First Principles Calculations for Structural, Electronic, and Magnetic

Article pubs.acs.org/JPCC

First Principles Calculations for Structural, Electronic, and Magnetic Properties of Gadolinium-Doped Alumina Clusters Amol B. Rahane,†,‡ Mrinalini D. Deshpande,*,† and Vijay Kumar§ †

Department of Physics, HPT Arts and RYK Science College, Nasik, Maharashtra 422 005, India Department of Physics, University of Pune, Pune, Maharashtra 411 007, India § Dr. Vijay Kumar Foundation, 1969 Sector 4, Gurgaon, Haryana 122 001, India ‡

S Supporting Information *

ABSTRACT: Atomic structures and physical properties of Gd-doped alumina clustersnamely, GdAl2n−1O3n and Gd2Al2n−2O3n with n = 1−10 have been studied within the framework of spin-polarized density functional theory and the projector augmented wave pseudopotential method. We find that the atomic structures of the host clusters (Al2O3)n are not changed significantly by the substitutional doping of a Gd atom on Al sites. Our results show that in the size range of the clusters we studied, a Gd atom prefers a maximum 4-fold-coordinated Al-site, except for n = 8, in which a 5-foldcoordinated Al site is favored. The substitution of Al with Gd atom is energetically favorable. This is in contrast to the substitutional doping of Gd in the bulk alumina corundum structure that is endothermic. There is a net magnetic moment of 7 μB per Gd atom, which is mostly localized on the Gd atom. Further substitution of an Al atom with Gd in GdAl2n−1O3n clusters results in the lowest-energy configuration's being either ferromagnetic or antiferromagnetic, the difference between the two magnetic states being very small. The variation in the magnetic state is found to be associated with the variation in the coordination number of Gd atoms and the sites of the two Gd atoms. Our results suggest that Gd doping of nanoparticles offers an interesting way to prepare Gd-doped ceramic materials.

1. INTRODUCTION Doping of rare earth (RE) elements in oxides is widely used to produce luminescent and magnetic materials. By doping different RE elements, it is possible to obtain three colors required for color imaging.1 Recently, luminescence studies on RE-doped Al2O3 powders under UV excitations showed bright red luminescence due to Eu3+ ions and green luminescence due to Eu2+ ions.2 Also in recent years, there has been an important development3 in which lasing quality Nd- or Gd-doped YAG crystals have been produced by using alumina and yttria nanoparticles. Using a ceramic particle route, it has been possible to produce crystal quality YAG samples with differing Nd or Gd (or both) concentrations and achieve high dopant concentrations, in contrast to normal crystal growth methods by which very small quantities of Nd (1%) could be doped into YAG.4,5 From these experiments, it appears that Nd or Gd doping is easier to achieve in nanoparticles compared with bulk. Furthermore, in recent years, doping with RE elements in alumina-based ceramics has received considerable attention because of significant improvement in the mechanical properties.6 The addition of a small amount of RE oxide in alumina sensitively changes the mechanical properties and reduces the creep rate by ∼2 orders of magnitude.7,8 Aluminum oxide has also recently been found to be thermally and chemically stable on Si and can serve as a high-k material.9 Some previous studies10,11 report an increase in the dielectric constant of metal oxides such as Ga2O3 and Al2O3 with the doping of RE ions © 2012 American Chemical Society

such as La and Gd. Doped oxide surfaces are also currently attracting interest in catalysis, and doped nanoparticles of oxides are being explored for catalytic activity. Aluminum oxide is also widely used as an insulating barrier in magnetic tunnel junctions because of its large forbidden gap. Studies in such tunnel junctions have been actively pursued in the past few years for their fundamental complexity as well as for their application potential in data storage industry.12 The charge-trapping properties of RE-doped Al2O3 suggests its potential application in nonvolatile memory devices.13 Future higher communication rates and greater data density will likely depend on new RE-ion-doped materials in which the local environment is manipulated to alter the magnetic and optical behavior. To understand the physics and chemistry of surfaces and nanostructures, we consider ternary clusters of gadolinium and aluminum oxide because an understanding of the doping of Gd in alumina nanoparticles could be very important for the processing of RE-doped ceramic materials. Recently, we initiated a systematic study of the evolution of the structural and electronic properties of metal oxide clusters and obtained the equilibrium structures, bonding nature, and other electronic properties of (Al2O3)n, n = 1−10 clusters.14 In the present Received: January 4, 2012 Revised: February 14, 2012 Published: February 15, 2012 6115

dx.doi.org/10.1021/jp300086y | J. Phys. Chem. C 2012, 116, 6115−6126

The Journal of Physical Chemistry C

Article

Figure 1. Atomic structures of the lowest and some of the low-lying isomers of GdAl2n−1O3n clusters along with the host cluster (Al2O3)n (n = 1−5). The white, red, and gray spheres represent Al, O, and Gd atoms, respectively.

