Ab initio investigation of electronic structure, equilibrium geometries, and finite-temperature behavior of Sn-doped Li_{n} clusters

Physica C 512 (2015) 22–27

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Physica C

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Ab-initio investigation of the electronic structure inthe superconducting EuFe2(As1�xPx)2

http://dx.doi.org/10.1016/j.physc.2015.02.0450921-4534/� 2015 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: Djillali Liabès University, Sidi Bel-Abbès 22000,Algeria. Tel.: +213 778 090 975, +213 773 802 694; fax: +213 48 54 11 52.

E-mail address: [email protected] (S. Kacimi).

F. Drief, A. Zaoui, S. Kacimi ⇑, B. MerabetLaboratoire de Physique Computationnelle des Matériaux, Université Djillali Liabès de Sidi Bel-Abbès, Sidi Bel-Abbès 22000, Algeria

a r t i c l e i n f o

Article history:Received 17 January 2015Received in revised form 16 February 2015Accepted 20 February 2015Available online 28 February 2015

Keywords:Ab-initio calculationsElectronic structureMagnetic propertiesFermi surfacesIron pnictide alloys

a b s t r a c t

The electronic structure and magnetic properties of EuFe2(As1�xPx)2 were investigated by means the localspin density approximation (LSDA) with the on-site Hubbard Ueff parameter (LSDA+U). The charge andspin densities, densities of states, band structures and Fermi surfaces as a function of the phosphorus per-centage in the ferromagnetic tetragonal EuFe2(As1�xPx)2 have been presented and discussed. For all stud-ied concentrations, our alloys keep both the ferromagnetic order and the metallic character. LSDA+Uelectronic structure calculations show that the tetragonal phase is characterized by the 4f localized elec-trons of the rare earth element Eu from where originates the magnetism, and by their 3d-Fe electronsresponsible for superconductivity. The substitution of As by P leads to a decrease in the volume and toa slight influence of magnetism of the Eu sublattice. LSDA+U calculations reproduce successfully theobserved experimental findings. Finally, we provide indications on the coexistence of superconductivityand magnetism for few concentrations.

� 2015 Elsevier B.V. All rights reserved.

1. Introduction

The discovery of the series of iron pnictides offers a newapproach to understanding the high-temperature superconduc-tivity mechanism. The magnetism seems to be the critical factorin determining the physical properties such as superconductivitythat emerges with suppression of the magnetic order in the FeAslayers [1]. The 122-type ternary compounds are quickly advancedand are model systems because of the availability of good singlecrystals. EuFe2As2 is a prominent member of the 122-series witha maximum critical temperature Tc = 32 K in the Eu0.5K0.5Fe2As2

system [2] because in addition to the anti-ferromagnetic order(AFM) of itinerant electrons, a magnetic order of localized ionsEu2+ is observed at lower temperatures [3]. Eu2+ ion has a widemagnetic moment and an anti-ferromagnetic order belowTN = 19 K, which means that the moments are ferromagnetic alongthe a-axis and anti-ferromagnetic along the c-axis [4–7]. Theappearance of the magnetic order in these systems attracts moreand more attention [8,9]. The charge carrier doping [2,10,11], thesubstitution of the P element on the As site [12–15], and the pres-sure effect [16–18] modify the magnetic order of Eu2+ and also theelectronic properties of the system, eventually leading to

superconductivity. So, the magnetic order arises from the europi-um has a perceptible impact on superconductivity in FeAs layers,revealing an extraordinary opportunity to study the interactionbetween magnetism and superconductivity [19]. It is thereforerather surprising that at present, there is no clear vision to explainhow the order of Eu2+ element changes with doping or pressure. Inaddition, there is still under debate, which type of magnetic orderof Eu2+ coexists with superconductivity [8,13–15]. In the following,we focus on EuFe2(As1�xPx)2 alloy and we discuss the effect of thesubstitution of P on the electronic and magnetic structure througha careful analysis of liaison mechanisms.

