Hole-Doped Antiferromagnets: Relief of Frustration Through Stripe Formation

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Hole-Doped AntiferromagnetsRelief of
Frustration Through Stripe Formation
John Tranquada

International Workshop on Frustrated Magnetism
September 13 - 17, 2004 Montauk, New York
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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?

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Andersons 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 S1/2 on a triangular
lattice
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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
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Frustration by AF next-nearest-neighbor exchange
spin-Peierls order
Sachdev and Read, Int. J. Mod. Phys. B 5, 219
(1991)
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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) HasenfratzNiedermayer, PL B 268,
231 (1991)
Expt Birgeneau et al., JPCS 56, 1913 (1995)
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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)
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Typical Phase Diagram La2-xSrxCuO4
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Doping kills LRO but not SRO
Phase diagram for La2-xSrxCuO4 and Y1-2xCa2xBa2Cu3
O6 psh x
Local magnetic field at T 1 K measured by muon
spin rotation
Niedermayer, Budnick, et al. PRL 80, 3843 (1998)
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Magnetic dilution
Experimental results for La2Cu1-z(Zn,Mg)zO4 Vajk
et al., Science 295, 1691 (2002)
Destruction of LRO requires 40 dilution!
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Competing Interactions
Motion of hole lowers kinetic energy
but costs superexchange energy
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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 ltlt 4t
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Hole segregation to antiphase domain walls
1D model
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Charge and spin stripe order
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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
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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)
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Stripe ORDER seen only in special cases
LTT
1/8 problem
LTO
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Antiferromagnetic resonance in SC cuprates
YBa2Cu3O7 Mook et al., PRL 70, 3490 (1993)

• T-dependent resonance observed by Keimer and
  coworkers in
• YBa2Cu3O6x bilayer
• Bi2Sr2CaCu2O8? bilayer
• Tl2Ba2CuO6 ? single layer
• (But not in La2-xSrxCuO4)

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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)
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Large crystals of La1.875Ba0.125CuO4 studied on
MAPS
MAPS spectrometer at ISIS
Diameter 8 mm Length 140 mm Mass gt 40 g
Crystals grown at BNL by Genda Gu
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Constant-energy slices through magnetic scattering
Stripe-ordered La1.875Ba0.125CuO4 T 12
K Tc lt 6 K
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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
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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

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How can we understand the stripe excitation
spectrum?
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Comparison with ladder model
2-leg, AF spin ladder J 100 meV two domains
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Evidence for spin gap
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Better theoretical models
Weakly-coupled stripes Vojta and Ulbricht
cond-mat/0402377 Uhrig, Schmidt, and
Grüninger cond-mat/0402659 included
4-spin cyclic exchange
Mean-field stripe order fluctuations Seibold
and Lorenzana cond-mat/0406589 dispersion is
more 2D-like
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Universal Spectrum Spin gap
LSCO(?)
YBCO(?)
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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)
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Collaborators
BNL Hyungje Woo Genda Gu Guangyong Xu
IMR, Tohoku Univ. Masa Fujita Hideto
Goka Kazu Yamada
ISIS Toby Perring
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Resonance effects can be incommensurate
Superconducting Normal state
LSCO x 0.16 Christensen et al. cond-mat/0403439
Effect of magnetic field in LSCO x0.18 PRB 69,
174507 (2004)
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Expected scattering patterns in reciprocal space
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Single-domain YBa2Cu3O6.85
E 35 meV Eres 41 meV
Hinkov et al., Nature 430, 650 (2004)