Accepted Manuscript Investigation of structural and multiferroic properties of three phases of BiFeO3 using modified Becke Johnson potential technique Elle Sagar, R. Mahesh, N. Pavan Kumar, P. Venugopal Reddy PII:
S0022-3697(17)30269-X
DOI:
10.1016/j.jpcs.2017.06.023
Reference:
PCS 8106
To appear in:
Journal of Physics and Chemistry of Solids
Received Date: 12 February 2017 Revised Date:
30 May 2017
Accepted Date: 20 June 2017
Please cite this article as: E. Sagar, R. Mahesh, N. Pavan Kumar, P. Venugopal Reddy, Investigation of structural and multiferroic properties of three phases of BiFeO3 using modified Becke Johnson potential technique, Journal of Physics and Chemistry of Solids (2017), doi: 10.1016/j.jpcs.2017.06.023. 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.
ACCEPTED MANUSCRIPT Investigation of structural and multiferroic properties of three phases of BiFeO3 using modified Becke Johnson Potential Technique 1
2
1,2
Elle Sagar , R.Mahesh , N. Pavan Kumar
1,2*
and P.Venugopal Reddy
1.Dept. of Physics, Osmania University, Hyderabad, Telangana State-500007-India. 2.Vidya Jyothi Institute of Technology, Aziz Nagar Gate, Hyderabad-500075-India. Abstract
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Electronic band structure, ferroelectric and ferromagnetic properties of Cubic, Tetragonal and Rhombohedral (hexagonal axis) phases of multiferroic BiFeO3 compound has been investigated using first-principles calculations under the generalized gradient (GGA) and TBmBJ semi local (Tran-Blaha modified Becke-Johnson) potential approximations using
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WIEN2k code. For this purpose, the total energies were calculated as a function of reduced volumes and the data were fitted to Brich Murnaghan equation. The estimated ground state
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parameters are found to be comparable with those of experimental ones. The semiconducting behavior of the material was obtained using TB-mBJ method in the spin polarized mode. Analysis of the density of states indicates that the valence band consists of Fe-d and O-p states, while the conduction band is composed of Fe-d and Bi-p states. The analysis of electron localization function shows that stereochemically active lone-pair electrons are present at Bi sites of Rhombohedral and Tetragonal phases and are responsible for the displacements of Bi
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atoms from the centro-symmetric to the non-centrosymmetric structure leading to the exhibition of ferroelectricity. Further, it has been concluded that the “lone pair” may have been formed due to the hybridization of 6s and 6p atomic orbitals with 6s2 electrons filling one of the resulting orbitals in Bi. The Polarization and the magnetic properties including
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susceptibility were obtained. The calculated magnetic moments at the iron sites are not integer
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values, since Fe electrons have a hybridization interaction with the neighboring O ions. Key words: Multiferroics, TB-mBJ exchange potential, Boltztrap Code, Electron localization Function, charge density.
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fax: +9140 27009002.
E-mail of corresponding author:
[email protected] (P.Venugopal Reddy)
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1. Introduction.
The materials possessing at least two out of the three well- known ferroic orders viz., ferroelectric, ferromagnetic or ferroelastic are called as multiferroics [1, 2]. In recent times these materials have drawn the attention of scientific community due to their potential applications, such as in multifunctional devices, wherein the interaction between the magnetic and electronic degrees of freedom allows both charge and spin can be manipulated by the
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electric or magnetic fields [3,4]. Moreover; the fundamental Physics of these materials is rich, interesting and useful. Among the family of multiferroic materials, BiFeO3 (BFO) has attracted attention of researchers due to its ability to exhibit both ferromagnetic and G-type AFM and ferroelectric properties above the room temperature [5]. In fact, enormous experimental and the
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work based on first principles are going on for the last few years [6–8] mainly to understand the origin of its ferroelectric polarization, weak spontaneous magnetization and high conduction behavior. Recently, Weiwei Mao et.al.[9]
reported that the X-ray diffraction
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analysis confirmed a lattice distortion from a rhombohedral to a tetragonal structure upon doping with Dy and Cr in BFO. Infact, the co-doping in BFO helped in a improving its magnetic behavior. The role of intrinsic factors such as defects, oxygen vacancies in the observation of ferroelectricity and weak ferromagnetism in these materials is still not fully understood. Although, BFO exists in the Rhombohedral phase at room temperature, its high
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temperature phase (Cubic) and its thin film phase (tetragonal) are also interesting because of their close proximity. A systematic investigation of all the three phases and a comparison of electronic, electrical and magnetic properties will throw some more light in understanding
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complex behaviour of BFO.
