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Charge transfer effects on the Fermi surface of Ba0.5K0.5Fe2As2

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Ann. Phys. (Berlin) 523, No. 3, 259 – 264 (2011) / DOI 10.1002/andp.201000113
Charge transfer effects on the Fermi surface of Ba0.5K0.5Fe2 As2
S. Nazir∗ , Z. Y. Zhu∗∗ , and U. Schwingenschlögl∗∗∗
KAUST, PSE Division, Thuwal 23955-6900, Kingdom of Saudi Arabia
Received 5 September 2010, revised 26 December 2010, accepted 7 January 2011 by U. Eckern
Published online 31 January 2011
Key words Pnictide, density functional theory, charge transfer, hybridization.
Ab-initio calculations within density functional theory are performed to obtain a more systematic understanding of the electronic structure of iron pnictides. As a prototypical compound we study Ba0.5 K0.5 Fe2 As2
and analyze the changes of its electronic structure when the interaction between the Fe2 As2 layers and their
surrounding is modified. We find strong effects on the density of states near the Fermi energy as well as
the Fermi surface. The role of the electron donor atoms in iron pnictides thus cannot be understood in a
rigid band picture. Instead, the bonding within the Fe2 As2 layers reacts to a modified charge transfer from
the donor atoms by adapting the intra-layer Fe-As hybridization and charge transfer in order to maintain an
As3− valence state.
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction
The recent discovery of new superconductors such as LaO1−x Fx FeAs (transition temperature TC ∼ 26 K)
[1,2], CeO1−x Fx FeAs (TC = 41–55 K) [3], SmO1−x Fx FeAs [4], LaO1−x Fx FeAs [5], or NdO1−x Fx FeAs
[6] has opened a new field in superconductivity research. Yet, the search for new high-TC superconductors
is still a very prospective task. Structural analysis of the iron pnictides reveals that both superconductivity
and magnetism are related to the Fe2 As2 layers, in which the Fe ions are arranged in a square lattice and
the As ions occupy apical positions.
The bonding and hybridization in the Fe basal plane are strong and it has been shown that the physical
properties heavily depend on the exact position of the As ion with respect to the Fe square lattice [7, 8].
Such a strong interdependence between structural details and the electronic structure is characteristic of
transition metal systems due to the localized d states [9,10]. In the case of the iron pnictides the As position
particularly influences the magnetic coupling between the Fe atoms. For AFe2 As2 with A = Ca, Sr, Ba,
Eu [11–16] the interaction along the crystallographic c-axis is found to be one order of magnitude weaker
than the corresponding intra-planar interaction [17]. In contrast, in RO1−x Fx FeAs, where R represents a
rare-earth ion, the inter-planar interactions are much weaker [1–6].
In both AFe2 As2 and RO1−x Fx FeAs the Fe2 As2 layers are stacked along the crystallographic c-axis and
separated by electron donor layers which consist either of an electropositive element A or of a rare-earth
oxide. It is interesting to note that O defects in the R-O sublattice of RO1−x Fx FeAs and hole doping in the
A sublattice of AFe2 As2 have similar effects on the crystal chemistry as well as the physical properties. To
preserve the chemical valence neutrality the Fe valence is modified, which may enhance TC in both classes
of materials. While a TC of 55 K can be attained in disordered RO1−x Fx FeAs [19–22], the maximum TC
found in hole doped AFe2 As2 is 38 K [23]. In general, the appearance of superconductivity seems to be
triggered by the electronic structure of the Fe2 As2 layers, whereas the other ions are charge reservoirs. The
∗
∗∗
∗∗∗
E-mail: safdar.nazir@kaust.edu.sa
E-mail: zhiyong.zhu@kaust.edu.sa
Corresponding author E-mail: udo.schwingenschlogl@kaust.edu.sa
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
260
S. Nazir et al.: Charge transfer effects on the Fermi surface of Ba0.5 K0.5 Fe2 As2
special geometry of the Fermi surface (FS) is commonly assumed to be essential for understanding the superconducting state [23, 24], but the mechanism is not finally resolved. Only few theoretical investigations
have been reported for the doped Ba1−x Kx Fe2 As2 compounds [25, 26].
In the following, we apply the density functional theory to prototypical Ba0.5 K0.5 Fe2 As2 . We aim at
clarifying the dependence of the electronic states on the interaction between the Fe2 As2 layers and their
surrounding. Thus, we elongate artificially the distance between the Fe2 As2 layers along the c-axis, while
keeping the intra-layer Fe-As bond lengths and angles constant. We study the density of states (DOS) as
well as the FS as function of the interaction in order to establish a comprehensive picture.
