Defect formation energy and magnetic properties of aluminum-substituted M-type barium hexaferrite

Accepted Manuscript Defect formation energy and magnetic properties of aluminum-substituted M-type barium hexaferrite Amitava Moitra, Sungho Kim, Seong-Gon Kim, S.C. Erwin, Yang-Ki Hong, Jihoon Park PII:

S2352-2143(14)00009-4

DOI:

10.1016/j.cocom.2014.11.001

Reference:

COCOM 8

To appear in:

Computational Condensed Matter

Received Date: 21 July 2014 Revised Date:

5 November 2014

Accepted Date: 6 November 2014

Please cite this article as: A. Moitra, S. Kim, S.-G. Kim, S.C. Erwin, Y.-K. Hong, J. Park, Defect formation energy and magnetic properties of aluminum-substituted M-type barium hexaferrite, Computational Condensed Matter (2014), doi: 10.1016/j.cocom.2014.11.001. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

*Manuscript

Defect formation energy and magnetic properties of aluminum-substituted M-type barium hexaferrite

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Amitava Moitraa , Sungho Kimb , Seong-Gon Kimc,b , S. C. Erwind , Yang-Ki Honge , Jihoon Parke a S.N.

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Bose National Centre for Basic Sciences, Sector-III, Block - JD, Salt Lake, Kolkata-98, India b Center for Computational Sciences, Mississippi State University, MS 39762, USA c Department of Physics and Astronomy, Mississippi State University, MS 39762, USA d Center for Computational Materials Science, Naval Research Laboratory, Washington DC, USA e Department of Electrical and Computer Engineering, University of Alabama, AL 35487, USA

Abstract

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The site occupancy and magnetic properties of aluminum-substituted barium hexaferrite BaAlx Fe12−x O19 , with the fraction of Al between x = 0.5 and x = 4, has been investigated using density-functional theory within the spin-polarized generalized-gradient approximation. Our results show that Al3+ ions preferentially occupy the 2a and 12k sites, and exclude the occupancy of 4f1 and 4f2 sites (which were not ruled out in previous experimental studies due to the lack of conclusive data). Our results also show that the saturation magnetization decreases monotonically with the increase of Al concentration in agreement with the available experimental data.

1. Introduction

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Keywords: 75.50.Gg, 75.50.Ww, 07.05.Tp

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Barium hexaferrite BaFe12 O19 (BFO) is one of the most extensively studied permanent magnetic materials among various M-type hexaferrites MFe12 O19 (M = Sr, Ba, or Pb) owing to its high saturation magnetization, good chemical stability, high coercivity and large magneto-crystalline anisotropy.[1, 2, 3] Recently, the material has drawn even more attention for its application in high density magnetic recording media, microwave devices, phase shifter applications and electromagnetic wave absorbers.[4, 6, 5] The knowledge of magnetic interactions among Fe ions on different sites is critical to understanding and predicting several material properties of barium hexaferrite. N´eel[7] and Anderson[8] proposed that these interactions are mediated by superexchange through the oxygen ions.[9] Gorter later proposed a different mechanism based on indirect exchange.[10] The electronic structure of the stoichiometrically similar compound strontium hexaferrite has been calculated by Fang et al. using density-functional theory.[11] Recently, Nov´ak et al. calculated exchange interactions in BFO from the total-energy differences of different collinear spin configurations.[12]

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Email address: [email protected] (Amitava Moitra) Preprint submitted to Computational Condensed Matter

