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Spinons and triplons in spatially anisotropic frustrated antiferromagnets

Nature Physics volume 3, pages 790795 (2007) | Download Citation

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Abstract

The search for elementary excitations with fractional quantum numbers is a central challenge in modern condensed-matter physics. It has long been speculated that two-dimensional frustrated magnets might support quantum disordered states with neutral spin-1/2 excitations known as spinons. Despite decades of search, however, no clear experimental examples have been found. We explore the possibility for several materials using a realistic model, the spin-1/2 spatially anisotropic frustrated Heisenberg antiferromagnet in two dimensions. Here, we derive an effective Schrödinger equation valid in the weak interchain coupling regime. The dynamical spin correlations from this approach agree quantitatively without fitting parameters with inelastic neutron measurements of the triangular antiferromagnet Cs2CuCl4. In such antiferromagnets, the spectrum is composed of an incoherent continuum arising from the effects of one-dimensional spinons of individual chains, and a sharp dispersing peak, due to coherently propagating ‘triplon’ bound states of two spinons. We argue that triplons are generic features of spatially anisotropic frustrated antiferromagnets, which arise because the bound spinon pair lowers its kinetic energy by propagating between chains.

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References

  1. 1.

    ‘Luttinger liquid theory’ of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas. J. Phys. C 14, 2585–2609 (1981).

  2. 2.

    & What is the spin of a spin wave? Phys. Lett. A 85, 375–377 (1981).

  3. 3.

    “Spinon gas” description of the S=1/2 Heisenberg chain with inverse-square exchange: Exact spectrum and thermodynamics. Phys. Rev. Lett. 66, 1529–1532 (1991).

  4. 4.

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

  5. 5.

    The spin-wave theory of antiferromagnetics. Phys. Rev. 87, 568–580 (1952).

  6. 6.

    Resonating valence bonds: A new kind of insulator? Mater. Res. Bull. 8, 153–160 (1973).

  7. 7.

    , & Topology of the resonating valence-bond state: Solitons and high-Tc superconductivity. Phys. Rev. B 35, 8865–8868 (1987).

  8. 8.

    & New functional integral approach to strongly correlated Fermi systems: The Gutzwiller approximation as a saddle point. Phys. Rev. Lett. 57, 1362–1365 (1986).

  9. 9.

    & Neutral fermion, charge-e boson excitations in the resonating-valence-bond state and superconductivity in La2CuO4-based compounds. Phys. Rev. B 37, 627–630 (1988).

  10. 10.

    , & Doping a Mott insulator: Physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).

  11. 11.

    , , , & Deconfined quantum critical points. Science 303, 1490–1494 (2004).

  12. 12.

    & Magnetic and metal-insulator transitions through bandwidth control in two-dimensional Hubbard models with nearest and next-nearest neighbor transfers. J. Phys. Soc. Jpn. 70, 3052–3067 (2001).

  13. 13.

    , & Nonmagnetic insulating states near the Mott transitions on lattices with geometrical frustration and implications for κ-(ET)2Cu2(CN). J. Phys. Soc. Jpn. 71, 2109–2112 (2002).

  14. 14.

    , , & Experimental realization of a 2D fractional quantum spin liquid. Phys. Rev. Lett. 86, 1335–1338 (2001).

  15. 15.

    , & Extended scattering continua characteristic of spin fractionalization in the two-dimensional frustrated quantum magnet Cs2CuCl4 observed by neutron scattering. Phys. Rev. B 68, 134424 (2003).

  16. 16.

    , , , & Spin liquid state in an organic Mott insulator with a triangular lattice. Phys. Rev. Lett. 91, 107001 (2003).

  17. 17.

    et al. Spin dynamics of the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2. Phys. Rev. Lett. 98, 107204 (2007).

  18. 18.

    et al. Ground state and excitation properties of the quantum kagomé system ZnCu3(OH)6Cl2 investigated by local probes. Preprint at <> (2006).

  19. 19.

    , & Gapless spin liquid behavior in two-dimensional solid 3He. Phys. Rev. Lett. 92, 025301 (2004).

  20. 20.

    et al. Direct measurement of the spin hamiltonian and observation of condensation of magnons in the 2D frustrated quantum magnet Cs2CuCl4. Phys. Rev. Lett. 88, 137203 (2002).

  21. 21.

    , & Large-N solutions of the Heisenberg and Hubbard–Heisenberg models on the anisotropic triangular lattice: Application to Cs2CuCl4 and to the layered organic superconductors kappa-(BEDT-TTF)(2)X. J. Phys. Condens. Matter 13, 5159–5181 (2001).

  22. 22.

    & Quantum orders and spin liquids in Cs2CuCl4. Preprint at <> (2002).

  23. 23.

    , & Statistics of spinons in the spin-liquid phase of Cs2CuCl4. Phys. Rev. B 68, 094412 (2003).

  24. 24.

    & Resonating valence bond wave function for the two-dimensional fractional spin liquid. Phys. Rev. Lett. 92, 157003 (2004).

