Systematic Spin Dynamics Measurement of La2Cu1xLixO4 x0'04, 0'06

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Systematic Spin Dynamics Measurement of
La2Cu1-xLixO4 (x0.04, 0.06 0.1) and Comparison
with Quantum Critical Theory

• Wei Bao
• Los Alamos National Laboratory
• Collaborators
• Y. Chen (NIST), J.E. Lorenzo (CNRS-Grenoble),
• J.L. Sarrao (LANL), A. Stunault (ILL), Y. Qiu
  S. Park (NIST)
• Discussions
• S. Sachdev, J.W. Ye, A.V. Chubukov, X.G. Wen, T.
  Senthil, Q.M. Si, F.C. Zhang, C.M. Varma, Z.Y.
  Weng, L. Yu,
• A.V. Balatsky, A. Castro Neto, O.P. Sushkov

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MotivationWhy do we bother with Quantum Critical
Theory

• Magnetic excitations important for high-Tc SC
• Few prediction for S(q,?) from microscopic models
  of underdoped cuprates
• Concrete prediction for S(q,?) by quantum
  critical theory (Sachdev Ye 93, ...)

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Universality treat frustration instead of
dopingto avoid randomness, disorder, etc, from
doping
X-order (ZTPG)
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Universal scaling at long wavelengths (low
energies) near a quantum critical point
frustration

• 2D quantum Heisenberg system maps to 21D
  classical Heisenberg system with ?Thc/kBT
• When kBTltJ, ?Tgta. Quantum effect becomes
  important.
• At T0, ?T8 map to 3D classical system.
  ?0(y-yc)-?
• Length scale sets by ?min?T, ?0
• Energy scale Ehc/? (z1)
  
• kBT for TgtTx G(y-yc)? for TltTx. ?/T to
  ?/G scaling

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Samples La2Cu1-xLixO4

• ?/T scaling obseved for insulating LBaCO LSCO
  at x0.05 (Hayden et al. 91, Keimer et al. 91)
  for superconducting LSCO x0.14 (Aeppli et al.
  97)
• Advantage of nonsuperconducting LCLiO

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La2Cu0.94Li0.06O4 q scans
in-plane
out of plane
Bao et.al., PRL 91, 127005 (2003)
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La2Cu0.94Li0.06O4 energy scans
Bao et.al., PRL 91, 127005 (2003)
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From ?/T scaling to const-E scaling
Bao et.al., PRL 91, 127005 (2003)
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Local magnetic susceptibility in QD regime
gapped no fermion scattering with spins
pseudogapped moderate scattering broadening
gapless strong fermion scattering with spins
Y.L.Liu and Z. B. Su, Phys. Lett. A 200, 393
(1995) Sachdev, Chubukov, Sokol, PRB 51,14874
(1995)
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Measured local susceptibility below 50K
Bao et.al., PRL 91, 127005 (2003)
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Crossover around 50K
Bao et.al., PRL 91, 127005 (2003)
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Not Heisenberg to XY crossover
Anisotropic gap 2.5 meV at x0
Remain to be Heisenberg also seen in YBCO,
using polarized neutron Stock et al.,
cond-mat/0505083
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La2Cu0.90Li0.10O4 energy scans
Chen et.al., cond-mat/0408147
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Different exponent and scaling function for x0.04
Chen et.al., cond-mat/0408147
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Scaling plot for S(E)
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Below Tx at higher E, i.e., shorter length than
?0,?/T scaling restored as expected
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Changing exponent and scaling functioncontrolled
by a AF QCT unlikely

• crossover in all three samples
• the same gapless, instead of gapped, spectrum
  ?(?) in the QD regime. Hole scattering
• But critical exponent and scaling function change
  at x0.04
• One known mechanism from classical critical
  phenomena disorder

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Proposed theories for spin-glass in doped cuprates

• competing AF FM interactions in a 2D plane
• all spins freeze at low T, as in conventional
  concentrated (cluster) spin glass
• formation of ferromagnetic short-ranged clusters

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No ferromagenetic clusters of Mgt1.4mmB
\\(001)
Chen et al. PRB 72,184401 (2005)
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La2Cu0.96Li0.04O4 energy scans
Chen, Bao et.al., cond-mat/0408147
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Quasielastic scattering at (p,k,p)
Chen et al. PRB 72,184401 (2005)
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Looks like a Bragg peak but not static
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Relative spectral weights of 3 parts
3 parts to S(q,E) 2 glassy 1 liquid
1.5K
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Summary

• First observation of crossover from ?/T scaling
  to const-E scaling in hole doped cuprates
• Maybe related to QC to QD crossover
• Gapless spectrum in the QD regime
• Variable T exponent and scaling function with
  doping
• Likely due to disorder, which manifests itself in
  the spin-glass transition
• Quite different from conventional spin-glass
  disordered mainly along the interplane dir.
• Mechanism of spin-glass in spin stacking faults,
  beyond purely 2D models
• Similar scaling crossover in PLCCO (Wilson et
  al. 05) similar glassy central peak in LSCO
  (Sternlieb et al., 90, Bella ?), YBCO (Stock et
  al. 05)

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Phase diagram of (La,Sr)2CuO4 and (Y,Ca)Ba2Cu3O6
µSR, NMR/NQR, M LSCO Harshman et al. (1988),
Sternlieb et al. (1990) Chou et al. (1993)
(1995) YBCO Niedermayer et al. (1998)
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Gapless in QD regime
Chen et.al., cond-mat/0408147
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