November 3, 2014

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2. Method

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Several researchers have investigated the modification of magnetic properties of BFO by substituting Fe3+ with Mn3+ ,[13] Cr3+ ,[14], Al3+ [16] and recently with other materials. [15, 17, 18, 19] In this manner, Al-substituted BFO was found to have a very large coercivity. At the same time, however, it was shown that the saturation magnetization decreases monotonically with increasing Al concentration. Understanding these phenomena at the microscopic level requires an investigation of the site preference for substituted Al atoms. Magnetism in BFO arises from five crystallographically distinct layers, each of which contains one of the five in-equivalent Fe sites: three octahedral site (12k, 4f2 , 2a), one tetrahedral site (4f1 ), and one trigonal bipyramid or hexahedral site (2b). The Curie temperature of bulk BFO is 740 K,[20] while nanoparticles of BFO have been reported to have the Curie temperature as high as 789 K.[2] A few reports conclude that substituted Al atoms occupy the 2a, 12k, and 4f1 sites,[21, 1] while others report the 4f2 site to be occupied as well.[22, 23] The hyperfine parameters for 2a and 4f1 are difficult to distinguish experimentally.[25] Studies also revealed that Al substitution occurs initially at the 2a, 4f1 , 12k, and 4f2 sites at low concentrations and then at the 12k site at higher concentrations.[25] The coercivity increases up to x = 2, while higher Al content leads to a decrease in coercivity. Although theoretical studies have been done on the exchange integrals[12] and electronic structure[11] of BFO and Sr-hexaferrite, respectively, no theoretical studies have yet addressed the site preference of dopant atoms. The main objective of the present paper is to determine the site preference for Al impurities in BFO by comparing the formation energies of different configurations using first-principles total-energy calculations. We find that Al3+ ions preferentially occupy the 2a and 12k sites, and not the 4f1 and 4f2 sites that were reported earlier.[21, 1, 22, 23] Our results also show that the total magnetic moment of BFO decreases monotonically with increased Al content, in agreement with experiment.

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Although a recent neutron diffraction result [24] shows a gradual transformation of the (Sc-doped) same system into a complex canted structure with spins pointing out of the axial direction, we made our model simple co-linear focusing on the Al-substitutional effect into the system. We use a unit cell containing two formula units of metallic BFO, which allows us to explicitly consider Al concentrations in BaAlx Fe12−x O19 from x = 0.5 to x = 4 in steps of 0.5. Experimentally, Al atoms are introduced to BFO in several different ways, using either a wet chemical process,[23] microwave adsorption,[22] or solgel methods.[1] M¨ ossbauer spectroscopy data[23] show that Al atoms always substitute for Fe atoms, probably because of their similar valence. Hence, in this work we consider that Al only substitutes for Fe. To determine the site preference of subsitutional Al atoms we compare the formation energies ∆Ef , defined as

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∆Ef = Etot − EBF O − NAl (ǫAl − ǫF e )

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where Etot is the total energy of Al-substituted BFO, EBF O is the total energy of pure BFO, NAl is the number of Al atoms that replace Fe atoms, and ǫF e and ǫAl are the atomic chemical potentials of Fe and Al. Atomic chemical potentials (negative quantities 2

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Wyckoff site 2d 2a 2b 4f1 4f2 12k 4e 4f 6h 12k 12k

Symmetry 6m2 3m 6m 3m 3m m 3m 3m mm m m

Atom coordinates 0.3333, 0.6667, 0.7500 0.0000, 0.0000, 0.0000 0.0000, 0.0000, 0.2500 0.3333, 0.6667, 0.0241 0.3333, 0.6667, 0.1912 0.1700, 0.3401, 0.8903 0.0000, 0.0000, 0.1560 0.0000, 0.0000, 0.9456 0.1917, 0.3834, 0.2500 0.1823, 0.3464, 0.0495 0.4880, 0.0139, 0.1542

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Atoms Ba Fe(1) Fe(2) Fe(3) Fe(4) Fe(5) O(1) O(2) O(3) O(4) O(5)

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Table 1: The sublattices and their computed fractional coordinates of M-type barium hexaferrite with a = 5.35 ˚ A and c = 21.19 ˚ A used in the present work.

