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Quantum Magnetism with Time-of-Flight Neutron Scattering

Quantum Magnetism with Time-of-Flight Neutron Scattering. Collin Broholm Johns Hopkins University NIST Center for Neutron Research. Conventional Spin Ordered Magnetism. Ferromagnetic EuO. Antiferromagnetic KNiF 3. Extreme case of decoupled spin pairs. 2 ×(2S+1).

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Quantum Magnetism with Time-of-Flight Neutron Scattering

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  1. Quantum Magnetism with Time-of-Flight Neutron Scattering Collin Broholm Johns Hopkins University NIST Center for Neutron Research

  2. Conventional Spin Ordered Magnetism Ferromagnetic EuO Antiferromagnetic KNiF3 CINS meeting on Canadian Participation at the SNS

  3. Extreme case of decoupled spin pairs 2×(2S+1) CINS meeting on Canadian Participation at the SNS

  4. Conceptual Phase Diagram for Quantum Magnets Chakravarty, Halperin, Nelson Sachdev T/J Quantum Critical 1/S, frustration, 1/z, H, P, x, … CINS meeting on Canadian Participation at the SNS

  5. A brief story of Antiferromangetism 1970 Nobel Prize in Physics to Hannes Alfvén and Louis Néel From Nobel lecture L. Néel 1904-2000 CINS meeting on Canadian Participation at the SNS

  6. Staggered magnetization or QM singlet 1962 Nobel Prize in Physics L. D. Landau 1908-1968 CINS meeting on Canadian Participation at the SNS L. D. Landau from Phys. Zs. UdSSR (1933).

  7. Conceptual Phase Diagram for Quantum Magnets T/J Quantum Critical 1/S, frustration, 1/z, H, P, x, … CINS meeting on Canadian Participation at the SNS

  8. Outline of talk • Introduction • Quantum magnetism • Neutron scattering (TOF and TAS) • Making waves • Waves in spin ordered system • Waves in quantum ordered system • Excitations at a quantum critical point • Spinon domain walls of spin-1/2 chain • Thermal anomalies at quantum critical point • High field anomalies at quantum critical point • Outlook and conclusions • Challenges for the future • Conclusions CINS meeting on Canadian Participation at the SNS

  9. Inelastic Magnetic Neutron Scattering • We can measure dispersion relations • We determine structure through transition rate CINS meeting on Canadian Participation at the SNS

  10. ki kf Q SPINS cold neutron spectrometer at NCNR CINS meeting on Canadian Participation at the SNS

  11. Disc Chopper TOF spectrometer From NCNR/DCS web site CINS meeting on Canadian Participation at the SNS

  12. MAPS Spectrometer at ISIS in UK CINS meeting on Canadian Participation at the SNS

  13. IRIS cold neutron TOF backscattering CINS meeting on Canadian Participation at the SNS

  14. Waves in spin ordered system T/J H, P, x…

  15. From A. Zheludev’s web page Spin wave eigenstates in ordered magnet La2CuO4 Coldea et al. PRL (2001) CINS meeting on Canadian Participation at the SNS

  16. Waves in quantum ordered system T/J H, P, x…

  17. Inter-atomic singlet in dimerized spin-1/2 chain Cu(NO3)2.2.5D2O : dimerized spin-1/2 system D CINS meeting on Canadian Participation at the SNS

  18. “Triplons” in dimerized copper nitrate CINS meeting on Canadian Participation at the SNS Xu et al PRL (2000)

  19. Qualitative description of triplons J • A spin-1/2 pair with AFM exchange has a singlet - triplet gap: • Inter-dimer coupling allows coherent triplet propagation andproduces well defined dispersion relation CINS meeting on Canadian Participation at the SNS

  20. 0.5 0.4 0 0.2 0.4 0.6 q (p) Single mode approximation CINS meeting on Canadian Participation at the SNS

  21. Qualitative description of triplons J • A spin-1/2 pair with AFM exchange has a singlet - triplet gap: • Inter-dimer coupling allows coherent triplet propagation andproduces well defined dispersion relation • Triplets can also be produced in pairs with total Stot=1 CINS meeting on Canadian Participation at the SNS

  22. Creating two triplets with one neutron Two magnon One magnon CINS meeting on Canadian Participation at the SNS Tennant et al (2003)

  23. Excitations at a quantum critical point T/J H, P, x…

  24. Quantum critical uniform spin chain 2 3 4 5 1 0 CINS meeting on Canadian Participation at the SNS Damle and Huse PRL (2002)

