Electronic Structure and Spontaneous Polarization in BiFeO3

electronic Structure and Spontaneous Polarization in BiFeO3Electronic structure and offhanded polarization in multiferroic passel BiFeO3Z. Mahhouti 1,2,3,* , H. El Moussaoui 1 , M. Hamedoun 1 , M. El Marssi 3 , A. Lahmar 2 , A. El Kenz 2 , and A. Benyoussef 1,2,4AbstractThe electronic structure, charismatic properties and spontaneous polarization in Bismuth ferrite BiFeO3 ar investigated using first-principle calculations. The computed results show that the ground state of bulk BiFeO3 is rhombohedral R3c symmetry with G-type antiferromagnetic ordering and insulating, the computed results are in good treaty with available look intos. The electronic structure has been studied using the full voltage linearized augmented plane wave (FP-LAPW) method wi comminuted generalized gradient similarity (GGA) and modified Becke-Johnson potential (mBJ). Therefore, the finding tie gap value is equal to the experimental value (Eg=2.5 eV) and much ruin than separate metaphysical values, th e local magnetic moment at the Fe atoms reaches the experimental value and it is in good agreement with previously account theoretical, with the bulky atomic displacement the modern possible action of polarization predicts a large spontaneous polarization in multiferroic bulk BiFeO3.INTRODUCTIONThe multiferroic term de zero(pre zero(prenominal)einal)es the coexistence of several ferroic orders (ferroelectric automobile, ferromagnetic, and ferroelastic) in one material1, coupled or not. Multiferroic materials are very rare because the origins of ferroelectricity and ferromagnetism are hardly compatible as shown by Hill et al.23. However, there are some exceptions such as La0.1Bi0.9MnO3 which is ferroelectric below 770 K and ferromagnetic below 105 K4. The definition of multiferroic has therefore been extended to materials with antiferroic orders such as BiFeO3 which is ferroelectric and antiferromagnetic. Bismuth ferrite BiFeO3 (BFO) is one of the few magnetoelectric multiferro ics who has simultaneously ferroelectric and antiferromagnetic orders under close conditions of temperature and pressure. Indeed, its high Curie temperature (TC = 1103 K)5 and Nel temperature (TN = 643 K)6 provide a wide range of applications at different temperatures7 such as spintronics, data storage and microelectronic devices89, In improver, a magnetoelectric coupling is possible at room temperature.Recently, BFO has seen a considerable increase in interest since the discovery of a much better spontaneous polarization, greater than 150 C/cm2, when the material is grown in thin layers10. This discovery aroused great enthusiasm among the scientific community who precious to explain the origin of some phenomenon and explore this material again.The phase diagram established accord to the reference11 shows the succession of three phases with increasing of temperature denoted , ,and , respectively. In its bulk course of instruction and at room temperature, BFO has a distorted pero vskite structure with rhombohedral symmetry and space group R3c (a = b = c = 5.63 , = 59.4)128. The primitive unit kiosk contains cardinal formula units (ten atoms), each Fe atom is surrounded by six antiparallel spin neighbors, the magnetic moments are oriented perpendicularly to the 111 direction, which leads to develop a G-type antiferromagnetic order on the whole of the material. However, new observations have revealed that the direction in which antiferromagnetism manifests rotates through the crystal13. This noncollinearity propagates within the material with a period from 620 to 640 1314 and superimposes on the G-type antiferromagnetic order. As the noncollinearity is quite minimal, the simplification to a collinear magnetic structure is possible15. In this paper, the noncollinearity effects were not taken during our calculations.Since BFO is grown as a thin layers, the material may undergo a compressive or extensive stress due to the exit between the primitive cell of t he material in its bulk form and those of the monocrystalline substrate, the small grown thickness is able to accept any relaxation of the structure. This can cause changes in the structure parameters of the crystal compared to its bulk form. However, other experimental works1617 showed that even BFO grown in thin layers, retains its rhombohedral symmetry.For a long time BFO considered too low to be exploitable ( Ps = 6.1 C/cm2 ) according to the first criterions of Teague et al.5, the ferroelectricity of BFO was studied again following the results of Young et al.10 on thin layers of BFO ( Ps = 158 C/cm2). However, many experimental studies carried out during this period gave a confound results, the spontaneous polarization varying from 2.2 C/cm2 18 to 158 C/cm2 10. The prove of the ferroelectricity of BFO is a concrete example to combine experimental results and theoretical calculations. In this case, the calculation methods take to explain the difference between the first meas ured values of bulk BFO and those admited on the same material grown in thin layers.In this paper, we study in detail the magnetic properties of bulk BFO, while considering a G-type antiferromagnetic order. But it is necessary to determine first the electronic manakin and to calculate the passel gap, in order to understand and obtain the theoretical model which corresponds to the reality of the material, and then to determine the spontaneous polarization using modern supposition of polarization. regularityThe