3. Results

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for stable compounds) are obtained in the ground-state bulk phases – i.e. bcc Fe and fcc Al. The total-energy calculations and geometry optimizations were performed within density-functional theory (DFT) [26, 27] using the projector-augmented-wave method.[28, 29] All calculations were spin polarized. We used the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation.[30] The plane-wave cutoff energy was 400 eV. A conjugate-gradient method[31] was used to relax the ionic positions. Geometry relaxations were performed until the energy difference between two successive ionic optimizations was less than 0.001 eV, which typically makes the magnitude of the force on each atom smaller than 0.001 eV/˚ A. The Brillouin zone was sampled with 50 k-points using the Monkhorst-Pack scheme.[32]

3.1. Pure Ba-hexaferrite (x = 0)

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The hexagonal crystal structure of BFO has the space group P 63 /mmc and is shown in Fig. 1. [9, 33] This structure can be symbolically described as RSR∗ S ∗ where R denotes 2− a three-layer block containing two O4 and one BaO3 with the composition Ba2+ Fe3+ 6 O11 , 3+ 2− while S denotes a two-layer block containing two O4 with the composition Fe6 O8 .[22] The asterisk denotes a rotation of the corresponding block by 180◦ about the c-axis.[9] By optimizing the volume and shape of the unit cell and the internal coordinates we obtained a = 5.35 ˚ A and c = 21.19 ˚ A as the equilibrium lattice constants of the hexagonal unit cell, in a fair agreement with the experimental values of 5.90 ˚ A and 23.24 ˚ A, respectively.[1] Table 1 lists the Wyckoff positions of the 11 in-equivalent atomic sites in the unit cell of BFO: one Ba (multiplicity 2), five Fe (multiplicity 2, 2, 4, 4, and 12), and five oxygen (multiplicity 4, 4, 6, 12, and 12). The total number of atoms occupying these sites in this primitive unit cell is 64. Table 1 also shows the optimized internal degrees of freedom determined in our first-principles calculations.

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Figure 1: (Color online) Crystal structure of M-type barium hexaferrite BaFe12 O19 . Red, pink, gray, blue and yellow colored spheres represent iron atoms in 2a, 4f1 , 12k, 4f2 , and 2b sites respectively. Small green spheres represent oxygen atoms, while larger cyan spheres represent barium atoms.

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4f1 − − − − + −

4f2 − − − + − −

2a + + − + + +

12k + + + + + −

2b + − + + + +

∆E (eV) 0.00 0.84 1.21 2.86 4.25 4.99

σ (µB ) 39.82 19.94 19.59 52.70 66.61 45.92

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Table 2: Relative total energies (∆E) and total magnetic moments (σ) per unit cell of different spin configurations of BFO.

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In Table 2 we compare the total energies and corresponding total magnetic moments of BFO in a number of different spin configurations. Our result confirms that the spin configuration suggested by Gorter[23, 10] – Fe moments in the 4f1 and 4f2 aligned and anti-parallel to those in the 2a, 12k, and 2b sites – indeed has the lowest total energy. Deviations from this configuration impose a substantial energy penalty of at least 0.84 eV. Our result also shows that reversing the spins of tetrahedral ferrite ions at 4f1 site costs more energy than reversing the spins of octahedral ferrite ions at 4f2 . This behavior has also been reported previously for strontium hexaferrite,[11] which is isomorphous with the magnetoplumbite (Pb,Mn)(Fe,Mn)12 O19 .[34] It can also be seen that 12k site costs the most energy (5 eV) to reverse its spin direction compared to other sites. Note that these energies are obtained by reversing the spin direction of itall atoms in particular sublattices. 3.2. x = 0.5

