Multiferroics are compounds that show ferroelectricity and magnetism. BiFeO3, by far the most studied, has outstanding ferroelectric properties, a cycloidal magnetic order in the bulk, and many unexpected virtues such as conductive domain walls or a low bandgap of interest for photovoltaics. Although this flurry of properties makes BiFeO3 a paradigmatic multifunctional material, most are related to its ferroelectric character, and its other ferroic property--antiferromagnetism--has not been investigated extensively, especially in thin films. Here we bring insight into the rich spin physics of BiFeO3 in a detailed study of the static and dynamic magnetic response of strain-engineered films. Using Mössbauer and Raman spectroscopies combined with Landau-Ginzburg theory and effective Hamiltonian calculations, we show that the bulk-like cycloidal spin modulation that exists at low compressive strain is driven towards pseudo-collinear antiferromagnetism at high strain, both tensile and compressive. For moderate tensile strain we also predict and observe indications of a new cycloid. Accordingly, we find that the magnonic response is entirely modified, with low-energy magnon modes being suppressed as strain increases. Finally, we reveal that strain progressively drives the average spin angle from in-plane to out-of-plane, a property we use to tune the exchange bias and giant-magnetoresistive response of spin valves.

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An effective Hamiltonian is developed to investigate the magnetic cycloid of the BiFeO3 (BFO) multiferroic. This approach reproduces many complex features of this cycloid, such as its plane of rotation containing the polarization and the newly discovered spin density waves resulting from the canting of magnetic dipoles out of this cycloidal plane. It also suggests that the energetic origin of the cycloid can be thought of in terms of the converse spin-current model, and reveals the mechanisms responsible for the spin density waves. Finally, this atomistic scheme resolves an ongoing controversy about the cycloid anharmonicity, and revisits a recent misconception about the relationship between out-of-plane spin-density waves and the weak magnetization associated with the spin-canted structure of BFO.

Properties of BiFeO_{3} under an electric field are simulated using an ab initio-based approach. Complex paths and anomalous phenomena occur, depending on the direction of the field. Examples of such phenomena are the rotations of the polarization and of the axis about which the oxygen octahedra tilt; isostructural transitions; disappearance and reappearance of the tilting of the oxygen octahedra; and reentrance into specific crystallographic classes.The magnetic order parameter is not always perpendicular to the polarization, especially when the tilting of the oxygen octahedra disappears. The governing "rule" is that the magnetic order parameter remains orthogonal to the axis about which the oxygen octahedra tilt.

Using a first-principles-based effective Hamiltonian within molecular dynamics simulations, we discover that applying an electric field that is opposite to the initial direction of the polarization results in a switching of both the polarization and the magnetic chirality vector of multiferroic BiFeO3 at an ultrafast pace (namely, of the order of picoseconds). We discuss the origin of such a double ultrafast switching, which is found to involve original intermediate magnetic states and may hold promise for designing various devices.