2. COMPUTATIONAL DETAILS

study, we aim to understand the variation in the structural, electronic, and magnetic properties of Gd-doped alumina clusters as the cluster size and Gd concentration are varied. Specifically, we focus on the study of the atomic structure and magnetic properties of GdAl2n−1O3n and Gd2Al2n−2O3n clusters using density functional theory. The rest of the paper is organized as follows. Section 2 describes the computational method. The results are presented and discussed in Section 3 and 4. A summary of the results is given in Section 5.

The calculations have been performed using spin-polarized density functional theory within the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof.15 The projector augmented wave pseudopotential method16,17 as implemented in the Vienna Ab Initio Simulation Package (VASP)18,19 has been used. The clusters were placed in a cubic supercell with an edge of 24 Å, and periodic boundary conditions were imposed. The cutoff energy for the plane wave was set to 282.8 eV, as recommended in the VASP code for oxygen with medium precision. The geometries of the host (Al2O3)n clusters were taken from our earlier work,14 where it 6116



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Figure 2. Atomic structures of the lowest and some of the low-lying isomers of GdAl2n−1O3n clusters along with the host cluster (Al2O3)n (n = 6− 10). Other details are the same as in Figure 1.

bulk α-Al2O3 phase using VASP by keeping the same exchangecorrelation functional. For the bulk calculations the energy cutoff for the plane wave expansion was increased by 25% than that of the cluster calculations as in this case we also performed optimization of the cell volume and shape as well. Further for the Gd-doped cases, full optimization of the lattice parameters is performed by substituting one of the 6-fold-coordinated Al atoms with a Gd. These calculations have been done by considering a large (3 × 3 × 1) supercell consisting of 270 atoms to represent bulk α-Al2O3. A large supercell is needed to understand the effects of the doping of Gd atom. In these cases with large supercells, we have performed Brillouin zone

was also shown that the present method gives a good description of the atomic structures and bonding in these clusters. For the doped clusters, the lowest-energy structure was obtained by changing the position of the Gd atoms at different Al sites. The structures were optimized without any symmetry constraint, and the calculations were considered to be converged when the force on each ion was 6, the coordination number of both the Gd atoms is 4, except for n = 8, in which case the coordination number for both the Gd atoms is 5. Overall, in the lowest-energy configurations, both Gd atoms minimize Gd−Gd interactions by selecting the farthest equivalent sites of the Al atoms. The configurations where both the Gd atoms are interacting via an O atom are the low-lying configurations. It is found that in Gd-doped alumina clusters, the Gd−O bonds are longer than the Al−O bonds of the host clusters. The magnetic coupling (FM or AFM) between the two Gd atoms is weak, and both FM and AFM states are nearly degenerate in most