calculations which we present in the remainder of this paper use the meanness functional theory (DFT) implemented in WIEN2k code. The interactions between electrons and ions are described in the good example of full potential linearized augmented plane wave (FP-LAPW) method. As the 3d electrons in diversity -metal Fe atom are incompletely filled, the spin density approximation was employed withinstry the Perdew-Burke-Ernzerhof (PBE) form of the generalized gradient appro ximation (GGA) and modified Becke-Johnson potential (mBJ). The new version of the exchange potential, proposed for the first time by the Becke and Johnson19, was lately published by Tran and Blaha20. The modified Becke-Johnson potential (mBJ) proposed by Tran and Blaha isWith is the electronic density, is kinetic energy density and is the potential of Becke-Roussel. In this work, the mBJ potential is used in compounding with the GGA-PBE approximation to compute the electronic structure, magnetic properties and spontaneous polarization in multiferroic bulk BFO. Our calculations do not include the spin-orbit interactions and the noncollinearity effects. The mesh of the first Brillouin zone in the reciprocal space was carried out using a 4 x 4 x 4 Monkhorst-Pack k-points grid. The structural parameters of BFO in space group R3c ( i.e, the grille constant and atomic positions ) are considered as calculated by Wang et al.8 as given from Kubel et al.12. The results of relaxing the ce ll volume, rhombohedral angle, and atomic positions within the R3c symmetry in reference8 show that there is an alternation of Bi3+ and Fe3+ ions along the 111 axis Each of these atoms is surrounded by six oxygen atoms, which thus form an octahedron around each cation. Inside the octahedron FeO6, the Fe3+ ion is distant the FeO2 plane (forming the base of the octahedron), which leads a distortion of the octahedron.The calculation of the spontaneous polarization using the modern theory of polarization is carried out by determining the difference in polarization between two symmetry (The non-centrosymmetric phase R3c which is ferroelectric and the centrosymmetric phase R-3c supposed paraelectric). In order to evaluate the polarization of the structure studied, we mustiness therefore use a structure (centrosymmetric) as a reference with the same unit cell as the real structure (non-centrosymmetric), but its atomic positions do not induce electrical dipoles. Energetically, these two s tructures are very close, which confirms our choice of R-3c symmetry as a centrosymmetric reference. They differ by the addition of a center of inversion within the symmetry, and the passage from one symmetry to the other is due to the displacement of the atoms along the 111 direction which is accompanied with a revolution of the FeO6 octahedra perpendicular to the same direction. This evolution of the paraelectric phase to the ferroelectric phase allows us to explain the birth of ferroelectricity within the bismuth ferrite BFO and to reproduce it efficiently in our calculations. The modern theory of polarization was applied for the first time to compute the ferroelectricity within the cubic perovskite-type KNbO3. The results obtained ( P = 35 C/cm2 2122) showed excellent agreement with the experimental data ( P = 37 C/cm223). Other studies were carried out subsequently, confirming the reliability of this method with respect to the experimental reality. Today, the modern theory of p olarization is widely used.Results and DiscussionElectronic and magnetic propertiesIn this section, we study the electronic structure of bulk BFO in ferroelectric R3c structure, considering the relaxing values of cell parameter, rhombohedral angle and atomic positions by Wang et al.8. We computed and plan the criminalised structure and electronic state densities with the same parameters mentioned at the paragraph II. The band gap value are calculated using mBJ potential in combination with the GGA-PBE approximation, our calculated band gap value is the same as the value measured by Gao et al.24 from the UV-visible diffuse reflectance spectrum witch is equal to 2.5 eV, our computed band gap is much better than other theoretical works such as Neaton et al.15 who found an indirect band gap of 0.4, 1.3, and 1.9 eV using LSDA+U approximation with U=0, 2, and 4 eV, respectively. The same for Ttnc et al.25 they found an indirect band gap of 0.9, 1.4, and 2.1 eV using LSDA+U approximation with U=0, 2, and 4 eV, respectively. Our band structure results (Fig.1) indicate an indirect band gap of approximately 2.5 eV witch is in excellent agreement to the experimental mensuration of about 2.5 eV 2426. Therefore, this equality between our calculated band gap and the experimental value confirms the insulating character of bulk BFO.In order to understand why the magnetic moments of the Fe atoms were arranged antiparallel within bulk BFO, we relaxed it according to different magnetic configurations paramagnetic, ferromagnetic, and antiferromagnetic. The ground-state energy of the various possible magnetic configurations shows that the G-type antiferromagnetic configuration is the one which offers the material its greatest stability. FIG. 1. Calculated band structure for rhombohedral BiFeO3.FIG. 2. Calculated total density of states for rhombohedral BiFeO3.Calculated density of state (Fig.2) for R3c BFO indicates an indistinguishable distribution between electronic states u p and down, which clearly exhibits the antiferromagnetic order of