Skip to main content
SpringerLink
Log in

Spin Nematic Phases in Quantum Spin Systems

  • Chapter
  • First Online:
Introduction to Frustrated Magnetism

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

Abstract

In this chapter, we explore the possibility for spin systems to develop a type of order that breaks the O(3) spin symmetry but does not have a magnetic moment. Such ordering is usually referred to as multipolar or nematic, with quadrupolar being the simplest example. These phases have been found in S=1 Heisenberg models extended with biquadratic exchange, in certain S=1∕2 Heisenberg models with both ferromagnetic and antiferromagnetic exchange couplings, and in models with cyclic ring-exchange terms. We present theoretical and numerical methods which can be used to understand and characterize quadrupolar and nematic phases. While quadrupolar/nematic ordering is well documented in model systems, it has not yet been identified unambiguously in real materials, although there exist some promising candidates which we also review.

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. G. Misguich, C. Lhuillier, in Frustrated Spin Systems, ed. by H.T. Diep (World Scientific, Singapore, 2005)

    Google Scholar 

  2. M. Blume, Y.Y. Hsieh, J. Appl. Phys. 40, 1249 (1969)

    Article  ADS  Google Scholar 

  3. A.F. Andreev, I.A. Grishchuk, Zh. Eksp. Teor. Fiz. 87, 467 (1984) [Sov. Phys. JETP 60, 267 (1984)]

    Google Scholar 

  4. V. Barzykin, L.P. Gor’kov, Phys. Rev. Lett. 70, 2479 (1993)

    Article  ADS  Google Scholar 

  5. S. Nakatsuji et al., Science 309, 1697 (2005)

    Article  ADS  Google Scholar 

  6. H. Tsunetsugu, M. Arikawa, J. Phys. Soc. Jpn. 75, 083701 (2006)

    Article  ADS  Google Scholar 

  7. H. Tsunetsugu, M. Arikawa, J. Phys. Cond. Mat. 19, 145248 (2007)

    Article  ADS  Google Scholar 

  8. A. Läuchli, F. Mila, K. Penc, Phys. Rev. Lett. 97, 087205 (2006)

    Article  ADS  Google Scholar 

  9. S. Bhattacharjee, V.B. Shenoy, T. Senthil, Phys. Rev. B 74, 092406 (2006)

    Article  ADS  Google Scholar 

  10. E.E. Kaul, H. Rosner, N. Shannon, R.V. Shpanchenko, C. Geibel, J. Magn. Magn. Mater. 272–276, 922 (2004)

    Article  Google Scholar 

  11. N. Kini, E.E. Kaul, C. Geibel, J. Phys. Condens. Matter 18, 1303 (2006)

    Article  ADS  Google Scholar 

  12. H. Kageyama, T. Kitano, N. Oba, M. Nishi, S. Nagai, K. Hirota, L. Viciu, J.B. Wiley, J. Yasuda, Y. Baba, Y. Ajiro, K. Yoshimura, J. Phys. Soc. Jpn. 74, 1702 (2005)

    Article  ADS  Google Scholar 

  13. H.T. Ueda, K. Totsuka, Phys. Rev. B 76, 214428 (2007)

    Article  ADS  Google Scholar 

  14. P. Santini, S. Carretta, G. Amoretti, R. Caciuffo, N. Magnani, G.H. Lander, Rev. Mod. Phys. 81, 807 (2009)

    Article  ADS  Google Scholar 

  15. J.A. Paixao, C. Detlefs, M.J. Longfield, R. Caciuffo, P. Santini, N. Bernhoeft, J. Rebizant, G.H. Lander, Phys. Rev. Lett. 89, 187202 (2002)

    Article  ADS  Google Scholar 

  16. Y. Tokunaga, D. Aoki, Y. Homma, S. Kambe, H. Sakai, S. Ikeda, T. Fujimoto, R.E. Walstedt, H. Yasuoka, E. Yamamoto, A. Nakamura, Y. Shiokawa, Phys. Rev. Lett. 97, 257601 (2006)

