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Electronic structure of BaFe2As2 as obtained from DFTASW first-principles calculations.

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Ann. Phys. (Berlin) 522, No. 8, 594 – 600 (2010) / DOI 10.1002/andp.201000070
Electronic structure of BaFe2As2 as obtained from DFT/ASW
first-principles calculations
Udo Schwingenschlögl∗ and Cono Di Paola
KAUST, PSE Division, 23955-6900 Thuwal, Kingdom of Saudi Arabia
Received 27 November 2009, revised 10 March 2010, accepted 14 June 2010 by U. Eckern
Published online 2 July 2010
We use ab-initio calculations based on the augmented spherical wave method within density functional theory to study the magnetic ordering and Fermi surface of BaFe2 As2 , the parent compound of the hole-doped
iron pnictide superconductors (K,Ba)Fe2 As2 , for the tetragonal I4/mmm as well as the orthorhombic
F mmm structure. In comparison to full potential linear augmented plane wave calculations, we obtain
significantly smaller magnetic energies. This finding is remarkable, since the augmented spherical wave
method, in general, is known for a most reliable description of magnetism.
c 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction
Recently a new class of high-temperature superconductors, based on iron-arsenides, has been found [1].
This discovery has generated an intensive interest in establishing the physical properties of these materials
and especially the mechanism of the superconductivity [2, 3]. Similar to the cuprate superconductors, the
properties of a FeAs-based superconductor depend strongly on the doping. This led to the discovery of a
number of new materials, including oxy-arsenides, which reach critical temperatures exceeding 55 K when
they are electron doped [4, 5].
A very prospective family is given by compounds crystallising in the body-centered tetragonal ThCr2 Si2
structure with I4/mmm symmetry. The parent compound of this class of materials is BaFe2 As2 , where
the FeAs layers are stacked such that the As atoms face each other. In addition, the Ba atoms are located in
the resulting eightfold coordinated (square prismatic) sites between them. The magnetic order of BaFe2 As2
is dominated by a spin density wave (SDW), where the magnetic phase transition is probably connected to
a structural transition at similar temperature. This feature is common to nearly the whole family, including
the oxy-arsenides [6, 7]. Despite this similarity, the oxy-arsenide superconductors in general are electron
doped, while BaFe2 As2 -type and KFe2 As2 -type superconductors are hole doped. However, in BaFe2 As2
the superconductivity, apparently, is associated with the suppression of the SDW. Spin fluctuations have
been observed by neutron scattering studies [8, 9] and addressed by first-principles calculations [10]. They
appear to play an important role for the pairing mechanism [11].
In addition, the BaFe2 As2 compound exhibits a SDW anomaly with a structural and magnetic phase
transition at 140 K, accompanied by a symmetry change from the I4/mmm tetragonal to the F mmm
orthorhombic space group [7, 12, 13]. Angle resolved photoemission spectroscopy has been performed
and the results have been compared to first-principles results [14–18]. Density functional theory (DFT)
shows that BaFe2 As2 can be seen as a quasi two-dimensional ionic metal [19], as the bonding between
the Ba and the conductive Fe-As layers is ionic. The conduction therefore becomes strongly anisotropic,
and is restricted to the Fe-As layers [20]. In the whole class of iron-arsenides superconductors, the Fermi
surfaces and electronic states are qualitatively similar according to electronic structure calculations [21–
∗
Corresponding author
E-mail: udo.schwingenschlogl@kaust.edu.sa
c 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Ann. Phys. (Berlin) 522, No. 8 (2010)
595
24]. Small compensating electron and hole Fermi surfaces have been observed, whereas the density of
states (DOS) is quite high. The effect of high pressure on the superconductivity of BaFe2 As2 has been
analysed experimentally in [25–28] and theoretically in [29].
It has been reported for DFT calculations that a structure optimisation for the iron pnictides LaFeAsO,
BaFe2 As2 and LaFePO, results in Fe–As/P bond lengths which are much shorter than the experimental
values [2]. The effect is smaller when spin-polarisation is included, reflecting a strong interrelation between
the magnetism and the crystal structure. However, in this case one obtains a Fe magnetic moment of 1–
2 μB , which is considerably larger than predicted by experiment. For BaFe2 As2 , a variety of DFT studies
have been performed, which either rely on the I4/mmm tetragonal [19, 22, 30] or on the low temperature
orthorhombic unit cell [31–33]. In this context, we analyse the electronic structure using the augmented
spherical wave (ASW) method.
