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.
BiFeO @math (BFO) is one of the most studied (probably most studied) multiferroic material. BFO is known to be multiferroic (or more precisely: AFM and ferroelectric) already since the early 1960s @cite_36 . However, for a long time it was not considered as a very promising material for applications, since the electric polarization was believed to be rather small @cite_97 and the AFM order does not lead to a net magnetization @cite_65 @cite_85 .
@cite_36 @cite_97 @cite_85 @cite_65
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Single crystals of BiFeO3 of perovskite structure were grown with dimensions of greater than 1 mm from a Bi2O3 flux. Dielectric hysteresis loops were measured on these crystals. While the loops were not fully saturated, they confirm that BiFeO3 is ferroelectric. 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. 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.