higher energy for Al2O3. The Gd−O and Gd−Gd BLs are 2.09 and 2.82 Å, respectively, which agree with the previous results.29,37 The ground state is an antiferromagnetic (AFM) state with 0 μB, the ferromagnetic (FM) state with 14 μB magnetic moment being 0.015 eV higher in energy. This result is in agreement with the previous studies.37,38 For n = 2−5, the geometries of the lowest-energy Gd2-doped configurations are similar to those of configurations with one doped Gd. All the Gd atoms in this size range are 3-fold coordinated, and the second Gd atom prefers the same coordination site as the first Gd atom, except for n = 4. For n = 4, one Gd atom is 4-fold coordinated, and the other Gd atom is 3-fold coordinated. For n = 5, for one 3-fold-coordinated Gd atom, the Gd−O BLs are ∼2.1 Å, and for the other Gd atom, two oxygen atoms are at a distance of 2.05 Å and the third oxygen atom is at a distance of 2.41 Å. The minimum Al−O and Gd−O BLs in the lowest-energy isomers for n = 2−5 are in the ranges of 1.69−1.72 and 2.05−2.1 Å, respectively. This suggests that doping of a second Gd tends to decrease the nearest Al−O BLs. The FM state is preferred for n = 2 and 3, where the coordination number of both Gd atoms is 3. For n = 4 and 5, the AFM state is preferred. Our results show that the difference in energies of FM and AFM isomers is very small. For example, for n = 4, the ground state has an AFM configuration, but the FM state is nearly degenerate (ΔE = 0.0004 eV). For n = 6−10, with the increase in cluster size, the coordination of the Gd atom also increases. For n = 6, the second Gd atom in Gd2Al10O18 prefers a 4-fold-coordinated Al site in GdAl11O18 that has a 3-fold-coordinated Gd atom. The minimum Gd−O BL for the 3-fold-coordinated Gd atom is 2.07 Å, and for the 4-fold-coordinated Gd atom, it is 2.11 Å. The configuration in which both the Gd atoms substitute for 4fold-coordinated Al atoms as shown in 6b is 0.44 eV higher in energy. In isomer 6c, both the Gd atoms are 3-fold coordinated, and it lies 1.31 eV higher in energy than the lowest-energy 6123



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Note that the doping of REs in bulk alumina is generally endothermic.39 The cohesive energies for α-Al2O3, Gd-doped α-Al2O3, and Gd2-doped α-Al2O3 are 6.455, 6.452, and 6.450 eV/atom, respectively. The total cost to dope a Gd atom at an octahedral site in alumina is 0.76 eV. This is because of the larger size of an Gd atom compared with that of an Al atom. The atomic size mismatch appears to be the origin of the lower stability of Gd-doped α-Al2O3. However, in clusters, the doping occurs on the surface, and the strain due to the large size can be reduced; that is why the doping becomes energetically favorable. With the increase in cluster size, the doping would continue to be favored on a surface Al site; that is why we can expect that the gain due to Gd doping will saturate. These results also point to the possibility of energetically favorable doping of Gd atoms on the surfaces of large nanoparticles as well as bulk surfaces. Because the Gd atoms tend to occupy the farthest sites in nanoparticles, by using smaller nanoparticles, it should be possible to accommodate high concentrations of Gd atoms; therefore, our results indicate that the use of alumina nanoparticles for ceramic preparation makes it easier to dope Gd, and in general, we shall expect similar results for the doping of other rare earth elements. The enhanced stability of the Gd-doped clusters is further reinforced by examining the fragmentation energies involving the fragmentation channels via dissociation of Al2O3 and Gd2O3 units. The fragmentation energy is defined as

cases. The Gd−O BLs for the AFM state are slightly smaller (0.004%) than in the FM state.

4. STABILITY AND MAGNETIC PROPERTIES The stability of these clusters can be found by calculating the BE per atom (Eb). The BE is calculated as Eb[Al(2n − m)O3nGd m] = ( −E[Al(2n − m)O3nGd m] + (2n − m)E[Al] + 3nE[O] + mE[Gd])/(5n)

where E is the total energy of the system. Figure 6 shows that the BE per atom of (Al2O3)n, n = 1−10, clusters increases with the cluster size,14 and approaching

Δ1E = E⎡⎣Al(2n − m)O3nGd m⎤⎦ − E⎡⎣Al(2n − m − 2)O(3n − 3)

(

Gd m⎤⎦ + E[Al2O3]

)

for the dissociation of the Al2O3 unit and Figure 6. The BE (eV/atom) for the lowest-energy configurations of (Al2O3)n, GdAl2n−1O3n, and Gd2Al2n−2O3n (n = 1−10) clusters. The BE (eV/atom) for the two Gd doped in the supercell of bulk α-Al2O3 configuration is also shown.