It is well known that the band gap values calculated using local density
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approximation (LDA) and GGA are very low when compared with the experimental ones [10]. However, the modified Becke- Johanson potential (TB-mBJ) proposed by Tran and Blaha [11] is found to yield more accurate energy band gap values for a wide range of materials [12-18]. The semiconductor gap calculated with mBJ, substantially larger than that with GGA, is in good agreement with recent experimental values.In the present investigation, DFT calculations were performed for band gap calculations using the electron full potential linearizedaugmented-plane-wave (FP-LAPW) method along with Tran and Blaha's modified BeckeJohnson (TB-mBJ) exchange potential and GGA correlation potential. In this work, to compute the electronic and magnetic properties of BiFeO3 compound TB-mBJ potential technique adopting WIEN2k code was used. Efforts have also been made to understand how the first principle methods are useful in elucidating the physical origin of the observed behavior of
Bismuth ferrite. In order to refine the TB-mBJ calculations of BFO samples of the present
ACCEPTED MANUSCRIPT investigation, spin–orbit coupling (SOC) interactions were also considered here. The present study also explains how the electron localization function (ELF) is useful in understanding the hybridization between Bi and O ions. Finally, the role of 6s2 lone pair in explaining the ferroelectric behavior of the material has also been investigated. The results of all these investigations are presented in this paper.
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2. Method of calculations. A systematic investigation of the electronic, optical and thermodynamic properties of three different phases of BiFeO3 compound was carried out using the full potential LAPW method using the WIEN2k [19] code within the generalized gradient approximation (GGA) and TB-
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mBJ to the exchange correlation potential as per the Perdew-Burke-Ernzerhof parameterization with spin polarised calculations [20]. The Brillouin zone sampling was performed using the Monkhorst-Pack scheme [21], for k-space integration of 5000 points in the entire Brillouin
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zone. The number of plane waves in a Fourier expansion of potential in the interstitial region was restricted to RMT×kmax = 8, whereas the Fourier expansion of the charge density was taken as, Gmax=12(a.u)-1. For the total energy calculations, the energy convergence criterion was considered as 10-6 Ry. The full relativistic effects were calculated using Dirac equations for the core states while the scalar relativistic approximation was used for valence states [22]. The electronic contribution to the polarization was calculated as a Berry phase using King-
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Smith and Vanderbilt method [23]. For calculating the temperature versus susceptibility behaviour of BFO, the code Boltztrap [24] with interface with WIEN2k was used. This calculation is based on the semi classical treatment given by the solution of Boltzmann
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equation by embedding certain approximations such as the relaxation time and rigid band. In order to understand the influence of spin–orbit coupling (SOC) on the values of band gap, Density of states and the magnetic behavior of Bismuth ferrite of the present investigation, the
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Spin Orbit Coupling ( SOC ) corrections have been made to the TB-mBJ calculations. For this purpose, the cut-off energy was set to a value of -6 Ry mainly to separate the core states from valance states, while k-mesh size of 10 x 10 x 10 (First Brillouin zone) was used [22]. The self-consistent calculations were considered to be converged only when the integration of absolute charge density difference per formula unit between the successive loops was less than 0.0001|e|, where e is the electron charge. 3. Crystal Structure The simulated crystal structures of BFO are shown in Figures.1. In the unit cell of cubic structure with space group Pm-3m (No. 221), Bi is located at the origin (0, 0, 0), Fe is at the
central position (0.5, 0.5, 0.5) and the three O atoms are at (0.5, 0.5, 0.0), (0.5, 0.0, 0.5) and
ACCEPTED MANUSCRIPT (0.0, 0.5, 0.5) positions as shown in Fig(1a). The lattice parameter value of a=3.9878 Å along with atomic positions were taken from the literature [25]. For tetragonal P4mm phase, the lattice parameters a = 3.67 Å and c = 4.64 Å with Wyckoff atomic positions of Bi (0, 0, 0), Fe (0.5, 0.5, 0.4390), O1 (0.5, 0.5, 0.8540) and O2 (0.0, 0.5, 0.3080) were used, and the simulated crystal structure is shown in Fig.1b [26, 27]. For R3c phase, the lattice parameters, a = 5.5733 Å and c = 13.8424 Å with Wyckoff atomic positions of Bi (0, 0, 0), Fe (0, 0, 0.22046), and O
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(0.44506, 0.01789, 0.95152) atoms were used for simulating the crystal structure [28] as shown in Fig.1.c. The calculated optimized lattice parameters of all the three structures are comparable with the reported (experimental) ones and are given in table.1.
