Skip to main content
SpringerLink
Log in

Geometrically Frustrated Antiferromagnets: Statistical Mechanics and Dynamics

  • Chapter
  • First Online:
Book cover Introduction to Frustrated Magnetism

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 164))

Abstract

These lecture notes provide a simple overview of the physics of geometrically frustrated magnets. The emphasis is on classical and semiclassical treatments of the statistical mechanics and dynamics of frustrated Heisenberg models, and on the ways in which the results provide an understanding of some of the main observed properties of these systems.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.P. Ramirez, Annu. Rev. Mater. Sci. 24, 453 (1994)

    Article  ADS  Google Scholar 

  2. P. Schiffer, A.P. Ramirez, Comments Cond. Mat. Phys. 18, 21 (1996)

    Google Scholar 

  3. M.J. Harris, M.P. Zinkin, Mod. Phys. Lett. B10, 417 (1996)

    ADS  Google Scholar 

  4. R. Moessner, Can. J. Phys. 79, 1283 (2001)

    Article  ADS  Google Scholar 

  5. C.L. Henley, Can. J. Phys. 79, 1307 (2001)

    Article  ADS  Google Scholar 

  6. P. Chandra, B. Doucot, Phys. Rev. B 38, 9335 (1988)

    Article  ADS  Google Scholar 

  7. P.W. Anderson, Phys. Rev. 102, 1008 (1956)

    Article  ADS  Google Scholar 

  8. J. Villain, Z. Phys. B 33, 31 (1979)

    Article  ADS  Google Scholar 

  9. R. Moessner, J.T. Chalker, Phys. Rev. Lett. 80, 2929 (1998)

    Article  ADS  Google Scholar 

  10. R. Moessner, J.T. Chalker, Phys. Rev. B 58, 12049 (1998)

    Article  ADS  Google Scholar 

  11. M. Harris, S.T. Bramwell, D.F. McMorrow, T. Zeiske, K.W. Godfrey, Phys. Rev. Lett. 79, 2554 (1997)

    Article  ADS  Google Scholar 

  12. J.N. Reimers, A.J. Berlinsky, A.-C. Shi, Phys. Rev. B 43, 865 (1991)

    Article  ADS  Google Scholar 

  13. J.N. Reimers, J.E. Greedan, M. Björgvinsson, Phys. Rev. B 45, 7295 (1991)

    Article  ADS  Google Scholar 

  14. N. Raju, M. Dion, M.J.P. Gingras, T.E. Mason, J.E. Greedon, Phys. Rev. B 59, 14489 (1999)

    Article  ADS  Google Scholar 

  15. S.E. Palmer, J.T. Chalker, Phys. Rev. B 62, 488 (2000)

    Article  ADS  Google Scholar 

  16. M. Elhajal, B. Canals, R. Sunyer, C. Lacriox, Phys. Rev. B 71, 94420 (2005)

    Article  ADS  Google Scholar 

  17. O. Tchernyshyov, R. Moessner, S.L. Sondhi, Phys. Rev. B 66, 64403 (2002)

    Article  ADS  Google Scholar 

  18. E.F. Shender, V.B. Cherepanov, P.C.W. Holdsworth, A.J. Berlinsky, Phys. Rev. Lett. 70, 3812 (1993)

    Article  ADS  Google Scholar 

  19. R. Moessner, A.J. Berlinsky, Phys. Rev. Lett. 83, 3293 (1999)

    Article  ADS  Google Scholar 

  20. T.E. Saunders, J.T. Chalker, Phys. Rev. Lett. 98, 157201 (2007)

    Article  ADS  Google Scholar 

  21. A.P. Ramirez, G.P. Espinoza, A.S. Cooper, Phys. Rev. Lett. 64, 2070 (1990)

    Article  ADS  Google Scholar 

  22. C. Broholm, G. Aeppli, G.P. Espinosa, A.S. Cooper, Phys. Rev. Lett. 65, 3173 (1990)

    Article  ADS  Google Scholar 

  23. B. Martinez, F. Sandiumenge, A. Rouco, A. Labarta, J. Rodriguez-Cavajal, M. Tovar, M.T. Causa, S. Gali, X. Obradors, Phys. Rev. B 46, 10786 (1992)

    Article  ADS  Google Scholar 

  24. S.H. Lee, C. Brohlom, G. Aeppli, A. Ramirez, T.G. Perring, C.J. Carlile, M. Adams, T.L. Jones, B. Hessen, Europhys. Lett. 35, 127 (1996)

