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.
From these calculation a spontaneous polarization of bulk BFO of @math @math C cm @math has been obtained. This is an order of magnitude larger than what was previously believed to be the case, based on the measurements in Ref. @cite_97 , and even exceeds the polarization of typical prototype ferroelectrics such as BaTiO @math , PbTiO @math , or PbZr @math Ti @math O @math (PZT). Variation of @math within reasonable limits changes the calculated value for the electric polarization by only @math @math C cm @math , i.e. the large value of the polarization is rather independent from the precise value of the Hubbard parameter. This is consistent with the assumption that the transition met al @math states do not play an active role for the ferroelectric instability in BFO. The calculated large spontaneous polarization for bulk BFO is also consistent with the large ionic displacements in the experimentally observed @math structure of BFO (see Fig. c), compared to an appropriate centrosymmetric reference configuration. Recently, the large polarization of @math @math C cm @math along (111) for bulk BFO has also been confirmed experimentally by new measurements on high-quality single crystals @cite_41 .
@cite_41 @cite_97
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Electric polarization loops are measured at room temperature on highly pure BiFeO3 single crystals synthesized by a flux growth method. Because the crystals have a high electrical resistivity, the resulting low leakage currents allow the authors to measure a large spontaneous polarization in excess of 100μCcm−2, a value never reported in the bulk. During electric cycling, the slow degradation of the material leads to an evolution of the hysteresis curves eventually preventing full saturation of the crystals. 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.