B 69, 064416 (2004)

    Article  ADS  Google Scholar 

  22. K. Majumdar, T. Datta, J. Phys.: Condens. Matter 21, 406004 (2009)

    Google Scholar 

  23. H.T. Ueda, T. Momoi, Phys. Rev. B 87, 144417 (2013)

    Article  ADS  Google Scholar 

  24. M.R. Pantic, D.V. Kapor, S.M. Radosevic, P. Mali, Solid State Commun. 182, 55 (2014)

    Article  ADS  Google Scholar 

  25. J. Kondo, K. Yamaji, Prog. Theor. Phys. 47, 807 (1972)

    Article  ADS  Google Scholar 

  26. E. Rhodes, S. Scales, Phys. Rev. B 8, 1994 (1973)

    Article  ADS  Google Scholar 

  27. H. Shimahara, S. Takada, J. Phys. Soc. Jpn 60, 2394 (1991)

    Article  ADS  Google Scholar 

  28. F. Suzuki, N. Shibata, C. Ishii, J. Phys. Soc. Jpn 63, 1539 (1994)

    Article  ADS  Google Scholar 

  29. A.F. Barabanov, V.M. Berezovskii, J. Phys. Soc. Jpn 63, 3974 (1994)

    Article  ADS  Google Scholar 

  30. A.F. Barabanov, V.M. Berezovskii, Phys. Lett. A 186, 175 (1994)

    Article  ADS  Google Scholar 

  31. A.F. Barabanov, V.M. Berezovskii, Zh. Eksp. Teor. Fiz. 106, 1156 (1994) [J. Exp. Theor. Phys. 79, 627 (1994)]

    Google Scholar 

  32. S. Winterfeldt, D. Ihle, Phys. Rev. B 56, 5535 (1997)

    Article  ADS  Google Scholar 

  33. L. Siurakshina, D. Ihle, R. Hayn, Phys. Rev. B 61, 14601 (2000)

    Article  ADS  Google Scholar 

  34. W. Yu, S. Feng, Eur. Phys. J. B 13, 265 (2000)

    Article  ADS  Google Scholar 

  35. L. Siurakshina, D. Ihle, R. Hayn, Phys. Rev. B 64, 104406 (2001)

    Article  ADS  Google Scholar 

  36. B.H. Bernhard, B. Canals, C. Lacroix, Phys. Rev. B 66, 104424 (2002)

    Article  ADS  Google Scholar 

  37. D. Schmalfuß, J. Richter, D. Ihle, Phys. Rev. B 70, 184412 (2004)

    Article  ADS  Google Scholar 

  38. I. Juhasz Junger, D. Ihle, J. Richter, A. Klümper, Phys. Rev. B 70, 104419 (2004)

    Article  ADS  Google Scholar 

  39. I. Juhasz Junger, D. Ihle, J. Richter, Phys. Rev. B 72, 064454 (2005)

    Article  ADS  Google Scholar 

  40. D. Schmalfuß, J. Richter, D. Ihle, Phys. Rev. B 72, 224405 (2005)

    Article  ADS  Google Scholar 

  41. D. Schmalfuß, R. Darradi, J. Richter, J. Schulenburg, D. Ihle, Phys. Rev. Lett. 97, 157201 (2006)

    Article  ADS  Google Scholar 

  42. T.N. Antsygina, M.I. Poltavskaya, I.I. Poltavsky, K.A. Chishko, Phys. Rev. B 77, 024407 (2008)

    Article  ADS  Google Scholar 

  43. I. Juhasz Junger, D. Ihle, L. Bogacz, W. Janke, Phys. Rev. B 77, 174411 (2008)

    Article  ADS  Google Scholar 

  44. I. Juhasz Junger, D. Ihle, J. Richter, Phys. Rev. B 80, 064425 (2009)

    Article  ADS  Google Scholar 

  45. M. Härtel, J. Richter, D. Ihle, Phys. Rev. B 83, 214412 (2011)

    Article  ADS  Google Scholar 

  46. I.I. Poltavsky, T.N. Antsygina, M.I. Poltavskaya, K.A. Chishko, Physica B 407, 3925 (2012)

    Article  ADS  Google Scholar 

  47. M. Härtel, J. Richter, O. Götze, D. Ihle, S.-L. Drechsler, Phys. Rev. B 87, 054412 (2013)

    Article  ADS  Google Scholar 

  48. G.S. Rushbrooke, G.A. Baker, P.J. Wood, in Phase Transitions and Critical Phenomena, edited by C. Domb, M.S. Green (Academic Press, London, 1974), Vol. 3, p. 245

  49. J. Oitmaa, C.J. Hamer, W.H. Zheng, Series Expansion Methods (Cambridge University Press, Cambridge, 2006)

  50. H.-J. Schmidt, A. Lohmann, J. Richter, Phys. Rev. B 84, 104443 (2011)

    Article  ADS  Google Scholar 

  51. A. Lohmann, H.-J. Schmidt, J. Richter, Phys. Rev. B 89, 014415 (2014)

    Article  ADS  Google Scholar 

  52. S.V. Tyablikov, Methods in the Quantum Theory of Magnetism (Plenum, New York, 1967)

  53. W. Gasser, E. Heiner, K. Elk, Greensche Funktionen in Festkörper- und Vielteilchenphysik (Wiley-VCH, 2001)

  54. W. Nolting, A. Ramakanth, Quantum Theory of Magnetism (Springer, Berlin, 2010)

  55. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C++, The Art of Scientific Computing (Cambridge University Press, Cambridge, 2007)