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4. Results and Discussions. 4.1 Electronic properties
The band structure calculations of cubic BFO were carried out using TB-mBJ spin
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polarized method and are found to be better than those obtained from GGA spin polarized ones. The Fermi energy in these calculations is set to zero energy. From the calculated band structure (GGA) of BFO in Pm3m cubic phase is found to have zero energy band gap indicating that the highest valence band overlaps with the lowest conduction band of both spins are shown in (Fig.2(a&d) ). In contrast, the calculations made using TB-mBJ method are found
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to exhibit a small band gap of 0.1eV in spin up and 1.8eV in spin down positions (Fig.2.(b&e)) indicating that in TB-mBJ based calculations, Fe 3d states might have shifted to higher energies and blur along the VB. This might have lead to the separation of the bands near the Fermi level. In fact a similar behavior has been reported in the case of d-states in NiO [29]. In
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order to understand the influence of Spin -Orbit coupling on the band structure of Cubic phase BFO, computations were undertaken by applying corrections to the TB-mBJ calculations and
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the results are shown in Fig. 2(c) and 2(f). It can be seen from the figures that the band gap are found to decrease and the values are given in Table -2. This is possible because the Fe 3d and Bi 4f bands become wider due to the application of SOC corrections. Fig. 2(c) and 2(f) explicitly demonstrates the energy bands obtained using mBJ + SOC. It can be seen from the figures that the energy bands, especially the conduction bands, in both of the spin channels hybridize with each other. Density of states calculations of Pm3m cubic BFO phase were also performed using GGA and TB-mBJ functions with spin polarized method and its variation with energy is shown in Fig. 3. The total and partial density of states (DOS) of cubic BiFeO3 calculated with GGA and the semi local TB-mBJ are shown in Fig.3 (X&Y). Similarly, the influence of SOC on the TB-mBJ calculations is also shown in Fig. 3(c & f). DOS calculations show that both the
valence and conduction bands are occupied with O-2p, Fe-3d and Bi-6p states with significant
ACCEPTED hybridization between Bi-6p, Fe-3d and O-2pMANUSCRIPT states in the range of + 5eV to –5eV. Therefore, the hybridization of Bi-6p – O-2p states in addition to Bi-6s states in DOS demonstrated the absence of lone pair around Bi3+ cations. The band gap values obtained by GGA method both in spin up and spin down positions in the case of tetragonal BFO is found to be zero. However, in the case of TB-mBJ methods the band gap values are found to be 2.1eV (in spin up) and 1.4eV (spin down)
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respectively (Figs. 4 b&d). The zero band gap value obtained using GGA calculations is not unexpected due to the fact that the failure of GGA schemes in predicting the correct electronic band structure especially near Fermi level for transition-metal oxides is well documented. For example, within the LSDA scheme, qualitatively wrong metallic ground state was predicted
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[29, 30]. Application of LSDA+ U scheme is found to produce correct results. For FeO a choice of U = 4.3 eV has been found to produce the observed insulating behaviour [10]. In view of this, in the present investigation, for calculating the band structure of tetragonal BFO,
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the TB-mBJ scheme was adopted and the results are shown in Fig.4. An effort was made to understand the influence of SOC on the band structure of tetragonal BFO and the results are also shown in Fig.4. It can be seen from the figures that the band gap values after applying SOC correction [Fig. 4(c) and 4(f)] are found to have gone down [Table 2]. . In TB-mBJ calculations, near the Fermi level the spin-up band is pushed down and the
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spin-down band is pushed up. The spin-polarized total and partial density of states of different atomic species of tetragonal phase are shown in Figs.5 (X&Y). In order to understand the behavior of the material in the band-gap region, the features near the Fermi level EF are focused more. The total DOS curves suggest that Fe 3d contributions are larger for the spin-up