2 Methodolody
The calculations are performed using the full-potential linearized augmented plane-wave plus local orbitals
(FP-LAPW+lo) scheme implemented in the WIEN2k package [27]. As compared to other schemes, this
method seems to provide a reliable description of BaFe2 As2 compounds [15]. The exchange-correlation
potential is treated in the local density approximation [28]. For the core states the relativistic effects are
taken into account, while the scalar relativistic approximation is used for the valance states. A mesh of
108 k-points within the irreducible wedge of the Brillouin zone is sampled in the DOS calculations. For
the Fermi surface calculations a dense mesh of 5600 k-points is used. Furthermore, in the wave function
expansion inside the atomic spheres the maximum value of the angular momentum amounts to lmax = 12
and a plane-wave cutoff of RMT Kmax = 7.0 with Gmax = 24 is applied. Our valence states consists of Ba
6s, K 4s, Fe 3d/4s, and As 4s/4p orbitals. The radii of the muffin-tin spheres (in atomic units) are chosen
to be 2.5 for both Ba and K, 2.38 for Fe, and 2.11 for As. The unit cell of Ba0.5 K0.5 Fe2 As2 is obtained
from a 1 × 1 × 2 supercell of tetragonal BaFe2 As2 . This supercell approach does not capture the statistical
distribution of the Ba/K ions in the real compound. However, a drawback of this fact on the following
conclusions is not to be expected, because the Ba/K ions mainly act as charge donors, whereas the Fermi
surface is due to the Fe2 As2 layers.
In general, hole doping has a strong effect on the crystal structure of BaFe2 As2 . It affects both the Fe-Fe
bond lengths and the As-Fe-As bond angles within the Fe2 As2 layers. Because hole doping reduces the
electron count, antibonding bands at the Fermi energy (EF ) are depopulated, which strengthens the Fe-Fe
bonding [29]. The compound Ba0.5 K0.5 Fe2 As2 crystallizes in a tetragonal ThCr2 Si2 -type structure with
space group I4/mmm. In our calculations we use the experimental lattice constants a = 3.9090 Å and
Fig. 1 (online colour at: www.ann-phys.org) Schematic representation of
the crystal structure of Ba0.5 K0.5 Fe2 As2 for (a) d = 0 Å and (b) d = 1.5 Å,
see the text for details.
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.ann-phys.org
Ann. Phys. (Berlin) 523, No. 3 (2011)
261
c = 13.2122 Å with the positional parameter zAs = 0.3538 [23]. The Ba and K atoms occupy 2a Wyckoff
positions, while the Fe and As atoms occupy 4d and 4e positions, respectively. We distort the bulk crystal
structure by inserting empty space above and below the Fe2 As2 layers, i.e., between these layers and the
Ba/K ions. Importantly, we maintain the individual layers in their original form. The ideal and a distorted
structure are shown in Fig. 1, where d denotes the thickness of the inserted empty space layers. In addition,
we address for comparison an isolated Fe2 As2 layer which we model by removing all other atoms from
the I4/mmm unit cell.
3 Results and discussion
In Fig. 2 we show the partial DOS of Ba0.5 K0.5 Fe2 As2 in comparison to an isolated Fe2 As2 layer with
identical intra-layer bond lengths and bond angles. According to Fig. 2(a), we find significant contributions
of the As 4p states only in the energy range from approximately −4.8 to −1.9 eV, showing a distinct
hybridization with the Fe 3d states. Above −1.9 eV there are almost only Fe 3d states. As compared to
the parent compound BaFe2 As2 , the DOS at EF increases by K (i.e. hole) doping, which has already been
reported in Ref. [25]. The increase is a consequence of a shift of EF , as expected for hole-doped materials,
and points to an enhanced instability against magnetism. On the contrary, an almost constant DOS at EF
has been found by Singh [7].
Fig. 2 (online colour at: www.ann-phys.org) Partial DOS of (a) Ba0.5 K0.5 Fe2 As2 and (b) an isolated Fe2 As2 layer.
In order to address the interaction between the Fe2 As2 layers and the adjacent Ba and K ions we
present in Fig. 2(b) the DOS calculated for an isolated Fe2 As2 layer. We find distinct differences to
Ba0.5 K0.5 Fe2 As2 , compare Fig. 2(a). We obtain a shift of spectral weight to higher energies with respect
to EF , which increases the DOS at EF . As a consequence, the system is more likely to develop magnetic
ordering. In turn, a first important function of the electron donor Ba and K ions for the superconductivity
in AFe2 As2 compounds thus is to provide a charge state which reduces the magnetic instability. Moreover,
the Fe and As states are stronger localized in an isolated Fe2 As2 layer, which is reflected by a shift of the
www.ann-phys.org
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
262
S. Nazir et al.: Charge transfer effects on the Fermi surface of Ba0.5 K0.5 Fe2 As2
lower band edge to higher energies, i.e. a reduction of the total band width, and by a sharpening of the
DOS peaks. The bonding between the Fe and the As atoms therefore is significantly modified.
1+
2.25+
The formal valence state Ba2+
As3−
0.5 K0.5 Fe2
2 arises from considering As to be fixed in a 3− state
and Ba/K to be fully ionized. Therefore, 2.25 valence electrons have to be provided by each Fe atom. It
is generally assumed that Fe donates its two 4s electrons to the As 4p orbitals, such that the Fe 3d states
give rise to the bands at EF and therefore play the main role for the emergence of superconductivity.
