Electronic structure and superconductivity of rare-earth pnictides

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Electronic structure and superconductivity of rare-earth pnictides Kh. Dine , S. Abbaoui , A. Dahani , A. Zaoui , S. Kacimi , A. Kadiri , A. Boukortt PII: DOI: Reference:

S0921-4534(19)30248-5 https://doi.org/10.1016/j.physc.2019.1353542 PHYSC 1353542

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Physica C: Superconductivity and its applications

Received date: Revised date: Accepted date:

11 July 2019 1 October 2019 7 October 2019

Please cite this article as: Kh. Dine , S. Abbaoui , A. Dahani , A. Zaoui , S. Kacimi , A. Kadiri , A. Boukortt , Electronic structure and superconductivity of rare-earth pnictides, Physica C: Superconductivity and its applications (2019), doi: https://doi.org/10.1016/j.physc.2019.1353542

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Highlights  LDA+U calculations were performed on RFePO compounds.  The electronic structure are presented and discussed.  The superconducting state is studied via Fermi surfaces.  The Hubbard potential effect has been shown on various properties.

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Corresponding author: Pr. Salima KACIMI Physics department, Djillali Liabès University, Sidi Bel-Abbès 22000, ALGERIA E-mail address: [email protected] Phone: +213-541 408 792 Fax: +213-48-54-11-52

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Electronic structure and superconductivity of rare-earth pnictides Kh. Dine1, 2, S. Abbaoui1, A. Dahani1, 2, A. Zaoui1,, S. Kacimi1, *, A. Kadiri1 and A. Boukortt3 *Corresponding author: E-mail address: [email protected], Phone: +213-778-090-975, Fax: +213-48-54-11-52

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Laboratoire Physique Computationnelle des Matériaux, Université Djillali Liabès de Sidi Bel-Abbès, Sidi BelAbbès 22000, Algérie. 2 Faculty of Technology, University of Saida, Algeria 3 Laboratoire d’Elaboration et Caractérisation Physico Mécanique et Métallurgique des Matériaux (ECP3M). Département de Génie Electrique, Faculté des Sciences et de la Technologie, Université Abdel Hamid Ibn Badis de Mostaganem, 27000, Algérie.

Abstract In this work, we have studied the electronic structure of iron-based superconductors LnFePO (Ln = La, Pr, Nd, Sm and Gd) and their non-superconducting analogue CeFePO using a first principles method through the band structure calculations. Fe 3d electronic bands are at the origin of the fascinating electronic properties of these materials. The height of the pnictogen hPn and the bond angle Fe-Pn-Fe have been calculated and discussed. We have shown that the behavior of Fe-dz2 and Fe-dxy orbitals under the effect of the rare earth element variation is responsible for the increase of the critical temperature in these systems.

Author keywords: DFT+U; Band structures; Fermi surfaces; Fe-pnictides.

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I. INTRODUCTION The iron-based pnictides

[1]

represent the second class of superconducting materials in terms

of superconducting critical temperature (TC), just behind the cuprates whose maximum critical temperature today reaches 56 K

[2]

. The main element that constitutes this kind of

compound is the iron atom. This raises important fundamental questions about the phenomenon of superconductivity in these materials. We must find a new theoretical framework to explain the origin of superconductivity in these compounds. Many FeSC families with different structures and compositions are already known,

[3, 4]

have a common

plane Fe-pnictide (P, As) or Fer-chalcogen (Se, Te). These compounds have also a similar electronic band structure in which the electronic states at the Fermi level are occupied mainly by Fe 3d electrons: three bands (holes) around the center and two others (electrons) around the corners. These five conduction bands (Fermi surfaces) lead to many unusual superconducting properties. R. Baumbach et al.

[5]

found that the LnFePO (Ln = La, Pr and

Nd) compounds have superconducting critical temperature values TC of 6, 3.2 and 3.1 K, respectively. The metal parent compounds LnFeAsO exhibits a structural instability near to 150 K and become superconducting via the doping or the pressure [6]. On the other hand, their analogs based phosphorus LaFePO and SmFePO

[7]

are superconductors at ambient pressure.

