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Superconductivity with Tc up to 4.5 K
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3d5
3d6
Crystal field splitting
Low-spin state
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x0.82
Co4
Co3
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Muon Spin Rotation establishes - bulk magnetic
order - commensurate order (guess A-type
AF) -the moment is about 0.3 mB.
Meanwhile confirmed by neutrons S. Bayrakci et
al, PRL 94, 157205 (2005) L.M. Helme et al.,
PRL 94, 157206 (2005).
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Ist not likely to be a spin density wave (SDW)
state ! -Strictly commensurate magnetic
order. - Nearly doping independent transition
temperature -Almost isotropic exchange coupling
despite of large FS anisotropy. µSR S. Bayrakci
et al., Phys. Rev. B 69, 100410 (2004), P.
Mendels et al., Phys. Rev. Lett. 94, 136403
(2005). Neutrons S. Bayrakci et al., Phys. Rev.
Lett. 94, 157205 (2005) L.M. Helme et al., Phys.
Rev. Lett. 94, 157206 (2005)
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Idea of Giniyat Khaliullin Hole doping induced
Co spin-state transition.
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Reduced Symmetry
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May sound like a wear idea but its actually
realized in the isoelectronic compound La1-xSrxCoO
3 New buzz-word Spin-state degree of freedom
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Important differences to La1-xSrxCoO3

• gtAntiferromagnetic clusters with small total spin
  of S1/2.
• gt Strong geometrical frustration!

G. Khaliullin, Prog. Theor. Phys. 160, 155
(2005). M. Daghofer, P. Horsch, and HG.
Khaliullin, cond-mat/0605334.
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Bulk magnetic state _at_ x0.75
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LS, S1/2
_at_ x0.75
IS, S1
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Ellipsometry on Na0.82(2)CoO2
C. Bernhard et al., PRL 93, 167003 (2004).
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8066 cm-1 1 eV
C. Bernhard et al., PRL 93, 167003 (2004).
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x0.97
Co4
Co3
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Muon Spin Rotation (mSR) on Na0.97CoO2
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• µSR data on Na0.97CoO2 establish
• Magnetic volume fraction of ? 40
• with sizeable magnetic moments.
• Glassy freezing transition around Tf?20-50 K
• Evidence for nanoscopic clusters.

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Na-content from EDX and ICPS analysis Consistent
with c-axis parameters from x-ray Q. Huang et
al., Phys. Rev. B 70, 184110 (2004). Chemical
phase separation due to segregation of Na
vacancies? C. de Vaulx et al., Phys. Rev. Lett.
95, 186405 (2005) G. Lang et al., Phys. Rev. B
72, 094404 (2005). We investigated two growth
batches with x0.97 - one is pure a-phase - other
has a minor phase with lower Na content ? Both
give virtually identical µSR results! Chemical
segregation is NOT the primary mechanism!
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Optics shows that the x0.97 sample is on the
verge of percolation ! Consistent with 40
volume fraction from µSR
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Na0.97CoO2
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dc-suszeptibility ? small moment of J?1/2 per
cluster.
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Evolution with hole doping, 1-x.
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Evolution of magnetic signal with hole doping, 1-x
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x0.75
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Na0.78CoO2 TN22 K
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Evidence for geometrical frustration from µSR
data at TgtTN,Tf
Very fast spin fluctuations for bulk magnetic
state at x0.78 (?lt10-9 s at TgtTN) Very slow
spin fluctuations for nanoscopic clusters at
x0.97 (?gt10-9 s up to 250 KgtgtTf20 K)
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• Inconsistent with chemical phase separation
• since fluctuations should be enhanced for finite
  size clusters!
• Evidence for frustrated magnetic interaction in
  ordered state!
• ? SST model gives a Kagome lattice geometry.
• Degeneracy is lifted for isolated clusters.
• - Disorder due to interaction with Na vacancies.
• - Single, double and triple hole clusters.
• - Weak dipolar interaction between clusters.

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Remember this is just a naive model that
neglects all additional complexities of
NaxCoO2! The IS Co3 ions (S1) form a Kagome
lattice with geometrical frustration and thus
strong fluctuations. The amplitude of the
charge modulation may be smaller. Charge order
may not be static.
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This is the end of the talk but not the end of
the story !