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Hole-Doped Antiferromagnets: Relief of Frustration Through Stripe Formation

Hole-Doped Antiferromagnets: Relief of Frustration Through Stripe Formation. John Tranquada. International Workshop on Frustrated Magnetism September 13 - 17, 2004 Montauk, New York. Outline. Early ideas about La 2 CuO 4 : quantum spin liquid

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Hole-Doped Antiferromagnets: Relief of Frustration Through Stripe Formation

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  1. Hole-Doped Antiferromagnets:Relief of Frustration Through Stripe Formation John Tranquada International Workshop on Frustrated Magnetism September 13 - 17, 2004 Montauk, New York

  2. Outline • Early ideas about La2CuO4: quantum spin liquid • Reality: La2CuO4 is a good antiferromagnet • Hole doping frustrates commensurate Néel order • Formation of charge stripes reduces magnetic frustration (and lowers KE) • Are stripe correlations relevant to superconducting cuprates?

  3. Anderson’s RVB proposal for La2CuO4 PW Anderson, Science 235, 1196 (1987) “The oxide superconductors, particularly those … base on La2CuO4, … tend … to occur near a metal-insulator transition … . This insulating phase is proposed to be the long-sought ‘resonating-valence-bond’ state or ‘quantum spin liquid’ hypothesized in 1973. This insulating magnetic phase is favored by low spin, low dimensionality, and magnetic frustration.” PW Anderson, Mat. Res. Bull. 8, 153 (1973) “Resonating Valence Bonds: A New Kind of Insulator” Proposal for S=1/2 on a triangular lattice

  4. Local RVB singlets Kivelson, Rokhsar, and Sethna, PRB 35, 8865 (1987) Existence of a spin gap leads to Bose condensation of doped holes Requires dynamic modulation of superexchange by phonons Reality: Cu-O bonds are stiff

  5. Frustration by AF next-nearest-neighbor exchange spin-Peierls order Sachdev and Read, Int. J. Mod. Phys. B 5, 219 (1991)

  6. Reality: An isolated CuO2 plane would order at T = 0 • S(q2D) ~ 1 / [(q2D)2 + -2] • = spin-spin correlation length -1 ~ exp(-J/T) J = 135 meV ~ 1500 K    as T  0 Theory: Chakravarty, Halperin,+Nelson, PRB 39, 2344 (1989) Hasenfratz+Niedermayer, PL B 268, 231 (1991) Expt: Birgeneau et al., JPCS 56, 1913 (1995)

  7. Spin waves in La2CuO4: No sign of frustration J = 146 meV Jc = 61 meV at T = 10K J’ = J’’ = 2 meV Coldea et al., PRL 86, 5377 (2001)

  8. Typical Phase Diagram: La2-xSrxCuO4

  9. Doping kills LRO but not SRO Phase diagram for La2-xSrxCuO4 and Y1-2xCa2xBa2Cu3O6 psh = x Local magnetic field at T = 1 K measured by muon spin rotation Niedermayer, Budnick, et al. PRL 80, 3843 (1998)

  10. Magnetic dilution Experimental results for La2Cu1-z(Zn,Mg)zO4 Vajk et al., Science 295, 1691 (2002) Destruction of LRO requires 40% dilution!

  11. Competing Interactions Motion of hole lowers kinetic energy but costs superexchange energy

  12. One hole in an antiferromagnet Dispersion measured by angle-resolved photoemision in Sr2CuO2Cl2 Wells et al., PRL 74, 964 (1995). Bandwidth for occupied states is ~ 2J << 4t

  13. Hole segregation to antiphase domain walls 2D extrapolation 1D model

  14. Charge and spin stripe order

  15. Early stripe predictions Zaanen and Gunnarson Phys. Rev. B 40, 7391 (1989) Hubbard model Mean-field solution White and Scalapino, PRL 80, 1272 (1998) t-J model Density matrix renormalization group

  16. Alternative: Frustrated Phase Separation Analysis of t-J model by Emery and Kivelson: Holes tend to phase separate! t-J model lacks long-range part of Coulomb interaction Long-range Coulomb repulsion frustrates phase separation Competing interactions result in striped and checkerboard phases Löw, Emery, Fabricius, and Kivelson, PRL 72, 1918 (1994)

  17. Stripe ORDER seen only in special cases LTT 1/8 problem LTO

  18. Antiferromagnetic “resonance” in SC cuprates • T-dependent resonance observed by Keimer and coworkers in • YBa2Cu3O6+x bilayer • Bi2Sr2CaCu2O8+ bilayer • Tl2Ba2CuO6+  single layer (But not in La2-xSrxCuO4) YBa2Cu3O7 Mook et al., PRL 70, 3490 (1993)

  19. Spin fluctuations in YBCO do not look like spin waves YBa2Cu3O6.85 La1.79Sr0.31NiO4 Bourges et al., PRL 90, 147202 (2002) Bourges et al., Science 288, 1234 (2000)

  20. Large crystals of La1.875Ba0.125CuO4 studied on MAPS MAPS spectrometer at ISIS Diameter = 8 mm Length = 140 mm Mass > 40 g Crystals grown at BNL by Genda Gu

  21. Constant-energy slices through magnetic scattering Stripe-ordered La1.875Ba0.125CuO4 T = 12 K Tc < 6 K

  22. 105 meV La2-xBaxCuO4 x = 1/8 Normal state with Stripe order YBa2Cu3O6.6 Superconducting state 66 meV Hayden et al., Nature 429, 531 (2004) 34 meV 24 meV k h

  23. Comparison of LBCO and YBCO • Magnetic excitation spectra look the same! (ELBCO ~ 1.5 EYBCO) • Implies same mechanism at work in both • Excitations in LBCO associated with stripes • Suggests stripe correlations present in YBCO • “Resonance peak” is just the most visible part of the spectrum • Present even in non-superconducting LBCO

  24. How can we understand the stripe excitation spectrum?

  25. Comparison with ladder model 2-leg, AF spin ladder J = 100 meV two domains

  26. Evidence for spin gap

  27. Better theoretical models Weakly-coupled stripes Vojta and Ulbrichtcond-mat/0402377 Uhrig, Schmidt, and Grüningercond-mat/0402659 included 4-spin cyclic exchange Mean-field stripe order + fluctuations Seibold and Lorenzanacond-mat/0406589 dispersion is more 2D-like

  28. Universal Spectrum + Spin gap LSCO(?) YBCO(?)

  29. Conclusions • Stripes form due to competing interactions (frustration) • Magnetic excitation spectrum of a stripe-ordered cuprate is same as in good superconductors • Suggests a universal spectrum • Quantum spin gap of two-leg ladders may be important for hole pairing LBCO results: Nature 429, 534 (2004)

  30. Collaborators BNL Hyungje Woo Genda Gu Guangyong Xu IMR, Tohoku Univ. Masa Fujita Hideto Goka Kazu Yamada ISIS Toby Perring

  31. “Resonance” effects can be incommensurate Superconducting Normal state LSCO x = 0.16 Christensen et al. cond-mat/0403439 Effect of magnetic field in LSCO x=0.18 PRB 69, 174507 (2004)

  32. Expected scattering patterns in reciprocal space

  33. Single-domain YBa2Cu3O6.85 E = 35 meV Eres = 41 meV Hinkov et al., Nature 430, 650 (2004)

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