    Article  ADS  Google Scholar 

  17. O. Sakai, R. Shiina, H. Shiba, J. Phys. Soc. Jpn. 74, 457 (2005)

    Article  ADS  Google Scholar 

  18. R. Shiina, H. Shiba, P. Thalmeier, J. Phys. Soc. Jpn. 66, 1741 (1997)

    Article  ADS  Google Scholar 

  19. T. Takimoto, J. Phys. Soc. Jpn. 75, 034714 (2006)

    Article  ADS  Google Scholar 

  20. Y. Kuramoto, H. Kusunose, A. Kiss, J. Phys. Soc. Jpn. 78, 072001 (2009)

    Article  ADS  Google Scholar 

  21. C.V. Ciobanu, S.-K. Yip, T.L. Ho, Phys. Rev. A 61, 33607 (2000)

    Article  ADS  Google Scholar 

  22. H.H. Tu, G.M. Zhang, L. Yu, Phys. Rev. B 74, 174404 (2006)

    Article  ADS  Google Scholar 

  23. A.M. Turner, R. Barnett, E. Demler, A. Vishwanath, Phys. Rev. Lett. 98, 190404 (2007)

    Article  ADS  Google Scholar 

  24. K.I. Kugel, D.I. Khomskii, Sov. Phys. Usp. 25 231 (1982)

    Article  ADS  Google Scholar 

  25. A. Mishra, M. Ma, F.-C. Zhang, S. Guertler, L.-H. Tang, S. Wan, Phys. Rev. Lett. 93, 207201 (2004); Phys. Rev. B 72, 024448 (2005)

    Google Scholar 

  26. B. Douçot, M.V. Feigel’man, L.B. Ioffe, A.S. Ioselevich, Phys. Rev. B 71, 024505 (2005)

    Article  ADS  Google Scholar 

  27. Z. Nussinov, M. Biskup, L. Chayes, J. van den Brink, Europhys. Lett. 67, 990 (2004)

    Article  ADS  Google Scholar 

  28. J. Dorier, F. Becca, F. Mila, Phys. Rev. B 72, 024448 (2005)

    Article  ADS  Google Scholar 

  29. R. Barnett, A. Turner, E. Demler, Phys. Rev. Lett. 97, 180412 (2006)

    Article  ADS  Google Scholar 

  30. B.A. Ivanov, A.K. Kolezhuk, Phys. Rev. B 68, 052401 (2003)

    Article  ADS  Google Scholar 

  31. B. Sutherland, Phys. Rev. B 12, 3795 (1975)

    Article  ADS  Google Scholar 

  32. I. Affleck, Phys. Rev. Lett. 54, 966 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  33. N. Papanicolaou, Nucl. Phys. B 305, 367 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  34. C.D. Batista, G. Ortiz, Phys. Rev. B 65, 180402(R) (2002)

    Google Scholar 

  35. A.V. Chubukov, D.V. Khveschenko, J. Phys. C Solid State Phys. 20, L505 (1987)

    Article  ADS  Google Scholar 

  36. A.V. Chubukov, Phys. Rev. B 44, 4693 (1991)

    Article  ADS  Google Scholar 

  37. F. Heidrich-Meisner, A. Honecker, T. Vekua, Phys. Rev. B 74, 020403(R) (2006)

    Google Scholar 

  38. T. Vekua, A. Honecker, H.-J. Mikeska, F. Heidrich-Meisner, Phys. Rev. B 76, 174420 (2007)

    Article  ADS  Google Scholar 

  39. L. Kecke, T. Momoi, A. Furusaki, Phys. Rev. B 76, 060407(R) (2007)

    Google Scholar 

  40. T. Hikihara, L. Kecke, T. Momoi, A. Furusaki, Phys. Rev. B 78, 144404 (2008)

    Article  ADS  Google Scholar 

  41. J. Sudan, A. Lüscher, A.M. Läuchli, Phys. Rev. B 80, 140402(R) (2009)

    Google Scholar 

  42. A.M. Läuchli, J. Sudan, A. Lüscher, J. Phys. Conf. Ser. 145, 012057 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  44. C. Knetter, A. Bühler, E. Müller-Hartmann, G.S. Uhrig, Phys. Rev. Lett. 85, 3958 (2000);