  56. A. Du, G.Z. Wei, J. Magn. Magn. Mater. 137, 343 (1994)

    Article  ADS  Google Scholar 

  57. P. Froebrich, P.J. Kuntz, Phys. Rep. 432, 223 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  58. H.-J. Schmidt, J. Schnack, M. Luban, Phys. Rev. B 64, 224415 (2001)

    Article  ADS  Google Scholar 

  59. G.A. Baker, Phys. Rev. 124, 768 (1961)

    Article  MathSciNet  ADS  Google Scholar 

  60. G.S. Rushbrooke, P.J. Wood, Proc. Phys. Soc. A 68, 1161 (1955)

    Article  MATH  ADS  Google Scholar 

  61. G.S. Rushbrooke, P.J. Wood, Molecular Physics 1, 257 (1958)

    Article  ADS  Google Scholar 

  62. J.M. Yeomans, Statistical Mechanics of Phase Transitions (Oxford University Press, Oxford, 1962)

  63. A.J. Guttmann, Asymptotic Analysis of Power Series Expansions (Academic Press, 1989)

  64. A.J. Guttmann, G.S. Joyce, J. Phys. A 5, L81 (1972)

    Article  ADS  Google Scholar 

  65. D.L. Hunter, G.A. Baker, Phys. Rev. B 19, 3808 (1979)

    Article  ADS  Google Scholar 

  66. M.E. Fisher, H. Au-Yang, J. Phys. A 12, 1677 (1979)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  67. M. Roger, Phys. Rev. B 58, 11115 (1998)

    Article  ADS  Google Scholar 

  68. J. Oitmaa, E. Bornilla, Phys. Rev. B 53, 14228 (1995)

    Article  ADS  Google Scholar 

  69. J. Oitmaa, W. Zheng, J. Phys.: Condens. Matter 16, 8653 (2004)

    ADS  Google Scholar 

  70. P. Müller, J. Richter, D. Ihle, in preparation

  71. R.A. Tahir-Kheli, H.S. Jarrett, Phys. Rev. 135, A1096 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  72. C. Yasuda, S. Todo, K. Hukushima, F. Alet, M. Keller, M. Troyer, H. Takayama, Phys. Rev. Lett. 94, 217201 (2005)

    Article  ADS  Google Scholar 

  73. C. Schneiweiss, Z. f. Physik 182, 466 (1965)

    Article  ADS  Google Scholar 

  74. R.G. Bowers, M.E. Woolf, Phys. Rev. 177, 917 (1969)

    Article  ADS  Google Scholar 

  75. C. Holm, W. Janke, Phys. Rev. B 48, 936 (1993)

    Article  ADS  Google Scholar 

  76. M.D. Kuz’min, Phys. Rev. Lett. 94, 107204 (2005)

    Article  ADS  Google Scholar 

  77. M.D. Kuz’min, M. Richter, A.N. Yaresko, Phys. Rev. B 73, 100401(R) (2006)

    Article  ADS  Google Scholar 

  78. D.W. Wood, N.W. Dalton, Phys. Rev. 159, 384 (1967)

    Article  ADS  Google Scholar 

  79. S.W. Lovesey, J. Phys. C 10, L455 (1977)

    Article  ADS  Google Scholar 

  80. Shih-Jye Sun, Hsiu-Hau Lin, Eur. Phys. J. B 49, 403 (2006)

    Article  ADS  Google Scholar 

  81. A.N. Ignatenko, A.A. Katanin, V.Yu. Irkhin, J. Exp. Theor. Phys. Lett. 97, 209 (2013).

    Article  Google Scholar 

  82. F.J. Lazaro, J. Bartolome, R. Burriel, J. Pons, J. Casabo, P.R. Nugteren, J. Phys. Colloques 49, C8-825 (1988)

    Google Scholar 

  83. G. Cao, S. Chikara, E. Elhami, X.N. Lin, P. Schlottmann, Phys. Rev. B 71, 035104 (2005)

    Article  ADS  Google Scholar 

  84. Lei Zhang, Jiyu Fan, Li Li, Renwen Li, Langsheng Ling, Zhe Qu, Wei Tong, Shun Tan, Yuheng Zhang, Europhys. Lett. 91, 57001 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Magdeburg, 39016, Magdeburg, Germany

    Patrick Müller, Johannes Richter & Andreas Hauser

  2. Institut für Theoretische Physik, Universität Leipzig, 04109, Leipzig, Germany

    Dieter Ihle

Authors
  1. Patrick Müller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Johannes Richter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andreas Hauser
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dieter Ihle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Johannes Richter.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Müller, P., Richter, J., Hauser, A. et al. Thermodynamics of the frustrated J1-J2 Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin. Eur. Phys. J. B 88, 159 (2015). https://doi.org/10.1140/epjb/e2015-60113-7

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2015-60113-7

Keywords

Search

Navigation