The Lithium (Li) Doping Effect for Enhancing Thermoelectric and Optoelectronic Performances of Co2NbAl

Cobalt -rich Heusler compounds represent a very interesting family among Heusler alloys due to their performance in the field of spintronics and magnetic devices. The quaternary Heusler created by swapping of an anti-atom site by an alkali element improves the performance of physical properties for new applications. In this study, the electronic structures and magnetic properties before and after swapping cobalt (Co) by lithium (Li) in the Co 2 NbAl compound have been investigated using first-principle computational calculations. Our findings revealed that the swapping Co antisite by Li keeps the half-metallic character in the CoLiNbAl. Analysis of band structures show that ternary Heusler compound is ferromagnetic half-metallic with half metallic gap (band gap in minority channel ) equal 0.134 eV but the swapping Co with Li leads the material to change its behavior and becomes a semiconductor with a gap equal 1.043 eV using HSE06 approach. The results of optical and thermoelectric properties such as absorption coefficient, reflectivity or thermopower and figure of merit are very interesting in the optoelectronic field and encourages the researchers to realize photovoltaic cell and thermoelectric generator with a higher efficiency . These interesting features suggest that Co 2 NbAl and LiNbAlCo Heusler compounds could be good candidates for applications of antiferromagnetic spintronics and optoelectronics in commercial semiconductor industry.


Introduction
Heusler alloys have undergone rapid growth in the last decade, due to their outstanding performance in technological and spintronics applications. The spintronic devices are based on the exceptional nature of the electronic structures and semi-metallic properties of this type of materials. There are several applications of these devices such as the giant magnetoresistance spin valves [1], magnetic tunnel junctions [2], spin-injecting [3] and spintransfer torque devices [4]. Theoretical and experimental research focuses on Heusler alloys due to the diversity of their functional characteristics. From a purely theoretical point of view most of the Heusler alloys have the same crystallographic structure and some of them even are very close in composition and electronic structure [5][6][7]. These characteristics can minimize the mismatching of lattice and electronic structure. Another very important point is the crystallographic similarity between most of the Heusler alloys and semiconductors, because we can distinguish them in two groups the diamond or zinc blend structure. Several investigations have been made in the literature to switch from a Heusler semiconductor to a diluted magnetic semiconductor. Recently, it has been found that the diluted magnetism in semiconductor with Heusler structure can be induced by the atomic anti-site disorder between the different crystallographic sites [8]. The replacement of cobalt which resides in a 4c atomic site by an alkali metal atom leads to two very important consequences such as the destruction of the half metallicity caused by the opening another gap in the majority spin leading to a semiconductor material. In this study, we have analyzed the effect of anti-site disorder of lithium (Li) on the structural parameters, dynamic stability, the electronic structures and magnetic properties of the Co2NbGa alloy.

METHODOLOGY
The first-principle calculations of the density functional theory (DFT) via the full-potential linearized augmented plane wave method (FP-LAPW) implemented in the WIEN2k software [9] are employed to predict the structural, electronic, magnetic, optical and thermal properties of Li doped Co2NbGa alloy. The generalized gradient approximation (GGA-PBE) proposed by Perdew-Burke-Ernzerhof [10] is considered as exchange-correlation potential for our calculations. The muffin-tin sphere radii of 2.3, 2.05, 2.1, and 2.0 a.u for Li, Nb, Al and Co were used for calculations, respectively. The 2s 1 , 5s 2 4d 4 ,3s 2 3p 1 , and 4s 2 3d 7 respectively for Li, Nb, Al and Co are considered as valence states due to their high energies.
The densities of states were performed by the tetrahedral integration method, where the RMT×Kmax = 7 was used for the number of plane waves, and the expansion of the wave functions was set to lmax = 10 inside of the muffin tin spheres. The k-point mesh for sampling the Brillouin zone is performed by a Monkhorst-Pack scheme of 12×12×12 point mesh. The 10 -6 eV value for criterion convergence is used for the total energy. To determine the band gaps, optical properties, and dielectric constants we have used the screened hybrid Heyd-Scuseria-Ernzehof (HSE06) [11] exchange-correlation functional with a 4 × 4 × 4 k-mesh. To obtain accurate results for transport properties, we have used the BoltzTraP code [12] with a high k-point density of 20 × 20 × 20 mesh and a constant relaxation-time approximation.

Structural properties and dynamical stability
The Co2NbAl Heusler compound is 2:1:1 stoichiometric ternary intermetallic with inverse Heusler structure. This material crystallizes in the cubic structure with AgLi2Sb as prototype structure with space group F43m No. 216, its primitive cell is described by four interpenetrating fcc sublattices, which contains three atoms Co, Nb and Al that form the base In Table 1, we have summarized the values of formation energies. The formation energy of our quaternary Heusler is negative value, which means that the LiNbAlCo care thermodynamically stable and can be obtained in equilibrium conditions. We noted that the formation energy of our ternary material is in agreement with the result found by Shakeel Ahmad Sof et al., [13].
Our lattice constant of LiNbAlCo compound has an accuracy of 98.51 % compared to the value calculated in the reference [14]. In the cubic lattice of LiNbAlCo, when the Co atom is replaced by the Li less electronegative atom, the lattice parameter increases slightly due to the ionic nature of the bond between the Co-Li couple. Consequently, the hardness of material decreases.  [13] given in Table 1. We have found a total magnetic moment of 1.989 μB for Co2NbAl compound, which is very significant with respect to the value of magnetic moment given by the Slater-Pauling rule. The cobalt (Co) atom has a main contribution to the total magnetic moment thanks owing to its partially filled d states. The deviation of calculated magnetic moment is 0.55 % from the value found by Srikrishna et al., [15]. Moreover, a good agreement of the magnetic moment of Co is mentioned.

Electronic band structures and densities of states
The addition of Li instead of Co destroys the half-metallic behavior and hence the LiNbAlCo We can see that the hybrid functional gives the same description of the band structure of reference [14], where our calculated band gap of 1.043 eV is closed to the value of 1.041 eV [14] given in the Table1. Our predicted ZT value based on HSE06 approach in the temperature range from 300-1100 K for LiNbAlCo is very attractive and decreases with the increase of temperature. The Figure   5.d shows the dimensionless figure of merit ZT of Li swapping Co. Due to the significant suppression of thermal conductivity, the ZT reached a value of 1.05 at room temperature.

Optical properties
The processing of optical properties is carried out using the Ehrenreich and Cohen's equation [17] which gives the frequency dependent complex dielectric function. This equation is given by the following relation: This expression represents the optical response of a material to an external electric field . The Kramers -Kronig relation [18] allows us to determine the real and imaginary part of equation 1. The different optical parameters as the refractive index n(ω) , the extinction coefficient k(ω), reflectivity R(ω) and absorption coefficient α(ω) are calculated from the real and imaginary part of the dielectric function [19][20][21]. The calculated imaginary part of the dielectric function 2 ( ) with PBE and HSE06 approaches of our compound is depicted as a function of energy in Fig.6

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.