Transcript Slide 1

Modeling of LaO1-xFxFeAs from the
Strong Coupling Perspective: the
Magnetic Order and Pairing
Channels.
Adriana Moreo
Dept. of Physics and ORNL
University of Tennessee, Knoxville,
TN, USA.
Collaborators: M.Daghofer, J. Riera., E. Arrigoni, D.
Scalapino and E. Dagotto.
Supported by NSF grants DMR-0706020.
F doped LaOFeAs
• Quaternary oxypnictides:
LnOMPn (Ln: La, Pr;
M:Mn, Fe, Co, Ni; Pn: P,
As).
• Fe –As planes.
• La-O planes.
• Fe form a square lattice.
• F replaces O and
introduces e- in Fe.
Experimental Properties
• Tc up to 28K (above
50K replacing La by
other rare earths).
Chen et al., cond-mat:0803.0128
• Bad metal or semiconductor in
undoped regime.
•Anomalous specific heat. Suggest
nodes in SC state.
Dong et al., cond-mat: 0803.3426
•Anomaly in resistivity at 150K.
Parent compound
• Long range
magnetic
order.
• Small order
parameter:
suggests
small or
intermediate
U and J.
De la Cruz et al., cond-mat: 0804.0795. See
also McGuire et al., cond-mat:0804.0796;
Dong et al., cond-mat:0803.3426 and others.
Doped compound
• No magnetic order
(neutrons, NMR,
Mossbauer).
• Nodal Gap (specific
heat,NMR) or large
ungapped regions
(integrated PES).
• Two gaps (NMR).
• Unconventional
mechanism, singlet
pairing (mSR, NMR).
• Hole doping also occurs.
(La1-xSrxOFeAs).
La1-xSrxOFeAs
Wen et al., cond-mat:0803.3021.
Theory
• Band Structure: 3d Fe
orbitals are important.
(LDA)
• dxz and dyz most
important close to eF.
(Korshunov et al., condmat:0804.1793).
• Metallic state.
• Possible itinerant
magnetic order.
Singh et al., cond-mat:
0803.0429; Xu et al., condmat:0803.1282; Giovannetti et
al., cond-mat: 0804.0866.
Fermi Surface
• Two hole pockets at G
point.
• Two electron pockets at
M.
• dxz and dyz orbitals (with
some dxy hybridization).
ARPES
Liu et al.,
cond-mat:
0806.2147
NdFeAsO1-xFx
LDA
Singh et al., cond-mat:
0803.0429
Interactions: strong or weak
electronic correlations?
• X-ray spectra: weak correlation (Kurmaev et al.,
cond.-mat.: 0805.0668).
• DMFT : strong correlation (Haule et al., condmat: 0803.1279).
• RPA: U~3, J=0 (Raghu et al., cond.-mat:
0804.1113).
• RPA and mean field calculations including
Coulomb and Hund interactions are predicting
the expected magnetic order and all possible
variations of the order parameter.
Numerical Simulations
(Daghofer et al., cond-mat:0805.0148).
• Relevant degrees of freedom need to be
identified.
• Construct the minimal model.
• Exact diagonalization in a small cluster.
• Very successful with the cuprates: found
magnetic order and correct pairing symmetry.
Minimum Model
• Consider the Fe-As
planes.
• Two d orbitals dxz and dyz
based on LDA and
experimental results.
• Consider electrons
hopping between Fe ions
through a double
exchange process Fe-AsFe. Square Fe lattice.
• Interactions: Coulomb
and Hund.
a/ 2
/ 2
 /a
2

a
2

a
Hoppings
H k  t1  (d i, x , d i  x , x ,  d i, y , d i  y , y ,  h.c.)
i ,
 t 2  (d i, y , d i  x , y ,  d i, x , d i  y , x ,  h.c.)
i ,
 t3  (d i, x , d i  x  y , x ,  d i, x , d i  x  y , x ,
i ,
 d i, y , d i  x  y , y ,  d i, y , d i  x  y , y ,  h.c.)
 t 4  (d i, x , d i  x  y , y ,  d i, y , d i  x  y , x ,  h.c.)
i ,
 t 4  (d i, x , d i  x  y , y ,  d i, y , d i  x  y , x ,  h.c.)
i ,
Obtain from Slate-Koster overlap integrals between Fe-d and As-p orbitals and
Fe-As-Fe double exchange hopping.
Hoppings
t1  2[(b  a )  g ]  dd
2
2
2
t 2  2[(b 2  a 2 )  g 2 ]  dd
t3  2(a  b  g )
2
2
2
t 4  (ab  g )
2
a  0.324( pd )  0.374( pd )
b  0.324( pd )  0.123( pd )
g  0.263( pd )  0.310( pd )
pd=1
pd=-0.2
dd=-pd
dd=0.1pd
The hoppings are obtained in terms of the lattice parameters and the pd overlap
Integrals.
Interaction
H int
J
 U  ni , , ni , ,  (U ' ) ni , x ni , y
2 i
i ,
 2 J  Si , x .Si , y  J  (d
i
U '  U  2J
i

i , x ,
d

i , x ,
d i , y , d i , y ,  h.c.)
Numerical Results: no doping
• U<1 for metal in
undoped case.
• If J=U/4, U<1 to
reproduce
experimental order
parameter in parent
compound.
• S(k) peaks at (0,)
and (,0).
Electron Doping
Spin singlet
J=U/4
 (k )   (cos k x  cosk y )d k, , d k ,  ,

Spin triplet
 (k )1  (cos k x  cosk y )(d k, x, d k , y ,  d k, y , d k , x, )
Symmetry of the Pairing Operator
#
9
12
IR
Basis
Spin
Orbital
Parity
B2g
(coskx+cosky)
t1
S
E
Nodal
A2g
(coskx+cosky)
it2
T
O
Gapless
According to D4h point group
Gap
See Y. Wan and Q-H Wang, condmat:0805.0923.
Sixteen possible pairing operators.
Gap Symmetry
s
H BCS
  xx

  xy

0

V

 xy
 yy
V
V
  xx
0
  xy
0
V  V0 cos k x  cos k y 
V 

0 
T
H
BCS
  xy 

  yy 
  xx

  xy

0

 V

 xy
 yy
V
V
  xx
0
  xy
0
V  V0 cos k x  cos k y 
V 

0 
  xy 

  yy 
Band Structure
gap
Y
M
singlet
triplet
X
G
node
Fermi Surface
Two Gaps
• Experimental
indications of
two gaps.
• Experiments
indicate “dwave” gap.
Y. Wang et al.,
cond-mat: 0806.1986;
K. Matano et al.,
cond-mat: 0806.0249;
F. Hunte et al.,
cond-mat:0804.0485.
Singlet (from numerical
simulations)
• No gap
on epockets.
• Nodes
on hpockets.
• Two
gaps.
• “d-wave”
Conclusions
• U and J have to be small or intermediate.
• The above does not mean “weak coupling” since
the ground state in the undoped case appears to
be a magnetically highly correlated state.
• In the region of parameter space explored the
favored singlet pairing state has “d-wave”
symmetry.
• Hole FS develop gaps with nodes. No gaps on
electron FS.
• The spin singlet pairing operator that we
obtained does not disagree with any of the
experimental results currently available.
Symmetry breaking for (0,)
U=0.5, J=0.125, pd=-0.2
U=1., J=0.25, pd=-0.5