The magnetoelectric behavior of BiFeO3 has been explored on the basis of accurate density functional calculations. We are able to predict structural, electronic, magnetic, and ferroelectric properties of BiFeO3 correctly without including any strong correlation effect in the calculation. Unlike earlier calculations, the equilibrium structural parameters are found to be in very good agreement with the experimental findings. In particular, the present calculation correctly reproduced experimentally-observed elongation of cubic perovskite-like lattice along the [111] direction. At high pressure we predicted a pressure-induced structural transition from rhombohedral (R3c) to an orthorhombic (P nma) structure. The total energy calculations at expanded lattice show two lower energy ferroelectric phases (with monoclinic Cm and tetragonal P 4mm structures), closer in energy to the ground state phase. Spin-polarized band-structure calculations show that BiFeO3 will be an insulator in A-and G-type antiferromagnetic phases and a metal in C-type antiferromagnetic, ferromagnetic configurations, and in the nonmagnetic state. Chemical bonding in BiFeO3 has been analyzed using partial density-of-states, charge density, charge transfer, electron localization function, Born-effective-charge tensor, and crystal orbital Hamiltonian population analyses. Our electron localization function analysis shows that stereochemically active lone-pair electrons are present at the Bi sites which are responsible for displacements of the Bi atoms from the centro-symmetric to the noncentrosymmetric structure and hence the ferroelectricity. A large ferroelectric polarization of 88.7 µC/cm 2 is predicted in accordance with recent experimental findings, but differing by an order of magnitude from earlier experimental values. The strong spontaneous polarization is related to the large values of the Born-effective-charges at the Bi sites along with their large displacement along the [111] direction of the cubic perovskite-type reference structure. Our polarization analysis shows that partial contributions to polarization from the Fe and O atoms almost cancel each other and the net polarization present in BiFeO3 mainly (> 98%) originates from Bi atoms. We found that the large scatter in experimentally reported polarization values in BiFeO3 is associated with the large anisotropy in the spontaneous polarization.
The computational framework of this study is based on the local-spin-density approximation with firstprinciples full-potential linear muffin-tin orbital calculations including orbital polarization ͑OP͒ correction. We have studied the magnetic anisotropy for a series of bilayer CuAu͑I͒-type materials such as FeX, MnX (X ϭNi,Pd,Pt), CoPt, NiPt, MnHg, and MnRh in a ferromagnetic state using experimental structural parameters to understand the microscopic origin of magnetic-anisotropy energy ͑MAE͒ in magnetic multilayers. Except for MnRh and MnHg, all these phases show perpendicular magnetization. We have analyzed our results in terms of angular momentum-, spin-and site-projected density of states, magnetic-angular-momentumprojected density of states, orbital-moment density of states, and total density of states. The orbital-moment number of states and the orbital-moment anisotropy for FeX (XϭNi,Pd,Pt) are calculated as a function of band filling to study its effect on MAE. The total and site-projected spin and orbital moments for all these systems are calculated with and without OP when the magnetization is along or perpendicular to the plane. The results are compared with available experimental as well as theoretical results. Our calculations show that OP always enhances the orbital moment in these phases and brings them closer to experimental values. The changes in MAE are analyzed in terms of exchange splitting, spin-orbit splitting, and tetragonal distortion/crystal-field splitting. The calculated MAE is found to be in good agreement with experimental values when the OP correction is included. Some of the materials considered here show large magnetic anisotropy of the order of meV. In particular we found that MnPt will have a very large MAE if it could be stabilized in a ferromagnetic configuration. Our analysis indicates that apart from large spin-orbit interaction and exchange interaction from at least one of the constituents, a large crystal-field splitting originating from the tetragonal distortion is also a necessary condition for having large magnetic anisotropy in these materials. Our calculation predicts large orbital moment in the hard axis in the case of FePt, MnRh, and MnHg against expectation.
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