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For Al concentration x = 0.5, one Al atom is substituted in different Fe sites of the unit cell. Since all Fe sublattices listed in Table 1 have more than one equivalent atomic site, this substitution breaks the symmetry among the atomic sites of the affected sublattices. Table 3 shows the relative formation energies of different configurations. The number under each column denotes the number of Al atoms substituted in each Fe sublattice. For Table 3, all spin orientations of the remaining Fe atoms are kept in the Gorter’s configuration as given in Table 2. We constructed all other spin configurations listed in Table 2 and compared their formation energies. We found that whenever the spin configuration is altered from the Gorter’s, the total energy is increased by a substantial amount. For instance, in the case of one Al atom substituted at 2a site (the first row of Table 3), the total energy is increased by 0.72 eV when the spin of 2b Fe atoms is reversed from the minimum energy configuration (the excitation that costs the least amount of energy in Table 2). Table 3 indicates that it is the most energetically favorable to substitute an Al atom into 2a site at the concentration of x = 0.5. 12k is the next probable site for Fe atoms to be substituted by Al atoms. Hence in a diluted limit of x ≤ 0.5, the substituted Al atoms will preferentially occupy 2a site. The positive values for ∆Ef in the last two rows of Table 3 indicate that the substitution of Al atoms into 4f2 or 4f1 site will be energetically unstable compared to pure BFO and separate bulk Al phase. Therefore, we conclude that at the concentration of x = 0.5, one Al atom in the unit cell prefers to occupy 2a site with the Gorter’s spin configuration.

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4f1 0 0 0 0 1

4f2 0 0 0 1 0

2a 1 0 0 0 0

12k 0 1 0 0 0

2b 0 0 1 0 0

∆Ef (eV) -0.75 -0.60 -0.14 0.05 0.24

σ (µB ) 34.31 28.21 34.16 43.89 40.41

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Table 3: Relative formation energies (∆Ef ) and total magnetic moments (σ) per unit cell for Alsubstituted BFO BaAlx Fe12−x O19 for x = 0.5. The number under each column denotes the number of Al atoms substituted in each Fe sublattice.

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3.3. x = 1 For Al concentration x = 1, two Al atoms are substituted in different Fe sites of the unit cell. Two Al atoms can be placed in any two Fe atomic sites that can belong to the same or different Fe sublattices listed in Table 1. Consequently, in most cases this substitution breaks symmetry among the atomic sites of the affected sublattices except in the cases that both Al atoms go in 2a or 2b sublattices. Table 4 shows the relative formation energies and corresponding magnetic moments of different configurations. The number under each column denotes the number of Al atoms substituted in each Fe sublattice. When more than one configuration is possible in each row, only the one with the minimum relative formation energy is given. During the process of finding the minimum energy configuration in each row, we observed that the minimum energy occurs when the distance between Al atoms are greatest. This information will be used to reduce the number of configurations to search for higher Al concentration in later sections. Similar to x = 0.5 case, all spin orientations of the remaining Fe atoms of Table 4, are kept in the Gorter’s configuration. We constructed all other spin configurations listed in Table 2 and compared their formation energies. We again found that whenever the spin configuration is altered from the Gorter’s, the total energy is increased by a substantial amount. For instance, in the case of two Al atoms substituted at 2a site (the first row of Table 4), when the spin of 2b Fe atoms is reversed (the excitation that costs the least amount of energy in Table 2) the total energy is increased by 0.78 eV. Table 4 indicates that both 2a and 12k sites are equally favored by Al atoms at this Al concentration. We note that when two Al atoms are shared in 2a and 12k sites (the second row in Table 4), the relative formation energy increase difference is too small (0.03 eV) to be treated as an excited state. We also note that these two cases produce nearly identical magnetic moments. Therefore, we conclude that at the concentration of x = 1, two Al atoms prefer to occupy 2a site only or one 2a and one 12k sites with the Gorter’s spin configuration.

