Layered cobaltates : CoO2 planes filled by a variable number of electrons

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Layered cobaltates CoO2 planes filled by a
variable number of electrons
Misfit cobaltates
Na cobaltates
Edge-shared octahedra, 90-degree Co-O-Co bonds
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Layered cobaltates

• Extraordinary narrow (200 meV) qp-bands
• Large thermopower, magn.field sensitive
• Magnetic and charge orderings
• Superconductivity (NaxCoO2 water)

Strongly correlated CoO2 planes
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Co3 (t2g6 S0) Co4 (t2g5 S1/2)
Two relevant valence states
Two regimes accessible
Small x many S1/2 Co4, few S0 Co3
(doped Mott insulator)
(strong corr.)
Large x few S1/2 Co4, many S0 Co3
(doped band insulator)
(weak corr.)
Small x paramagnetic metal, Pauli
susceptibility, FL Large x magn. order,
enhanced thermopower, NFL, QCP
Experiment
opposite trend to what expected !
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FL
NFL
Enhanced th.el. power
QCP?
SC
S1/2
S0
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Co-valence in superconducting NaxCoO2 H2O
as measured
1-x counting
Milne et al. PRL (2004) Water intercalation
addes electrons into CoO2
SC-dome located far away from the
Mott limit
Different result NMR by Alloul et al.
Similar conclusion Takada et al. (2004)
Karppinen et al. (2004)
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Bobroff et al., 2007
Strong correlations develop at large x, near the
band insulator (!) limit
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ARPES in misfits near the band insulator regime
(x0.7)
Brouet et al., 2007
qp-damping
strong scattering at 150 meV
(c)
?
(a) peak-dip-hump structure (b) strongly renorm.
qp-band
Spin-diluted system but correlations as strong as
in doped Mott insulators
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Experiment

• Correlations are enhanced at large x,
• near the spinless band-insulator limit
• SC dome is located at valence compositions
• far away from the Mott limit
• .things are very different from
  cuprates!

Different origin functionality of correlations
no double occupancy principle as in cuprates is
insufficient
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Oxide families

• Ti, V weak JT t2g orbital
  (orbital fluctuation)
• Cr,Mn large spin, DE
  (half metallicity)
• Mn JT eg orb., polarons
  (CMR effect)
• Fe,Ni proxim. to M/I trans.
  (spin-helix order)
• Co spin-state degen.
  (high th.el.power)
• Cu quant.spin, no orbital
  (high-Tc SC)

Correlations universal Functionality
different
valence orbital spin lattice str.
local Hilbert space communication rules

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The origin of strong correlations in layered
cobaltates

• Spin-state quasidegeneracy of Co ions
• Edge-sharing octahedra, 90 d-p-d path

G.Khaliullin J.Chaloupka
Phys.Rev.Lett., 2007 Phys.Rev.B,
2008 Prog.Theor.Phys.Suppl.,2008
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A.
Spin-state quasidegeneracy in cobaltates
Co(2) high-spin 3/2 (Hund
coupling dominates) Co(4) low-spin
1/2 (favored by 10Dq crystal field)
Co(3) S 0, 1, 2 states are energetically
close !
S1 t2g5eg1 S2
t2g4eg2 S0 t2g6
Co3O6 octahedron
?ES
?ES 10Dq - 2JH
is small, fraction of eV only SPIN-STATE
TRANSITIONS driven by temperature, doping (
LaCoO3)
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(t2g and eg sectors separated)
B.
strong mixing between t2g and eg
eg
t2g5eg S1 states are generated by this hopping
Spin-state fluctuations
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Electron transfer matrix depends on MeOMe bond
angle
t2g eg overlap the largest element
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Model
H Ht Ht

