Structural, elastic, electronic and magnetic properties of Fe3AC; A = Al, Ga and In

We report first principle calculations on the structural, electronic and magnetic properties of antiperovskite Fe3AC; A = Al, Ga and In. Calculations show that these compounds are more stable in the magnetic states, the estimated equilibrium lattice parameters (a and V ) are in agreement with the experimental data. From the single crystal elastic constants, the polycrystalline elastic moduli is estimated. Similar to previous studies on carbides antiperovskite, these compounds are good electrical conductors. The analysis of the total and partial densities of states shows that the conductivity is assured by d electrons of the transition metal atoms. The magnetic character in these compounds is mainly related to the spin polarization of Fe-d electrons. The magnetic moment per unit formula is found to decrease from 3.52 μB to 3.06 μB corresponding to Fe3InC and Fe3AlC respectively.


INTRODUCTION
Ternary transition metal carbides (or nitrides) have shown attractive and unusual properties, which made them of potential use in a number of applications, extend from semiconducting to superconducting. Among these carbides and nitrides are the antiperovskite compounds with the general formula M 3 AX where X is C or N, while both A and M are metal atoms [1]. The discovery of superconductivity at 8 K for the Ni 3 MgC [2], highlights these materials and stimulates more experimental and theoretical works to investigate the origin of this behaviour.
The present work is carried out on Fe 3 AC; A = Al, Ga and In, both of them have a cubic structure with A elements at the cubic corner, Fe atoms at the face centres and C atom at the body centre [1][2][3][4].

COMPUTATIONAL METHODS
Our calculations were carried out using the CASTEP (Cambridge Serial Total Energy Package) code [5], in which the density functional theory [6] and the Kohn-Sham approach were used to calculate the fundamental eigenvalue. In order to reduce the basis set of plane wave (PW) functions used to describe the real electronic functions, the pseudopotential (PP) approximation was introduced, where the nucleus and the core electrons were replaced by an effective potential. The exchange correlation energy was estimated using the generalized gradient approximation with the Perdew-Burke-Ernzerhof functional (PBE) [7]. Brillouin zone sampling was done by the Monkhorst-Pack scheme [8] and was sampling on 10 × 10 × 10 irreducible k points. The ultra-soft pseudopotential was employed with a cut off energy E cut off = 400 eV, with an energy tolerance of 5.10 −6 eV/atom.

Structural and elastic properties
To achieve the ground state properties, we have performed both spin polarized and non spin polarized calculations as presented in Fig. 1. The energy difference: E = E S P − E SN P for Fe 3 AlC, Fe 3 GaC and Fe 3 InC is about −0.10, −0.13 and −0.20 eV respectively. These quantities ensure a good stability of these compounds in the magnetic state. From Table 1, the calculated lattice parameter a and the equilibrium volume V are in well satisfactory with the experimental results reported in Ref. [1].
According to Hooke's law, single crystal elastic constants of Fe 3 AC; A= Al, Ga and In, were determined by a linear fit of the stress-strain data. The elastic behaviour can be described by three independent elastic constants [9] C 11 , C 12 and C 44 . C 11 values are higher about 84%, 84% and 77% than C 44 for Fe 3 AlC, Fe 3 GaC and Fe 3 InC respectively.
Polycrystalline elastic constants B and G are obtained with the Hill's assumption. The bulk modulus B and G MATEC Web of Conferences  [3]. The obtained bulk modulus of Fe 3 AlC is about 16% higher than the reported one by Ouyang et al. [4]. Shear modulus G is defined as the response of a material against hydrostatic pressure within shape change [9], G decreases by 9% from 110 to 100 GPa for Fe 3 AlC and Fe 3 InC respectively. The results show that the ratio G/B is around 0.5 for all compounds under study suggesting a ductile behaviour of these materials.

Electronic and magnetic properties
Since the equilibrium ground state was defined to be stable in the magnetic state, we have calculated the band structure (BS), the total (TDOS) and the partial (PDOS) densities of states for both spin up and down states. Only the results for Fe 3 GaC are presented. The band structure reported in Fig. 2 shows an important overlapping around the Fermi level, pointing out to the electrical conduction state in these compounds.
The spin polarized results for both TDOS and PDOS are presented in Fig. 3, for Fe 3 GaC. The valence band structure of Fe 3 AC is formed from two parts. The lower part located under −12 eV originates from C(s), and Fe (s, d) electrons. The upper one, extend from −9 eV to Fermi level, originates from A(s,d), Fe d and C p electrons. The conduction band above the Fermi level is a contribution  The estimated magnetic moment of Fe atom is 1.16 µ B in Fe 3 AlC and increases to 1.32 µ B in Fe 3 InC, it is mainly arises from d electrons. The magnetic moment of Fe in Fe 3 AlC is in good agreement with that reported in Ref. [4].
From Fig. 4, it was observed that Fe-C bonds in Fe 3 AC are very strong and of covalent-ionic nature. Fe-A are less strong and show ionic nature, A-A bonds are the weakest and exhibit metallic character. These results are in agreement with the observed hybridized states in Fig. 3.

CONCLUSION
The calculated lattice parameter a and the equilibrium volume V are in agreement with the experimental results. The results show that these compounds are more stable in the magnetic state. The bulk modulus B and G decrease with the atomic number Z of A elements. Based on the BS and the PDOS, we have observed that only the Fe d electrons are involved in the electrical conduction. The plot of the valence charge density shows a mixture of covalent, ionic and metallic bonds which maintain the crystal stability.