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Quantum spin dynamics in 1D antiferromagnets.

Quantum spin dynamics in 1D antiferromagnets. Igor Zaliznyak. Neutron Scattering Group. Outline. Excitation continuum in 1D S=1 Heisenberg antiferromagnet (Haldane chain). Luttinger liquid behavior in the high-field phase of a Haldane chain

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Quantum spin dynamics in 1D antiferromagnets.

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  1. Quantum spin dynamics in 1D antiferromagnets. Igor Zaliznyak Neutron Scattering Group Outline Excitation continuum in 1D S=1 Heisenberg antiferromagnet (Haldane chain). Luttinger liquid behavior in the high-field phase of a Haldane chain Fundamental importance: instability of the coherently propagating excitations in quantum (spin) liquid High-energy spinons in S=1/2 chain copper oxides. Fundamental importance: electronic structure of cuprates, spin-charge separation, log(T) corrections at low T Practical importance: relaxation channel in optoeletronic devices, anisotropic heat transport, …

  2. Collaboration • C. Broholm, D. Reich • S.-H. Lee, R. Erwin • L.-P. Regnault, M. Enderle • M. Sieling BENSC Hahn-Meitner Institute • P. Vorderwisch, M. Meissner • T. Perring, C. Frost • S. V. Petrov • H. Takagi ISSP University of Tokyo

  3. “Heisenberg model systems”: why bother? H = JSSiSi+1+ JS SiSi+D+ DS(Siz)2 , J/J>> 1 (<<1) 1D • What are the “model” assumptions? • spins are on localized electrons • near(est) neighbor exchange • coupling lattice: 1D, 2D, 3D? 2D • good approximation for many systems • simple and general Hamiltonian • great variety of fundamental phenomena Example: CsNiCl3. J = 2.3 meV = 26 K J= 0.03 meV = 0.37 K = 0.014 J D = 0.002 meV = 0.023 K = 0.0009 J 3D magnetic order below TN = 4.84 K

  4. Understanding antiferromagnetic spin chain: history. Spectrum for S=1 is not intermediate case between S=1/2 and S>>1 S >> 1 S = 1/2 S = 1 Single mode, no gap (Anderson, 1952) Continuum, no gap (Bethe, 1931) Gap at q=p (Haldane, 1983) e(q) > p/2Jsin(q) e(q) < pJsin(q/2) e(q) = 2J(S(S+1))1/2sin(q) e2 (q) = D2 + (cq)2 e(q)/J/(S(S+1))1/2

  5. Understanding S=1 chain: theory. Mostly - numerical studies on finite chains. • Quantum Monte-Carlo: • Takahashi (1989), Meshkov (1993), Dietz et. al. (1993), Yamamoto (1995), … • Exact diagonalization: • Golinelli et. al. (1990), Haas et. al. (1995), … • Density matrix renormalization group: • White et.al. (1993), ….

  6. Understanding S=1 chain: theory. Quantum Monte-Carlo results for 128-spin chain indeed indicated existence of a continuum. QMC by S. Meshkov (1993). Since S(q)=>0 at q=0, S(q,w)/S(q) is shown.

  7. Interesting detail: excitations are non-interacting fermions! L.P.Regnault, S. Meshkov and I. Zaliznyak J. Phys. Condens. Matter (Letter),1993 How could we know? Receipt is simple: take the spectrum, calculate free energy, and compare with measured thermodynamic quantities.

  8. Understanding S=1 chain: experiment. NENP: Haldane gap confirmed, no continuum observed.

  9. Cross-over from single-mode to continuum in spectrum of 1D S=1 Heisenberg antiferromagnet observed. I. A. Zaliznyak, S.-H. Lee, S. V. Petrov, PRL 017202 (2001) Color contour map of the spectral density of raw magnetic scattering ~ dynamic spin susceptibility

  10. Instability of coherently propagating mode at the top of the excitation band in Haldane spin chain. Haldane mode becomes a continuum at q <~ 0.5 J = 2.275(5) meV, v = 2.49(4)J

  11. Spectral density measured in two configurations. Resolution is better and more round in the “E-resolved 2-axis mode”. Continuum confirmed, starts at q < 0.6.