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3.4. x = 1.5 For Al concentration x = 1.5, three Al atoms are substituted in different Fe sites of the unit cell. Table 5 shows the relative formation energies and corresponding magnetic moments of different configurations. The number under each column denotes the number of Al atoms substituted in each Fe sublattice. When more than one configuration is possible in each row, only the one with the minimum relative formation energy is given. However, the number of possibilities of putting three Al atoms at all 24 available Fe sites (24 C3 = 2024) is rather large for us to compute the relative formation energies 6

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2a 2 1 0 1 0 1 1 0 0 0 0 0 0 0 0

12k 0 1 2 0 1 0 0 1 1 0 0 0 0 0 0

2b 0 0 0 0 1 1 0 0 0 1 1 2 0 0 0

∆Ef (eV) -1.70 -1.67 -1.18 -1.03 -0.92 -0.90 -0.83 -0.80 -0.74 -0.21 -0.06 -0.05 0.26 0.30 0.46

σ (µB ) 29.48 29.49 24.35 29.44 29.28 25.62 38.87 39.29 39.07 31.44 39.07 21.63 45.22 41.39 41.54

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4f2 0 0 0 0 0 0 1 0 1 1 0 0 1 2 0

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4f1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 2

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Table 4: Relative formation energies (∆Ef ) and total magnetic moments (σ) per unit cell for Alsubstituted BFO BaAlx Fe12−x O19 for x = 1. The number under each column denotes the number of Al atoms substituted in each Fe sublattice.

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using first-principles calculations for all possible cases. Therefore, we made a couple of assumptions to reduce the total number of required calculations based on the results of lower concentration cases. For the first two rows of Table 5, energies were calculated for all possible configurations and the ones with the minimum relative formation energies are given. For the remaining rows of Table 5, we made following two assumptions. First, all spin orientations of the remaining Fe atoms are assumed to be in the Gorter’s configuration. This is a well justified assumption since for all Al concentrations we considered so far (x = 0.5 and 1), it has been clearly demonstrated that any deviation from the Gorter’s spin configuration for the remaining Fe atoms costs a substantial amount energy (typically in the order of 1 eV even for the least energy-costing cases). Second, we assume that the minimum energy will occur when the distances between Al atoms are greatest, as demonstrated for x = 1.0 case. For the first two rows of Table 5, we constructed all other spin configurations listed in Table 2 and compared their formation energies. We again found that whenever the spin configuration is altered from the Gorter’s, the total energy is increased by a substantial amount. For instance, in the case of the first row of Table 5 (two Al atoms at 2a site and one at 12k site), when the spin of 2b Fe atoms is reversed (the excitation that costs the least amount of energy in Table 2) the total energy is increased by 1.2 eV. Table 5 indicates that both 2a and 12k sites are equally favored by Al atoms at Al concentration of x = 1.5. Similar to x = 1 case, we note that when three Al atoms are shared in 2a and 12k sites (the first two rows in Table 5), the difference in relative formation energies is too small (0.04 eV) to treat the second one as an excited state. Therefore, we conclude that for x = 1.5 case, three Al atoms prefer to be shared between 2a and 12k sites with the Gorter’s spin configuration. We also note that these two cases produce nearly identical magnetic moments. Therefore, we conclude that at the concentration of x = 1.5, three Al atoms prefer to occupy 2a and 12k sites equally with 7

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the Gorter’s spin configuration. 3.5. Higher Al concentration