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(down) states below & above the Fermi level EF. It is also clear from the figure that in the immediate vicinity of EF, the contribution from the oxygen atoms is almost negligible while
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that of Bi 6p states is approximately one tenth of the total value. In view of this, one may conclude that the dominant contribution is from Fe 3d states. The calculated electronic energy band gap of R3c BFO (3.6 eV ) for spin up is
comparable with that of optical energy gap 3.00 eV [31] while for that for spin down position (1.7 eV ) is comparable with that of the experimental one [32] and are shown in Figs 6(X&Y). The DOS of Fe 3d obtained by TB- mBJ method is found to be in the range of zero to 6 eV. The main difference in DOS between GGA and TB-mBJ appears in the middle of the VB (5eV to - 8 eV) and connects with Fe 3d orbital. In GGA approach, this region is dominated by the strongly localized Fe 3d orbital for all the structures. However, in the case of TB-mBJ method, Fe 3d states of all the structures are found to shift to higher energies and blur along the VB leading to the separation of bands near the Fermi level. The lower part of the valence band
consists of Bi 6s state with some admixture of O 2p states (around 9 eV). The differences in
MANUSCRIPT DOS observed in unoccupied ACCEPTED states for GGA and TB-mBJ calculations are associated with exact peak positions and relative intensities are shown in Figs.7. In order to understand the influence of SOC on the band gap and density of states values of rhombohedral phase of BFO, corrections have been made to the TB-mBJ calculations. The band gap values after applying SOC correction are given Table 2. The correctness of the DOS for applied approaches may be verified using the
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experimental electron energy loss spectra. The conduction band is characterized mainly by the empty Fe 3d states with admixture of Bi 6p and O 2p states. The Bi 6s and O 2p orbital in the lower part of VB and near the Fermi level form a pair of occupied bonding and anti- bonding states respectively. The contribution from Bi 6s states near the top of the VB increases in the
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TB-mBJ scheme. Such a situation is typical in the formation of lone pairs [33]. Calculated partial DOS shows that the valence band (VB) region consists of mainly O 2p states with a small contribution from Fe 3d, Bi 6s and Bi 6p states. Further, the conduction band (CB)
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region is dominated with Fe 3d states with a small contribution from O 2p states and Bi 6p states. The predicted Fe 3d states at the bottom of VB indicate a stronger hybridization between O 2p states and Fe 3d states than hybridization between O 2p states and Bi 6s and 6p states. 4.2 Charge density analysis
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Additional evidence of partial covalency of the chemical bonding and stereo chemically active lone pair activity in BFO emerges from the calculated electron-charge density data. Therefore, the electron charge density for all the phases has been computed the
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results are shown in Fig.8. It can be seen from the figure that the electron distribution around Bi atom is found to be a symmetrical sphere for cubic, whereas in the case of tetragonal and rhombohedral phases the electron distribution is found to be asymmetrical sphere. This
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distribution is clearly shown by the isosurface of electron density (black solid circles). The asymmetrical isosurface sphere and electron distribution around Bi atom indicate the presence of stereo chemically active lone pair that contributes to the polar behaviour of BFO in tetragonal and rhombohedral phases. Therefore, one may conclude that the stereo chemically active lone pair of Bi 6s2 might be responsible for the observed ferroelectric polarization in these two phases of BFO. In fact, M. K. Yaakob et. al [34] reported that the calculated effective charge of Bi in hexagonal phase is lower than in orthorhombic phase, wherein a longer Bi-O bond length is predicted.
