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 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?
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
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
Frustration by AF next-nearest-neighbor exchange
Sachdev and Read, Int. J. Mod. Phys. B 5, 219 (1991)
spin-Peierls order
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
Theory:
Chakravarty, Halperin,+Nelson,PRB 39, 2344 (1989)
Hasenfratz+Niedermayer,PL B 268, 231 (1991)
Expt: Birgeneau et al., JPCS 56, 1913 (1995)
as T 0
Spin waves in La2CuO4: No sign of frustration
J = 146 meVJc = 61 meV at T = 10KJ’ = J’’ = 2 meV
Coldea et al., PRL 86, 5377 (2001)
Doping kills LRO but not SRO
Phase diagram for La2-xSrxCuO4 andY1-2xCa2xBa2Cu3O6
psh = x
Local magnetic field at T = 1 Kmeasured by muon spin rotation
Niedermayer, Budnick, et al.PRL 80, 3843 (1998)
Magnetic dilution
Destruction of LRO requires 40% dilution!
Experimental resultsfor La2Cu1-z(Zn,Mg)zO4
Vajk et al., Science 295, 1691 (2002)
One hole in an antiferromagnet
Dispersion measured by angle-resolved photoemision in Sr2CuO2Cl2Wells et al., PRL 74, 964 (1995).
Bandwidth for occupied states is ~ 2J << 4t
Early stripe predictions
Zaanen and GunnarsonPhys. Rev. B 40, 7391 (1989)
Hubbard modelMean-field solution
White and Scalapino, PRL 80, 1272 (1998)
t-J modelDensity matrix renormalization group
Alternative: Frustrated Phase Separation
Löw, Emery, Fabricius, andKivelson, PRL 72, 1918 (1994)
Competing interactions result in striped and checkerboard phases
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
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)
Spin fluctuations in YBCO do not look like spin waves
Bourges et al., Science 288, 1234 (2000)
YBa2Cu3O6.85
Bourges et al., PRL 90, 147202 (2002)
La1.79Sr0.31NiO4
Large crystals of La1.875Ba0.125CuO4 studied on MAPS
Diameter = 8 mmLength = 140 mmMass > 40 g
MAPS spectrometer at ISIS
Crystals grown at BNLby Genda Gu
Constant-energy slices through magnetic scattering
Stripe-ordered La1.875Ba0.125CuO4
T = 12 K
Tc < 6 K
24 meV
34 meV
66 meV
105 meV
h
k
La2-xBaxCuO4
x = 1/8
Normal state with Stripe order
YBa2Cu3O6.6
Superconducting state
Hayden et al.,Nature 429, 531 (2004)
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
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
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)
Collaborators
BNL Hyungje Woo Genda Gu Guangyong Xu
IMR, Tohoku Univ. Masa Fujita Hideto Goka Kazu Yamada
ISIS Toby Perring
“Resonance” effects can be incommensurate
LSCO x = 0.16Christensen et al.cond-mat/0403439
SuperconductingNormal state
Effect of magnetic field in LSCO x=0.18PRB 69, 174507 (2004)