    Article  ADS  Google Scholar 

  25. A.S. Wills, A. Harrison, S.A.M. Menthink, T.E. Mason, Z. Tun, Europhys. Lett. 42, 325 (1998)

    Article  ADS  Google Scholar 

  26. M.J.P. Gingras, C.V. Stager, N.P. Raju, B.D. Gaulin, J.E. Greedan, Phys. Rev. Lett. 78, 947 (1997)

    Article  ADS  Google Scholar 

  27. J.S. Gardner, B.D. Gaulin, S.-H. Lee, C. Broholm, N.P. Raju, J.E. Greedan, Phys. Rev. Lett. 83, 211 (1999)

    Article  ADS  Google Scholar 

  28. J.C. Maxwell, Philos. Mag. 27, 294 (1864)

    Google Scholar 

  29. J.T. Chalker, P.C.W. Holdsworth, E.F. Shender, Phys. Rev. Lett. 68, 855 (1992)

    Article  ADS  Google Scholar 

  30. I. Ritchey, P. Chandra, P. Coleman, Phys. Rev. 47, 15342 (1993)

    Article  Google Scholar 

  31. J. Villain, R. Bidaux, J.P. Carton, R.J. Conte, J. Phys. Paris 41, 1263 (1980)

    MathSciNet  Google Scholar 

  32. E.F. Shender, Sov. Phys. JETP 56, 178 (1982)

    Google Scholar 

  33. A.V. Chubukov, Phys. Rev. Lett. 69, 832 (1992)

    Article  ADS  Google Scholar 

  34. C.L. Henley, Phys. Rev. Lett. 96, 47201 (2006)

    Article  ADS  Google Scholar 

  35. A.G. Gukasov, T. Brückel, B. Dorner, V.P. Plakhty, W. Prandtl, E.F. Shender, O.P. Smirnov, Europhys. Lett. 7, 83 (1988)

    Article  ADS  Google Scholar 

  36. T. Brückel, B. Dorner, A.G. Gukasov, V.P. Plakhty, Phys. Lett. A 162, 357 (1992)

    Article  ADS  Google Scholar 

  37. S.V. Isakov, K. Gregor, R. Moessner, S.L. Sondhi, Phys. Rev. Lett. 93, 167204 (2004)

    Article  ADS  Google Scholar 

  38. C.L. Henley, Phys. Rev. B 71, 014424 (2005)

    Article  ADS  Google Scholar 

  39. M. Zinkin, M.J. Harris, T. Zeiske, Phys. Rev. B 56, 11786 (1997)

    Article  ADS  Google Scholar 

  40. B. Canals, D. Garanin, Can. J. Phys. 79, 1323 (2001)

    Article  ADS  Google Scholar 

  41. T. Fennell, S.T. Bramwell, D.F. McMorrow, P. Manuel, Nat. Phys. 3, 566 (2007)

    Article  Google Scholar 

  42. D.A. Huse, W. Krauth, R. Moessner, S.L Sondhi, Phys. Rev. Lett. 91, 167004 (2003)

    Google Scholar 

  43. L. Jaubert, J.T. Chalker, P.C.W. Holdsworth, R. Moessner, Phys. Rev. Lett. 100, 067207 (2008)

    Article  ADS  Google Scholar 

  44. M.J. Harris, M.P. Zinkin, T. Zeiske, Phys. Rev. B 52, R707 (1995)

    Article  ADS  Google Scholar 

  45. S.-H. Lee, Ph.D. thesis, Johns Hopkins University (1996)

    Google Scholar 

  46. J. van Duijn, N. Hur, J.W. Taylor, Y. Qiu, Q.Z. Huang, S.-W. Cheong, C. Broholm, T.G. Perring, arXiv:0707.2678 (2007)

    Google Scholar 

  47. P. Conlon, J.T. Chalker, Phys. Rev. Lett. 102, 237106 (2009)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

I am very grateful to my collaborators in the research on geometrically frustrated antiferromagnets that I have been involved with, especially E.F. Shender, P.C.W. Holdsworth and R. Moessner, and also J.F.G. Eastmond, S.E. Palmer, P. Hogan, M.Y. Veillette, R. Coldea, T.E. Saunders, M.J. Bhaseen and T.S. Pickles. In addition, I have benefitted from discussions with many other colleagues. I thank EPSRC for supporting this work.

Author information

Authors and Affiliations

  1. Theoretical Physics, Oxford University, 1, Keble Road, Oxford, OX1 3NP, UK

    John T. Chalker

Authors
  1. John T. Chalker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to John T. Chalker .

Editor information

Editors and Affiliations

  1. Laboratoire Louis Néel, CNRS, Grenoble CX, France

    Claudine Lacroix

  2. CNRS, Labo. Physique Solides, Université Paris-Sud XI, Orsay CX, 91405, France

    Philippe Mendels

  3. Inst. Physique Théorique, Ecole Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland

    Frédéric Mila

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Chalker, J.T. (2011). Geometrically Frustrated Antiferromagnets: Statistical Mechanics and Dynamics. In: Lacroix, C., Mendels, P., Mila, F. (eds) Introduction to Frustrated Magnetism. Springer Series in Solid-State Sciences, vol 164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10589-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-10589-0_1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10588-3

  • Online ISBN: 978-3-642-10589-0

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation