Structural and electronic properties of the iron pnictide compound EuFe2As2 from first principles

We report results of the electronic and mechanical structure properties of the iron pnictide compound EuFe2As2, at zero pressure. The open source computer code Quantum Espresso, which incorporates the Density Functional Theory (DFT), Pseudo Potentials (PP) and the Plane Wave (PW) were used to perform calculations from first principles. Projector-Augmented Wave (PAW) Pseudo Potentials were used in these calculations. The Density of States exhibits a sizeable superconducting gap and the band structure has no bandgap. Calculations were performed from scratch.


Introduction
Iron Pnictides have been studied for their potential application in technology due to their exhibition of high temperature superconductivity [1][2][3]. Superconductivity at high temperature has been discovered in iron-Pnictide compounds and this has ignited numerous interest and research on the properties of these compounds [4][5][6]. In previous studies, iron Pnictides have been seen to exhibit superconductivity up to high temperatures of ∼26K [7][8][9]. Compounds based on iron are classified as '1111', '122', '111', and '11' families, depending on their structure and make up [10,11]. In the 122 family of compounds, AFe 2 As 2 (A=Ba, Ca, Sr, Eu) have stimulated high interest in research since they are easier to synthesize [11]. EuFe As 2 2 is unique in the 122 family since the Eu atom undergoes Spin Density Wave and Antiferromagnetic ordering magnetic transitions, leading to antiferromagnetic ground state [12,13]. Other compounds in the 122 Iron Pnictide family include BaFe 2 As 2 and CaFe 2 As 2 , which have a relatively similar structure to that of EuFe 2 As 2 [14].
EuFe 2 As 2 is one of the 122 iron Pnictide compounds with a Body-Centered Tetragonal crystal structure [7][8][9] and also exhibits superconductivity on application of pressure of up to ∼2.5Gpa [7,[15][16][17][18][19]. Superconductivity in these compounds can be achieved through doping or application of pressure on the material [20], for example, application of pressure on BaFe 2 As 2 and CaFe 2 As 2 tunes superconductivity [7,15] with T c of up to 38K [21]. In this article, we report on the mechanical and electronic structure properties of EuFe 2 As 2 as studied from first principles.

Computational details
In our study, we used the Plane Wave method to investigate the electronic and mechanical structure properties of EuFe As 2 2 from first principles, using the open source computer code Quantum Espresso [22][23][24][25]. Self -Consistent Calculations were run to obtain the total and Fermi energy of the system, which is a useful parameter in describing the electronic structure properties of the compound [26]. The input files were designed such that the mechanical properties including the Bulk, Shear and Young moduli, and Poisson ratio were obtained. Quantum Espresso supports the use of Projector-Augmented Wave (PAW), Ultra Soft Pseudo Potentials (USPP), which are Norm Conserving. Norm Conserving Pseudo Potentials are well normalized, a feature useful for an accurate description of bonding in the compound [27,28]. The PAW Non Linear Correction Pseudo Potentials were used in these calculations [29][30][31][32][33]. Before running the Self-Consistent Calculations, the Variable Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Cell relax( vc-relax )calculation was performed to obtain relaxed atomic positions and then optimization of cell dimensions, K-points, and the kinetic energy cut off was also done so as to obtain a relaxed crystal structure, to ensure that the ground state crystal structure is obtained and that the results are free from stress [8,[34][35][36]. The initial k-point sampling was done using p , a 2 where a is the lattice parameter [19]. Optimization of the K-points yielded the converged K-points, convergence ensuring a stress and strain free system [37]. The Density Functional Theory which focuses on the electron density to study the properties of a many-body system was employed.

