Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Order-by-disorder and spiral spin-liquid in frustrated diamond-lattice antiferromagnets

Nature Physics volume 3, pages 487–491 (2007)Cite this article

Abstract

Frustration refers to competition between different interactions that cannot be simultaneously satisfied—a familiar feature in many magnetic solids. Strong frustration leads to highly degenerate ground states and a large suppression of ordering by fluctuations. Key challenges in frustrated magnetism include the characterization of the fluctuating spin-liquid regime and determination of the mechanism of eventual order at lower temperature. Here, we study a model of a diamond-lattice antiferromagnet appropriate for numerous spinel materials. With sufficiently strong frustration, a massive ground-state degeneracy develops amongst spirals whose propagation wavevectors reside on a continuous two-dimensional ‘spiral surface’ in momentum space. We argue that an important ordering mechanism is entropic splitting of the degenerate ground states, an elusive phenomenon called ‘order by disorder’. A broad spiral spin-liquid regime emerges at higher temperatures, where the underlying spiral surface can be directly revealed through spin correlations. We discuss the agreement between these predictions and the well-characterized spinel MnSc2S4.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Spin-spiral state on the diamond lattice.
Figure 2: Spiral surfaces.
Figure 3: Phase diagram.
Figure 4: Spiral surface measured from Monte Carlo simulation.
Figure 5: Correlation function of the spiral spin-liquid.
Figure 6: Powder-averaged structure factor.

References

  1. Ramirez, A. P. Strongly geometrically frustrated magnets. Annu. Rev. Mater. Sci. 24, 453–480 (1994).

    Article  ADS  Google Scholar 

  2. Lee, S.-H et al. Emergent excitations in a geometrically frustrated magnet. Nature 418, 856–858 (2002).

    Article  ADS  Google Scholar 

  3. Isakov, S. V., Gregor, K., Moessner, R. & Sondhi, S. L. Dipolar spin correlations in classical pyrochlore magnets. Phys. Rev. Lett. 93, 167204 (2004).

    Article  ADS  Google Scholar 

  4. Henley, C. L. Power-law spin correlations in pyrochlore antiferromagnets. Phys. Rev. B 71, 014424 (2005).

    Article  ADS  Google Scholar 

  5. Hermele, M., Fisher, M. P. A. & Balents, L. Pyrochlore photons: The U(1) spin liquid in a s=1/2 three-dimensional frustrated magnet. Phys. Rev. B 69, 064404 (2004).

    Article  ADS  Google Scholar 

  6. Bramwell, S. T. & Gingras, M. J. P. Spin ice state in frustrated magnetic pyrochlore materials. Science 294, 1495–1501 (2001).

    Article  ADS  Google Scholar 

  7. Yamashita, Y. & Ueda, K. Spin-driven Jahn–Teller distortion in a pyrochlore system. Phys. Rev. Lett. 85, 4960–4963 (2000).

    Article  ADS  Google Scholar 

  8. Veillette, M. Y., Chalker, J. T. & Coldea, R. Ground states of a frustrated spin-(1/2) antiferromagnet: Cs2CuCl4 in a magnetic field. Phys. Rev. B 71, 214426 (2005).

    Article  ADS  Google Scholar 

  9. Villain, J., Bidaux, R., Carton, J. P. & Conte, R. Order as an effect of disorder. J. Physique 41, 1263–1272 (1980).

    Article  MathSciNet  Google Scholar 

  10. Rastelli, E. & Tassi, A. Order produced by quantum disorder in the Heisenberg rhombohedral antiferromagnet. J. Phys. C 20, L303–L306 (1987).

    Article  ADS  Google Scholar 

  11. Henley, C. L. Ordering due to disorder in a frustrated vector antiferromagnet. Phys. Rev. Lett. 62, 2056–2059 (1989).

    Article  ADS  Google Scholar 

  12. Chubukov, A. Order from disorder in a kagomé antiferromagnet. Phys. Rev. Lett. 69, 832–835 (1992).

    Article  ADS  Google Scholar 

  13. Henley, C. L. Ordering by disorder: Ground-state selection in fcc vector antiferromagnets. J. Appl. Phys. 61, 3962–3964 (1987).

    Article  ADS  Google Scholar 

  14. Gvozdikova, M. V. & Zhitomirsky, M. E. Monte Carlo study of first-order transition in Heisenberg fcc antiferromagnet. JETP Lett. 81, 236–240 (2005).

    Article  ADS  Google Scholar 

  15. Reimers, J. N. Absence of long-range order in a three-dimensional geometrically frustrated antiferromagnet. Phys. Rev. B 45, 7287–7294 (1992).

    Article  ADS  Google Scholar 

  16. Moessner, R. & Chalker, J. T. Low-temperature properties of classical geometrically frustrated antiferromagnets. Phys. Rev. B 58, 12049–12062 (1998).