Δ2E = E⎡⎣Al(2n − m)O3nGd m⎤⎦ − E⎡⎣Al(2n − m)O(3n − 3)

( Gd(m − 2)⎤⎦ + E[Gd2O3])

slowly towards the bulk Al2O3 value.21,22 A comparison of the BE of Gd and Gd2-doped clusters with the BE of the host (Al2O3)n clusters (n = 1−10) clearly indicates that the substitution of Al atoms by Gd is energetically favorable. Up to n = 4, for Gd-doped clusters, the BE increases substantially as compared with the BE of the host cluster. After n ≥ 5, it increases with n slowly. The BE curve of Gd2Al2n−2O3n shows a nature similar to that of the host and GdAl2n−1O3n clusters with a decreasing energy difference between doped and undoped clusters. For n ≥ 6, the structures are stabilized with the coordination of approximately four oxygen atoms for each Gd. Although the energy gain due to Gd doping in a cluster is similar with increasing size, the gain in BE per atom decreases, which is expected.

for the dissociation of the Gd2O3 unit. Here, E is the total energy of the system. The fragmentation energies for the dissociation of an Al2O3 unit from the host as well as from Gd- and Gd2-doped clusters are in the range of 7.7−9.4 eV, which indicates that the given clusters are quite stable against dissociation of an Al2O3 unit. The energies for the dissociation of Gd2O3 from Gd2Al2n−2O3n clusters are in the range 6.4−7.8 eV. This means that it is easier to dissociate a Gd2O3 molecule than Al2O3. It is because the BE of the Gd2O3 molecule is higher compared with the BE of an Al2O3 molecule. We have compared the HOMO−LUMO gap for GdAl2n−1O3n and Gd2Al2n−2O3n clusters with that of (Al2O3)n clusters in Figure 7. Note that the experimental value of the band gap in bulk Gd2O3 crystal is 5.44 eV, and that of the bulk

Table 2. Fragmentation Energies Δ1E (Al2O3) and Δ2E (Gd2O3) in eV of the Ground State Configurations of the Gd(Al2n−1O3n) and Gd2(Al2n−2O3n) (n = 1−10) Clusters n (Al2O3)n Gd(Al2n−1O3n) Gd2(Al2n−2O3n) Gd2(Al2n−2O3n) a

Δ1E wrt Al2O3a

Δ2E wrt Gd2O3a

1

2

3

4

5

6

7

8

9

10

0

9.06 8.75 7.83 7.83

8.65 8.47 8.09 6.86

8.25 8.56 8.94 7.15

8.60 8.08 7.72 6.40

7.51 9.12 9.39 7.40

8.46 8.93 9.16 7.48

9.06 8.22 8.53 7.28

8.24 9.36 8.55 7.77

7.25 9.27 9.10 6.90

wrt = with respect to. 6124



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around the Gd ions, and there is a very weak induced polarization of opposite spin on neighboring O ions. The charge density isosurface is shown for Gd2Al2O6 in Figure 8(a). It shows that there is negligible charge around Al ions, and most of the charge is around O and Gd ions. The charge around Gd ions is due to 4f localized states. The nature of bonding is therefore strongly ionic. Furthermore, it is noted from the charge densities of different clusters that the charge density isosurfaces are similar and that the bonding characteristics remain the same in the series, which explains why the average Al−O and Gd−O BLs remain almost constant with the increase in cluster size. Further, we have calculated the Bader charges for Gd-doped bulk phase. For α-Al2O3, the Bader charges on all the Al atoms are +2.45e, and on the O atoms, they are −1.61e to −1.65e. In Gd-doped α-Al2O3, the Bader charge on a Gd atom is +2.01e, which is lower than that of an Al atom. The Bader charges on the nearest oxygen atoms are in the range of −1.55e and −1.58e. The Bader charges on nearest-neighbor Al atoms increase to +2.46e, as compared with the charges on Al in αAl2O3. Therefore, charge transfer from Gd to O atoms is lower compared with Al atoms. With the increase in coordination of a Gd atom, the charge transfer from Gd to oxygen atoms increases. For n = 5, in the lowest-energy configuration the Bader charge on 3-fold-coordinated Gd is +1.98e (Figure 3), and for 2- and 3-fold-coordinated oxygens, it is −1.39e and −1.55e, respectively. With the increase in cluster size, the coordination number of Gd atom increases. For 4- and 5-foldcoordinated Gd atoms, the Bader charges are +2.02e and +2.01e, respectively. For 3- and 4-fold-coordinated oxygen atoms, these are −1.50e and −1.59e, respectively. Overall, with the increase in cluster size and coordination number, the charge transfer from Gd to O approaches the bulk value.

Figure 7. The HOMO−LUMO gap (eV) for the lowest-energy configurations of (Al2O3)n, GdAl2n−1O3n, and Gd2Al2n−2O3n (n = 1− 10) clusters. The band gaps (eV) for the bulk α-Al2O3, Gd-doped αAl2O3, and Gd2-doped α-Al2O3 configurations are also shown.

α-Al2O3 is 8.7 eV.23 Our calculated value of the band gap for bulk α-Al2O3 is 5.85 eV. The HOMO−LUMO gap for both Gd- and Gd2-doped clusters is in the range of 2.1−3.7 eV. In addition, the band gap for the Gd- and Gd2-doped bulk α-Al2O3 decreases with the Gd concentration. The lower value in our calculations is due to the use of GGA and also due to nonbonding states in clusters that are mostly localized on 2fold-coordinated oxygen atoms. It is found that for Gd2-doped clusters, the HOMO−LUMO gap in AFM state decreases compared with the host clusters. The HOMO level for (Al2O3)n clusters consists of a contribution from the 2-foldcoordinated O atoms only and no contribution from Al atoms is seen. When we substitute Gd for Al, the HOMO level now has contributions from the 2-fold-coordinated oxygen atoms plus a small contribution from the Gd-4f orbitals. It is seen that for clusters with a single Gd, the magnetic moment is 7 μB. The calculated magnetic moment of Gd2Al2n−2O3n clusters oscillates between 0 and 14 μB. The clusters with n = 4, 5, 6, 9, and 10 prefer the AFM state, but in general, the AFM and FM states for the lowest-energy atomic structure of a given cluster are nearly degenerate. The variation in the magnetic moment is found to be associated with the variation in the coordination number of Gd atoms and the sites of the two Gd atoms. The magnetic polarization for the Gd2Al2O6 cluster in the AFM and FM states is shown in Figure 8(b) and 8(c). It can be seen that the polarization is strongly

5. CONCLUSIONS Stability and magnetic properties of GdAl2n−1O3n and Gd2Al2n−2O3n clusters with n = 1−10 have been studied from ab initio calculations. In a cluster, the Gd atom prefers to substitute on a 4-fold-coordinated Al site, which facilitates a stronger coupling between Gd-sd and O-p orbitals. Our results show that substitution of an Al with a Gd atom is energetically favorable, but in the case of bulk α-Al2O3, Gd doping is energetically unfavorable, and with the increase in the concentration of Gd atoms, the stability decreases. This is because of the larger size of an Gd atom compared with that of an Al atom. The atomic size mismatch appears to be the origin of the lower stability of Gd-doped α-Al2O3. These results suggest that doping of Gd and, in general, rare earths in nanoparticles offers an attractive route to prepare rare-earthdoped ceramic materials, such as YAG, which has been attracting much interest in recent years. The HOMO−LUMO gap of Al2O3 clusters is affected by the doping of Gd atoms, but in many cases, the change is small. It is found that in the bulk phase, the band gap decreases with the increase in the Gd concentration. The substitution of Al with Gd leads to a large magnetic moment of the host clusters. In the case of GdAl2n−1O3n, the magnetic moment becomes 7 μB and for Gd2Al2n−2O3n, it becomes 14 μB for the FM and 0 μB for the AFM states. In the case of Gd 2 -doped α-Al 2 O 3 , ferromagnetic behavior is observed. The present study may also have important implications for potential applications of Gd-doped Al2O3 nanoparticles in magnetic refrigeration as well as MRI contrast agents. The

Figure 8. (a) The total charge density, (b) the total magnetization density [ρ↑−ρ↓] for the FM configuration, and (c) the total magnetization density [ρ↑−ρ↓] for the AFM configuration of the Gd2Al2O6 cluster. The red and blue colors represents the positive and negative spin densities, respectively. Most of the polarization is around Gd ions, and a small polarization is induced on neighboring O ions. 6125