2. Methodology

For the DFT calculations we use the Wien2k code [20], wherethe so called full-potential (linear) augmented plane-wave pluslocal orbitals method [21] has been implemented. In this method,wave functions, charge density, and potential are expanded inspherical harmonics inside no overlapping muffin-tin spheres,and plane waves are used outside in the remaining interstitialregion of the unit cell. In the code, core states are treated different-ly within a multi-configuration relativistic Dirac–Fock approach,while valence states are calculated in a scalar relativistic approach.For the exchange-correlation energy we used LSDA+U approach[22]. From the total energy, we computed equilibrium latticeconstants and bulk moduli by fitting energy versus volume to

EuFe2(As1/2P1/2)2

Fig. 2. The charge distribution of the ferromagnetic EuFe2(As1/2P1/2)2 alloy.

Fig. 3. The calculated spin density of EuFe2(As1/4P3/4)2 et EuFe2(As3/4P1/4)2 in (110)

F. Drief et al. / Physica C 512 (2015) 22–27 23

Murnaghan’s equation [23]. The total energy was determined usinga set of 39, 40 and 8 k-points in the irreducible sector of Brillouinzone for EuFe2P2, EuFe2As2 and their alloy EuFe2(AsxP1�x)2 respec-tively. The RKmax = 7 was used and we have adopted the values of2.3 Bohr for europium element, 2.00, 1.80 and 1.70 Bohr for Fe, Asand P atoms respectively, as MT radii. The coulomb potential Ueff

for the Eu 4f– is fixed about 8 eV.

3. Results and discussion

3.1. Structural properties

The localized Eu 4f states were treated using the LSDA+U. Thevalue of the strong Coulomb repulsion U4f of the Eu ion is takenfrom the literature [13]. The Fe 3d states were treated on an itiner-ant level without additional correlations. The partial P substitutionwas modeled by the construction of supercells of 40-atoms.Furthermore, the variation of energy according to an applied stress(here it is the variation of the volume) allows to determine by asimple processing the equilibrium properties of the consideredmodels. It is proved that any small external effects like impurities,doping, external pressure and fields can easily flip the Eu spinsfrom anti-ferromagnetic (AFM) to ferromagnetic (FM). Recently,It has been shown that for the phosphorus concentration x > 0.2,FM inter-layer coupling between the Eu moments becomes favor-able and continues to remain so for larger P substitutions, consis-tent with the present experimental observations [13–15]. Forthis, we have considered the EuFe2(As1�xPx)2 as tetragonal ferro-magnetic system. The lattice parameters and the bulk modulusfor the various phosphorus concentration of EuFe2(As1�xPx)2 alloyin the tetragonal structure were obtained by using LSDA+U andare reported in Fig. 1. The curves show that the behavior of the lat-tice parameters and c/a of the various concentrations correspondswell with the experimental trends. The equilibrium volumes (Veq)are 4.66% and 3.18% smaller than the experimental data. Thus,the doping of As by P introduces a volume compressive inEuFe2(As1�xPx)2. This is due to the DFT that is known to

Fig. 1. Lattice parameters a0, c/a and the bulk modulus B0 as a function of thephosphorus concentration of EuFe2(As1�xPx)2 alloy.

plane using LSDA+U approximation.

Fig. 4. The variation of the magnetic moments as a function of the phosphorusconcentration of EuFe2(As1�xPx)2 alloys using LSDA+U approximation.

underestimate the lattice constants and inter-atomic distances.The obtained values of B0 show that the phosphorus incorporationin the place of Arsenic increases the bulk modulus going fromx = 0.125 to x = 0.875. The experimental volumes are well repro-duced well as the properties related to the total energy such asthe bulk modulus. Phosphorus ion is smaller than the Arsenicion, and the volume is reduced with increasing phosphorus

Fig. 5. The densities of states (a) total (b) of d-Fe character (c) s and p characters of P and As atoms and (d) d and f characters of europium atom as a function of theconcentration using LSDA+U approximation.

24 F. Drief et al. / Physica C 512 (2015) 22–27

content. The same observation is valid for c/a (see Fig. 1). Thesefirst results, if they do not allow to be categorical about the behav-ior of 4f electrons of our ferromagnetic alloy EuFe2(As1�xPx)2, indi-cate that at least part of them is localized.

