Gap Doped Antiferromagnets: Relief of Frustration Through Stripe Formation

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Plot. Early thoughts regarding La2CuO4: quantum turn liquidReality: La2CuO4 is a decent antiferromagnetHole doping disappoints similar N

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Gap Doped Antiferromagnets: Relief 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 thoughts regarding La 2 CuO 4 : quantum turn fluid Reality: La 2 CuO 4 is a decent antiferromagnet Hole doping baffles comparable Néel arrange Formation of charge stripes diminishes attractive disappointment (and brings down KE) Are stripe connections important to superconducting cuprates?

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Anderson's RVB proposition for La 2 CuO 4 PW Anderson, Science 235 , 1196 (1987) "The oxide superconductors, especially those … base on La 2 CuO 4 , … tend … to happen almost a metal-protector move … . This protecting stage is proposed to be the long-looked for 'resounding valence-bond' state or 'quantum turn fluid' guessed in 1973. This protecting attractive stage is supported by low turn , low dimensionality , and attractive dissatisfaction ." PW Anderson, Mat. Res. Bull. 8 , 153 (1973) "Resounding Valence Bonds: A New Kind of Insulator" Proposal for S=1/2 on a triangular grid

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Local RVB singlets Kivelson, Rokhsar, and Sethna, PRB 35 , 8865 (1987) Existence of a turn hole prompts to Bose buildup of doped gaps Requires dynamic adjustment of superexchange by phonons Reality : Cu-O bonds are solid

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Frustration by AF next-closest neighbor trade turn Peierls arrange Sachdev and Read, Int. J. Mod. Phys. B 5 , 219 (1991)

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Reality: A segregated CuO 2 plane would arrange at T = 0 S( q 2D ) ~ 1/[( q 2D ) 2 +  - 2 ] = turn relationship 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)

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Spin waves in La 2 CuO 4 : No indication of disappointment J = 146 meV J c = 61 meV at T = 10K J' = J'' = 2 meV Coldea et al ., PRL 86 , 5377 (2001)

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Typical Phase Diagram: La 2-x Sr x CuO 4

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Doping murders LRO however not SRO Phase chart for La 2-x Sr x CuO 4 and Y 1-2x Ca 2x Ba 2 Cu 3 O 6 p sh = x Local attractive field at T = 1 K measured by muon turn pivot Niedermayer, Budnick, et al. PRL 80 , 3843 (1998)

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Magnetic weakening Experimental outcomes for La 2 Cu 1-z (Zn,Mg) z O 4 Vajk et al ., Science 295 , 1691 (2002) Destruction of LRO requires 40% weakening!

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Competing Interactions Motion of gap brings down motor vitality yet costs superexchange vitality

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One gap in an antiferromagnet Dispersion measured by point settled photoemision in Sr 2 CuO 2 Cl 2 Wells et al ., PRL 74 , 964 (1995). Data transfer capacity for possessed states is ~ 2J << 4t

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Hole isolation to antiphase space dividers 2D extrapolation 1D show

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Charge and turn stripe arrange

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Early stripe expectations Zaanen and Gunnarson Phys. Rev. B 40 , 7391 (1989) Hubbard show Mean-field arrangement White and Scalapino, PRL 80, 1272 (1998) t-J demonstrate Density grid renormalization amass

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Alternative: Frustrated Phase Separation Analysis of t-J display by Emery and Kivelson: Holes tend to stage partitioned! t-J show needs long-run some portion of Coulomb connection Long-extend Coulomb repugnance disappoints stage division Competing collaborations result in striped and checkerboard stages Löw, Emery, Fabricius, and Kivelson, PRL 72 , 1918 (1994)

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Stripe ORDER seen just in uncommon cases LTT 1/8 issue LTO

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Antiferromagnetic "reverberation" in SC cuprates T-subordinate reverberation saw by Keimer and colleagues in YBa 2 Cu 3 O 6+x bilayer Bi 2 Sr 2 CaCu 2 O 8+  bilayer Tl 2 Ba 2 CuO 6+  single layer (But not in La 2-x Sr x CuO 4 ) YBa 2 Cu 3 O 7 Mook et al ., PRL 70 , 3490 (1993)

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Spin variances in YBCO don't look like turn waves YBa 2 Cu 3 O 6.85 La 1.79 Sr 0.31 NiO 4 Bourges et al., PRL 90 , 147202 (2002) Bourges et al., Science 288 , 1234 (2000)

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Large precious stones of La 1.875 Ba 0.125 CuO 4 examined on MAPS spectrometer at ISIS Diameter = 8 mm Length = 140 mm Mass > 40 g Crystals developed at BNL by Genda Gu

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Constant-vitality cuts through attractive scrambling Stripe-requested La 1.875 Ba 0.125 CuO 4 T = 12 K T c < 6 K

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105 meV La 2-x Ba x CuO 4 x = 1/8 Normal state with Stripe arrange YBa 2 Cu 3 O 6.6 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 appear to be identical! ( E LBCO ~ 1.5 E YBCO ) Implies same instrument at work in both Excitations in LBCO related with stripes Suggests stripe connections display in YBCO "Reverberation pinnacle" is quite recently the most obvious piece of the range Present even in non-superconducting LBCO

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How would we be able to comprehend the stripe excitation range?

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Comparison with stepping stool demonstrate 2-leg, AF turn step J = 100 meV two areas

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Evidence for turn hole

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Better hypothetical models Weakly-coupled stripes Vojta and Ulbricht cond-tangle/0402377 Uhrig, Schmidt, and Grüninger cond-tangle/0402659 included 4-turn cyclic trade Mean-field stripe arrange + vacillations Seibold and Lorenzana cond-tangle/0406589 scattering is more 2D-like

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Universal Spectrum + Spin hole LSCO(?) YBCO(?)

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Conclusions Stripes shape because of contending communications (dissatisfaction) Magnetic excitation range of a stripe-requested cuprate is same as in great superconductors Suggests an all inclusive range Quantum turn crevice of two-leg stepping stools might be imperative for gap blending LBCO comes about: 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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"Reverberation" impacts can be disproportionate Superconducting Normal state LSCO x = 0.16 Christensen et al. cond-tangle/0403439 Effect of attractive field in LSCO x=0.18 PRB 69 , 174507 (2004)

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Expected scrambling designs in equal space

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Single-area YBa 2 Cu 3 O 6.85 E = 35 meV E res = 41 meV Hinkov et al ., Nature 430 , 650 (2004)

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