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(12) de Groot, C. H.; Ouyang, Y.; Koo, S.-M.; Kendall, E.; Shu, Q. Q.; Moodera, J. S. J. Phys.: Condens. Matter 2002, 14, 5153. (13) Kim, D. H.; Lim, D. J. Korean Phys. Soc. 2010, 57, 1444. (14) Rahane, A. B.; Deshpande, M. D.; Kumar, V. J. Phys. Chem. C 2011, 115, 18111. (15) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (16) Blöchl, P. E. Phys. Rev. B 1994, 50, 17953. (17) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758. (18) Kresse, G.; Furthmuller, J. Phys. Rev. B 1996, 54, 11169. (19) Vienna Ab initio Simulation Package (VASP); Technische Universität Wien: Wien, 1999. (20) Lewis, J.; Schwarzenbach, D.; Flack, H. D. Acta Crystallogr. A 1982, 38, 733. (21) Tefft, W. E. J. Res. Natl. Bur. Stand. A 1966, 70, 277. (22) Weast, R. C. CRC Handbook of Chemistry and Physics, 67th ed.; CRC Press: Boca Raton, FL; 1983. (23) French, R. H. J. Am. Ceram. Soc. 1990, 73, 477. (24) Yadav, B. R.; Rai, S. B.; Rai, D. K. J. Mol. Spectrosc. 1981, 89, 1. (25) Carette, P.; Hocquet, A.; Douay, M.; Pinchemel, B. J. Mol. Spectrosc. 1987, 124, 243. (26) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure. Constants of Diatomic Molecules; Van Nostrand Reinhold: New York; 1979; Vol. VI. (27) Murad, E.; Hildenbrand, D. L. J. Chem. Phys. 1980, 73, 4005. (28) Doi, K.; Fujitani, K.; Kadowaki, N.; Nakamura, K.; Tachibana, A.; Hattori, T. Jpn. J. Appl. Phys. 2005, 44, 6115. (29) Dolg, M.; Liu, W.; Kalvoda, S. Int. J. Quantum Chem. 2000, 76, 359. (30) Neukermans, S.; Veldeman, N.; Janssens, E.; Lievens, P.; Chen, Z.; Schleyer, P. v. R. Eur. Phys. J. D. 2007, 45, 301. (31) Herzberg, G. Spectra of Diatomic Molecules; Van Nostrand: New York, 1950. (32) Gingerich, K. A. Faraday Symp. Chem. Soc. 1980, 14, 109. (33) Rajesh, C.; Majumder, C. J. Chem. Phys. 2009, 130, 234309. (34) Nayak, S. K.; Khanna, S. N.; Jena, P. Phys. Rev. B 1998, 57, 3787. (35) Kant, A.; Lin, S. S. Monatsh. Chem. 1972, 103, 757. (36) Tang, W.; Sanville, E.; Henkelman, G. J. Phys.: Condens. Matter 2009, 21, 084204. (37) Ayuela, A.; March, N. H.; Klein, D. J. J. Phys. Chem. A 2007, 111, 10162. (38) Moon, R. M.; Koehler, W. C. Phys. Rev. B 1975, 11, 1609. (39) Yang, T.; Wang, H.; Lei, M. K. Mater. Chem. Phys. 2006, 95, 211. (40) Jung, R.; Lee, J.-C.; So, Y.-W.; Noh, T.-W.; Oh, S.-J.; Lee, J.-C.; Shin, H.-J. Appl. Phys. Lett. 2003, 83, 5226.

small difference in the AFM and FM energies indicates that the spin ground states and exited states are close in energy, and the spin reversal barrier can be easily compromised by their thermal population. As earlier studies report an increase in the dielectric constant of the metal oxides such as Ga2O3 and Al2O3 with the doping of RE ions such as Gd,11 our results show that doping of RE is achieved more easily in nanoparticles because in nanoparticles, the rare earth dopants can reduce strain due to size mismatch more effectively than in the bulk, and it leads to a gain in energy of the host nanoparticles. Therefore, processing of RE-doped alumina and other oxides could be better achieved via the nanoparticle route, and this material can serve as a promising candidate for an alternative gate oxide replacing silica40 as well as for the preparation of other rare-earth-doped oxide materials for optical and magnetic applications using the nanoparticle route.

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ASSOCIATED CONTENT

S Supporting Information *

The Cartesian coordinates for the lowest-energy configurations for Gd- and Gd2-doped Al2O3 clusters. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS M.D.D. and A.B.R. acknowledge financial assistance from the Department of Science and Technology (DST), Government of India and University Grants Commission (UGC). M.D.D. acknowledges the Center for Development of Advance Computing (CDAC), Pune and Bangalore, for providing the supercomputing facility. M.D.D. and A.B.R. also gratefully acknowledge the Dr. Vijay Kumar Foundation (VKF) for providing local hospitality. V.K. acknowledges financial support from the Asian Office of Aerospace Research and Development (AOARD).

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REFERENCES

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First Principles Calculations for Structural, Electronic, and Magnetic

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