4.3. ELF studies
ACCEPTED Ravindran et. Al [35] studied that the MANUSCRIPT electron localization function in BFO compound and indicated that the negligibly small ELF value between atoms indicate the presence of dominant ionic bonding in this material. In fact, the ELF distribution shows a maximum value at the O sites and minimum value at the Fe and Bi sites indicating the charge-transfer interaction from Bi/Fe to O sites. It is well- known that the Electron Localization Function (ELF) is very useful parameter to understand the separation of spatial regions characterizing
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the shared and unshared electron interactions such as the covalent, metallic and ionic bonding. The ELF values computed for three different phases of BiFeO3 are shown in Fig.9. One may see from the figure that in the case of cubic structure since ELF value is negligibly small, one may conclude that it might be having purely ionic bonding between Bi and O. However, in the
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case of tetragonal phase as the ELF is large, the bonding may be totally covalent. Finally, in the case of Rhombohedral phase , as the ELF value is neither small nor large, the bonding may be partially ionic and partially covalent. Based on these results, one may conclude that
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tetragonal phase may exhibit more ferroelectricity than the rhombohedral one. The DOS values for all the three phases are shown in Fig.10. From DOS figures, one may understand O p states in all the three phases are present at the top of the valence band, while a few O p electrons are found to be present around −10 eV of energy along with Bi 6s electrons, indicating the interaction between O p and Bi 6s electrons . From the DOS of cubic
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structure, since O p electrons are negligibly small, the hybridization between the Bi-s and O-p atoms around -10eV is negligibly small. On the other hand, in the case of tetragonal phase, since O p electrons are very large in number, the hybridization between Bi-s and O-p atoms around -10eV may be maximum. Finally, in the case of rhombohedral phase since O p
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electrons are moderate in numbers, hybridization between O p and Bi 6s electrons might be between the two phases. In fact, the conclusions arrived at on the basis of the ELF studies
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corroborates with those obtained from the DOS studies. Using the optimized crystal structure of all the three phases, the bond lengths
among various ions along with bond angles have been calculated and are given in Table.3. It can be seen from the table that since in the case of cubic phase since O-Fe-O angle is 90◦ its behaviour might be non polar indicating that it may not exhibit ferroelectricity. However, in the case of Rhombohedral O-Fe-O angle is 166.98◦ while in the case of Tetragonal it is 84.3980 indicating that both the phases might be having polar behaviour along with the exhibition of ferroelectricity. It can also be seen from the table that Bi-O bond lengths are higher for cubic and are lesser for the other two phases. The observed behaviour may be attributed to the fact that cubic structure is having higher symmetry when compared with the other two structures. In
the case of Fe-O bond, for Rhombehedral phase is having higher value followed by the cubic
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phase.
Finally, Fe-O bond in the case of tetragonal phase is having the least. The lesser O-O bond length exhibited by the tetragonal phase is least among the three phases and may be attributed to the deformation of oxygen octahedra caused by increased O-O repulsion. The FeO bond is found to be lowest in the case of tetragonal phase among the three phases, while it is highest in the case of Bi-O bond indicating the larger repulsive force between the lone pair of
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Bi6s2 with other bonded electron pairs [36]. Based on these observations one may conclude that the strongest hybridization Bi-O bonds indicating that there may be a large cation displacement.
It can be seen from Fig.9, that the lone pair lobe is absent in the case of cubic while
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in the case of rhombehedral it is found to emerge slowly. However, as in the case of tetragonal phase the lone pair lobe is very strong, one may conclude the presence of more polarization leading to higher ferroelectricity. Further, in the Bi-O plane, since the lone pair lobes are
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localized at Bi sites (each Bi bonded with two oxygen ions), one may notice the increased contribution from Bi 6p states and diminished contribution from Bi 6s states, when compared with those in the case of case of hexagonal BFO. It has been observed that the calculated electronic DOS using TB-mBJ method is found to be more accurate and is comparable with the experimental values [37]. The calculated partial DOS shows better hybridization between Bi 6s
lone pair. [38,39]. 4.4 Magnetic Properties:
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states and O 2p states, suggesting that hybridization is essential to the stereo chemically active
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The magnetic moments of Fe of all three phases were calculated using TB- mBJ method and the values are given in Table.4. It can be seen from the table that the magnetic moments of Fe obtained by are comparable with those available in the literature [40-42] suggesting that
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TB-mBJ method might have given satisfactory results. In order to understand the influence of SOC on the magnetic behavior of BFO of the present investigation, corrections have been applied to TB- mBJ method, the and the magnetic moments of Fe are given in Table 4. The Oxygen ions are also found to have a very low value of magnetic moment of
0.05µB, indicating that there might be hybridization between Fe 3d and O 2p states. The local magnetic moments show that the major contribution to the total moment is coming from the Fe atoms. Small induced magnetic moments at O sites due to Fe-O hybridization can also be seen. In the all three structures, due to different Fe-O bond length, oxygen atoms have different magnetic moments. These different local moments of oxygen show different crystal symmetry of BFO [41].