  12. Conclusions. Instability of the coherent propagating mode at high energies is a universal feature of quantum liquid close to criticality? • Dispersion of the in-chain excitation is asymmetric, as expected for disordered S=1 HAFM chain. • In the coherent part of the spectrum dispersion parameters agree with those measured in NENP and in Monte Carlo calculations. • Single-mode excitation in a Haldane chain becomes unstable around the top of the dispersion band. • Continuum excitation spectrum, whose width increases with decreasing q, is observed at q < 0.6 . Acknowledgement This work was carried out under Contract DE-AC02-98CH10886, Division of Materials Sciences, US Department of Energy. The work on SPINS was supported by NSF through DMR-9986442

  13. Haldane chain in magnetic field. L.P. Regnault, I. Zaliznyak, J.P. Renard, C. Vettier, PRB 50, 9174 (1994). 3,5,…-particle continuum 3,5,…-particle continuum Macroscopic quantum phase in the string operator at H>Hc results in the shift in q-space between fermions and magnons. H=0 H~Hc ? particles particles holes I. Zaliznyak, unpublished (2002). H>Hc

  14. Haldane chain in magnetic field: H>Hc. I. Zaliznyak, M. Enderle, C. Broholm, et al, to be published (2002).

  15. Haldane chain in magnetic field H>Hc: Luttinger liquid? H=0 H>~Hc H<Hc H>Hc H~Hc I. Zaliznyak, et al (2002).

  16. Chain copper oxides: 1D Mott-Hubbard insulators. Cu-O bond length  1.95 Å, exchange coupling J ~ 0.2-0.3 eV (!) Sr2CuO3 SrCuO2

  17. What is interesting about chain copper oxides? • Electronic band structure and model Hamiltonian for cuprates • Y. Mizuno et al, PRB 58 (1998), W. C. Makrodt, H. J. Gotsis, PRB 62 (2000), H. Rosner et al, PRB 63 (2001)) • Spin-charge separation • C. Kim et al, PRL 77 (1996), PRB 56 (1997) , H. Fujisawa et al, PRB 59 (1999), H. Suzuura and N. Nagaosa, PRB 56 (1997), F. Essler and A. Tsvelik, PRB (2001) • log(T) corrections to low-T magnetic susceptibility • N. Motoyama et al, PRL 76 (1996), K. R. Thurber et al, PRL 87 (2001) • Heat transport by spinons: giant heat conductance along the chains • A. V. Sologubenko et al, PRB 62 (2000), PRB 64 (2001) • Ultrafast relaxation of the optical nonlinear absorption • T. Ogasawara et al, PRL 85 (2000), H. Kishida et al, PRL 87 (2001)

  18. t1 t2 Electronic band structure of chain copper oxides and spin-charge separation. Effective single-band Hubbard model at half-filling HEH= -S tm(cj,+cj+m, + H.c.) + (U/2) S(n jn j- + H.c.) + VS(n jn j+1 + H.c.) - |K|S SjSj+1 Electron spectral function A(k,): holon-spinon continuum Parametri-zation: U, t vc(k-kf) • Band gap 1.5 eV • Exchange J =? vs(k-kf)  Ef kf k/ ARPES measurement, C. Kim et al, PRL (1996) Essler and Tsvelik cond-mat/0108382

  19. How do we know exchange coupling J? “Inelastic neutron scattering experiments are much desired”, Maekawa & Tohyama, Rep. Prog. Phys. (2001), T. Rice, Physica B (1992). • Temperature dependence of the magnetic susceptibility (N. Motoyama et al, PRL (1996)) J = 0.19(2) eV ? • Infrared absorption below the optical band gap (H. Suzuura et al, PRL (1996)) J = 0.26(1) eV • Electron + Xray spectroscopy + band structure calculations (R. Neudert et al, PRL 81 (1998), Rosner et al, PRB 56 (1997)) • U  4.2 eV • V  0.8 eV • t  0.55 eV J = 4t2/(U-V) - |K| ~ 0.25-0.36 eV (!?) J~ 0.5 - 1 meV Record-high J, record-low J/J

  20. Two-spinon continuum in SrCuO2: direct measurement MAPS@ISIS, Ei = 98 meV. Color contour map of the scattering intensity. White lines are gaps in the detectorr array. Vertical lines at l = n/2 are spinons. qchain/2

  21. Two-spinon continuum in SrCuO2: direct measurement MAPS@ISIS, Ei = 241 meV. Color contour map of the scattering intensity. qchain/2

  22. Two-spinon continuum in SrCuO2: direct measurement MAPS@ISIS, Ei = 520 meV. Color contour map of the scattering intensity. qchain/2

  23. Two-spinon continuum in SrCuO2: direct measurement Best fit: J = 280(20) meV, higher than usually believed. Agrees with midinfrared absorption result J = 260(10) meV. qchain/2

