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.

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Multiferroic and magnetoelectric materials

Recent research activities on the linear magnetoelectric (ME) effect?induction of magnetization by an electric field or of polarization by a magnetic field?are reviewed. Beginning with a brief summary of the history of the ME effect since its prediction in 1894, the paper focuses on the present revival of the effect. Two major sources for 'large' ME effects are identified. (i) In composite materials the ME effect is generated as a product property of a magnetostrictive and a piezoelectric compound. A linear ME polarization is induced by a weak ac magnetic field oscillating in the presence of a strong dc bias field. The ME effect is large if the ME coefficient coupling the magnetic and electric fields is large. Experiments on sintered granular composites and on laminated layers of the constituents as well as theories on the interaction between the constituents are described. In the vicinity of electromechanical resonances a ME voltage coefficient of up to 90?V?cm?1?Oe?1 is achieved, which exceeds the ME response of single-phase compounds by 3?5 orders of magnitude. Microwave devices, sensors, transducers and heterogeneous read/write devices are among the suggested technical implementations of the composite ME effect. (ii) In multiferroics the internal magnetic and/or electric fields are enhanced by the presence of multiple long-range ordering. The ME effect is strong enough to trigger magnetic or electrical phase transitions. ME effects in multiferroics are thus 'large' if the corresponding contribution to the free energy is large. Clamped ME switching of electrical and magnetic domains, ferroelectric reorientation induced by applied magnetic fields and induction of ferromagnetic ordering in applied electric fields were observed. Mechanisms favouring multiferroicity are summarized, and multiferroics in reduced dimensions are discussed. In addition to composites and multiferroics, novel and exotic manifestations of ME behaviour are investigated. This includes (i) optical second harmonic generation as a tool to study magnetic, electrical and ME properties in one setup and with access to domain structures; (ii) ME effects in colossal magnetoresistive manganites, superconductors and phosphates of the LiMPO4 type; (iii) the concept of the toroidal moment as manifestation of a ME dipole moment; (iv) pronounced ME effects in photonic crystals with a possibility of electromagnetic unidirectionality. The review concludes with a summary and an outlook to the future development of magnetoelectrics research.

https://iopscience.iop.org/article/10.1088/0022-3727/38/8/R01/pdf

Revival of the Magnetoelectric Effect

The magnetoelectric effect--the induction of magnetization by means of an electric field and induction of polarization by means of a magnetic field--was first presumed to exist by Pierre Curie, and subsequently attracted a great deal of interest in the 1960s and 1970s (refs 2-4). More recently, related studies on magnetic ferroelectrics have signalled a revival of interest in this phenomenon. From a technological point of view, the mutual control of electric and magnetic properties is an attractive possibility, but the number of candidate materials is limited and the effects are typically too small to be useful in applications. Here we report the discovery of ferroelectricity in a perovskite manganite, TbMnO3, where the effect of spin frustration causes sinusoidal antiferromagnetic ordering. The modulated magnetic structure is accompanied by a magnetoelastically induced lattice modulation, and with the emergence of a spontaneous polarization. In the magnetic ferroelectric TbMnO3, we found gigantic magnetoelectric and magnetocapacitance effects, which can be attributed to switching of the electric polarization induced by magnetic fields. Frustrated spin systems therefore provide a new area to search for magnetoelectric media.

Magnetic control of ferroelectric polarization

Magnetism and ferroelectricity are essential to many forms of current technology, and the quest for multiferroic materials, where these two phenomena are intimately coupled, is of great technological and fundamental importance. Ferroelectricity and magnetism tend to be mutually exclusive and interact weakly with each other when they coexist. The exciting new development is the discovery that even a weak magnetoelectric interaction can lead to spectacular cross-coupling effects when it induces electric polarization in a magnetically ordered state. Such magnetic ferroelectricity, showing an unprecedented sensitivity to ap plied magnetic fields, occurs in 'frustrated magnets' with competing interactions between spins and complex magnetic orders. We summarize key experimental findings and the current theoretical understanding of these phenomena, which have great potential for tuneable multifunctional devices.