3.2. Electronic properties

The analysis of the charge distribution is carried out to revealvaluable information about the nature of the liaison and the basic

features of the structures. Despite the ambiguity in determiningrigorous values, the charge transfer calculation between the atomsor atomic layers may be useful in understanding the consideredsystems. We present in Fig. 2, the contours of the valence chargedensity of the ferromagnetic ground state of EuFe2(As1/2P1/2)2 alloyon the (110) plane in both spin directions. It is clearly visible thatthe metal bond is localized between Eu atoms inside the layers.The high charge density around Fe ions is due to the Fe-3d orbitals.Each iron atom forms a Fe–As type of covalent bond which is

EuFe2As2

EuFe2P2

Fig. 6. Band structures of the ferromagnetic parent compounds calculated by the LSDA+U approach.

EuFe 2(As 1/2P1/2 )2

Fig. 7. Band structures of the ferromagnetic EuFe2(As1�xPx)2 alloys using LSDA+U approach.

F. Drief et al. / Physica C 512 (2015) 22–27 25

x=0.25 x=0.1875

Fig. 8. Fermi surfaces of the tetragonal superconductor EuFe2(As1�xPx)2 alloys for the majority spin.

26 F. Drief et al. / Physica C 512 (2015) 22–27

obtained via the hybridization of Fe-3d and As-4p orbitals. On theother hand, the charge transfer of the Fe atom toward the As atomobeys to the concept of electronegativity and therefore gives rise toionic character between the Fe–As bonds. Overall, there is a mix-ture of covalent and ionic bonds. The distribution of the corre-sponding spin density in the (110) plane is shown in Fig. 3. Themajority of the spin magnetic moments are found on the 4f statesof the rare earth element which is the main contributor with a veryweak contribution of iron atoms. The calculated magneticmoments as a function of the phosphorus concentration of the fer-romagnetic alloy EuFe2(As1�xPx)2 are shown in Fig. 4. From this fig-ure, the phosphorus incorporation slightly affects the values of themagnetic moments which are highly localized on the europiumsites with negligible contributions of the other atoms. These resultsare consistent with the recently reported experimental findings[3,8,9,13–15].

The total (TDOS) and partial (PDOS) densities of states areshown in Fig. 5(a)–(d). In the plots, the energies are reported atthe Fermi level EF. This protocol is respected in all figures ofTDOS and PDOS. The Fermi level separates the valence band fromthe conduction ones. The total densities as a function of the phos-phorus concentration presented in Fig. 4a, show great topologicalsimilarity of the distribution of electrons in the two regions, andchanges reside in the positions of bands caused by the variationof the phosphorus percentage in the ferromagnetic alloys. Fig. 5bshows that the Fermi level EF is positioned between the two max-ima of the iron atom. In the case of parents, our systems are metal-lic. We notice that Fe-d bands are narrow and are located at ahigher binding energy, more than 1 eV of both sides of the Fermienergy (EF). We also note that our results are very similar by vary-ing the phosphorus concentration, where the Fe itinerant statesstill dominate the Fermi region. The only difference between thedensities of states is the appearance of some narrow peaks in bothvalence and conduction bands as a result of the incorporation ofphosphorus atoms to the Arsenic sites. Therefore, two hybridiza-tions of p-d type will take place; the metallic character and the fer-romagnetic order are preserved. The rest of the partial densities ofstates for each atomic site (PDOS) as a function of the phosphorusconcentration are shown in Fig. 5c and d. Figures show that thebottom of the valence band (VB), located between �7 and �3 eV,is dominated by the p-states of As and/or P atoms. The Fermi level

region (�3 eV and 3 eV) is predominated by iron states with a sig-nificant contribution of p-As and/or -P states. From 3 eV, the con-duction band (CB) has a variety of states (s, p states of As and Patoms and d states of Eu and Fe ions). The As 4p states are moreextended than P 3p states, which when combined with a strongdecrease of the volume tends to reduce the strength of the FMinteraction between the inter-layer Eu ions, always keeping theferromagnetic order.

The strongly localized 4f states of the europium atom, which arecharacterized by an intense peak at 1.8 eV, remain unchanged byvarying the phosphorus concentration. These states hybridize withthe d-Fe states and giving another hybridization of d-f type.