Results and discussion
In this section, we report the various results obtained from the theoretical computation. Figure 1(b) shows the optimized crystal structure for EuFe 2 As 2 . There are three types of atoms in the crystal, namely: Europium, Iron and Arsenic. The number of atoms we considered in these calculations were five, one Europium, two iron, and two arsenic. There exists a Europium atom at the center of the structure hence the structure is Body Centered Tetragonal [7,9], since our optimized structure had the Eu atom in the middle. Below is the crystal structure (b), obtained after vc-relax and optimization. The optimized structure has an Eu atom at the center and shows similar bonding of atoms as other iron Pnictides [13].
In this section, we present results for the optimization of K-points, cell dimensions and kinetic energy cutoff that were used throughout the calculation.
On optimization, the following curves were obtained for the cell dimensions, K-points and kinetic energy cut off. The optimized cut off kinetic energy and k-point value as from figure 2 below is ∼45 and ∼4 respectively. The optimized cell dimension as from figure 3 below is ∼7 Bohr units.
The optimized cell dimension three as from the optimization curve is ∼4.2 Bohr units.
In this section, we report on the calculations of the electronic structure properties which included the band structure calculation, Density of States and Partial Density of States.
EuFe As There is a band gap of 0.0eV, which is in agreement with other theoretical studies on the compound [39]. The density of states curve for the compound was obtained as below.
The Density Of States with the. long and sharp peaks are between energies of ∼7.8 eV and ∼10.2 eV as shown in Figure 4 above, and they represent the core electrons that have a minimal contribution to determining the properties of the electrons since they are considered to be chemically inert [42]. The Density of States between ) there exists an atom at the center of the structure, hence the Body Centered Tetragonal structure for this 122 family of iron pnictides [15]. (b) The crystal structure of EuFe 2 As 2 as drawn using a Quantum Espresso package Xcrysden. A body centered structure is portrayed as seen above. The Europium atom is located at the center, giving it the mentioned structure.
the peaks is zero since states do not exist there as seen in Figure 4 above. A Kondo-like peak is as shown above, in agreement with results from similar iron Pnictides which show similar peaks [36].
Similar pnictide such as BaCa 2 As 2 also exhibits a sizeable gap far from the Gamma-X high symmetry line [43], similar to the one present in the band structure in Figure 5 below and the Density of States.    [40] which yield coulomb parameters of ∼4 eV [8,36]. It is within this gap that there exists the superconducting state of the compound. The Partial Density of States shows Europium and Iron atoms to be the major contributors to the projecting states. Other minor curves are left out in the illustration since their contribution to the Partial Density of States was minimal. The density of states of other Pnictides shows similar gaps [41].
The mechanical properties we obtained from the computation are summarized in Table 1 below. The Poisson's ratio was found to be ∼0.32 at absolute zero temperature, our result compared well to a value of 0.302 for other families of Pnictides [41], the difference may be as a result of varying atoms present in the two compounds and a slight difference in the crystal structure. This value further confirmed that EuFe 2 As 2 is a stable and metallic [45, ] Other Pnictides such as SrFe 2 As 2 have a Poisson's ratio of ∼0.48 upon application of pressure [47], which causes the lattice parameters to change. The Bulk modulus, Shear modulus, and Young's modulus were found to be ∼346 Gpa, ∼136 Gpa and ∼362 Gpa respectively, implying that the material is hard since the moduli are greater than 200 [48].

Conclusion
In this study, the electronic structure properties-Density Of States, Partial Density Of States, bands structure and structural properties including Bulk, Shear and Young's Modulus and Poisson's ratio of EuFe 2 As 2 were investigated using the open source computer code Quantum Espresso. The compound was stable and the crystal structure was Body Centered Tetragonal, just like experimental details suggested [15]. The band structure and Density of States graph showed a sizable gap, the superconducting gap, implying that the material exhibits superconductivity, in agreement with previous studies on the material. The Poisson's ratio of the compound implied that the compound was a stable metal.

Acknowledgments
We thank Dr Ketui D, Dr Nyawere P and Mr Agora J for their informative contributions in support of this research. There exists no bandgap in the material as seen from the graph above, similar to previous results from studies on the pnictide [39], hence the material is a conductor. The Density of States and Band structure of the compound show very close similarity as seen above. The zero binding energy and Fermi level correspond, in agreement with previous studies on the material [44].