A short review is given of the recent work on single-phase crystals that are ferroelectric and ferromagnetic at or near room temperature. BiFeO 3 is mentioned only briefly, because it has been reviewed in detail elsewhere very recently; emphasis instead is on copper oxide, perovskite oxides with mixed B-site occupancy (such as Pb(Fe 1/2 Ta 1/2 ) x (Zr y Ti
INTRODUCTIONMultiferroics are usually defined as single-phase crystals exhibiting at the same temperature and pressure both ferromagnetism (or antiferromagnetism) and ferroelectricity (or antiferroelectricity). As most ferroelectrics are also ferroelastic 1 (hysteretic stress-strain relationships), the 'multi-ferro' label often includes three coupled order parameters. (As a peripheral comment, we note that it is necessary and sufficient 2 for a ferroelectric to be ferroelastic if its phase transition changes the crystal class-for example, from orthorhombic to tetragonal-treating hexagonal and trigonal as a single super-class. Examples of nonferroelastic ferroelectrics include KTiOPO 4 and LiNbO 3 , whose ferroelectric transitions are, respectively, orhorhombic-orthorhombic and trigonal-trigonal.)The interest in multiferroics at present is growing rapidly, and the interest is twofold: from a fundamental point of view the coupling between spins and lattices in crystals-between magnetism and ferroelectricity and/or structural phase transitions-has been recognized as complex and fascinating for several decades, generally requiring low-symmetry materials that were carefully avoided in earlier days of solid state theory. A good reason why it is presented in the elegant work by Schmid and Trooster 3 on the boracites: These materials (for example, nickel-iodine boracite) are multiferroic only at cryogenic temperatures and grow in needle-like structures, making them impractical for commercial device applications; and theoretically they exhibit low symmetry (monoclinic or triclinic) and have as many as 96 atoms per unit cell, making them theoretically formidable. Despite these drawbacks, multiferroics present a possible avenue for the next generation of computer digital memories, combining at least in principle, the high-speed and low-power consumption 4,5 of a ferroelectric random access memory (FRAM) with the nondestructive READ operation of a magnetic RAM. We discuss below why these goals will not be easy to achieve in commercial products:The most serious problems are operational temperature (most multiferroics operate well below ambient) and magnitudes of magnetization (all multiferroics with reasonably high operating temperatures are weak ferromagnets-canted antiferromagnetswhereas a strong ferromagnet is desired), and the switched polarization is also extremely weak. The polarization in most multiferroics is so weak that authors measure it in nC m À2 rather than the older customary mC cm À2 . Keep in mind that equally good SI units would be C hectare À1 for these multiferroics, a value far lower than the roughly 1 mC cm À2 required by a computer memory sense ampl...