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Scattering Neutrons from Magnons, Spinons, Solitons, and Breathers

Scattering Neutrons from Magnons, Spinons, Solitons, and Breathers. Neutron Scattering and 1D magnetism Spin-1 chains & Summer in Aspen Toward Quantum Criticality strongly interacting dimers (PHCC) Quantum critical spin-1/2 chain Field Effects at Criticality H>0: Extended Critical phase

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Scattering Neutrons from Magnons, Spinons, Solitons, and Breathers

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  1. Scattering Neutrons from Magnons, Spinons, Solitons, and Breathers • Neutron Scattering and 1D magnetism • Spin-1 chains & Summer in Aspen • Toward Quantum Criticality • strongly interacting dimers (PHCC) • Quantum critical spin-1/2 chain • Field Effects at Criticality • H>0: Extended Critical phase • hs>0: From spinons to solitons • Conclusions Collin Broholm, Johns Hopkins University and NIST Center for Neutron Research

  2. Acknowledgements G. Aeppli UCL C. D. Batista Los Alamos Y. Chen LANL D. C. Dender NIST T. Hong JHU M. Kenzelmann JHU & NIST C. P. Landee Clarke University K. Lefmann Risø National Lab Y. Qiu NIST & Univ. Maryland D. H. Reich JHU C. Rische Univ. of Copenhagen M. B. Stone Penn State University M. M. Turnbull Clarke University I. Zaliznyak BNL

  3. Neutron Scattering and 1D Magnetism

  4. Magnetic Neutron Scattering The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function

  5. NIST Center for Neutron Research

  6. pi pf ħQ SPINS cold neutron spectrometer at NCNR

  7. Better Instrumentation at Existing Sources 2 cm 4 cm Jose A. Rodriguez, NIST

  8. 20+20 Channel MACS detection system

  9. Spallation Neutron Source at ORNL, TN Neutrons + B>30 Tesla One of 18 instruments

  10. Spin-1 Chains at Summer 1991 (?)

  11. Neutrons Create magnons in spin-1 chain NENP=Ni(C2H8N2)2NO2ClO4 Ma et al. PRL (1992)

  12. Experiments and Theory of spin-1 chain

  13. Single mode approximation for spin-1 chain Dispersion relation Equal time correlation function Ma et al. PRL (1992)

  14. Bound state meets continuum

  15. Neutrons Create magnons in spin-1 chain NENP=Ni(C2H8N2)2NO2ClO4 Ma et al. PRL (1992)

  16. Approaching Quantum Criticality

  17. Strongly Interacting Dimers in PHCC hw(meV) (C4H12N2)Cu2Cl6(PHCC) Stone et al. PRB (2001)

  18. Magnon decay in two-magnon continuum Stone et al. Nature (2006)

  19. Uniform spin chain: Unbound spinons Exact 2-spinon contribution Cu(C4H4N2)(NO3)2 Stone et al. (2003).

  20. Finite T scaling at the QCP Exact low energy scaling form is known for spin-1/2 chain Here we measure the q-integrated “local” response H. J. Schultz PRB (1986)

  21. Local response of spin-1/2 chain Dender Ph. D. thesis JHU (1997)

  22. Spin-½ chain in uniform field

  23. Spinons in magnetized spin-½ chain (XY case for simplicity)

  24. Uniform Spin ½ chain 0.0 T Stone et al. (2003)

  25. Uniform Spin ½ chain 8.7 T || ^ Stone et al. (2003)

  26. Spin-½ chain in a staggered field

  27. Why staggered field yields bound states Zero field state quasi-long range AFM order Without staggered field distant spinons don’t interact With staggered field solitons separate “good” from “bad” domains, which leads to interactions and bound states

  28. Spin-½ chain with two spins per chain unit Landee et al. (1986) CuCl2.2(dimethylsulfoxide) Xia and Riseborough (1988) ~ Oshikawa and Affleck (1997)

  29. 3 2 ħw (meV) 1 0 0 0.2 0.4 0.6 0.8 1 H=0 T Kenzelmann et al. (2003)

  30. 3 2 ħw (meV) 1 0 0 0.2 0.4 0.6 0.8 1 H=11 T Kenzelmann et al. (2003)

  31. Bound states from 2-spinon continuum Kenzelmann et al. (2003)

  32. Sine-Gordon mapping of spin-1/2 chain Effective staggered + uniform field spin hamiltonian Spin operators are represented through a phase field relative to incommensurate quasi-long-range order with Lagrangian density • This is sine-Gordon model with interaction term proportional to hs • Spectrum consists of • Solitons, anti-solitons • Breather bound states Oshikawa and Affleck (1997)

  33. Bound states from 2-spinon continuum Breathers n=1,2 and possibly 3 Soliton, M Kenzelmann et al. (2003)

  34. Testing sine-Gordon predictions Theory by Essler-Tsvelik (1998) Cu-Benz Dender et al. (1997). Neel order 0 Neel order Kenzelmann et al. (2003)

  35. MFT of fermions in a staggered field Kenzelmann, Batista, et al. (2005)

  36. Mean Field Dispersion Relations

  37. High energy bound states Kenzelmann et al. (2005)

  38. Conclusions • Single mode approximation • Good for spin-1 chain when q>0.3π • A versatile tool for experimentalists & theorists • Decay of bound state in near critical spin-1/2 bi-layer • Spin-1/2 chains: Physical realization of QCP • Uniform field exposes extended critical state • Staggered fields • inherent to multi-atom cells • produce rich spectrum of bound states • Sine-Gordon model describes • Bound state energies • Breather intensities • Field dependent incommensurability • High-E bound states predicted & observed

  39. Some Challenges in Quantum Magnetism • Identify isotropic D>1 critical phase • Isolated critical phase via perturbations • Purify known glassy quantum magnets • “Vortex lattice” in quantum magnet • High field phase of spin-1/2 ladder • Correlations in magnetization plateau • Structure & dynamics of quantum impurities in D>1 • Itinerant quantum magnetism • Frustration+low D+mobile fermions

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