The substitution of La with Ce, Pr, Nd, Sm or Gd lanthanides in As-based oxypnictides leads to a near doubling of Tc. There is also a lack of theoretical and experimental data on phosphorus-based iron pnictides. Although the LaFePO compound has received special attention, recently SmFePO has been found to be superconducting non-superconducting up to 400 mK

[6]

, and CeFePO remains

[8]

. The electronic structure of LnFePO (Ln = Pr, Nd and

Gd) compounds has not yet been studied theoretically. So, a comparative study between the electronic properties is needed to track the changes in orbital physics in the vicinity of the 4

Fermi level. In this work, the superconductivity was investigated through the band structure and the topology of the Fermi surface in the LnFePO compounds (Ln = Ce, Pr, Nd, Sm and Gd), and we focus our attention on the occupancy of the atomic orbitals in the Fermi level region. II. METHODOLOGY The calculations were made in the context of functional theory (DFT) implemented in the Wien2k package

[9]

. The atoms were represented by the L/APW+lo method

[10]

. In this

method, the wave functions, charge density and potential are extended into spherical harmonics without overlapping muffin-tin spheres, and plane waves are used in the remaining interstitial region of the unit cell. In the code, the states of heart and valence are treated differently. The core states are treated by a relativistic approach of Dirac-Fock, while the valence states are treated by a scalar relativistic approach. The electronic exchange and correlation functions were processed using the local density approximation LDA [11] as well as their added versions on the Coulomb interaction, LDA+U

[12]

. At the same time, we used an

appropriate set of k-points to calculate the total energy. The electronic states of the atoms in the crystal have been chosen with the valence configurations of rare earth elements [Kr] 4d10/5s2 5p6 6s2 5d1 4fn , Fe: [Ne]3s2/3p6 3d6 4s2, P: [Ne]/ 3s2 3p3 and O: [He]/ 2s2 2p4. The values of 2.5 bohr for rare earth elements, 2.0 bohr for iron, 1.8 bohr for phosphorus, and 1.5 for oxygen as the muffin-tin (MT) radii, were used. The total energy was minimized using a set of 84 k-points in the irreducible sector of the Brillouin zone for the quadratic function of the tetragonal-P4/nmm structure, and the value of 8 for the cutoff energy were used. The selfconsistent calculations are considered to be converged only when the calculated total energy of the crystal converged to less than 1 mRy.

5

III. RESULTS AND DISCUSSION The study of the electronic properties of LnFePO (Ln = La, Pr, Nd, Sm and Gd) compounds requires the use of the experimental parameters, in order to ensure a good description of the band structure. Experimental parameters of the five studied compounds were taken from references

[7, 13-15]

Fermi surfaces

. Generally, the electronic structure of Fe-based superconductors has five

[16]

. The displacement of the maximum of the valence band, which is

represented by the d-Fe states, towards higher energies is caused by the presence of the 4f states below the Fermi energy. This strong correlation clearly influences the construction of the band structure in the vicinity of the Fermi level causing several changes. So, to solve this problem, we studied the properties by varying the Hubbard's potential from 0 to 9eV up to have five bands that cross the Fermi level as in the normal state like LaFePO system. Our selection of the suitable Coulomb parameter Ueff is based on two points: i) Only five bands that crossing the Fermi level to lead a five Fermi surfaces sheet and ii) these five Fermi surfaces have the same dispersion as well as LaFePO

[17]

. Two electron and two hole pockets

of dxz/yz character, centered around M and gamma points respectively. The fifth consists of a 3D dispersion hole pocket around Z with mainly d3z2-r2 character. 4f-states of rare earth elements are more degenerate in the vicinity of the Fermi level; this is due to the effect of the LDA approach. The role of Coulomb parameter Ueff is to lift this degeneracy by splitting and moving them from the Fermi level [18]. From the literature, in iron based superconductors, 3dFe bands that constitute the Fermi surfaces are weakly affected by 4f-states of rare earth elements when using different values of Ueff [19-24]. The degree of influence of the 4f states on the 3d-Fe orbital’s is shown by the points mentioned above (number of bands that crossing the Fermi level and their dispersion in Γ-Z direction). In the case of CeFePO compound only four bands cross the Fermi level reported 6

by M. G. Holder et al. using angle-resolved resonant photoemission (ARPES)

[25]

. They

observe that the 4f-Ce states hybridize with the 3(d3z2-r2)-Fe states near the Fermi level and consequently, the superconductivity disappears. These results are confirmed by the calculations the local-density approximation (LDA) with addition of a Coulomb repulsion value of U =7 eV. In our calculations, we have used 8, 4, 4.5, 5.5 and 7 eV for Ce, Pr, Nd, Sm, and Gd respectively, which are sufficiently to reproduce the experimental data found in the case of LaFePO compound [17]. The calculated densities of states by the LDA+U approach in the tetragonal phase are shown in Figure 1. The electron distribution of the total and partial densities in these compounds is very similar to that determined in the LaFePO compound [26]. FeP hybridization is localized in all compounds and the only change is in the location of f-orbitals near the Fermi level. Unlike the other materials, CeFePO compound, which does not have a low temperature superconducting phase [27], presents four bands crossing the Fermi level. This is argued by the presence of 3d-Fe/4f-Ce hybridization

[22]

. To study the exceptional case of the CeFePO

compound, we have calculated their band structure with character. Indeed, the hybridization of the 4f states of Ce with the dxz and dyz states of the iron is clearly shown in the Figures 2. The similarity of the electron property in the other iron-based superconductors, LnFePO (Ln = Pr, Nd, Sm and Gd) is verified by our results and the five-band model is respected. But the question that arises: How can one explain the emergence of the critical temperature TC from 3 K to 6 K in the series from La to Gd? All iron pnictures respect the five-band model, but the rearrangement of orbitals and occupied energy levels, which produces superconductivity in the vicinity of the Fermi level, is totally different and can be considered as robust remarks to understand the mechanism of superconductivity. Using first principles calculations of the electronic structure of LaFeAsO and LaFePO compounds, Verónica Vildosola et al.

[28]

have observed that the electronic

7

structure of iron oxypnictides is highly dependent on changes in interatomic distances and FePn-Fe bond angles. So, the Curie temperature can be controlled by the Fe-Pn-Fe bonding angle (Pn = pnictogen), which is one of the most attractive characteristics of iron-based superconductors. Then, orbital physics, which dominates the Fermi level for the band structure and the Fermi surface, are the key factor in understanding the emergence of superconductivity in Iron pnictures. In Figures 3 and 4, 3d orbitals of iron vary systematically with the change of the rare earth atom. For example, the orbital dz2 occupies the energy bands below the Fermi level and moves to the higher energy bands from Ce to Gd; while, the dxy orbital is located above EF in the case of the PrFePO compound and to low energy levels for the GdFePO. This observation was confirmed by V. Vildosola et al.

[28]

.

They found that the Fermi surface of iron-based superconductors is mainly controlled by the Fe-Pn-Fe binding angle or the pnictogen height measured from the Fe plane

[29]

. Another

important remark, when the classification of the compounds studied according to the position of the orbital dz2, the parent compound LaFePO is located in fourth place after the NdFePO. We note that the critical temperature respects this rule and systematically emerges with the position of this orbital. The Curie temperature is of the order of 3.1 K for Pr and Nd and 5 K for La and it reaches the value of 6 K in the case of Gd. Figure 5 shows the lattices of the FeP layer, the pnictogen height hPn and the Fe-Pn-Fe bond angle. To verify the influence of the Fe-Pn-Fe bond angle or the pnictogen height measured from the Fe plane of all systems, we calculated the angle and the height using the following equations:

θ2 is the angle formed by Fe-P bond with the base plane as illustrated in Figure 5, and it is expressed as: 8

The calculated values are shown in the following table: Table 1 - Fe-Pn-Fe bond angles and the pnictogen heights measured from the iron plane of all systems. Compounds

hpn

TC

LaFePO

1.1400 Å

CeFePO

1.0866 Å 29.12° 121.76° Non-superconducting

PrFePO

1.1683 Å 30.85° 118.30°

3.20 K[30]

NdFePO

1.1622 Å 30.80° 118.40°

3.10 K[30]

SmFePO

1.1651 Å 31.00° 118.00°

3-5 K[31]

GdFePO

1.1547 Å 30.90° 118.20°

6.1 K[32]

29.9°

3-5 K[30]

121.60°

Figures 6-9 show the band structures and Fermi surfaces of LnFePO (Ln = Pr, Nd, Sm et Gd) compounds. It has been reported in references

[28, 32-36]

that the hpn [hpn = hAs (1.32 Å) - hP

(1.14 Å) = 0.18Å] controls the position of the dz2 and dxy bands near the Γ point in the Brillouin zone. In LnFePO systems, the control of these bands is manipulated by the effect of the variation of the rare earth element since the variation of hpn is almost negligible [hpn= hP/Gd (1.16 Å)-hP/La (1.14 Å) = 0.02Å]. V. Vildosola et al.

