Indian Journal of Materials Science

Volume 2015, Article ID 296095, 11 pages

http://dx.doi.org/10.1155/2015/296095

## Electronic Structure, Electronic Charge Density, and Optical Properties Analysis of GdX_{3} (X = In, Sn, Tl, and Pb) Compounds: DFT Calculations

^{1}Department of Physics, National Defence Academy, Pune 411023, India^{2}Department of Physics, Sarojini Naidu Government Girls P. G. Autonomous College, Bhopal 462016, India^{3}Department of Physics, Barkatullah University, Bhopal 462026, India

Received 5 May 2015; Revised 10 July 2015; Accepted 12 July 2015

Academic Editor: Andres Sotelo

Copyright © 2015 Jisha Annie Abraham et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The electronic properties of magnetic cubic AuCu_{3} type GdX_{3} (X = In, Sn, Tl, and Pb) have been studied using first principles calculations based on density functional theory. Because of the presence of strong on-site Coulomb repulsion between the highly localized 4f electrons of Gd atoms, we have used LSDA + *U* approach to get accurate results in the present study. The electronic band structures as well as density of states reveal that the studied compounds show metallic behavior under ambient conditions. The calculated density of states at the Fermi level *N*() shows good agreement with the available experimental results. The calculated electronic charge density plots show the presence of ionic bonding in all the compounds along with partial covalent bonding except in GdIn_{3}. The complex optical dielectric function’s dispersion and the related optical properties such as refractive indices, reflectivity, and energy-loss function were calculated and discussed in detail.

#### 1. Introduction

The rare earth based intermetallics, REX_{3} (X = In, Sn, Tl, and Pb), have been investigated extensively because they show a variety of interesting physical properties: magnetism, de Haas-van Alphen (dHvA) effect, and thermal, transport, and electronic properties [1, 2]. They have cubic 1_{2} (AuCu_{3}) crystal structure, space group . Electron-transport properties of GdIn_{3} in the paramagnetic range are similar to those for other REIn_{3} compounds and its Fermi surface is almost the same as that of the nonmagnetic compound LaIn_{3} [3, 4]. Grechnev et al. [5] have studied GdM (M = Cu, Ag, and Mg) and RIn_{3} (R = Gd, Tb, and Dy) with LMTO method within the atomic sphere approximation. They have done investigations of RM and RM_{3} compounds in CsCl and AuCu_{3}-type structures, in which the R sublattice is simple cubic and in which the energy band occupancy can be varied. They have chosen the position of Gd at (0, 0, 0) and M at (0.5, 0.5, 0.5) in the case of GdM and R at (0, 0, 0) and In at (0, 0.5, 0.5) in the case of RIn_{3} compounds. Magnetic neutron studies at pressures above 40 GPa have been used for GdX (X = As, Sb, and Bi) compounds by Goncharenko et al. [6]. They have reported that these compounds are stable up to 40 GPa in antiferromagnetic ordering. Duan et al. [7] have studied the magnetic ordering in Gd monopnictides using Heisenberg model. They have reported that the magnetic ordering in GdN undergoes a transition from ferromagnetic to antiferromagnetic state among the Gd monopnictides. The hyperfine fields in ferromagnetically ordered cubic Laves phase compounds of gadolinium with nonmagnetic metals (GdX_{2}: X = Al, Pt, Ir, and Rh) have been investigated by Dormann and Buschow [8]. Pressure-induced structural phase transition of gadolinium monopnictides GdX (X = As and Sb) has been studied theoretically using interionic potential theory as reported by Pagare et al. [9]. Magnetic measurements have been performed for cubic Laves phase compounds RFe_{2} (R = Gd, Tb, Dy, Ho, Er, and Y) and (R = Gd, Tb, and Er) in fields up to 30 kOe and for temperatures between 4.2° and 1000°K by Buschow and Van Stapele [10]. The structural and elastic properties of GdX (X = Bi, Sb) using FP-LMTO have been studied by Boukhari et al. [11]. The experimental data and results of* ab initio* calculations of the volume derivatives of the band structure and the exchange parameters for the corresponding series of compounds have been used to analyze the nature of the f-f interactions. Possibility of Kondo effect in Gd intermetallic compound has been studied by Yazdani and Khorassani [12]. They also showed that, with increasing electron concentration, Gd experiences electronic and magnetic instability, and these behaviors point to the appearance of the Kondo Lattice. The electronic structure of the intermetallic compound Gd_{3}Pd has been studied by Punkkinen et al. [13] using the local spin-density approximation (LSDA) and the LSDA + approximation to the exchange-correlation potential of the spin-density functional theory. They found that the “” states of Gd play an important role in a correct description of the magnetic state of the Gd_{3}Pd. They also suggested that the crystal and magnetic structure of the Gd_{3}Pd is more complicated at low temperatures than at temperatures just below the transition temperature.

It is revealed from the literature that no efforts have so far been made to study the electronic and optical properties of GdX_{3} (X = In, Sn, Tl, and Pb) compounds either theoretically or experimentally. In the present paper, we therefore aim to study theoretically the electronic structure and optical and magnetic properties of the above class of compounds using density functional theory within LSDA + method. This method explicitly includes on-site Coulomb interaction term in the conventional Hamiltonian and influence of electronic and magnetic properties of such systems [14, 15].

#### 2. Crystal Structure and Computational Details

The crystal structure of GdX_{3} is stable in cubic AuCu_{3} structure (). The ground state calculations were carried out using the full-potential linearized augmented plane wave (FP-LAPW) method [16] as implemented in the WIEN2k code [17]. The exchange-correlation effects were described with LSDA + [18] approximation. In the calculations reported here, we have used the parameter = 7 to determine the matrix size (convergence), where is the plane wave cut-off and is the smallest atomic sphere radius. Within these spheres, the charge density and potential are expanded in terms of the crystal harmonics up to an angular momentum of . A plane wave expansion has been used in the interstitial region. was set to 14 (a.u)^{−1}, where is defined as the magnitude of the largest vector in the charge density Fourier expansion. Brillouin zone sampling was performed by the Monkhorst-Pack scheme [19] with 10 × 10 × 10 mesh based on Hohenberg and Kohn theorems [20, 21]. The values of the kinetic energy cut-off and the grid were determined by ensuring the convergence of total energies within an accuracy of 1 meV/atom. Due to the strong on-site Coulomb repulsion between the highly localized electrons of RE atoms, the local spin-density approximation (LSDA) with additional Hubbard correlation terms (LSDA + approach) [18] is also used to calculate the accurate results. Thus, we present LSDA + approach in order to obtain the appropriate results. In the LSDA + calculations we have used an effective parameter = , where is the Hubbard parameter and is the exchange parameter. We set = 6.70 eV and = 0.70 eV. We have optimized the atomic positions taken from XRD data [22] by minimization of the forces acting on the atoms. From the relaxed geometry, the electronic structure, electronic charge density, and the optical properties are determined. The optimized geometry along with the experimental values [22] is listed in Table 1.