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For further Al substitution calculations (x ≥ 2), the number of possibilities of putting Al atoms at all 24 available Fe sites becomes prohibitively large for us to compute the relative formation energies using first-principles calculations. For example, the number of possibilities for x = 2 (four Al atoms in the unit cell) is 24 C4 = 10626. Therefore, we again make a couple of assumptions to reduce the number of required calculations based on the results of lower concentration cases. Firstly, all spin orientations of the remaining Fe atoms are assumed to be in the Gorter’s configuration. For all Al concentrations we considered so far (x = 0.5, 1, and 1.5), it has been clearly demonstrated that any deviation from the Gorter’s spin configuration for the remaining Fe atoms costs a substantial amount energy (typically in the order of 1 eV even for the least energy-costing cases). Secondly, we construct the unit cells of higher Al concentrations by adding additional Al atoms to the ones used to make the first two rows of Table 5 (x = 1.5). For instance, for Al concentration of x = 2, four Al atoms are substituted in different Fe sites of the unit cell. Instead of considering all possible combinations of selecting 4 atomic sites out of 24 Fe atomic sites, we put first three Al atoms in the positions used to make the first two rows of Table 5 and consider the possibilities of placing the last Al atom in the remaining Fe sites only. We computed and compared relative formation energies of all configurations constructed in this manner for Al concentrations of x = 2.0 and 2.5. The results for the configurations with minimum formation energies are listed in Table 6 along with the results of other Al concentrations. For the Al concentrations of x = 1.0 and 1.5 in Table 6, we also show the secondary configurations with nearly identical formation energies as described in the previous sections. We note that these secondary configurations have very similar magnetization with the primary ones. As it is demonstrated in Table 6, the site preference to 2a and 12k sites of Al atoms is clearly established. Therefore, for the last three cases of the Table 6 at the Al concentrations of x = 3, 3.5 and 4.0, we have calculated only the configurations with two Al atoms at 2a sites and the rest of Al atoms at 12k sites with the Gorter’s spin configuration for remaining Fe atoms. In Fig. 2, we plotted the saturation magnetization of Al-substituted BAFO BaAlx Fe12−x O19 as a function of the Al concentration x from our calculations summarized in Table 6. The computed magnetization decreases linearly as the Al concentration x increases, as observed experimentally by Choi et al.[1] The linear reduction of magnetization with the increase of the Al concentration is similar to previously reported behavior.[1, 21] The overestimation of our calculated magnetization values from the experimental values are due to possible non-linearity of the spin system within the BaAlx Fe12−x O19 or due to the fact that we are dealing an infinite simulation cell compared to experiment, where they have used a truncated nanoparticle, or due to both of them. Our calculation shows that this decrease is due to the fact that Al atoms occupy the 2a and 12k sites only, which are majorly contributing towards the total magnetic moment of the system. Substitution of Al atoms of zero magnetic moment decreases the contribution of magnetic moment from those sites, and hence the reduction in total magnetic moment is expected.

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2b 0 0 0 1 0 1 1 0 0 0 0 0 1 1 2 1 2 0 0 1 0 0 0 0 2 1 1 2 0 1 0 0 0

∆Ef (eV) -2.59 -2.55 -2.39 -2.05 -1.97 -1.96 -1.77 -1.77 -1.76 -1.72 -1.71 -1.59 -1.43 -1.28 -1.19 -1.18 -1.15 -1.05 -1.02 -1.01 -0.89 -0.87 -0.73 -0.64 -0.46 -0.36 -0.32 -0.05 0.13 0.20 0.21 0.40 0.46

σ (µB ) 24.57 24.24 34.39 24.23 34.38 24.28 20.69 33.82 34.28 34.01 24.27 34.08 33.52 34.19 24.14 30.18 20.38 43.86 43.85 34.21 40.46 43.28 40.18 40.44 26.23 39.59 39.55 26.65 52.65 36.58 49.75 46.42 46.16

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12k 1 2 1 0 0 2 1 0 2 1 3 2 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0

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2a 2 1 1 2 2 0 1 2 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0

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4f2 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 2 0 0 2 1 0 1 2 1 0 3 0 2 1 0

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4f1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 2 0 1 2 0 0 1 1 0 2 1 2 3

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Table 5: Relative formation energies (∆Ef ) and the total magnetic moments (σ) per unit cell for Alsubstituted BFO BaAlx Fe12−x O19 for x = 1.5. The number under each column denotes the number of Al atoms substituted in each Fe sublattice.

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Table 6: Site preferences for Al atoms in Al-substituted BFO BaAlx Fe12−x O19 and their corresponding total magnetic moments (σ) per unit cell for different Al concentration x.

