Multiferroics, materials where spontaneous long-range magnetic and dipolar orders coexist, represent an attractive class of compounds, which combine rich and fascinating fundamental physics with a technologically appealing potential for applications in the general area of spintronics. Ab initio calculations have significantly contributed to recent progress in this area, by elucidating different mechanisms for multiferroicity and providing essential information on various compounds where these effects are manifestly at play. In particular, here we present examples of density-functional theory investigations for two main classes of materials: (a) multiferroics where ferroelectricity is driven by hybridization or purely structural effects, with BiFeO3 as the prototype material, and (b) multiferroics where ferroelectricity is driven by correlation effects and is strongly linked to electronic degrees of freedom such as spin-, charge-, or orbital-ordering, with rare-earth manganites as prototypes. As for the first class of multiferroics, first principles calculations are shown to provide an accurate qualitative and quantitative description of the physics in BiFeO3, ranging from the prediction of large ferroelectric polarization and weak ferromagnetism, over the effect of epitaxial strain, to the identification of possible scenarios for coupling between ferroelectric and magnetic order. For the second class of multiferroics, ab initio calculations have shown that, in those cases where spin-ordering breaks inversion symmetry (e.g. in antiferromagnetic E-type HoMnO3), the magnetically induced ferroelectric polarization can be as large as a few µC cm−2. The examples presented point the way to several possible avenues for future research: on the technological side, first principles simulations can contribute to a rational materials design, aimed at identifying spintronic materials that exhibit ferromagnetism and ferroelectricity at or above room temperature. On the fundamental side, ab initio approaches can be used to explore new mechanisms for ferroelectricity by exploiting electronic correlations that are at play in transition met al oxides, and by suggesting ways to maximize the strength of these effects as well as the corresponding ordering temperatures.
In addition to these structural studies, DFT calculations have also been used to investigate the magnetic properties of BFO, in particular the possible origin for the significant magnetization reported in Ref. @cite_58 . Bulk BFO is known to exhibit G-type'' AFM ordering @cite_65 , i.e. the magnetic moment of each Fe cation is antiparallel to that of its nearest neighbors. Superimposed to this G-type magnetic order a long-period cycloidal modulation is observed, where the AFM order parameter @math , defined as the difference between the two sublattice magnetizations @math , rotates within the (110) plane with a wavelength of @math @cite_85 .
@cite_85 @cite_58 @cite_65
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Enhancement of polarization and related properties in heteroepitaxially constrained thin films of the ferroelectromagnet, BiFeO 3 , is reported. Structure analysis indicates that the crystal structure of film is monoclinic in contrast to bulk, which is rhombohedral. The films display a room-temperature spontaneous polarization (50 to 60 microcoulombs per square centimeter) almost an order of magnitude higher than that of the bulk (6.1 microcoulombs per square centimeter). The observed enhancement is corroborated by first-principles calculations and found to originate from a high sensitivity of the polarization to small changes in lattice parameters. The films also exhibit enhanced thickness-dependent magnetism compared with the bulk. These enhanced and combined functional responses in thin film form present an opportunity to create and implement thin film devices that actively couple the magnetic and ferroelectric order parameters. The temperature dependence of structural and magnetic order parameters of ferroelectric-antiferromagnetic BiFeO3 with rhombohedral perovskite structure is investigated by means of neutron diffraction on a powder sample. The tilt angle of oxygen octahedra decreases from 12.5 degrees at 4.2K to 11.4 degrees at 878K. Associated with ferroelectricity the cation displacements diminish essentially with increasing temperature. Changes of cation shifts, tilt angle, distortion and strain of octahedra are discussed with respect to phase transitions. The ground-state structural and electronic properties of ferroelectric BiFeO 3 are calculated using density functional theory within the local spin-density approximation sLSDAd and the LSDA+U method. The crystal structure is computed to be rhombohedral with space group R3c, and the electronic structure is found to be insulating and antiferromagnetic, both in excellent agreement with available experiments. A large ferroelectric polarization of 90‐ 100 m C c m 2 is predicted, consistent with the large atomic displacements in the ferroelectric phase and with recent experimental reports, but differing by an order of magnitude from early experiments. One possible explanation is that the latter may have suffered from large leakage currents. However, both past and contemporary measurements are shown to be consistent with the modern theory of polarization, suggesting that the range of reported polarizations may instead correspond to distinct switching paths in structural space. Modern measurements on well-characterized bulk samples are required to confirm this interpretation. New information on the magnetic ordering of the iron ions in bismuth ferrite BiFeO3 was obtained by a study with a high-resolution time-of-flight neutron diffractometer. The observed splitting of magnetic diffraction maxima could be interpreted in terms of a magnetic cycloidal spiral with a long period of 620+or-20 AA, which is unusual for perovskites.