    Article  ADS  Google Scholar 

  17. Tristan, N. et al. Geometric frustration in the cubic spinels MAl2O4 (M=Co, Fe, and Mn). Phys. Rev. B 72, 174404 (2005).

    Article  ADS  Google Scholar 

  18. Suzuki, T., Nagai, H., Nohara, M. & Takagi, H. Melting of antiferromagnetic ordering in spinel oxide CoAl2O4 . J. Phys. Condens. Matter 19, 145265 (2007).

    Article  ADS  Google Scholar 

  19. Fritsch, V. et al. Spin and orbital frustration in MnSc2S4 and FeSc2S4 . Phys. Rev. Lett. 92, 116401 (2004).

    Article  ADS  Google Scholar 

  20. Smart, J. S. Effective Field Theories of Magnetism (W. B. Saunders Company, Philadelphia, 1966).

    Book  Google Scholar 

  21. Diep, H. T. & Kawamura, H. First-order phase transition in the fcc Heisenberg antiferromagnet. Phys. Rev. B 40, 7019–7022 (1989).

    Article  ADS  Google Scholar 

  22. Minor, W. & Giebultowicz, T. Studies of FCC Heisenberg antiferromagnets by Monte Carlo simulation on large spin arrays. J. Phys. Colloq. 49, 1551 (1988).

    Article  Google Scholar 

  23. Alonso, J. L. et al. Monte Carlo study of O(3) antiferromagnetic models in three dimensions. Phys. Rev. B 53, 2537–2545 (1996).

    Article  ADS  Google Scholar 

  24. Roth, W. L. Magnetic properties of normal spinels with only A–A interactions. J. Physique 25, 507–515 (1964).

    Article  Google Scholar 

  25. Krimmel, A. et al. Magnetic ordering and spin excitations in the frustrated magnet MnSc2S4 . Phys. Rev. B 73, 014413 (2006).

    Article  ADS  Google Scholar 

  26. Lyons, D. H., Kaplan, T. A., Dwight, K. & Menyuk, N. Classical theory of the ground spin-state in cubic spinels. Phys. Rev. 126, 540–555 (1962).

    Article  ADS  Google Scholar 

  27. Luttinger, J. M. & Tisza, L. Theory of dipole interaction in crystals. Phys. Rev. 70, 954–964 (1946).

    Article  ADS  Google Scholar 

  28. Luttinger, J. M. A note on the ground state in antiferromagnetics. Phys. Rev. 81, 1015–1018 (1951).

    Article  ADS  Google Scholar 

  29. Lyons, D. H. & Kaplan, T. A. Method for determining ground-state spin configurations. Phys. Rev. 120, 1580–1585 (1960).

    Article  ADS  MathSciNet  Google Scholar 

  30. Rastelli, E. & Tassi, A. The rhombohedral Heisenberg antiferromagnet: infinite degeneracy of the ground state and magnetic properties of solid oxygen. J. Phys. C 19, L423–L428 (1986).

    Article  ADS  Google Scholar 

  31. Garanin, D. A. & Canals, B. Classical spin liquid: Exact solution for the infinite-component antiferromagnetic model on the kagomé lattice. Phys. Rev. B 59, 443–456 (1999).

    Article  ADS  Google Scholar 

  32. Mucksch, M. et al. Multi-step magnetic ordering in frustrated thiospinel MnSc2S4 . J. Phys. Condens. Matter 19, 145262 (2007).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We would like to acknowledge R. Shindou, Z. Wang, C. Henley and M. P. A. Fisher for illuminating discussions, as well as T. Suzuki, M. Muecksch and A. Krimmel for sharing their unpublished results. This work was supported by the Packard Foundation (D.B. and L.B.) and the National Science Foundation through grants DMR-0529399 (J.A.) and DMR04-57440 (D.B. and L.B.).

Author information

Authors and Affiliations

  1. Department of Physics, University of California, Santa Barbara, California 93106-9530, USA

    Doron Bergman, Jason Alicea & Leon Balents

  2. Theoretische Physik, Eidgenössische Technische Hochschule Zürich, CH-8093 Zürich, Switzerland

    Emanuel Gull

  3. Microsoft Research, Station Q, University of California, Santa Barbara, California 93106, USA

    Simon Trebst

Authors
  1. Doron Bergman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jason Alicea
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Emanuel Gull
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Simon Trebst
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Leon Balents
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Doron Bergman.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bergman, D., Alicea, J., Gull, E. et al. Order-by-disorder and spiral spin-liquid in frustrated diamond-lattice antiferromagnets. Nature Phys 3, 487–491 (2007). https://doi.org/10.1038/nphys622

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys622

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing