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Computational Predictions of the Electronic and Magnetic Properties of Alkali Metal Chlorides A2MCl6 (A= Alkali Metal, M = Mn, Mo): A Density Functional Theory Study

Detailed first-principles calculations of the electronic structure inclusive of magnetic properties of alkali metal chlorides of the type A2MCl6 (A = Alkali metal, M= Mn, Mo) have been performed using the density functional theory (DFT). The calculated optimized lattice constants show close agreement with experimental results. The electronic band structure and density of states were investigated for the first time using different schemes of generalized gradient approximation (GGA) such as Wu-Cohen GGA, modified Becke Johnson potential and GGA plus Hubbard U parameter method. We found that the Hubbard U correction significantly improves the current DFT results. The calculated band structures of K2MoCl6 or Cs2MoCl6 indicate that the spin up electrons have metallic structure while the spin down configurations have semi-conducting nature together resulting in a half-metallic behavior. Finally, the analysis of magnetic properties indicates a ferromagnetic nature for all these compounds. These findings indicate that the alkali metal chlorides K2MoCl6 and Cs2MoCl6 are potentially promising candidates for future applications in the field of spintronics.

The so-called half-metallic compounds, whose one state is metallic and the other insulator (or semiconductor) has attracted growing interest in the recent past due to their use in spin based electronics [1]. However, most of these materials are inherently non-magnetic, restricting their applications to the field of spintronics [2]. For possible applications in spintronics, it is necessary to discover materials with ferromagnetism at room-temperature and complete (100%) spin polarization at Fermi level [3]. Half-metallic magnets, having a metallic state in one spin direction and a semiconducting/insulating nature in the other spin direction, are proved to be the favorable materials for spintronics [1]. These materials possess large magnetoresistance (MR) and can be practically used as spin valves, spin filters, and magnetic sensors [4,5]. In these materials, we not only consider charge of the electron but also its spin in order to produce faster processing speed in high-tech electronic devices [6]. The successful use of the electronic charge with its spin makes spintronic devices ideal and more useful than the ordinary devices. De Groot and Mueller first discovered half-metallicity in magnetic half-Heusler alloys NiMnSb and PtMnSb [7]. Since then, many reports have been published in the literature predicting half metallic characteristics in most of the new compounds. A large number of half metallic compounds have been predicted theoretically and confirmed experimentally including half and full-Heusler alloys, perovskite compounds, metallic oxides, chalcogenides, and transition metal pnictides [4,[8][9][10].
Here we present a detailed study of another kind of half metallic compounds, the alkali metal halides with anti-fluorite structure of the type A 2 MCl 6 (A= Alkali metals and M = Mn, Mo). In these compounds, half metallicity arises due to the strong spin polarization of transition metal dstate and halogens ion p-state [3]. A lot of literature data has been published on the structural properties of this important group of compounds [11][12][13][14][15][16]. However, very limited amount of data is available about the electronic properties of these compounds. Donald et al. [11] systematically studied the lattice energies and thermo-chemistry of hexachloromolybdates K 2 MoCl 6 and Rb 2 MoCl 6 . They found that the lattice energies of K 2 MoCl 6 and Rb 2 MoCl 6 are 1418 kJ/mol and 1347 kJ/mol, respectively. By performing first principles calculations, Deeth and Jenkins [12] predicted the heterolytic bond enthalpies E(M-X), bond lengths, and energies of hexahalometallate (IV) complexes. The calculated lattice energies are in fair agreement with the data published elsewhere [11]. Another extensive review by Douglas et al. [13] focuses on the structure of [MoCl 6 ] 2complexes. Based on their study, it is confirmed that A 2 MCl 6 (A=K, Rb, Cs; M = Mn, Mo) possesses cubic structure with space group 3 . Moews [14] successfully synthesized the crystal, as well as performed studies related with the visible and ultraviolet spectra of the single crystal K 2 MnCl 6 . They concluded that the compound exhibit anti-fluorite cubic structure with unit cell length of 9.6445 ± 0.0020 Å. The bond length for Mn-Cl is 2.276 Å while for K-Cl it is 3.412 Å. The rubidium and cesium hexachloride complexes (Rb 2 MnCl 6 and Cs 2 MnCl 6 ) were also prepared and are known to have the same structures as reported for K 2 MnCl 6 . Norman carried out magnetic susceptibility measurements of K 2 MnCl 6 , K 3 Cr(CN) 6 , and V(bipy) 3 (ClO 4 ) 2 in the low-temperature range from 76 K to 295 K [15]. The susceptibilities were found to increase upon decreasing the temperature. Furthermore, the magnetic moments were also measured and found in reasonable agreement with the spin only moment. Another group of researchers [16] successfully measured the magnetic susceptibility of A 2 MnCl 6 (A = NH 4 + , K + , Rb + ) salts at different temperatures. The same group also determined the crystal structure of hexametallates by powder X-ray diffraction technique.
The above discussion shows that considerable efforts have been made in the past to know the structural properties of alkali metal halides. However, the electronic and magnetic properties of these compounds are still largely unexplored. We hereby present the results of our computational investigation of the electronic and magnetic properties of alkali metal halides using the rapidly developing approach of density functional theory. Here we focus on calculating the lattice constant, bond length, band structure, electronic density of states, and magnetic properties of four different compounds, namely K 2 MnCl 6 , K 2 MoCl 6 , R 2 MnCl 6 , and Cs 2 MoCl 6 .

Calculations Method
The calculations presented in this work are based on the Kohn-Sham formalism of the density functional theory as implemented in the computer code Wien2k [17]. The exchange-correlation energy ( ) are treated with the Wu-Cohen GGA [18], Tran-Blaha modified Becke Johnson potential [19] and GGA plus Hubbard U functional [20] with spin polarization. The optimized crystal structure and lattice parameters are obtained using the Wu-Cohen GGA functional. The optimized structure geometry is then used to investigate the electronic band structure, the total and partial density of states, the elastic constants, different elastic moduli, and total cell magnetic moment. Due to the well-known underestimation problem of standard LDA/GGA in describing complex systems we use the on-site Coulomb energy (U) in our calculations for the transition metals (TMs) Mn and Mo which have partially filled d and f orbitals. In GGA scheme, the exchange-correlation energy ( ) is a functional of localized charge densities and their gradients: Where ρ ↑ , ρ ↓ are electron charge densities for the spin up and spin down configurations and ∇ρ ↑ , ∇ρ ↓ , are the corresponding gradients corrections. Further details about the spin polarized method (-GGA) and their formulas used in the present calculations were reported in earlier works [17,21].To account for the self-interaction error in TMs d and f states we used the DFT+U method introduced by Anisimov and co-workers [22][23][24], which meet the high proficiency of LDA/GGA and treatment of the electron correlation with Hubbard model. The parameter U can be determined with the help of linear response theory [25].
In the full-potential scheme, the core orbitals are treated fully relativistically, whereas the valence orbitals are treated semi-relativistically. All the calculations have a kinetic energy cutoff of 400 eV, which is fairly large for the compounds studied here. The size, shape, and the relative

Structural Properties
As a first step towards analysis of the structural properties of the compounds, all the lattice structures and atomic positions were optimized by minimizing the forces acting on the respective atoms using the WC-GGA approach. The optimized unit cell structure (a view along a-axis) is shown in Fig. 1a. The monovalent cation (K/Rb/Cs) is coordinated by twelve halogen ions, whereas each tetravalent cation (Mn/Mo) is coordinated by six halogen ions (Fig. 1b), forming an octahedron. The anion Cl is 6-fold coordinated. All the compounds investigated in the present study crystallize in anti-fluorite type structure with space-group   [14,16,27,28]. The increase in bond length, Mn-Cl and Mo-Cl, is observed as we move from K to Rb to Cs which is attributed to the larger atomic size of Cs than K and Rb.