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Multiferroics: a magnetic twist for ferroelectricity

Multiferroic materials, which show simultaneous ferroelectric and magnetic ordering, exhibit unusual physical properties — and in turn promise new device applications — as a result of the coupling between their dual order parameters. We review recent progress in the growth, characterization and understanding of thin-film multiferroics. The availability of high-quality thin-film multiferroics makes it easier to tailor their properties through epitaxial strain, atomic-level engineering of chemistry and interfacial coupling, and is a prerequisite for their incorporation into practical devices. We discuss novel device paradigms based on magnetoelectric coupling, and outline the key scientific challenges in the field.

Multiferroics: progress and prospects in thin films.

The physical properties of a topologically disordered amorphous material (glass), such as heat capacity and thermal conductivity, are markedly different from those of its ordered crystalline counterpart. The understanding of these phenomena is a notoriously complex problem. One of the universal features of disordered glasses is the 'boson peak', which is observed in neutron and Raman scattering experiments. The boson peak is typically ascribed to an excess density of vibrational states. Here, we study the nature of the boson peak, using numerical simulations of several glass-forming systems. We discovered evidence suggestive of the equality of the boson peak frequency to the Ioffe-Regel limit for 'transverse' phonons, above which transverse phonons no longer propagate. Our results indicate a possibility that the origin of the boson peak is transverse vibrational modes associated with defective soft structures in the disordered state. Furthermore, we suggest a possible link between slow structural relaxation and fast boson peak dynamics in glass-forming systems.

Universal link between the boson peak and transverse phonons in glass.

As a liquid approaches its glass transition its dynamics slow down and simultaneously the material becomes more heterogeneous. A static structural heterogeneity, now shown to be widely present in glass-forming liquids, is suggested to be the origin of this dynamic heterogeneity that links structural parameters to the glass transition.

Critical-like behaviour of glass-forming liquids

The evolution of spin- and orbital-ordered states has been investigated for a series of insulating perovskites $R{\mathrm{MnO}}_{3}$ $(R=\mathrm{L}\mathrm{a},\mathrm{P}\mathrm{r},\mathrm{N}\mathrm{d},\dots{}).$ $R{\mathrm{MnO}}_{3}$ with a large ${\mathrm{GdFeO}}_{3}$-type distortion is regarded as a frustrated spin system having ferromagnetic nearest-neighbor and antiferromagnetic (AF) next-nearest-neighbor (NNN) interactions within a ${\mathrm{MnO}}_{2}$ plane. The staggered orbital order associated with the ${\mathrm{GdFeO}}_{3}$-type distortion induces the anisotropic NNN interaction, and yields unique sinusoidal and up-up-down-down AF ordered states in the distorted perovskites with ${e}_{g}^{1}$ configuration.

Distorted perovskite with e g 1 configuration as a frustrated spin system

Some liquids do not crystallize below the melting point, but instead enter into a supercooled state and on cooling eventually become a glass at the glass-transition temperature. During this process, the liquid dynamics not only drastically slow down, but also become progressively more heterogeneous. The relationship between the kinetic slowing down and growing dynamic heterogeneity is a key problem of the liquid–glass transition. Here, we study this problem by using a liquid model, with a crystalline ground state, for which we can systematically control frustration against crystallization. We found that slow regions having a high degree of crystalline order emerge below the melting point, and their characteristic size and lifetime increase steeply on cooling. These crystalline regions lead to dynamic heterogeneity, suggesting a connection to the complex free-energy landscape and the resulting slow dynamics. These findings point towards an intrinsic link between the glass transition and crystallization.

Hiroshi Shintani

Papers

Magnetic control of ferroelectric polarization

Universal link between the boson peak and transverse phonons in glass.

Critical-like behaviour of glass-forming liquids

Distorted perovskite with e g 1 configuration as a frustrated spin system

Frustration on the way to crystallization in glass