2 Technical details
Our investigation is based on density functional theory within the local density approximation (the VoskoWilk-Nusair scheme). We apply the augmented spherical wave method, which has the advantage that the
band structure results can be interpreted intuitively in terms of atomic orbitals, by the spherical wave basis
set [34, 35]. The approach has been successfully used to describe a broad range of magnetic systems [36–
38]. Our basis set comprises Ba 6s, 6p, 5d, Fe 4s, 4p, 3d, and As 4s, 4p, 4d orbitals. In order to model the
shape of the crystal potential realistically, the basis is complemented by states of additional augmentation
spheres at carefully selected positions. The Brillouin zone sampling is performed by means of the linear
tetrahedron method on a mesh of an increasing number of k-points in order to ensure convergence of the
data with respect to the k-space grid.
3 Results
We turn to the results of our band structure calculations for the high temperature tetragonal phase, which
is shown in Fig. 1 in projections along the y and z-axes. Figure 2 shows the electronic bands, the partial
Fe 3d and As 4p DOSs, as well as the Fermi surface. These results have been obtained for the structural
parameters reported in [7] for a temperature of 175 K. We stress that we have not altered the internal atomic
coordinates, see the extended discussion in [30,39]. The fact that the experimental atomic coordinates of As
Ba
Fe
As
Y
X
Z
X
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Fig. 1 (online colour at: www.ann-phys.org) BaFe2 As2
crystal structure (I4/mmm space group) projection on the
top of the xz-plane (left) and on the top of the xy-plane
(right).
c 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
U. Schwingenschlögl and C. Di Paola: Electronic structure of BaFe2 As2
3
3
2
2
1
1
0
0
(E - EF) (eV)
(E - EF) (eV)
596
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
Z
Γ
X P
6
-6
Γ
N
Z
Γ
X
Γ
Y
6
Fe d
As p
5
5
4
4
DOS (1/eV)
DOS (1/eV)
-1
3
Fe d
As p
3
2
2
1
1
0
L
0
-6
-5
-4
-3
-2
-1
0
(E - EF) (eV)
1
2
3
-6
-5
-4
-3
-2
-1
0
(E - EF) (eV)
1
2
3
Fig. 2 (online colour at: www.ann-phys.org) Calculated electronic structure of spin-degenerate BaFe2 As2 at 175 K
(left column) and 5 K (right column): electronic bands (top) in the first Brillouin zone of the body centered tetragonal and face centered orthorhombic lattice, respectively, partial Fe 3d and As 4p DOSs (center), and Fermi surface
(bottom).
c 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.ann-phys.org
Ann. Phys. (Berlin) 522, No. 8 (2010)
597
are not correctly reproduced by electronic structure calculations points to a strong influence of electronic
correlations on the coupling between the structural, electronic, and magnetic degrees of freedom in iron
pnictides. The calculated electronic band structure on the left hand side of Fig. 2 refers to the body centered
tetragonal Brillouin zone, which is also used for representing the Fermi surface. For the latter, our findings
nicely coincide with previous spin-degenerate calculations. In particular, we obtain the distinct deviations
from a two dimensional electronic structure which are characteristic for iron pnictides and show that a
reduced dimensionality is not an indispensable prerequisite for high-temperature superconductivity. In
fact, the corrugations in the Fermi surface of (K,Ba)Fe2 As2 can explain the nearly isotropic critical field
found for this system [40].
Table 1 Energy gain (per Fe ion) with respect to the non-magnetic ASW solution as well as Fe magnetic
moments. An AF solution could not be obtained for the 5 K structure.
FM
AF
175 K, tetragonal
Energy gain Moment
2.0 meV
0.35 μB
4.2 meV
1.60 μB
5 K, orthorhombic
Energy gain Moment
0.14 meV
0.19 μB
–
–
While the electronic structure resulting from our calculations resembles earlier findings in much detail,
we obtain remarkable differences for the magnetic energies of different spin patterns. We have investigated
both a ferromagnetic coupling (FM pattern) between the Fe spins and the spin density wave type magnetic
order observed experimentally (AF pattern) [7]. In the latter the spins are aligned antiferromagnetically
along one axis of the xy-plane and ferromagnetically along the other. The magnetic energies (per Fe atom)
determined for the two patterns with respect to the non-magnetic ASW solution are summarised in Table
1, together with the calculated magnetic moments. Whereas these data nicely reproduce the spin-polarised
linear augmented plane wave (LAPW) results of Singh [30] (energy gain of 1 meV per Fe; 0.3 μB ) of
a weak instability against the FM pattern, we find also the instability against the AF pattern to be weak,
which strongly contradicts the LAPW result (energy gain of 92 meV per Fe; 1.75 μB ). In contrast to
such a robust magnetic state, our calculations thus are utterly in line with a suppression of the magnetic
ordering by fluctuations at a quantum critical point [39]. Experimentally, the compound quickly becomes
paramagnetic under doping.
