Multiferroics are defined as materials that exhibit more than one of the primary ferroic properties in the same phase: ferromagnetism – a magnetisation that is switchable by an applied magnetic field ferroelectricity – an electric polarisation that is switchable by an applied electric field ferroelasticity – a deformation that is switchable by an applied stress While ferroelectric ferroelastics and ferromagnetic ferroelastics are formally multiferroics, these days the term is usually used to describe the magnetoelectric multiferroics that are simultaneously ferromagnetic and ferroelectric. Sometimes the definition is expanded to include nonprimary order parameters, such as antiferromagnetism or ferrimagnetism. In addition, other types of primary order, such as ferroic arrangements of magnetoelectric multipoles of which ferrotoroidicity is an example, have also been recently proposed. Besides scientific interest in their physical properties, multiferroics have potential for applications as actuators, switches, magnetic field sensors and new types of electronic memory devices. History A Web of Science search for the term multiferroic yields the year 2000 paper "Why are there so few magnetic ferroelectrics?" from N. A. Spaldin (then Hill) as the earliest result. This work explained the origin of the contraindication between magnetism and ferroelectricity and proposed practical routes to circumvent it, and is widely credited with starting the modern explosion of interest in multiferroic materials. The availability of practical routes to creating multiferroic materials from 2000 stimulated intense activity. Particularly key early works were the discovery of large ferroelectric polarization in epitaxially grown thin films of magnetic BiFeO3, the observation that the non-collinear magnetic ordering in orthorhombic TbMnO3 and TbMn2O5 causes ferroelectricity, and the identification of unusual improper ferroelectricity that is compatible with the coexistence of magnetism in hexagonal manganite YMnO3. The graph to the right shows in red the number of papers on multiferroics from a Web of Science search until 2008; the exponential increase continues today. Magnetoelectric materials To place multiferroic materials in their appropriate historical context, one also needs to consider magnetoelectric materials, in which an electric field modifies the magnetic properties and vice versa. While magnetoelectric materials are not necessarily multiferroic, all ferromagnetic ferroelectric multiferroics are linear magnetoelectrics, with an applied electric field inducing a change in magnetization linearly proportional to its magnitude. Magnetoelectric materials and the corresponding magnetoelectric effect have a longer history than multiferroics, shown in blue in the graph to the right. The first known mention of magnetoelectricity is in the 1959 Edition of Landau &