  25. Two Particle Continuum at QCP SrCuO2 O Cu CINS meeting on Canadian Participation at the SNS Zaliznyak et al (2004)

  26. Disintegration of a spin flip Spinon Spinon CINS meeting on Canadian Participation at the SNS

  27. From band-structure to bounded continuum J w e/J h q (p) Q (p) CINS meeting on Canadian Participation at the SNS

  28. Neutron Scattering Stone et al. (2003). Exact two-spinon cross-section Karbach et al. 2000

  29. Finite T scaling at the QCP Exact low energy scaling form is known for spin-1/2 chain From it follow expressions for the critical q=p response And for the q-integrated “local” response H. J. Schultz PRB (1986) CINS meeting on Canadian Participation at the SNS

  30. Raw data from Copper Benzoate ħw=0.5meV T=1.5 K Dender Ph. D. thesis JHU (1997) CINS meeting on Canadian Participation at the SNS

  31. Critical q=p response of spin-1/2 chain Dender Ph. D. thesis JHU (1997) CINS meeting on Canadian Participation at the SNS

  32. Local response of spin-1/2 chain Dender Ph. D. thesis JHU (1997) CINS meeting on Canadian Participation at the SNS

  33. Spinons in magnetized spin- ½ chain Broholm et al. (2002) CINS meeting on Canadian Participation at the SNS

  34. Uniform Spin ½ chain 0.0 T CINS meeting on Canadian Participation at the SNS Stone et al. (2003)

  35. Uniform Spin ½ chain 8.7 T || ^ CINS meeting on Canadian Participation at the SNS Stone et al. (2003)

  36. Staggering to tie the knot 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 CINS meeting on Canadian Participation at the SNS

  37. Spin-½ chain with two spins per chain unit Landee et al. (1986) CuCl2.2(dimethylsulfoxide) Oshikawa and Affleck (1997) The staggered field is given by CINS meeting on Canadian Participation at the SNS

  38. 3 2 ħw (meV) 1 0 0 0.2 0.4 0.6 0.8 1 H=0 T Kenzelmann et al. (2003)

  39. 3 2 ħw (meV) 1 0 0 0.2 0.4 0.6 0.8 1 H=11 T Kenzelmann et al. (2003)

  40. Bound states from 2-spinon continuum Kenzelmann et al. (2003) CINS meeting on Canadian Participation at the SNS

  41. Sine-Gordon mapping of spin-1/2 chain Effective staggered + uniform field spin hamiltonian Spin operators are represented by a phase field within incommensurate quasi-order with Lagrangian density • This is sine-Gordon model with interaction term proportional • to hs. Thespectrum consists of : • Solitons, anti-solitons • Breather bound states CINS meeting on Canadian Participation at the SNS Oshikawa and Affleck (1997)

  42. Bound states from 2-spinon continuum Kenzelmann et al. (2003) Breathers n=1,2 and possibly 3 Soliton, M CINS meeting on Canadian Participation at the SNS

  43. Theory by Essler-Tsvelik (1998) Neel order Testing sine-Gordon predictions Neel order 0 CINS meeting on Canadian Participation at the SNS Kenzelmann et al. (2003)

  44. A complex quantum ordered system T/J H, P, x…

  45. Putative Spin ladder model for CuHpCl What kind of singlet in CuHpCl? • Negative QCW indicates AFM interactions • No phase transition and • Spin ladder model consistent withc(T) CINS meeting on Canadian Participation at the SNS

  46. ….and there are two modes when ladder gives only one Acid test for one-dimensionality ^ Q // to chain Q tochain CINS meeting on Canadian Participation at the SNS

  47. Measuring bond energies c* (001) (101) a* (100) CINS meeting on Canadian Participation at the SNS Point size First moment

  48. Frustrated three dimensional spin liquid CINS meeting on Canadian Participation at the SNS

  49. Experiments now beyond our reach • Fully map bound state dispersion to establish spin hamiltonian • Understand the role of frustration for stabilizing quantum ordered phase • Establish the nature of continuum excitations in a complex spin liquid • Probe the quantum critical properties at high pressure or fields • Probe excitations through magnetization plateau in quantum magnet • Probe spin correlations following pulsed perturbations • Couple quantum magnet to conduction electrons and probe the critical state CINS meeting on Canadian Participation at the SNS

  50. The Spallation Neutron Source CINS meeting on Canadian Participation at the SNS

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