    Article  ADS  Google Scholar 

  45. K. Totsuka, S. Miyahara, K. Ueda, Phys. Rev. Lett. 86, 520 (2001)

    Article  ADS  Google Scholar 

  46. R. Bendjama, B. Kumar, F. Mila, Phys. Rev. Lett. 95, 110406 (2005);

    Article  ADS  Google Scholar 

  47. K.P. Schmid, J. Dorier, A. Läuchli, F. Mila, Phys. Rev. B 74, 174508 (2006)

    Article  ADS  Google Scholar 

  48. A. Joshi, M. Ma, F. Mila, D.N. Shi, F.C. Zhang, Phys. Rev. B 60, 6584 (1999)

    Article  ADS  Google Scholar 

  49. P. Li, G.M. Zhang, S.Q. Shen, Phys. Rev. B 75, 104420 (2007)

    Article  ADS  Google Scholar 

  50. A. Chubukov, J. Phys. Condens. Matter 2 1593 (1990)

    Article  ADS  Google Scholar 

  51. V.M. Matveev, Zh. Eksp. Teor. Fiz. 65, 1626 (1973) [Sov. Phys. JETP 38, 813 (1974)]

    Google Scholar 

  52. K. Harada, N. Kawashima, J. Phys. Soc. Jpn. 70, 13 (2001)

    Article  ADS  Google Scholar 

  53. K. Harada, N. Kawashima, Phys. Rev. B 65, 052403 (2002)

    Article  ADS  Google Scholar 

  54. K. Harada, N. Kawashima, M. Troyer, Phys. Rev. Lett. 90, 117203 (2003)

    Article  ADS  Google Scholar 

  55. P.W. Anderson, Basic Notions of Condensed Matter Physics, Frontiers in Physics, vol. 55. (Benjamin Cummings, London, 1984)