Magnetic susceptibility (χ) plays an important role in explaining the magnetic
ACCEPTED MANUSCRIPT order of a magnetic material. Multiferroic BFO with Rhombohedral structure is known to have antiferromagnetic behavior at room temperature and it goes to antiferromagnetic to paramagnetic state at 643K(TN). Some experimental work has been done in the low temperature region [43,44]. According to these reports, as the temperature goes down to 5K or less, the magnetization is found to increase rapidly indicating that a transformation of Fe sublattice from antiferromagnetic to weak ferromagnetic at low temperatures. As there is no
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such work based on first principles, magnetization behavior of BFO sample has been investigated over a temperature range of 4 – 800K. To calculate the magnetic susceptibility of these materials post-DFT Boltztrap technique was used. The temperature versus susceptibility plots of three phases are shown in Fig. 11. There is a sudden fall in susceptibility between 0K
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to 25K and beyond 25K the behaviour is almost constant later on and the behaviour is consistent with the experimental results [43]. Further, the magnetic susceptibility value at 60K
4.5. Ferroelectric behavior.
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for cubic is 0.65 emu, for tetragonal is 0.64 emu and for Rhombohedral is 1.1emu.
As the Bismuth ferrite is basically a multiferroic material, an in depth knowledge of ferroelectricity and hence spontaneous polarization is essential. Therefore, the polarization values of all the three phases were calculated as a Berry phase using King-Smith and Vanderbilt’s method. In this approach, for a given crystalline geometry, the total polarization P
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was calculated as the sum of ionic and electronic contributions. The ionic contribution is obtained by summing the product of the position of each ion in the unit cell (with a given choice of basis vectors) with the nominal charge of its rigid core. The electronic contribution was determined by evaluating the phase of the product of overlaps between cell-periodic Bloch
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functions along a densely sampled string of neighboring points in k space. Here four symmetrized strings consisting of 15000 points were used to obtain the electronic contribution
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to the polarization and is calculated separately for each spin channel. As the cubic phase of BiFeO3 is metallic in nature, the spontaneous polarization values of the other two structures were calculated and the results are given in Table 5. The polarization values of the present investigation are comparable with those of reported ones [45]. From the table it is clear that the polarization value of Tetragonal phase is larger than rhombohedral phase indicating that tetragonal phase might be exhibiting better ferroelectricity.
CONCLUSION:
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The band structure calculations obtained by TB-mBJ method in the spin polarized mode indicate the semiconducting behavior of all the three phases.
2.
From the DOS of cubic structure, since O p electrons are negligibly small in the -10ev
region, the hybridization between Bi-s and O-p electrons might be also negligibly small. On the other hand, in the case of tetragonal phase, since O- p electrons are very large in number in
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the -10 eV regions, the hybridization between Bi-s and O-p atoms may be maximum, indicating large polarization. Finally, in the case of rhombohedral phase since O p electrons are moderate in numbers, the hybridization between O p and Bi 6s electrons might also be moderate. 3.
It has been concluded from the ELF and charge density behavior of three phases that the
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electron distribution around Bi atom is a symmetrical sphere for cubic phase, whereas an asymmetrical sphere is exhibited in tetragonal and rhombohedral phases. The asymmetrical
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isosurface sphere and electron distribution around Bi atom indicate stereochemically active lone pair that contributes to the polar behavior leading to ferroelectricity in BFO tetragonal and hexagonal phases of BFO.
4. From ELF studies of cubic phase it has been concluded that it is having purely ionic bonding between Bi and O. However, in the case of tetragonal phase as the ELF is large, the bonding may be totally covalent. Finally, in the case of rhombohedral phase, as the ELF value is
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intermediate, the bonding may be partially ionic and partially covalent. Based on these results, one may conclude that tetragonal phase may exhibit more ferroelectricity than rhombohedral one.
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5. The Oxygen ions are found to have a very low value of magnetic moment of 0.05µB, indicating that there might be hybridization between Fe 3d and O2p states. Similarly, the
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spontaneous polarization analysis demonstrates that the polarization arises due to the displacement of Bi relative to Fe-O octahedra. 6.
It has been concluded from these studies that TB-mBJ is very accurate and a direct method
in modelling and for predicting the properties of BFO materials. In fact, TB-mBJ calculations gave a meaningful information and excellent prediction in the development of new multiferroic materials with improved properties for various applications and new materials. 7.