  25. 25.

    , & Algebraic vortex liquid in spin-1/2 triangular antiferromagnets: Scenario for Cs2CuCl4. Phys. Rev. Lett. 95, 247203 (2005).

  26. 26.

    , & Ordering in Cs2CuCl4: Possibility of a proximate spin liquid. Phys. Rev. B 72, 174417 (2005).

  27. 27.

    , & Spin dynamics of the quasi-two-dimensional spin-1/2 quantum magnet Cs2CuCl4. Phys. Rev. B 72, 134429 (2005).

  28. 28.

    , , , & Spin structure factor of the frustrated quantum magnet Cs2CuCl4. Phys. Rev. B 73, 184403 (2006).

  29. 29.

    , , , & Anomalous excitation spectra of frustrated quantum antiferromagnets. Phys. Rev. Lett. 96, 057201 (2006).

  30. 30.

    , , , & Excitation spectra and ground state properties of the layered spin-1/2 frustrated antiferromagnets Cs2CuCl4 and Cs2CuBr4. Phys. Rev. B 75, 174447 (2007).

  31. 31.

    & Ordering in spatially anisotropic triangular antiferromagnets. Phys. Rev. Lett. 98, 077205 (2007).

  32. 32.

    , & Phase diagram for a class of spin-1/2 Heisenberg models interpolating between the square-lattice, the triangular-lattice, and the linear-chain limits. Phys. Rev. B 59, 14367–14375 (1999).

  33. 33.

    , , & Spin liquid phase in anisotropic triangular lattice Heisenberg model: Exact diagonalization and density-matrix renormalization group calculations. Phys. Rev. B 74, 012407 (2006).

  34. 34.

    Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atomkette. Z. Phys. 71, 205–226 (1931).

  35. 35.

    Über das Austauschproblem eines Kristalles. Arkiv Mat. Astron. Fysik 26A, 1–106 (1938).

  36. 36.

    & Spin-wave spectrum of the antiferromagnetic linear chain. Phys. Rev. 128, 2131 (1962).

  37. 37.

    , , & Quantum spin dynamics of the antiferromagnetic linear chain in zero and nonzero magnetic field. Phys. Rev. B 24, 1429–1467 (1981).

  38. 38.

    , & Exact two-spinon dynamical correlation function of the one-dimensional Heisenberg model. Phys. Rev. B 54, R12669–R12672 (1996).

  39. 39.

    , , , & Two-spinon dynamic structure factor of the one-dimensional s=1/2 Heisenberg antiferromagnet. Phys. Rev. B 55, 12510–12517 (1997).

  40. 40.

    & The 4-spinon dynamical structure factor of the Heisenberg chain. J. Stat. Mech.P12013 (2006).

  41. 41.

    , , & Finite-temperature dynamical magnetic susceptibility of quasi-one-dimensional frustrated spin-1/2 Heisenberg antiferromagnets. Phys. Rev. B 64, 094425 (2001).

  42. 42.

    , & Quasi-one-dimensional spin-1/2 Heisenberg magnets in their ordered phase: Correlation functions. Phys. Rev. B 56, 11001 (1997).

  43. 43.

    , & Form factors of the XXZ Heisenberg spin-1/2 finite chain. Nucl. Phys. B 554, 647 (1999).

  44. 44.

    , & Transition rates via Bethe ansatz for the spin-1/2 planar XXZ antiferromagnet. J. Phys. A 36, 5361 (2003).

  45. 45.

    , & Computation of dynamical correlation functions of Heisenberg chains: The gapless anisotropic regime. J. Stat. Mech.P09003 (2005).

  46. 46.

    & Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures. Phys. Rev. B 57, 8307 (1998).

  47. 47.

    & Excitations in one-dimensional S=1/2 quantum antiferromagnets. Phys. Rev. Lett. 90, 227204 (2003).

  48. 48.

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

  49. 49.

    & Dimerized phase and transitions in a spatially anisotropic square lattice antiferromagnet. Phys. Rev. Lett. 93, 127202 (2004).

  50. 50.

    et al. Magnetization plateaux of the S=1/2 two-dimensional frustrated antiferromagnet Cs2CuBr4. J. Phys. Condens. Matter 16, S773–S778 (2004).

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Acknowledgements

We would like to thank J. Alicea, M. P. A. Fisher and R. Shindou for discussions. This work is supported by the Grant-in-aid for Scientific Research (C) No. 10354143 from MEXT, Japan (M.K.), the Petroleum Research Fund ACS PRF 43219-AC10 (O.S.), NSF grant/DMR-0457440 (L.B.) and the Packard Foundation (L.B.). Part of this research was completed at KITP and supported in part by the NSF under Grant No. PHY05-51164.

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

    • Masanori Kohno
    •  & Leon Balents
  2. Computational Materials Science Center, National Institute for Materials Science, Tsukuba 305-0047, Japan

    • Masanori Kohno
  3. Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA

    • Oleg A. Starykh

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Correspondence to Leon Balents.

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https://doi.org/10.1038/nphys749

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