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Quantum criticality and universal scaling of a quantum antiferromagnet

Nature Materials volume 4, pages 329–334 (2005)Cite this article

Abstract

Quantum effects dominate the behaviour of many diverse materials. Of particular current interest are those systems in the vicinity of a quantum critical point (QCP). Their physical properties are predicted to reflect those of the nearby QCP with universal features independent of the microscopic details. The prototypical QCP is the Luttinger liquid (LL), which is of relevance to many quasi-one-dimensional materials. The magnetic material KCuF3 realizes an array of weakly coupled spin chains (or LLs) and thus lies close to but not exactly at the LL quantum critical point. By using inelastic neutron scattering we have collected a complete data set of the magnetic correlations of KCuF3 as a function of momentum, energy and temperature. The LL description is found to be valid over an extensive range of these parameters, and departures from this behaviour at high and low energies and temperatures are identified and explained.

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Figure 1: Inelastic neutron scattering data for KCuF3.
Figure 2: Inelastic neutron scattering data for KCuF3 measured well below TN and plotted as a function of energy and wavevector parallel to the chain direction.
Figure 3: Universal energy/temperature scaling in KCuF3.
Figure 4: Magnetic crossover diagram showing the different physical regimes of KCuF3 as a function of energy and temperature.

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References

  1. Sachdev, S. Quantum criticality: competing ground states in low dimensions. Science 288, 475–480 (2000).

    Article  CAS  Google Scholar 

  2. Hertz, J. A. Quantum critical phenomena. Phys. Rev. B 14, 1165–1184 (1976).

    Article  CAS  Google Scholar 

  3. Keimer, B. et al. Scaling behavior of the generalized susceptibility in La2-xSrxCuO4+y . Phys. Rev. Lett. 67, 1930–1933 (1991).

    Article  CAS  Google Scholar 

  4. Hayden, S. M. et al. Magnetic fluctuations in La1.95Ba0.05CuO4 . Phys. Rev. Lett. 66, 821–824 (1991).

    Article  CAS  Google Scholar 

  5. Aeppli, G., Mason, T. E., Hayden, S. M., Mook, H. A. & Kulda, J. Nearly singular magnetic fluctuations in the normal state of a high-TC superconductor. Science 278, 1432–1435 (1997).

    Article  CAS  Google Scholar 

  6. Aronson, M. C. et al. Non-Fermi-liquid scaling of the magnetic response in UCu5-xPdx (x=1,1.5). Phys. Rev. Lett. 75, 725–728 (1995).

    Article  CAS  Google Scholar 

  7. Grigera, S. A. et al. Magnetic field-tuned quantum criticality in the metallic ruthenate Sr3Ru2O7 . Science 294, 329–332 (2001).

    Article  CAS  Google Scholar 

  8. Schroder, A. et al. Onset of antiferromagnetism in heavy-fermion metals. Nature 407, 351–355 (2000).

    Article  CAS  Google Scholar 

  9. Gogolin, A. O., Nersesyan, A. A. & Tsvelik, A. M. Bosonization and Strongly Correlated Systems (Cambridge Univ. Press, Cambridge, 1998).

    Google Scholar 

  10. Luther, A. & Peschel, I. Single-particle states, Kohn anomaly, and pairing fluctuations in one dimension. Phys. Rev. B 9, 2911–2919 (1974).

    Article  CAS  Google Scholar 

  11. Luther, A. & Peschel, I. Calculation of critical exponents in two dimensions from quantum field theory in one dimension. Phys. Rev. B 12, 3908–3917 (1975).

    Article  Google Scholar 

  12. Faddeev, L. D. & Takhtajan, L. A. What is the spin of a spin-wave. Phys. Lett. A 85, 375–377 (1981).

    Article  Google Scholar 

  13. Haldane, F. D. M. Fractional statistics in arbitrary dimensions – a generalization of the Pauli principle. Phys. Rev. Lett. 67, 937–940 (1991).

    Article  CAS  Google Scholar 

  14. Muller, G., Thomas, H., Beck, H. & Bonner, J. C. Quantum spin dynamics of the antiferromagnetic linear chain in zero and nonzero magnetic field. Phys. Rev. B 24, 1429–1467 (1981).

    Article  Google Scholar 

  15. Karbach, M., Mü ller, G., Bougourzi, A. H., Fledderjohann, A. & Mütter, K.-H. Two-spinon dynamic structure factor of the one-dimensional S=1/2 Heisenberg antiferromagnet. Phys. Rev. B 55, 12510–12517 (1997).

    Article  CAS  Google Scholar 

  16. Schulz, H. J. Phase diagrams and correlation exponents for quantum spin chains of arbitrary spin number. Phys. Rev. B 34, 6372–6385 (1986).

    Article  CAS  Google Scholar 

  17. Anderson, P. W. An approximate quantum theory of the antiferromagnetic ground state. Phys. Rev. B 86, 694–701 (1952).