Although TB-mBJ is very accurate and a direct method in modelling and for predicting
the properties of BFO materials, Spin Orbit Coupling ( SOC ) corrections yielded refined and better results.
8.
A careful examination of the results indicates that the density functional theory may be
used to explore not only theACCEPTED structural andMANUSCRIPT magnetic properties but also the ferroelectric properties of various types of magneto electric materials. Acknowledgments The authors thank Professors Peter Blaha, Vienna University of Technology, Austria for providing WIEN2K code. The authors also thank DRDO, India and UGC, India for funding
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26. D. Ricinschi, K.-Y. Yun, and M. Okuyama, J. Phys.: Condens.Matter 18(2006) L97. 27. D. C. Arnold, K. S. Knight, G. Catalan, S. A. T. Redfern, J. F. Scott, P. Lightfoot, and F. D. Morrison, Adv. Funct. Mater 20 (2010) 1.
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29. M. Cococcioni and S. de Gironcoli, Phys. Rev. B 71 (2005) 035105
30. W. E. Pickett, S. C. Erwin, and E. C. Ethridge, Phys. Rev. B 58(1998) 1201
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32. T. Higuchi, Y.-S. Liu, P. Yao, P.-A. Glans, and J. Guo, Phys. Rev. B. 78(2008)085106. 33. H. M. Tutuncu and G. P. Srivastava, Phys. Rev. B. 78(2008) 235209. 34. M. K. Yaakob, M. F. M. Taib, M. S. M. Deni and M. Z. A. Yahya, Integrated
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Ferroelectrics, 155:134–142, 2014
35. P. Ravindran, R. Vidya, A. Kjekshus, and H. Fjellvåg, Phys. Rev. B 2006, 74, 224412. 36. R. Seshadri and N. A. Hill, Chem. Mater. 13 (2001) 2892. 37. G. W. Watson and S. C. Parker, Phys. Rev. B. 59(1999)8481.
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38. G.W. Watson and S.C. Parker, J. Phys. Chem. B 103(1999)1258. 39. R. Seshadri, Proc. Indian Acad. Sci. (Chem. Sci.), 113(2001)487.
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Table.1. Estimated lattice parameters, c/a ratio and Z parameters of BiFeO3.
Phase
a (Å)
c (Å)
c/a
ZFe
Cubic
3.991
-
-
-
Tetragonal
a (3.987) 3.660
4.630
(1.265)
0.4413
0.8612(0.8540) b
(3.670) b
(4.640) b
(1.264) b
(0.4390 ) b
0.31230(0.3080)b
5.562
13.792
2.479
0.2189
0.4541(0.4450) c
(5.573)c
(13.842) c
(2.483) c
(0.2205) c
0.0188(0.0179) c
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Rhombohedral
ZO
Expt: aref [25], bref [26, 27], b,cref [27, 28]
Table.2. Calculated Electronic Band gap values of three phases of BiFeO3,
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before and after applying SOC. Phase
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Tetragonal
Rhombohedral
GGA
TB-mBJ
mBJ + SOC
Spin-up
-
0.1
-
Spin-down
-
1.8
1.6
Spin-up
-
2.1
1.0
Spin-down
-
1.4
1.2
Spin-up
-
3.6
3.2
Spin-down
-
1.7
1.6
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Cubic
Band Gap (eV)
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Structure
Cubic
Tetragonal
Rhombohedral
Fe-O
1.9955
1.9580
2.0828
Fe-Bi
3.4563
3.7125
Bi-O
2.8211
2.3522
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Table.3. The bond length (Å) and bond angles (degree) of three phases of BiFeO3.
O-O
2.8211
Fe-O-Fe
90°
O-Fe-O
90°
Literature Values of Rhombohedral phase Ref. [28] 2.1144 3.0622
2.366
-
2.6304
2.728
-
-
155.05°
155.15°
84.39°
166.98°
165.22°
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3.0649
Table.4. The calculated Fe and O magnetic moment (µB) of Cubic, Tetragonal and
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Rhombohedral phase of BiFeO3.