To complete our discussion of the different electron contribu-tions of all atoms, we traced the band structures of the parent com-pounds and their corresponding alloys in both directions of spin(majority and minority) in Figs. 6 and 7. We have focused ourattention on the Fermi level because the magnetism and supercon-ductivity phenomena occur in this region. From LSDA+U PDOS cal-culations, we concluded that the Fermi region is dominated by the3d-Fe states with the presence of an intense peak of 4f originate ofEuropium. The current position of the 4f electrons do not reflectthe reality, for this reason that many studies consider them as coreelectrons and we really think that the electrons of the rare earthelement does not contribute in Fermi region. So, we confirm thatthe Fe 3d-electrons dominate the density of states near the Fermilevel; this indicates that these electrons could be the origin ofsuperconductivity in these materials. Several ab initio calculations[24–29] have shown that the electronic structure of many similarmaterials have a significant contribution of Fe 3d-electrons nearthe Fermi level, which are in excellent agreement with our results.

Recently, several researchers [13–15] confirmed the coexistenceof superconductivity and magnetism in the tetragonalEuFe2(As1�xPx)2. Experimental studies present a new vision todescribe both superconductivity and magnetism. They presented aphase diagram EuFe2(As1�xPx)2 as a function of the phosphorus.Their results suggest that the superconducting phase (SC) and theferromagnetic order (FM) are competing. The superconductingphase can be observed in two different concentration ranges0.16 6 x 6 0.22, [13] and 0.2 6 x 6 0.4 [14,15]. The studies show thatthis multifunctionality superconductivity-magnetism is still underdebate. From these findings, we decided to calculate the Fermi

F. Drief et al. / Physica C 512 (2015) 22–27 27

surfaces of EuFe2(As1�xPx)2 alloy in the tetragonal (FM) phase, select-ing two concentrations of these intervals to make the comparison.

The Fermi surfaces of tetragonal superconductorEuFe2(As1�xPx)2 are presented for only the spin-up, five bands of3d-Fe type cross the Fermi level for the two chosen concentrationsx = 0.1875 and x = 0.25. From Fig. 8, the calculation shows that twotypes of electron pockets centered at the Z point and two holestype pockets centered at the C point. Note that the holes coverthe C ? X direction, and present in some cases small sizes in theFermi surface, which result from the weak crossing of orbitals withthe Fermi level. These distortions are corrected by increasing theconcentration of phosphorus in supercells. All Fermi surfaces arepresented for the first time.

4. Conclusions

The objective of this paper was to present a theoretical studywithin the DFT of the ferromagnetic EuFe2(As1�xPx)2 alloy for dif-ferent phosphorous concentrations taking into account two majoraspects: (i) to study the induced magnetism of 4f states of the rareearth element, (ii) to study the 3d-Fe states that are responsible forsuperconductivity in these systems by examining their Fermi sur-faces which are a good indicator of this phenomenon. We investi-gated and explained the effect of the phosphorus incorporation forvarious concentrations on the electronic and magnetic structure.We were able to reproduce the crystallographic properties success-fully by comparing with the recent experimental results. On theother hand, we have also presented and discussed the magneticand electronic properties of these systems such as the charge andspin densities, the densities of states, the band structure and theFermi surfaces depending on the phosphorus percentage in a ferro-magnetic tetragonal EuFe2(As1�xPx)2. LSDA+U calculations showthat these all supercell models maintain both the metallic charac-ter and the ferromagnetic order by varying the phosphorus con-centration. Different types of hybridization are localized in thevicinity of the Fermi level: p-d between P, As and Fe atoms, andd-f between Fe and Eu elements. Our results show also that thesubstitution of phosphorus in place of Arsenic affects slightly themagnetic moments values that are highly localized on the europi-um site with very weak contributions of iron, phosphorus andArsenic atoms. By referring to some recent experimental work,we calculated the Fermi surfaces of EuFe2(As1�xPx)2 alloy in the tet-ragonal phase in order to provide indications on the superconduc-tivity phenomenon and consequently to show the coexistence thesuperconductivity and magnetism, which was already confirmedby several groups of researchers.

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