  24. Conclusions What did we learn? • Structure of the non-hydrodynamic part of the excitation spectrum in S=1antiferromagnetic Heisenberg chain • cross-over from the coherent propagating Haldane-gap mode to continuum occurs at q<~0.6 • experimental studies are the main source of insight • instability of the coherent spectrum is a general feature of quantum (spin) liquid close to phase transition (small gap)? • Spin excitation spectrum in the Mott-Hubbard insulator SrCuO2 supports evidence for spin-charge separation in -Cu-O- chains • two-spinon continuum directly observed • electron dynamics is dominated by spinons up to ~ 0.8 eV • J = 280(20) meV, not 190 meV => rethink/redo log corrections • large energy scale and fractional nature of excitations results in fascinating physical properties

  25. Understanding S=1 chain: theory. Somewhere q=p single mode should crossover to q=0 continuum. 2-particle continuum at q=>0 arise in simple fermion “toy model”, Gomez-Santos (1989) Hierarchy of excited levels after White and Huse (1993) What about continuum? No quantitative theory, difficult to measure: structure factor ->0 at small q. Not observed in NENP down to 0.3

  26. Model S=1 Haldane chain compound CsNiCl3. H = JSSiSi+1+ JS SiSi+D+ DS(Siz)2 , J/J>> 1 (<<1) J = 26 K, J= 0.033 J, D = 0.0009 J, TN = 4.84 K J J • “supercritical” J => not important for spin dynamics at high energies • the most isotropic of known materials

  27. New measurement: high-luminosity setups with ASD. Area sensitive detector (ASD) gives 4-6 fold increase in throughput without any loss in resolution and with very low background.

  28. SPINS@NG5.NCNR.NIST.GOV Area sensitive detector => 4-6 fold increase in throughput.

  29. Single-mode and continuum spectrum in one-dimensional S=1 Heisenberg antiferromagnet (Haldane chain). NENP (1992): gap+single mode CsNiCl3 (2001): +continuum

  30. Instability of coherently propagating mode at the top of the excitation band in two quantum liquids. Haldane mode becomes a continuum at q <~ 0.5 Top of the band “maxon” excitation in superfluid 4He broadens with pressure Graf, Minkiewicz, Bjerrum Moller, and Passell (1974)

  31. 3D corrections to the 1D excitation spectrum: MF-RPA estimates. Except at low energy, spectrum even at T=0 is 1D • In mean field random phase approximation (MF-RPA) corrections to the 1D • dispersion • static structure factor S(q) • are within ±10% for 0.2 < q < 0.8 , and within ±5% for 0.3 < q < 0.7 

  32. Weak inter-chain coupling of the S=1/2 -Cu-O-Cu- chains: long-range order and correlated spin glass. TN 5 K k h Q=(h,0.5,0.5) Points: magnetic scattering Line: nuclear scattering SrCuO2: decoupling in zigzag ladder results in short-range anisotropic static order Sr2CuO3: static long-range (Bragg) order

  33. Effect of the inter-chain coupling on spin dynamics in SrCuO2. J  280 meV, TN 5 K, <µ> 0.15µB I. Zaliznyak et al, PRL 83, 5370 (1999). • Extremely weak coupling between S=1/2 antiferromagnetic spin chains in Sr2CuO3 and SrCuO2 results in static order but marginal modulation of the inelastic spectrum.

  34. Weak inter-chain coupling of the S=1/2 chains: static order and effect on spin dynamics. A. Zheludev et al, cond-mat/0105223. J  24 meV, TN 9 K, <µ> 0.15µB A C A B B Magnon A C Magnetic Bragg peak

  35. Evidence for spin-charge separation in1D Mott-Hubbard insulator: ARPES in chain copper oxide SrCuO2. C. Kim et al, PRB 56, 15589 (1997).

  36. Spinons in chain copper oxides: picosecond relaxation of optical nonlinearity. T. Ogasawara et al, PRL 85, 2204 (2000). Sr2CuO3

  37. Spinons in chain copper oxides: giant heat conductance. A. V. Sologubenko et al, PRB 64, 054412 (2001).

  38. Future projects • Extend collaboration within BNL • femtosecond pump-probe measurements in SrCuO2 /Chemistry • gate/photodoping in thin films? • Continuum in better-1D Haldane material Y2BaNiO5, check for the effect of inter-chain coupling • High-field phase of the Haldane chain (NENP, in works): marginalization of quantum liquid? • Two-spinon excitation spectrum in Sr2CuO3 • Logarithmic corrections to the susceptibility - by neutrons! • Doping SrCuO2 and Sr2CuO3 away from half-filling • Doping the gapped (Haldane) -O-Ni-O- spin chains in SrNiO2, isostructural with SrCuO2 – new sub-gap physics?

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