t2g--t2g
t2g--eg
accompanied by S1 exciton (present in NaCoO2
but not in LaCoO3)
S1 exciton eg-orbital label
Fermions dressed by spin-state fluctuations
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ARPES spectra
1. Self-consistent Born approximation
Fermion selfenergy
Spin-exciton selfenergy
2. Exact diagonalization (one s1/2 hole on a
hexagon)
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perturbative (SCBA)
exact diagonalization
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Im G(E,k)
at x 0.7 (fermionic density 0.3)
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hump
qp
Exp ARPES in misfits x0.7
theory (x0.7)
Brouet et al. (2007)
With t 100 meV, theory reproduces both qp- and
hump dispersion
consistent with LDA value
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Brouet et al. ARPES in misfits near the band
insulator regime (x0.7)
quasiparticle damping
strong scattering at 150 meV
experiment
S1 virtual state energy
theory suggests
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ET
Scattering on spin-state fluctuations qp
destroyed below ET 150 meV
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Interaction between t2g holes mediated by S1
excitations
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Spin-correlated hopping via the S1 intermediate
states
Step 1 S1 exciton formed
Step 2 Exciton relaxed Process sensitive
to the spin orientation of holes
Effective interaction between fermions
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initial state
intermediate
final state
Exchange by S1 exciton fermionic
pair-hopping
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Interaction between t2g-fermions in terms of
singlet Sij and triplet Tij
dimer-hopping (SC pairing)
nonlocal charge and spin interactions
(spin/ch. order)

Vt2/ET
bond-charge bond-spin
(i) 1/3 factor Singlets move faster and gain
more kinetic energy
(ii) cos-factor Frustration
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Spin susceptibility
Hspin
Sq site-spin Dq bond-spin
RPA
2kF-fluctuations enhanced
bare
t
K
M
G
x0.5
Exp Bragg peak at M
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Interaction between t2g-fermions in terms
of pair hopping
Singlets
Triplets

Vt2/ET
(i) 1/3 factor Singlets move faster and gain
more kinetic energy
(ii) cos-factor Frustration
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Coulomb repulsion VC between t2g holes
suppresses Tc VC /t 0 3 20
0
3
20
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Summary

• Spin-state quasidegeneracy of Co3
• proximity to the Mott physics
• 90 d-p-d bonding in NaCoO2
• S1 states accessible by t2g- eg
  hopping,
• spin-polarons, incoherent ARPES,
• Superconductivity
• pairing mediated by spin-state
  fluctuations

Mott insulator
S1
entangled
band insulator
S0
? a t2g5, s1/2gt ß t2g6, s0gt ?
t2g5eg, s1gt
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t2geg hopping is orbital selective
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Coulomb repulsion between holes
reduces the pair-hopping process Vp(nd)V
spatially separated spin-polarons (trapped by
a random Na-potential) supports magnetic
and charge order, suppresses SC
p(nd)
classical Monte-Carlo
prob. of pair-hopping process
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How good are the conditions for pair-hopping
interaction?
Co3
Co4
1/ß kinetic energy
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LDA suggests band-flattening when water is
present Model predicts singlet s-wave Tc
enhanced
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Tc equation (both the pair-hopping V and
dispersion are renormalized by the Gutzwiller
factor)
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Pair-hopping term in cuprates is small
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G.Kh. Prog.Theor.Phys.Suppl.(2005)
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Cobaltates

• Undoped
• LaCoO3, 3D cubic nonmagnetic
  insulator
• NaCoO2, 2D triangular nonmagnetic insulator

• Doped by holes
• La1-xSrxCoO3 spin-glass
  ferromagnetic metal
• Na1-xCoO2 spin-glass
  ferro-planes metal (x lt 0.25)
• nonmagn.
  metal, supercond. (x gt 0.25)

Similar ionic structure but different hopping
geometry
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Exact diagonalization
Two contibutions central-spin ½ and ring-spins 1
M.Daghofer, P.Horsch, and G.Kh. (PRL 2006)
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Key control factors in oxides

• A. Internal structure of TM ions
  (Ti,Co,Cu)
• -- valence state, spin orbital
  degeneracy
• -- local Hilbert space ?1, ?2, ?3,
  
• B. Lattice symmetry
• -- dictates hopping geometry
• -- communication rules / structure of
  Bloch states