What Hartree-Fock tells us about
the magnetic state of
iron based superconductors
E. Bascones
Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC)
In collaboration with:
María José Calderón
Belén Valenzuela
Gladys E. León
The phase diagram
Structural
transition
Metallic
Antiferromagnetism
Zhao et al,
Nat. Mat. 7, 953 (2008),
Doping suppresses AFM &
superconductivity appears
Interested in understanding magnetic phase
Metallic antiferromagnetic state
Zhao et al, Nat. Mat. 7, 953 (2008),
Dong et al, arXiv:1012.5188
Columnar state
(p,0) ordering
Double Stripe
AF state
Focus on (p,0) magnetic state of iron pnictides
How correlated are the electrons? Which is the nature of magnetism?
Weak correlations
(Fermi surface instabilities,
Renormalized Fermi liquid)
Localized electrons
(J1-J2 model)
Antiparallel
orbital moments
Correlations due to
Hund’s coupling
Does orbital ordering
play any role?
Coexistence of localized
and itinerant electrons
Which ones?
Doped Mott insulators
(6 e in 5 orbitals)
Multiorbital character may play an important role
Outline
 A five orbital model for iron based superconductors
 The Hartree-Fock phase diagram
 The metallic (p,0) state:
Doped Mott insulators & orbital differentiation
The origin of orbital ordering and its role on magnetism
Nesting
 Pnictides in the phase diagram.
 Summary and more
Five orbital model
• FeAs layer. 2 Dimensional
• 5 Fe orbitals. 1 Fe unit cell
As not included explicitly, it mediates hopping
• Hopping parameters: Slater-Koster approach
• Possibility to change angle a between Fe-As
bond and Fe plane
xy
yz/zx
3z2-r2
x2-y2
M.J. Calderón, B. Valenzuela, EB,
Phys. Rev. B, 80, 094531 (2009)
600 meV
Five orbital model
• FeAs layer. 2 Dimensional
• 5 Fe orbitals. 1 Fe unit cell
As not included explicitly, it mediates hopping
• Hopping parameters: Slater-Koster approach
• Possibility to change angle a between Fe-As
bond and Fe plane (a= regular tetrahedra)
M.J. Calderón, B. Valenzuela, EB, Phys. Rev. B, 80, 094531 (2009)
Five orbital model
Tight-binding (hopping)
Inter-orbital
repulsion
Pair hopping
Intra-orbital
repulsion
Hund’s
coupling
Crystal-field
Approximate relations
U’=U – 2JH
J’= 2JH
Phase diagram as a function of U, J/U
Mapping to Heisenberg model. Hund’s coupling
Large U
Increasing Hund’s coupling JH
n=6 undoped
Ferromagnetic
(p,0) in x2-y2 configuration
Orbital reorganization
Crystal field sensitivity
(p,p) in 3z2-r2 configuration
M.J. Calderón et al , arXiv: 1107.2279 (2011)
Hartree-Fock phase diagram
(p,p) –(p,0) transition
with increasing
Hund’s coupling JH
Transition very sensitive to crystal
field changes.
It involves charge reorganization
between x2-y2 and 3z2-r2 orbitals.
Localized Physics
EB, M.J. Calderón, B. Valenzuela, PRL, 104, 227201 (2010) M.J. Calderón, G. León , B. Valenzuela, EB, arXiv: 1107.2279
Hartree-Fock phase diagram
What is the nature of this metallic (p,0) state?
The (p,0) state
Gap at the Fermi level
Insulating behavior
NM
LM
Deep in the
insulating region
EB, M.J. Calderón, B. Valenzuela, PRL 104, 227201 (2010)
The (p,0) metallic state
NM
LM
The (p,0) metallic state
LM
The (p,0) metallic state. The Mott gap
The gap opens when
the orbitals are half filled
U=2.5 eV J=0.25 U
Suggests HF evidence of Mott gap
Similar physics found in LDA+U Yin, Lin & Ku, arXiv: 1106.0881
The (p,0) metallic state
METALLIC
DOPED MOTT
INSULATORS
LM
The (p,0) state. Metallic doped Mott insulators
Orbital differentiation
NM
LM
Small gap & metallicity:
zx, 3z2-r2, x2-y2
Large gap (localization): xy, yz
The metallic (p,0) state. Localized & itinerant electrons
Orbital differentiation
NM
zx, 3z2-r2, x2-y2
Itinerant & no gap
LM
xy & yz
localized
The metallic (p,0) state. Localized & itinerant electrons
Decreasing localization
xy
More correlated in DMFT/slave U(1) spins. Localized in previous
minimal models. Close to half-filling in non-interacting bands.
yz
localized in our description
zx
3z2-r2
x2-y2
Less correlated in DMFT/slave U(1) spins. Localized in several
previous minimal models. Larger filling in non-interacting bands.
Itinerant in our description
The metallic (p,0) state. Localized & itinerant electrons
Decreasing localization
xy
More correlated in DMFT/slave U(1) spins. Localized in previous
minimal models. Close to half-filling in non-interacting bands.
yz
zx
3z2-r2
x2-y2
localized in our description
Different degree of localization
(AF state)
Less correlated in DMFT/slave U(1) spins. Localized in previous
minimal models. Larger filling in non-interacting bands.
Itinerant in our description
The metallic (p,0) state. Localized & itinerant electrons
Decreasing localization
xy
yz
zx
3z2-r2
x2-y2
Different degree of localization
(AF state)
Which is the role of
orbital ordering?
Origin of orbital ordering. Exchange in X direction
yz-yz exchange constant larger
in X direction
zx-zx exchange constant larger
In Y direction
EB, M.J. Calderón, B. Valenzuela, PRL 104, 227201 (2010)
Lee, Yin, Ku, PRL 103, 267001 (2009)
Origin of orbital ordering. Exchange in X direction
yz-yz exchange constant larger
in X direction
zx-zx exchange constant larger
In Y direction
xy-yz exchange constant in Y direction
opposes to (p,0) state
xy-zx exchange constant in X direction
would favor (p,0) state.
EB, M.J. Calderón, B. Valenzuela, PRL 104, 227201 (2010)
Lee, Yin, Ku, PRL 103, 267001 (2009)
The origin of orbital ordering. Exchange constants
Assume xy and yz orbitals localized
Exchange constants would
favor a reversal of orbital
ordering for slightly
elongated tetrahedra
Origin of orbital ordering. Kinetic energy in Y direction
Gain of kinetic energy
along FM direction thanks
to hybridization of zx, 3z2-r2
and x2-y2 orbitals
The (p,0) metallic state
METALLIC
DOPED MOTT
INSULATORS
orbital differentiation
NM
LM
ITINERANT +
LOCALIZED
The metallic (p,0) state.
Change in the behavior
of the magnetization
NM
LM
Orbital
differentiation
Itinerant
The metallic (p,0) state.
Transition between itinerant and
orbital differentiacion regimes
NM
LM
Pure itinerant in very small
range of parameters
Summary and more Metallic (p,0) magnetic state at HF level
Doped
Mott
NM
Orbital differentiation
zx, 3z2-r2, x2-y2 itinerant
yz, xy localized
Localized
+itinerant
LM
Gain in kinetic energy between
itinerant zx, 3z2-r2, x2-y2
along FM Y- direction at least
partly responsible for magnetism
and orbital ordering
From comparison between Hartree-Fock & mapping to Heisenberg
 Double stripe ordering as a compromise between FM exchange interactions
and cost in kinetic energy
 Asymmetry with electron-hole doping. (p,p) ordering appears with hole
doping. FM/DS tendencies are enhanced with electron doping.