Multiferroics: Past, present, and future
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Introduction Multiferroics are defined to be materials that combine two or more of the primary ferroic order parameters simultaneously in the same phase. The established primary ferroics are ferromagnets (materials with a spontaneous magnetization that is switchable by an applied magnetic field), ferroelectrics (materials with a spontaneous electric polarization that is switchable by an applied electric field), and ferroelastics (materials with a spontaneous deformation that is switchable by an applied stress).1 The primary ferroic phenomena are illustrated by the vertices of the triangle in Figure 1, where the ferromagnetic, ferroelectric, and ferroelastic switching are indicated by blue, yellow, and purple arrows, respectively. The most interesting aspect of multiferroics is the cross-coupling between the order parameters, represented by the sides of the triangle. Piezoelectricity, resulting from the coupling between polarization and deformation in ferroelectric ferroelastics (left edge of the triangle), is well established and widely exploited (e.g., in sonar detectors). Likewise, magnetism and structure are often strongly coupled (bottom edge of the triangle) leading to piezomagnetism, which can be used in magnetomechanical actuation or magnetic sensing. The multiferroics that combine ferromagnetism and ferroelectricity are represented by the right edge of the triangle and are much less common. They are appealing, however, since their coupling produces the so-called magnetoelectric effect, in which an electric field can induce or modify the magnetization, and a magnetic field affects the electrical polarization (green arrows in Figure 1). Electric-field control of magnetism in
particular is highly appealing for potential devices, since electric fields can be engineered to be far smaller and to use less power than their magnetic counterparts.
Why are there so few magnetic ferroelectrics? A Web of Science search returns a paper entitled Why are there so few magnetic ferroelectrics?2,3* as the earliest result for “multiferroic.” The answer to the question is simple. The chemistries of ions that tend to be magnetic in solids are different from those that tend to form electric dipoles. For an ion to carry a magnetic moment, its electrons, each of which have 1 Bohr magneton (μB) of spin-magnetic moment, must be arranged such that their magnetic moments do not cancel each other. This excludes all completely filled orbitals, so core electrons do not contribute to magnetism, and also, closed-shell ions are not magnetic. Among valence electrons in partially filled shells, the band energy is optimized when the lowest energy levels are occupied by nonmagnetic pairs of antiparallel electrons. This competes with Hund’s magnetic coupling, which favors parallel electrons to optimize the exchange energy. The magnetic state tends to win the competition when the electrons are localized, which in solids occurs for transition metals with partially filled 3d shells or lanthanides with partially filled 4f shells. For ferroelectricity, there i
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