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Origin of the anomalous Hall Effect in High-Tc
cuprates IR Hall angle, ARPES, and current
vertex corrections from fluctuating magnons
G. S. Jenkins, D.C. Schmadel, and H.D. Drew
University of Maryland, College Park
Collaborators

• Experimental
• A. Zimmers, Paris
• J. Cerne, Buffalo
• L. Shi, Maryland
• R. Greene, Maryland
• L. Rigal, Toulouse
• M. Grayson, WSI

• Theory
• T. D Stanescu, Maryland
• V. Galitski, Maryland
• P. Coleman, Rutgers
• H. Kontani, Nagoya
• A. Millis, Columbia
• V. Yakovenko, Maryland

• Materials
• I. Tsukada, CRIEPI, Tokyo
• Y. Ando, CRIEPI, Tokyo
• G. Gu, Brookhaven
• J. H. Cho, Pusan Un.
• P. Fournier, Sherbrooke

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High Tc Phase Diagram
YBa2Cu3O6x
Rigal PRL (93) 2004
La2-xSrxCuO4
Zimmers PRB (76) 2007
Jenkins, coming soon!
Jenkins, submitted, 2009
Bi2Sr2CaCu2O8x
Jenkins, Draft avail. 2009
Schmadel PRB (75) 2007
Jenkins, PhD Thesis
Pseudogap
Half filling x0
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Overdoped RCCO ARPES dc- RH
Pr2-xCexCuO4
DC Hall Dagan et al., PRL (92) 2004
Lin and Millis PRB (72) 2005
Anomalous T dep. in h-doped cuprates too
Matsui et al, PRB 2007 NCCO
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IR Hall Effect
Jenkins, PhD Thesis (2003) www.irhall.umd.edu
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Experimental Block Diagram
Design and build experiment sensitive to E-field
Polarization modulation --- Unique sensitive
system in FIR!
Polarizer limitations Extinction Coef 10-5
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No magnet
In situ WP calibration
FIR laser Dielectric Input/output coupler Single
freq Gas system
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Ref. Bolo
Rotator Bearings and surfaces timing-type
belt opt encoders programmable PID servo
motor 1/10000 angular freq accuracy
WPs Broadband AR coating 1st order, entire
set
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/-8T, cold finger cts flow probe
Kapton windows
Sensitive slight pressure on table causes
measurable rotations!
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Sample Through-put reflectivity, substrate AR
coating (sxx d) FTIR characterization for FA to
HA conversion Edge effects Graphite Ap.,
spatial filtering Minimize motion Cu plates,
clamp
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FIR Hall angle - Pr2-xCexCuO4
10.5 and 5.25 meV
Divide discussion into overdoped and underdoped
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Overdoped RCCO ARPES dc- RH
Pr2-xCexCuO4
DC Hall Dagan et al., PRL (92) 2004
Lin and Millis PRB (72) 2005
Slow tendency to return to h-like response
Proposed causal mechanism thermal fluctuations
Matsui et al, PRB 2007 NCCO
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FIR Hall angle - overdoped Pr2-xCexCuO4
Jenkins, submitted, 2009 arXiv0901.1701
Opt. Bi-2212 wH agrees with ARPES, essentially
same FS
Suppression of HA as T and freq increase, x
approaches xc
No thermal fluctuations in T? 0 limit
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FIR Hall angle - overdoped Pr2-xCexCuO4
Salient features captured as a function of
temperature, doping, and frequency!
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Kontani model description
Same model reproduces h-doped dc Hall Coef.
H. Kontani, Rep. Prog. Phys. 71, 026501 (2008)
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Underdoped RCCO ARPES dc- RH
Pr2-xCexCuO4
DC Hall Dagan et al., PRL (92) 2004
P. Fournier et al., unpublished
Lin and Millis PRB (72) 2005
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Underdoped NCCO ARPES
Armitage et al, PRL 2002, NCCO
Matsui et al, PRB 2007 NCCO
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FS reconstruction zone diagonal order
?
(?,?)
h- and e-like FS segments
Motoyama et al., Nature 445 (2007), NCCO
Park et al, PRB (75) 2007, 14 SCCO
Lin and Millis PRB (72) 2005
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IR Hall angle Pr2-xCexCuO4
10 meV
and
Low T
ARPES data qualitatively describe the Hall data
Large unreconstructed h-like FS yields mH 2.3
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IR Hall angle Pr2-xCexCuO4
and
Paramagnetic state mH 2.3 from ARPES
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DC Hall Coef. Pr2-xCexCuO4
P. Fournier et al., unpublished
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Conclusion
www.irhall.umd.edu

• We measure a new transport quantity, Re and Im qH
  at finite frequency (low optical excitation
  energies)
• Overdoped PCCO
• Low-temperature finite-frequency strong
  suppression of Hall angle rule out thermal
  fluctuations as root causal mechanism
• Fermi-liquid theory which include CVCs induced by
  AF fluctuations well describe frequency,
  temperature, and doping dependence of IR Hall
  data
• Underdoped PCCO
• IR Hall data is qualitatively consistent with
  pocket topology/ARPES/SDW
• Temperature dependence of Hall mass parameter
  suggests CVCs from AF fluctuations in
  paramagnetic state

H. Kontani, Rep. Prog. Phys. 71, 026501 (2008)
Jenkins et al., 2009, arXiv0901.1701