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
1993552027 2130156865 2112232168 2074950413
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. 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 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. We consider the change in polarization P which occurs upon making an adiabatic change in the Kohn-Sham Hamiltonian of the solid. A simple expression for P is derived in terms of the valence-band wave functions of the initial and final Hamiltonians. We show that physically P can be interpreted as a displacement of the center of charge of the Wannier functions. The formulation is successfully applied to compute the piezoelectric tensor of GaAs in a first-principles pseudopotential calculation.