    Article  CAS  Google Scholar 

  18. Satija, S. K., Axe, J. D., Shirane, G., Yoshizawa, H. & Hirakawa, K. Neutron scattering study of spin waves in one-dimensional antiferromagnet KCuF3 . Phys. Rev. B 21, 2001–2007 (1980).

    Article  CAS  Google Scholar 

  19. Haldane, F. D. M. O(3) nonlinear sigma-model and the topological distinction between integer-spin and half-integer-spin antiferromagnets in 2 dimensions. Phys. Rev. Lett. 61, 1029–1032 (1988).

    Article  CAS  Google Scholar 

  20. Hutchings, M. T., Samuelsen, E. J., Shirane, G. & Hirakawa, K. Neutron-Diffraction Determination of the Antiferromagnetic Structure of KCuF3 . Phys. Rev. 188, 919–923 (1969).

    Article  CAS  Google Scholar 

  21. Tennant, D. A., Cowley, R. A., Nagler, S. E. & Tsvelik, A. M. Measurement of the spin-excitation continuum in one-dimensional KCuF3 using neutron scattering. Phys. Rev B 52, 13368–13380 (1995).

    Article  CAS  Google Scholar 

  22. Tennant, D. A., Nagler, S. E., Welz, D., Shirane, G. & Yamada, K. Effects of coupling between chains on the magnetic excitation spectrum of KCuF3 . Phys. Rev. B 52, 13381–13389 (1995).

    Article  CAS  Google Scholar 

  23. Dender, D. C. et al. Magnetic properties of a quasi-one-dimensional S=1/2 antiferromagnet: Copper benzoate. Phys. Rev. B 53, 2583–2589 (1996).

    Article  CAS  Google Scholar 

  24. Zheludev, A. et al. Spin dynamics in the quasi-one-dimensional S =1/2 antiferromagnet BaCu2Si2O7 . Phys. Rev. B 65, 014402–014410 (2002).

    Article  Google Scholar 

  25. Lake, B., Tennant, D. A. & Nagler, S. E. Novel longitudinal mode in the coupled quantum chain compound KCuF3 . Phys. Rev. Lett. 85, 832–835 (2000).

    Article  CAS  Google Scholar 

  26. Lake, B., Cowley, R. A. & Tennant, D. A. dimer model of the magnetic excitations in the ordered phase of the alternating chain compound CuWO4 . J. Phys. Condens. Matter 9, 10951–10975 (1997).

    Article  CAS  Google Scholar 

  27. Essler, F. H. L., Tsvelik, A. M. & Delfino, G. Quasi-one-dimensional spin-1/2 Heisenberg magnets in their ordered phase: correlation functions. Phys. Rev. B 56, 11001–11013 (1997).

    Article  CAS  Google Scholar 

  28. Schulz, H. J. Dynamics of coupled quantum spin chains. Phys. Rev. Lett. 77, 2790–2793 (1996).

    Article  CAS  Google Scholar 

  29. Kittel, C. Introduction to Solid State Physics 6th edn, 443–450 (Wiley, New York, 1986).

    Google Scholar 

  30. Smirnov, F. A. Form Factors in Completely Integrable Models of Quantum Field Theory (World Scientific, Singapore, 1992).

    Book  Google Scholar 

  31. Bocquet, M. Finite temperature perturbation theory for quasi-one-dimensional spin-1/2 Heisenberg antiferromagnets. Phys. Rev. B 65, 184415–184425 (2002).

    Article  Google Scholar 

Download references

Acknowledgements

We thank J. S. Caux, R. Coldea, F. H. L. Essler and A. M Tsvelik for helpful discussions and G. Shirane for the loan of the crystal. ORNL is operated by UT-Battelle LLC., under contract no. DE-AC05-00OR22725 with the US Department of Energy.

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Author notes

  1. Bella Lake

    Present address: Department of Physics & Astronomy, Ames Laboratory, IOWA State University, Ames, Iowa, 50011, USA

  2. D. Alan Tennant

    Present address: Department of Magnetism (SF2), Hahn-Meitner Institute Berlin, Glienicker Str. 100, D-14109, Berlin, Germany

Authors and Affiliations

  1. Condensed Matter Sciences Division, Oak Ridge National Laboratory, Oak Ridge, 37831-6393, Tennessee, USA

    Bella Lake & Stephen E. Nagler

  2. Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK

    Bella Lake & D. Alan Tennant

  3. ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, UK

    D. Alan Tennant & Chris D. Frost

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  1. Bella Lake
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Correspondence to Bella Lake.

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Lake, B., Tennant, D., Frost, C. et al. Quantum criticality and universal scaling of a quantum antiferromagnet. Nature Mater 4, 329–334 (2005). https://doi.org/10.1038/nmat1327

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