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Emergent excitations in a geometrically frustrated magnet


Frustrated systems are ubiquitous1,2,3, and they are interesting because their behaviour is difficult to predict; frustration can lead to macroscopic degeneracies and qualitatively new states of matter. Magnetic systems offer good examples in the form of spin lattices, where all interactions between spins cannot be simultaneously satisfied4. Here we report how unusual composite spin degrees of freedom can emerge from frustrated magnetic interactions in the cubic spinel ZnCr2O4. Upon cooling, groups of six spins self-organize into weakly interacting antiferromagnetic loops, whose directors—the unique direction along which the spins are aligned, parallel or antiparallel—govern all low-temperature dynamics. The experimental evidence comes from a measurement of the magnetic form factor by inelastic neutron scattering; the data show that neutrons scatter from hexagonal spin clusters rather than individual spins. The hexagon directors are, to a first approximation, decoupled from each other, and hence their reorientations embody the long-sought local zero energy modes for the pyrochlore lattice.

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Figure 1: Lowest-energy spin configurations for four antiferromagnetically interacting spins on a square, a tetrahedron, and the pyrochlore lattice of corner-sharing tetrahedra.
Figure 2: Temperature dependence of the inverse correlation length, κ(T) = ξ(T)-1.
Figure 3: Wavevector dependence of the inelastic neutron scattering cross-section for ZnCr2O4.
Figure 4: Possible spin fluctuations in the classical ground-state manifold.


  1. Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001)

    ADS  CAS  Article  Google Scholar 

  2. Wolynes, P. G. & Eaton, W. A. The physics of protein folding. Phys. World 12, 39–44 (1999)

    CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  4. Ramirez, A. P. in Handbook on Magnetic Materials (ed. Busch, K. J. H.) Vol. 13, 423–520 (Elsevier Science, Amsterdam, 2001)

    Google Scholar 

  5. Moessner, R. & Chalker, J. T. Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet. Phys. Rev. Lett. 80, 2929–2932 (1998)

    ADS  CAS  Article  Google Scholar 

  6. Canals, B. & Lacroix, C. Pyrochlore antiferromagnet: a three-dimensional quantum spin liquid. Phys. Rev. Lett. 80, 2933–2936 (1998)

    ADS  CAS  Article  Google Scholar 

  7. Stormer, H. L., Tsui, D. C. & Gossard, A. C. The fractional quantum Hall effect. Rev. Mod. Phys. 71, S298–S305 (1999)

    MathSciNet  CAS  Article  Google Scholar 

  8. Laughlin, R. B. & Pines, D. The theory of everything. Proc. Natl Acad. Sci. USA 97, 28–31 (2000)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  9. Lovesey, S. W. Theory of Thermal Neutron Scattering from Condensed Matter (Clarendon, Oxford, 1984)

    Google Scholar 

  10. Birgeneau, R. J. et al. Instantaneous spin correlations in La2CuO4 . Phys. Rev. B 59, 13788–13794 (1999)

    ADS  CAS  Article  Google Scholar 

  11. Lee, S.-H. et al. Spin-glass and non-spin-glass features of a geometrically frustrated magnet. Europhys. Lett. 35, 127–132 (1996)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  13. Lee, S.-H., Broholm, C., Kim, T. H., Ratcliff, W. & Cheong, S-W. Local spin resonance and spin-Peierls-like phase transition in a geometrically frustrated antiferromagnet. Phys. Rev. Lett. 84, 3718–3721 (2000)

    ADS  CAS  Article  Google Scholar 

  14. Moessner, R. & Berlinsky, A. J. Magnetic susceptibility of diluted pyrochlore and SrCr9-9xGa3+9xO19 . Phys. Rev. Lett. 83, 3293–3296 (1999)

    ADS  CAS  Article  Google Scholar 

  15. Garcia-Adeva, A. J. & Huber, D. L. Quantum tetrahedral mean-field theory of the pyrochlore lattice. Can. J. Phys. 79, 1359–1364 (2001)

    ADS  CAS  Article  Google Scholar 

  16. Mekata, M. & Yamada, Y. Magnetic-ordering process in SrCr9(Ga-In)3O19 . Can. J. Phys. 79, 1421–1426 (2001)

    ADS  CAS  Article  Google Scholar 

  17. Uemura, Y. J. et al. Spin fluctuations in frustrated kagomé lattice system SrCr8Ga4O19 studied by muon spin relaxation. Phys. Rev. Lett. 73, 3306–3309 (1994)

    ADS  CAS  Article  Google Scholar 

  18. Ramirez, A. P., Espinosa, G. P. & Cooper, A. S. Elementary excitations in a diluted antiferromagnetic kagomé lattice. Phys. Rev. B 45, 2505–2508 (1992)

    ADS  CAS  Article  Google Scholar 

  19. Broholm, C., Aeppli, G., Espinosa, G. P. & Cooper, A. S. Antiferromagnetic fluctuations and short range order in a kagomé lattice. Phys. Rev. Lett. 65, 3173–3716 (1990)

    ADS  CAS  Article  Google Scholar 

  20. Pande, V. S., Grosberg, A. Yu. & Tanaka, T. Heteropolymer freezing and design: Towards physical models of protein folding. Rev. Mod. Phys. 72, 259–314 (2000)

    ADS  CAS  Article  Google Scholar 

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We thank O. Tchernyshyov, R. Moessner, S. L. Sondhi, A. B. Harris, G. Aeppli, N. Read and D. Weitz for discussions, J. J. Rush, A. P. Ramirez and P. M. Gehring for critical reading of the manuscript, and Z. Huang for assistance in making figures. This work was partially supported by the NSF and the BSF.

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Lee, SH., Broholm, C., Ratcliff, W. et al. Emergent excitations in a geometrically frustrated magnet. Nature 418, 856–858 (2002).

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