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.
Effects of epitaxial strain can be assessed from first principles by performing bulk calculations for a strained unit cell, where the lattice constant within a certain lattice plane (corresponding to the orientation of the substrate surface) is constrained, whereas the lattice constant in the perpendicular direction as well as all internal structural parameters are allowed to relax. Such calculations have been performed for BFO corresponding to a (111) orientation of the substrate @cite_52 . In this case the @math symmetry of the bulk structure is conserved and the epitaxial constraint is applied in the lattice plane perpendicular to the polarization direction. It was found that the sensitivity of the electric polarization to strain is surprisingly weak in BFO, much weaker than in other well-known ferroelectrics @cite_52 (see Fig. ). A systematic comparison of the strain dependence in various ferroelectrics, including BFO in both the @math and a hypothetical tetragonal phase with @math symmetry, has been performed in Ref. @cite_45 (see Fig. ). It was shown that the effect of epitaxial strain for all investigated systems can be understood in terms of the usual bulk linear response functions and that both strong and weak strain dependence can occur.
@cite_45 @cite_52
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We investigate the variation of the spontaneous ferroelectric polarization with epitaxial strain for BaTiO @math , PbTiO @math , LiNbO @math , and BiFeO @math using first principles calculations. We find that while the strain dependence of the polarization is very strong in the simple perovskite systems BaTiO @math and PbTiO @math it is only weak in LiNbO @math and BiFeO @math . We show that this different behavior can be understood purely in terms of the piezoelectric and elastic constants of the unstrained bulk material, and we discuss several factors that determine the strain behavior of a certain material. The dependencies on strain and oxygen vacancies of the ferroelectric polarization and the weak ferromagnetic magnetization in the multiferroic material bismuth ferrite, @math , are investigated using first principles density functional theory calculations. The electric polarization is found to be rather independent of strain, in striking contrast to most conventional perovskite ferroelectrics. It is also not significantly affected by oxygen vacancies, or by the combined presence of strain and oxygen vacancies. The magnetization is also unaffected by strain, however, the incorporation of oxygen vacancies can alter the magnetization slightly, and also leads to the formation of @math . These results are discussed in light of recent experiments on epitaxial films of @math , which reported a strong thickness dependence of both magnetization and polarization.