[28]

have shown that the change of

the Fermi surface leads to the increase of the critical temperature. In this work, we followed the behavior of the Fe-dz2 and Fe-dxy orbitals vs the variation of the rare earth element; which is responsible for the increase of the critical temperature in these systems. Our results are in excellent agreements with the experimental findings [28, 32-35]. From Figures 6-9, all materials have five bands of which two electron pockets (dxz and dyz) centered at the M point and three hole pockets centered at the Γ point with dxz, dyz and dxy characters. We notice that the hole with dxy character is two-dimensional in PrFePO and 9

NdFePO compounds, since it has no dispersion in the Z direction; unlike to SmFePO and GdFePO systems, it's a scattered 3D pocket with d3z2-r2 character. So, the studied superconductors show the same electronic property of the five band model. Note that the orbitals constituting the Fermi surface, which control the increase in superconducting temperature, are very important. IV. CONCLUSIONS In this work, we have studied the electronic structure of iron-based Superconductors LnFePO (Ln = La, Pr, Nd, Sm and Gd) and their non-superconducting analogue CeFePO using the L/APW+lo method. Calculations show that Fe-3d electronic bands are the source of the fascinating electronic properties of these materials. We have shown that it is possible to reproduce the electronic structure of these superconducting compounds using the LDA+U approach with a good choice of Hubbard potential. The ARPES experimental observations of the electronic structure are consistent with these predicted structures. To highlight the general trends appear in the properties common to these iron-based superconducting compounds, the electronic structures of the LnFePO compounds (Ln = Ce, Pr, Nd, Sm and Gd) belonging to the 1111-family have been compared. In all these systems the model of five Fermi surfaces is respected except in the CeFePO compound, where only four bands constitute the Fermi surfaces; this is due to the hybridization of the cerium 4f states with the dxz, dyz character of Fe-3d states. This hybridization results from the suppression of the superconducting phase thus confirming the results obtained by ARPES [25]. In the superconducting compounds LnFePO (Ln = Pr, Nd, Sm and Gd), the variation of the rare earth elements induces significant changes in the occupations of the atomic orbitals by comparing with those of the non-magnetic LaFePO compound. In the non-magnetic superconducting state, the orbital of the character dxy has no dispersion in the Z direction and is therefore two-dimensional. In the opposite case, we have a

10

pocket of 3D scattered with

character. LDA+U calculations show also that these

orbitals can be controlled by the Fe-Pn-Fe bond angle or by the pnictogen height measured from the Iron plane. It is very important to point out that the variation of the rare earth atom leads to a change in orbitals of the Fermi surface, which are responsible of the increase of the superconducting temperature. Conflict of Interest We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property.

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Figures Figure 1: The calculated densities of states by the LDA+U approach in the tetragonal phase. Figure 2: The band structures with characters of the CeFePO compound using the LDA+8 eV approach, Figure 3: The band structures of the LnFePO compounds (Ln = Ce, Pr, Nd, Sm and Gd) along the -Z direction using the LDA+U approach. Figure 4: The band structures of the LnFePO compounds (Ln = Ce, Pr, Nd, Sm and Gd) along the -M direction using the LDA+U approach. Figure 5: the lattices of the Fe-P layer, the pnictogen height hPn and the Fe-Pn-Fe bond angle Figure 6: Band structures and Fermi surfaces of PrFePO (U = 4 eV) compound. Figure 7: Band structures and Fermi surfaces of NdFePO (U = 4.5 eV) compound. Figure 8: Band structures and Fermi surfaces of SmFePO (U = 5.5 eV) compound. Figure 9: Band structures and Fermi surfaces of GdFePO (U = 7 eV) compound.

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Figure 1 14

Figure 2

15

Figure 3 16

Figure 4

17

Figure 5

18

Figure 6

Figure 7

19

Figure 8

Figure 9 20