Phase
Cubic
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Magnetic Moment of Fe(µB) Present study
Magnetic Moment of Oxygen(µB)
Literature
Present study
Literature
GGA
TB-mBJ
mBJ+SOC
values
GGA
TB-mBJ
mBJ+SOC
values
3.08
4.22
4.21
2.83d
0.05
0.07
0.26
(- 0.083)a
0.13
0.16
0.25
(0.19)d
0.15
0.18
0.26
(0.21)d
Tetragonal
3.60
4.12
4.13
4.065e 4.18b
Rhombohedral
3.31
4.19
4.21
3.87b 4.30c
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Reported:aref [8] bref [333] cref [40] dref [41] eref [42]
Table. 4. Polarization values of BiFeO3 compound obtained by TB-mBJ method.
160
Rhombohedral
103
143.5 93.1
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Cubic
Polarization values (µC/cm2) Present Study Literature Values Ref. [45] -
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Phase
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Rhombohedral R3c phase.
GGA
TB-mBJ
(X). Spin-up (b)
TB-mBJ+ SOC (c)
(Y). Spin-down
(e)
(f)
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Figure.1. Crystal structure of BiFeO3: (a) Cubic Pm3m phase (b) Tetragonal p4mm phase (c)
Figure.2. (X&Y). Electronic Band Structures of cubic phase BiFeO3. Calculated with GGA scheme (a & d), TB-mBJ scheme(b & e) and TB-mBJ + SOC scheme(c & f).
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GGA (X). Spin-up (a)
TB-mBJ
TB-mBJ+ SOC (c)
(Y). Spin-down (d)
(f)
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(b)
Fig.3 (X&Y). Density of states of cubic BiFeO3. Calculated with GGA scheme (a & d), TB-mBJ
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GGA
TB-mBJ
TB – mBJ + SOC
(X).Spin-Up (b)
(c)
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(a)
(Y).Spin-down (d)
(f)
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Figure.4. (X&Y). Electronic Band Structures of tetragonal phase BiFeO3. Calculated with GGA scheme (a & d), TB-mBJ scheme(b & e) and TB-mBJ + SOC scheme(c & f).
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GGA (X). Spin-up
TB-mBJ (b)
(c)
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(a)
TB – mBJ + SOC
(Y). Spin-down (d)
(f)
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Figure.5 (X&Y). Density of states of Tetragonal phase of BiFeO3. Calculated with GGA scheme (a & d), TB-mBJ scheme(b & e) and TB-mBJ + SOC scheme(c & f).
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GGA (X).Spin-up
TB-mBJ (b)
(c)
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(a)
TB – mBJ + SOC
(Y).Spin-down (d)
(f)
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Figure.6(X&Y). Electronic Band structure of Rhombohedral phase. Calculated with GGA scheme (a & d), TB-mBJ scheme(b & e) and TB-mBJ + SOC scheme(c & f).
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GGA (X).Spin-up
TB-mBJ (b)
(c)
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(a)
TB-mBJ + SOC
(Y).Spin-down (d)
(f)
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Figure.7(X&Y). Density of states of Rhombohedral phase BiFeO3. Calculated with GGA scheme (a &
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(b)
(c)
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Figure.8. Charge density of BiFeO3 (a) Cubic Pm3m phase (b) Tetragonal p4mm
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phase (c) Rhombohedral R3c phase.
Figure.9. Electron Localization Function of BiFeO3 for (a) Cubic Pm3m phase (b) Tetragonal p4mm
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(a)
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(c)
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Figure.10. Partial DOS of BiFeO3 for (a) Cubic Pm3m phase (b) Tetragonal p4mm phase (c)Rhombohedral R3c phase. 0.7
0.7
0.5
3
3
0.5
0.3
0.4
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0.4
0.3
(c) 1.0
0.8
3
χ mol (cm /mole)
0.6
χ mol (cm /mole)
0.6
χ mol (cm /mole)
1.2
(b)
(a)
0.6
0.4
0.2
0.2
0.2
0.1
0.1 200
300
400
T(K)
500
600
700
800
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0
100
200
300
400
500
600
700
800
T(K)
0
100
200
300
400
T(K)
Fig11. Susceptibility Vs Temperature graphs of three different phases of Multiferroic BFO. a) Cubic Phase, b) Tetragonal Phase, c) Rhombohedral Phase.
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500
600
700
800
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1. Structural, electronic and multiferroic properties of three phases of BiFeO3 are investigated. 2. Three types of methods like GGA, TB-mBJ and TB-mbj+SOC are used to do the calculations. 3. Magnetic susceptibility Vs Temperature measurements are done using Boltztrap Code.
