A ferroelectric crystal exhibits a stable and switchable electrical polarization that is manifested in the form of cooperative atomic displacements. A ferromagnetic crystal exhibits a stable and switchable magnetization that arises through the quantum mechanical phenomenon of exchange. There are very few 'multiferroic' materials that exhibit both of these properties, but the 'magnetoelectric' coupling of magnetic and electrical properties is a more general and widespread phenomenon. Although work in this area can be traced back to pioneering research in the 1950s and 1960s, there has been a recent resurgence of interest driven by long-term technological aspirations.

BiFeO3 is perhaps the only material that is both magnetic and a strong ferroelectric at room temperature. As a result, it has had an impact on the field of multiferroics that is comparable to that of yttrium barium copper oxide (YBCO) on superconductors, with hundreds of publications devoted to it in the past few years. In this Review, we try to summarize both the basic physics and unresolved aspects of BiFeO3 (which are still being discovered with several new phase transitions reported in the past few months) and device applications, which center on spintronics and memory devices that can be addressed both electrically and magnetically.

In the past year it has become possible to fabricate ferroelectric thin-film memories onto standard silicon integrated circuits that combine very high speed (30-nanosecond read/erase/rewrite operation), 5-volt standard silicon logic levels, very high density (2 by 2 micrometer cell size), complete nonvolatility (no standby power required), and extreme radiation hardness. These ferroelectric random-access memories are expected to replace magnetic core memory, magnetic bubble memory systems, and electrically erasable read-only memory for many applications. The switching kinetics of these films, 100 to 300 nanometers thick, are now well understood, with switching times that fit an activation field dependence that scales applied field and temperature. Earlier problems of fatigue and retention failure are also now understood and have been improved to acceptable levels.

Long viewed as a topic in classical physics, ferroelectricity can be described by a quantum mechanical ab initio theory. Thin-film nanoscale device structures integrated onto Si chips have made inroads into the semiconductor industry. Recent prototype applications include ultrafast switching, cheap room-temperature magnetic-field detectors, piezoelectric nanotubes for microfluidic systems, electrocaloric coolers for computers, phased-array radar, and three-dimensional trenched capacitors for dynamic random access memories. Terabit-per-square-inch ferroelectric arrays of lead zirconate titanate have been reported on Pt nanowire interconnects and nanorings with 5-nanometer diameters. Finally, electron emission from ferroelectrics yields cheap, high-power microwave devices and miniature x-ray and neutron sources.

This review covers the important advances in recent years in the physics of thin film ferroelectric oxides, the strongest emphasis being on those aspects particular to ferroelectrics in thin film form. We introduce the current state of development in the application of ferroelectric thin films for electronic devices and discuss the physics relevant for the performance and failure of these devices. Following this we cover the enormous progress that has been made in the first principles computational approach to understanding ferroelectrics. We then discuss in detail the important role that strain plays in determining the properties of epitaxial thin ferroelectric films. Finally, we look at the emerging possibilities for nanoscale ferroelectrics, with particular emphasis on ferroelectrics in non conventional nanoscale geometries.Comment: This is an invited review for Reviews of Modern Physics. We welcome feedback and will endeavour to incorporate comments received promptly into the final versio