Electronic Properties
To predict the electronic properties of A 2 MoCl 6 (A=K, Cs) and A 2 MnCl 6 (A=K, Rb) systems, the spin dependent electronic band structure and density of states are calculated using the optimized geometry. Different exchange-correlation energy functionals namely, spin polarized WC-GGA, TB-mBJ, and GGA+U accompanied with spin polarization are used in order to get the detailed information of the electronic nature for all these compounds. We also checked the electronic properties of the above compounds using non-spin GGA calculations. In simple GGA calculations, the band structures profile shows overlapping bands across the Fermi level (not shown for brevity), suggesting these compounds as metallic solids. Upon adding spin of the electron, the three different methods (GGA, TB-mBJ, and GGA+U) reveal an intriguing halfmetallic character of the compounds K 2 MoCl 6 and Cs 2 MoCl 6 . The majority spin-channel shows metallic character with zero bandgap, while the minority spin-channel shows a semiconducting nature with wide bandgap. The band structure plot of A 2 MoCl 6 obtained at GGA+U level is shown in Fig. 2(a, b). From the plot, it can be seen that the valence-band maximum (VBM) of  Table 3 shows that in both the calculations the bandgap decreases with replacing K by Rb or Cs. According to our calculations, the mBJ and GGA+U method produces quite better results as compared with simple GGA. As still there is no experimental and theoretical data available for comparison, we hope that our results may offer useful guidance for further experimental and theoretical research in this direction in the future.
For A 2 MnCl 6 (A=K, Rb) compounds, the band structure plots are obtained using exactly the same approach as described above for A 2 MoCl 6 . The WC-GGA and mBJ calculations predict the compound Rb 2 MnCl 6 as half metallic. However, when GGA+U method is employed, the compound shows spin polarized semiconducting nature. For K 2 MnCl 6 , the plots are shown in

Magnetic Properties
The magnetic properties of the selected compounds were investigated using the spin polarized calculations based on the DFT. The magnetic moments and spin-resolved density of states (DOS) were calculated in order to explain the complete magnetic nature of the compounds. Our calculations reveal that both the systems, A 2 MoCl 6 (A= K, Cs) and A 2 MnCl 6 (A= K, Rb), are in ferromagnetic state. Table 4 shows the total cell magnetic moment, partial magnetic moment, and interstitial region magnetic moments of A 2 MoCl 6 and A 2 MnCl 6 , calculated using GGA, mBJ, and GGA+U method. From the table, it is obvious that the total cell magnetic moment of the compounds calculated with mBJ method is an integral value, which meets the criteria of a half metal as suggested by Slater-Pauling rule [37]. The positive value of the magnetic moment indicates that the magnetic ground state is ferromagnetic for A 2 MoCl 6 and A 2 MnCl 6 . As addressed in Table 4, the magnetic moment of Mo is 1.9192μ B and 2.3900μ B in the compounds K 2 MoCl 6 and Cs 2 MoCl 6 while the magnetic moment of Mn is 3.0934μ B and 3.8928μ B in K 2 MnCl 6 and Rb 2 MnCl 6 , respectively. In all the compounds, the magnetic moment seems to be mostly contributed by Mo and Mn, while the remaining atoms i.e. K, Rb, and Cs have little contribution to the total cell magnetic moment. Further, the Cl-atom is polarized antiparallel with a negative value of the magnetic moment.
In order to gain more information about the magnetic moments shown in Table 4, we calculated the spin-resolved density of states ( Fig. 3 -4)

Conclusions
We have systematically performed electronic structure calculations of the alkali metal chlorides of the type A 2 MCl 6 (A= Alkali metals and M = Mn, Mo) using density functional theory. We used the spin-polarized WC-GGA, mBJ, and GGA+U method in order to accurately determine the structural, electronic, and magnetic properties of these compounds.   Table 3 The calculated energy bandgap (in eV) for K 2 MoCl 6 , Cs 2 MoCl 6 , K 2 MnCl 6 , and Rb 2 MnCl 6 using WC-GGA, mBJ, and GGA+U method. Table 4 The calculated partial and total magnetic moments for the family of the compounds A 2 MoCl 6 /A 2 MnCl 6 .        Table 3 The calculated energy bandgap (in eV) for K 2 MoCl 6 , Cs 2 MoCl 6 , K 2 MnCl 6 , and Rb 2 MnCl 6 using WC-GGA, mBJ, and GGA+U method.  Table 4 The calculated partial and total magnetic moments for the family of the compounds