    Google Scholar 

  56. B. Bernu, C. Lhuillier, L. Pierre, Phys. Rev. Lett. 69, 2590 (1992)

    Article  ADS  Google Scholar 

  57. B. Bernu, P. Lecheminant, C. Lhuillier, L. Pierre, Phys. Rev. B 50, 10048 (1994)

    Article  ADS  Google Scholar 

  58. G. Fáth, J. Sólyom, Phys. Rev. B 51, 3620 (1995)

    Article  ADS  Google Scholar 

  59. A.V. Chubukov, Phys. Rev. B 43, 3337 (1991)

    Article  ADS  Google Scholar 

  60. N. Kawashima, Prog. Theor. Phys. Suppl. 145, 138 (2002)

    Article  ADS  Google Scholar 

  61. D. Porras, F. Verstraete, J.I. Cirac, Phys. Rev. B 73, 014410 (2006)

    Article  ADS  Google Scholar 

  62. M. Rizzi, D. Rossini, G. De Chiara, S. Montangero, R. Fazio, Phys. Rev. Lett. 95, 240404 (2005)

    Article  ADS  Google Scholar 

  63. K. Buchta, G. Fáth, Ö. Legeza, J. Sólyom, Phys. Rev. B 72, 054433 (2005)

    Article  ADS  Google Scholar 

  64. A. Läuchli, G. Schmid, S. Trebst, Phys. Rev. B 74, 144426 (2006)

    Article  ADS  Google Scholar 

  65. S. Bergkvist, I. McCulloch, A. Rosengren, Phys. Rev. A 74, 053419 (2006)

    Article  ADS  Google Scholar 

  66. T. Grover, T. Senthil, Phys. Rev. Lett. 98, 247202 (2007)

    Article  ADS  Google Scholar 

  67. G. Fáth, J. Sólyom, Phys. Rev. B 44, 11836 (1991)

    Article  ADS  Google Scholar 

  68. K. Nomura, S. Takada, J. Phys. Soc. Jpn. 60, 389 (1991);

    Article  MathSciNet  ADS  Google Scholar 

  69. Y. Xian, J. Phys. Condens. Matter 5 7489, (1993)

    Article  ADS  Google Scholar 

  70. J. Sólyom, J. Zittartz, Europhys. Lett. 50 389 (2000);

    Article  ADS  Google Scholar 

  71. M. Greiter, S. Rachel, D. Schuricht, Phys. Rev. B 75, 060401(R) (2007)

    Google Scholar 

  72. A. Schmitt, K.-H. Mütter, M. Karbach, Y. Yu, G. Müller, Phys. Rev. B 58, 5498 (1998)

    Article  ADS  Google Scholar 

  73. C. Itoi, M. Kato, Phys. Rev. B 55, 8295 (1997)

    Article  ADS  Google Scholar 

  74. Ph. Corboz, A. Läuchli, K. Totsuka, H. Tsunetsugu, Phys. Rev. B 76, 220404(R) (2007)

    Google Scholar 

  75. K. Harada, N. Kawashima, M. Troyer, J. Phys. Soc. Jpn. 76, 013703 (2007)

    Article  ADS  Google Scholar 

  76. P. Lecheminant, K. Totsuka, Phys. Rev. B 74, 224426 (2006)

    Article  ADS  Google Scholar 

  77. A. Läuchli, J.-C. Domenge, C. Lhuillier, P. Sindzingre, M. Troyer, Phys. Rev. Lett. 95, 137206 (2005)

    Article  ADS  Google Scholar 

  78. P. Chandra, P. Coleman, Phys. Rev. Lett. 66, 100 (1991)

    Article  ADS  Google Scholar 

  79. P. Chandra, P. Coleman, A.I. Larkin, J. Phys. Condens. Matter 2, 7933 (1990)

    Article  ADS  Google Scholar 

  80. A.V. Chubukov, Phys. Rev. B 44, 5362 (1991)

    Article  ADS  Google Scholar 

  81. P. Azaria, B. Delamotte, D. Mouhanna, Phys. Rev. Lett. 68, 1762 (1992)

    Article  ADS  Google Scholar 

  82. M.E. Zhitomirsky, Phys. Rev. Lett. 88, 057204 (2002)

    Article  ADS  Google Scholar 

  83. B. Canals, M.E. Zhitomirsky, J. Phys. Condens. Matter 16, S759 (2004)

    Article  ADS  Google Scholar 

  84. N. Shannon, K. Penc, Y. Motome, Phys. Rev. B 81, 184409 (2010)

    Article  ADS  Google Scholar 

  85. T. Momoi, P. Sindzingre, N. Shannon, Phys. Rev. Lett. 97, 257204 (2006)

    Article  ADS  Google Scholar 

  86. M.E. Zhitomirsky, Phys. Rev. B 78, 094423 (2008)

    Article  ADS  Google Scholar 

  87. M. Enderle, C. Mukherjee, B. Fåk, R.K. Kremer, J.-M. Broto, H. Rosner, S.-L. Drechsler, J. Richter, J. Malek, A. Prokofiev, W. Assmus, S. Pujol, J.-L. Raggazzoni, H. Rakoto, M. Rheinstädter, H.M. Rønnow, Europhys. Lett. 70, 237 (2005)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute for Solid State Physics and Optics, 49, 1525, Budapest, Hungary

    Karlo Penc

  2. Max Planck Institut fur Physik komplexer Systeme, Nothnitzer Strasse 38, 01187, Dresden, Germany

    Andreas M. Läuchli

Authors
  1. Karlo Penc
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas M. Läuchli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karlo Penc .

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

Penc, K., Läuchli, A.M. (2011). Spin Nematic Phases in Quantum Spin Systems. 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_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-10589-0_13

  • 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