the material, in this case the antiferromagnetic order can only be G-type. The Fe atoms along the 111 axis have a local magnetic moment of 4.02 B comes from 3d states, this value is much better than 4.25 B and 4.17 B reported by Ttnc et al.25 using LSDA+U with U = 4 and 6 eV, respectively. Therefore, our computed local magnetic moment of Fe atoms is very close to the measurement value of about 3.75B 27.FIG. 3. Atomic projection of electronic PDOS for rhombohedral BiFeO3.Figure 3 shows atomic projected electronic density of states (PDOS) around the ban gap region for two spin channels. The results suggest that the valence band are predominantly formed by Fe 3d states, hybridized with a character from O 2p states. Conduction band states are occupied by a large amount of Fe 3d states, hybridized with a small contribution of Bi 6p states that also contains a significant amount of O 2p states.Spontaneous polarizationThe spontaneous polarization was calculated within bulk BFO using the ferroelectric structure R3c and the theoretical centrosymmetric phase R-3c. The centrosymmetric phase must be judiciously chosen, in order to found the difference of ferroelectric polarization between the centrosymmetric and non-centrosymmetric phases little than the quantum of polarization, Where is the electronic charge, is a lattice vector in the direction of polarization, and is the volume of the unit cell. Our calculations have shown that centrosymmetric phase R-3c is the structure closest to the ferroelectric structure R3c, both energetically as well as structural. This symmetry differs from the R3c only by the addition of a center of inversion. The transition from the paraelectric to the ferroelectric phase was characterized by a large displacement of the atoms along the 111 axis and a rotation of the FeO6 octahedra. Therefore, we expect that the spontaneous polarization develops along the 111 axis. In ord er to calculate the difference of polarization, we have considered that the transition from paraelectric to ferroelectric phase was done adiabatically and continuously. In this way, each atom moves along a path divided into segments of equal length. This method allowed us to follow the evolution of the spontaneous polarization during the whole paraelectric-ferroelectric transition. Throughout the paraelectric-ferroelectric transition, it is imperative to avoid any external contribution to symmetry, such as compression or expansion of the unit cell (in this case we do not calculate the real spontaneous polarization). For this reason, the structures used for our calculations have the same cell parameters, only the atomic positions were shifted.The modern theory of polarization compute the both, ionic and electronic contribution to the spontaneous polarization using the sum of the Wannier centers of the occupied bands. Our results showed that the spontaneous polarization developed alon g three directions, and was 58.8 C/cm2 along each axis, resulting a spontaneous polarization of 101.1 C/cm2 along the 111 axis which is in full agreement with the spontaneous polarization calculated by Neaton et al.15 using LSDA+U. Early measurements on bulk BFO single crystals5 found a small polarization of about 6.1 C/cm2. On the other hand, many experiment studies on thin film samples of BFO showed a large spontaneous polarization of about century-158 C/cm2 1610. The anomalously early value was caused by several explanations. First, the authors5 indicated that their hysteresis loops were not saturated. Second, maybe the small value limited by the poor of the sample quality. Finally, the third explanation is that the crystal structure is not the same. Recently, Lebeugle et al.28 have prepared a highly pure BFO single crystal (bulk BFO with a rhombohedral R3c symmetry) and measured the spontaneous polarization, they found a very large value of about 100 C/cm2 28 which is an intrins ic property of the bulk BFO, as expected by our theoretical studies.CONCLUSIONSIn summary, Bismuth ferrite BiFeO3 is one of a few magnetoelectric multiferroics who has simultaneously ferroelectric and ferromagnetic orders, it has seen a considerable increase in interest since the discovery of a high spontaneous polarization. The first principle calculations with our approximations and parameters chosen allowed us to understand and obtain the behaviors of electronic and magnetic properties which make possible the computing of the right band gap and local magnetic moment. The property intrinsic of the large spontaneous electric polarization in bulk BiFe2O3 showed by recently experiment studies was confirmed by our theoretical investigations using the modern theory of polarization. These good agreements between our theoretical investigation and experimental measurement allow the scientific community to compute other properties and understand the physics behind the measurement at the at omic level.References1H. Schmid, Multi-ferroic magnetoelectrics, Ferroelectrics, vol. 162, no. 1, pp. 317-338, Jan. 1994.2N. A. Hill, Why Are There so Few Magnetic Ferroelectrics?, J. Phys. Chem. B, vol. 104, no. 29, pp. 6694-6709, Jul. 2000.3N. A. Hill, Density Functional Studies of Multiferroic Magnetoelectrics, Annu. Rev. Mater. Res., vol. 32, no. 1, pp. 1-37, Aug. 2002.4A. Moreira dos Santos et al., Orbital ordering as the determiner for ferromagnetism in biferroic BiMnO 3, Phys. Rev. B, vol. 66, no. 6, Aug. 2002.5J. R. Teague, R. Gerson, and W. J. 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