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)

Typical Phase Diagram: La2-xSrxCuO4

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)

Competing Interactions

Motion of hole lowers kinetic energy

but costs superexchange energy

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

Hole segregation to antiphase domain walls

1D model

2Dextrapolation

Charge and spin stripe order

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

Stripe ORDER seen only in special cases

1/8 problem LTT

LTO

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

How can we understand the stripe excitation spectrum?

Comparison with ladder model

2-leg, AFspin ladder

J = 100 meV

two domains

Evidence for spin gap

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

Universal Spectrum + Spin gap

LSCO(?)

YBCO(?)

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)

Expected scattering patterns in reciprocal space

Single-domain YBa2Cu3O6.85

Hinkov et al., Nature 430, 650 (2004)

E = 35 meV

Eres = 41 meV