12k 0 0 0 1 1 2 2 3 4 5 6

2b 0 0 0 0 0 0 0 0 0 0 0

µ(µB ) 39.82 34.31 29.48 29.49 24.57 24.24 19.52 14.41 9.59 5.34 0.33

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2a 0 1 2 1 2 1 2 2 2 2 2

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Experiment by Choi et al. [Ref. 1]

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4f2 0 0 0 0 0 0 0 0 0 0 0

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Magnetic moment per unit cell (µΒ)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

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Figure 2: The dependence of saturation magnetization of Al-substituted BAFO BaAlx Fe12−x O19 as a function of the Al concentration x. The experimental values are obtained from Ref. [[1]].

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4. Discussions

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Our first-principles calculations show that the main driving force of site preference for Al atoms in BAFO is the formation energy. As shown in Table 3, Al atoms prefer to substitute Fe atoms in 2a, 12k, 2b, 4f2 and 4f1 in that order, gaining most formation energy (-0.75 eV) at 2a site while losing most formation energy (+0.24 eV) at 4f1 site. Throughout the cases for higher Al concentration up to x = 4.0, this trend was kept unchanged and caused first two Al atoms to go 2a sites and the rest to 12k sites. Several experimental observations using M¨ ossbauer spectroscopy support this preferential occupation of 2a and 12k sites by Al atoms.[21, 1, 22, 23] However, these experimental studies have not been conclusive enough to distinguish the nearly equal hyperfine parameters for 2a, 4f1 and 4f2 sites,[25] and rule out 4f1 and 4f2 sites. Our relative formation energy calculations show unambiguously that it is very unlikely for Al atoms to substitute Fe atoms at 4f1 and 4f2 sites. To further elucidate the Al substitution process into BFO, we may consider the contribution of exchange interaction energy (J) to the site preference. Nov´ak and Rusz calculated the exchange integrals of BFO for intersublattice and intra-sublattice interactions using GGA+U calculations.[12] Assuming the exchange interaction is short range, they showed that the intersite exchange interaction energies vary from 9 meV for the 2a sites to 20 meV for the 4f2 sites. In the present study, we further found that keeping the Gorters spin configuration for Al-substituted BFO, the total energy still depends on the distribution of Al in different sublattices. 5. Conclusions

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Using density functional theory within the spin-polarized generalized gradient approximation, we have shown that for Al-substituted BFO, Al atoms preferentially go to 2a sites first. Once 2a sites are filled, further substitutional Al atoms occupy the 12k sites. Our calculations also support the experimental fact that magnetic moment monotonically decreased as the concentration of Al is increased. This is due to the fact that non-magnetic Al atoms are substituting the Fe atoms that have majorly contributed toward the total magnetic moment of the system. Finally we showed that the exchange interaction energies are too small compared to the formation energies, and the total energy still depends on the distribution of Al in different sublattices. 6. Acknowledgment

This work was in part supported by the Center for Advanced Vehicular Systems (CAVS) at Mississippi State University and TUE-CMS at S. N. Bose National Centre for Basic Sciences. A.M. acknowledges support from Thematic Unit of Excellence in Computational Materials Sciences under Dept. of Science and Technology, Govt. of India. S.G.K. would like to acknowledge the support of the Henry Family Eminent Scholar Award. S.C.E acknowledges support from the Office of Naval Research. Computer time allocation has been provided by the High Performance Computing Collaboratory (HPC2 ) at Mississippi State University and CRAY computational resources at S. N. Bose Centre.

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 DFT results reveal the Al doped barium hexaferrite (BFO) system.  Saturation magnetization of BFO decreases as Al doping concentration increases.  Formation energies are compared, and found the site preference for Al atoms.  Al atoms substitute the majorly contributing magnetic Fe atoms.  Calculations support the experimental observance of reduced magnetization.