The situation basically does not change when we turn to the low temperature orthorhombic phase of
BaFe2 As2 . Corresponding electronic structure results are shown on the right hand side of Fig. 2. Both the
partial DOSs and the Fermi surface display (at most) minor modifications. The only remarkable difference
is the tightened waist of the cylindrical surface sheets (center of the Brillouin zone) induced by the distortions. However, according to Table 1, the stability of the FM pattern is reduced to only 0.14 meV per
Fe atom, which is very close to the paramagnet. For the AF pattern, we even could not attain a magnetic
solution but always ended up with the paramagnetic one. However, this fact is not surprising since the
calculated AF energy gain for the tetragonal phase amounts to only 4.2 meV and it is known that in DFT
calculations (in contrast to experimental results) the tetragonal-to-orthorhombic transition counteracts the
magnetism.
While we therefore cannot compare the changes of the electronic states in the AF phase, it still is helpful
to discuss the FM phase. To this aim, we show in Fig. 3 the results of our spin-polarized calculations with
presumed ferromagnetic coupling between all Fe ions for the high and low temperature crystal structure,
respectively. The DOS data are given separately for the spin majority and minority contributions. Comparison to Fig. 2 discloses that both spin manifolds originate from the spin-degenerate bands by rigid band
shifts. The spin splitting is reduced for the F mmm case, which also is reflected by a reduction of the
magnetic moment from 0.35 μB to 0.19 μB . A similar reduction for the AF pattern would lead to a value
very close to the experimental moment of 0.87 μB [7]. Figure 3 in addition shows spin majority (center)
www.ann-phys.org
c 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
598
U. Schwingenschlögl and C. Di Paola: Electronic structure of BaFe2 As2
3
Fe d
As p
2
2
1
1
DOS (1/eV)
DOS (1/eV)
3
0
0
-1
-1
-2
-2
-3
Fe d
As p
-3
-6
-5
-4
-3
-2
-1
0
(E - EF) (eV)
1
2
3
-6
-5
-4
-3
-2
-1
0
(E - EF) (eV)
1
2
3
Fig. 3 (online colour at: www.ann-phys.org) Calculated electronic structure of spin-polarised BaFe2 As2 at 175 K
(left column) and 5 K (right column): partial spin majority and spin minority Fe 3d and As 4p DOSs (top) as well as
corresponding Fermi surfaces (center: majority, bottom: minority).
c 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.ann-phys.org
Ann. Phys. (Berlin) 522, No. 8 (2010)
599
and minority (bottom) Fermi surfaces which display distinct differences, even though the alteration of the
DOS from the I4/mmm to the F mmm case is rather small.
4 Conclusion
In conclusion, we have applied DFT band structure calculations to the iron pnictide BaFe2 As2 , using the
all-electron ASW method. Remarkably, we obtain magnetic energies below 5 meV per Fe site, which is
significantly less than found in previous theoretical investigations of BaFe2 As2 , LaFeAsO, and LaFePO,
using full potential LAPW calculations. While the ASW approach usually leads to very accurate magnetic
energies, it appears to fail for the present compound. Therefore, it is interesting to analyze which origin the
discrepancies between the LAPW and ASW results may have.
Firstly, the convergence of the calculations with respect to the basis set in use may be incomplete. In
contrast to the LAPW approach, the ASW scheme requires inclusion of so-called empty spheres to correctly
describe the crystal potential within the voids between the nuclei. We have tested various choices of basis
sets and likewise have varied the maximal overlap allowed for the atomic spheres. We find no dependence
of our results on this choice, if the overlap is limited to 15% of the sphere radius. We therefore conclude
that our calculations are well converged with respect to the basis set. Beyond, the final energy convergence
of our self-consistency cycle in each case is at least one order of magnitude smaller than the lowest energy
value discussed above. Secondly, there may be an influence of the approximation used for the exchangecorrelation functional. However, this possibility can be excluded, since we compare only energies obtained
by the local density approximation. In addition, all energies under consideration have been obtained by all
electron calculations.
For these reasons, it seems that the full potential scheme implemented in the LAPW approach is essential
for the calculated magnetic energies of BaFe2 As2 , even though this is usually not the case. However, it is
well established that the iron pnictides are characterized by a close interplay between the crystal structure,
the electronic structure, and the magnetism. This fact is connected to the spatial anisotropy of the electronic
states involved in the magnetic coupling. One may speculate that the spherical approximation of the atomic
potential in the ASW approach in this situation affects the magnetic energies.
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