The As3− state is reached by a transfer of one electron from the Ba/K donor atoms. Since for an isolated
Fe2 As2 layer this charge transfer is prohibited, As has to adopt an additional electron from Fe, resulting in
3+
a formal As3−
2 Fe2 configuration. However, by the enhanced charge transfer we may expect that the FeAs hybridization becomes stronger, which is confirmed by our DOS. In turn, our results establish that the
second important function of the electron donor A ion in AFe2 As2 , besides providing charge carriers, is to
adjust the bonding within the Fe2 As2 layers. In fact, even a small modification of this intra-layer bonding
should be relevant for the occurrence of superconductivity in AFe2 As2 .
We next discuss the FS. Note that due to the occupation of the A site by both Ba and K ions the Brillouin
zone of Ba0.5 K0.5 Fe2 As2 is tetragonal, which is also the case for the supercell of an isolated Fe2 As2 layer.
In Fig. 3 we observe for the FS of Ba0.5 K0.5 Fe2 As2 the characteristic circular hole pockets at the Brillouin
zone center as well as the electron pockets at the zone corners [30, 31]. According to Figs. 3(a,b) the hole
pockets are larger and the electron pockets smaller than in the parent compound BaFe2 As2 . This fact is
associated to the disappearance of magnetic ordering [7, 24]. Reflecting the mentioned alterations in the
DOS of an isolated Fe2 As2 layer, the FS is likewise affected, compare Figs. 3(c,d). Not only the size of
the FS sheets changes (as the filling of the bands is reduced) but also the shape of the sheets is subject
to considerable modifications and additional sheets appear. The latter cannot be explained by a rigid band
shift but confirms that the Fe-As bonding is altered qualitatively.
Fig. 3 (online colour at: www.ann-phys.org) FS in
the (a) kz = 0 and (b) kz = 0.5 planes of
Ba0.5 K0.5 Fe2 As2 and the (c) kz = 0 and (d) kz = 0.5
planes of an isolated Fe2 As2 layer.
Since the FS of Ba0.5 K0.5 Fe2 As2 shows fundamental differences to the FS of an isolated Fe2 As2 layer,
the separation of the Fe2 As2 layers from their surrounding is an effective parameter to tailor the electronic
properties of AFe2 As2 compounds. Experimentally, the superconducting transition in fact depends strongly
on the choice of the substituents at the A site. As we will show in the following, the latter is not only a
consequence of changing the electron count, but results, to a large extend, from an alteration of the bonding
within the Fe2 As2 layers. In order to study the effect of the coupling to the surrounding separated from
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.ann-phys.org
Ann. Phys. (Berlin) 523, No. 3 (2011)
263
Fig. 4 (online colour at: www.ann-phys.org) FS in the kz = 0 plane compared for different distortions:
(a) d = 0.5 Å, (b) d = 1.5 Å, (c) d = 2.5 Å, and (d) d = 3.5 Å.
the doping effects, we show in Fig. 4 results of FS calculations for distorted Ba0.5 K0.5 Fe2 As2 with an
increased separation between the Fe2 As2 layers and the Ba/K layers along the c-axis, see Fig. 1.
We find significant changes in the shape of the hole and electron pockets when the separation grows,
i.e. the interaction along the c-axis decreases. The hole pockets grow, while the electron pockets shrink.
Moreover, additional FS sheets appear at the zone center as well as corners. A kind of saturation of these
alterations is reached for a separation of d = 3.5 Å, see Fig. 4(d). However, there remain some distinct
differences to the FS of an isolated Fe2 As2 layer, compare Fig. 4(d) to Fig. 3(c). This fact supports the
common picture of long range interactions along the c-axis in iron pnictides. On the other hand, a situation
similar to ideal Ba0.5 K0.5 Fe2 As2 is not reached until the separation is down to d = 0.5 Å, compare Fig. 4(a)
to Fig. 3(a). This value appears to be an effective scale on which the interaction with Ba/K is relevant for
the details of the bonding within the Fe2 As2 layers.
4 Conclusion
To conclude, we have investigated the electronic structure of the recently discovered high-TC superconductor Ba0.5 K0.5 Fe2 As2 . Our study has focussed on establishing an understanding of the interaction between
the Fe2 As2 layers (responsible for the superconducting properties of the compound) and their surrounding,
particularly the electron donor Ba/K ions. Reduction of this interaction has a strong effect on both the DOS
and the FS. First, by a shift of EF towards lower energies, the system becomes more instable against magnetic ordering. Second, the shape of the FS changes qualitatively. Therefore, the effect of the substituents at
the A site of AFe2 As2 cannot be understood in a rigid band picture, confirming the relevance of structural
distortions in iron pnictides [32]. However, charge transfer from the A ions to the Fe2 As2 layers alters the
Fe-As bonding. A reduced charge transfer results in an enhanced Fe-As hybridization, which allows the
As ions to keep the original 3− valence state by transferring charge from Fe.
Acknowledgements Fruitful discussions with J. J. Pulikkotil and support by the KAUST supercomputing laboratory
are gratefully acknowledged.
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www.ann-phys.org
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