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.

Multiferroics, defined for those multifunctional materials in which two or more kinds of fundamental ferroicities coexist, have become one of the hottest topics of condensed matter physics and materials science in recent years. The coexistence of several order parameters in multiferroics brings out novel physical phenomena and offers possibilities for new device functions. The revival of research activities on multiferroics is evidenced by some novel discoveries and concepts, both experimentally and theoretically. In this review, we outline some of the progressive milestones in this stimulating field, especially for those single-phase multiferroics where magnetism and ferroelectricity coexist. First, we highlight the physical concepts of multiferroicity and the current challenges to integrate the magnetism and ferroelectricity into a single-phase system. Subsequently, we summarize various strategies used to combine the two types of order. Special attention is paid to three novel mechanisms for multiferroicity generation: (1) the ferroelectricity induced by the spin orders such as spiral and E-phase antiferromagnetic spin orders, which break the spatial inversion symmetry; (2) the ferroelectricity originating from the charge-ordered states; and (3) the ferrotoroidic system. Then, we address the elementary excitations such as electromagnons, and the application potentials of multiferroics. Finally, open questions and future research opportunities are proposed.

Multiferroicity: the coupling between magnetic and polarization orders

The manipulation of magnetic properties by an electric field in magnetoelectric multiferroic materials has driven significant research activity, with the goal of realizing their transformative technological potential. Here, we review progress in the fundamental understanding and design of new multiferroic materials, advances in characterization and modelling tools to describe them, and the exploration of devices and applications. Focusing on the translation of the many scientific breakthroughs into technological innovations, we identify the key open questions in the field where targeted research activities could have maximum impact in transitioning scientific discoveries into real applications. Magnetoelectric multiferroics, where magnetic properties are manipulated by electric field and vice versa, could lead to improved electronic devices. Here, advances in materials, characterisation and modelling, and usage in applications are reviewed.

Advances in magnetoelectric multiferroics.

Perovskite lead-free dielectrics for energy storage applications

Ferroelectric materials have a spontaneous electric polarization and are widely used in electronic devices including memories. Conventional ferroelectricity arises from ionic displacement, but an alternative mechanism has been proposed based on ordered electrons. Evidence for the latter behaviour has now been found in a mixed valence oxide. This type of ferroelectricity may offer potential for devices with enhanced controllability. Ferroelectric materials are widely used in modern electric devices such as memory elements, filtering devices and high-performance insulators. Ferroelectric crystals have a spontaneous electric polarization arising from the coherent arrangement of electric dipoles1 (specifically, a polar displacement of anions and cations). First-principles calculations2,3 and electron density analysis4 of ferroelectric materials have revealed that the covalent bond between the anions and cations, or the orbital hybridization of electrons on both ions, plays a key role in establishing the dipolar arrangement. However, an alternative model—electronic ferroelectricity5—has been proposed in which the electric dipole depends on electron correlations, rather than the covalency. This would offer the attractive possibility of ferroelectric materials that could be controlled by the charge, spin and orbital degrees of freedom of the electron. Here we report experimental evidence for ferroelectricity arising from electron correlations in the triangular mixed valence oxide, LuFe2O4. Using resonant X-ray scattering measurements, we determine the ordering of the Fe2+ and Fe3+ ions. They form a superstructure that supports an electric polarization consisting of distributed electrons of polar symmetry. The polar ordering arises from the repulsive property of electrons—electron correlations—acting on a frustrated geometry.

Ferroelectricity from iron valence ordering in the charge-frustrated system LuFe2O4.

Magnetic Properties of Perovskite GdCrO3

The perovskite chromite La1−xPrxCrO3 shows an unusual positive exchange bias (PEB) and a negative exchange bias (NEB) associated with magnetization reversal, arising from an antiparallel Pr3+-Cr3+ coupling. Below ∼200 K, changing the cooling magnetic field switches the type of EB. A PEB appears in low cooling fields (<3–15 kOe), comparable with the internal magnetic field at the Pr site. The appearance of PEB or NEB depends on the orientation of the Pr3+ moment with respect to the canted Cr3+ component.

Positive exchange bias from magnetization reversal in La1−xPrxCrO3 (x ∼ 0.7–0.85)

The magnetic and dielectric properties have been investigated for the isostructural oxides of $R{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$, $R\mathrm{Fe}M{\mathrm{O}}_{4}$, and $R\mathrm{Ga}\mathrm{Cu}{\mathrm{O}}_{4}$ ($R=\mathrm{Yb}$ and Lu, $M=\mathrm{Co}$ and Cu). The magnetization measurements for $R{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ showed ferrimagnetic ordering at $\ensuremath{\sim}250\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. This system also exhibited large dielectric constants of $\ensuremath{\sim}10\phantom{\rule{0.2em}{0ex}}000--30\phantom{\rule{0.2em}{0ex}}000$ at around room temperature, which is attributable to the charge-ordering-induced ferroelectricity, as was proposed in our recent paper. The magnetic transition temperatures are lowered to $\ensuremath{\sim}45--90\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ for $R\mathrm{Fe}M{\mathrm{O}}_{4}$. Magnetic ordering is not found for $R\mathrm{Ga}\mathrm{Cu}{\mathrm{O}}_{4}$. ac magnetic susceptibility measurements indicate that magnetic ordering becomes short-ranged by the substitution at the Fe site. The overall characteristic behavior of the magnetic properties is explained in terms of the change of a spin value as well as the dilution of magnetic interactions. Although the ac dielectric measurements show the existence of polar regions in each material, the dielectric constants below $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ become smaller in the order of $R{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$, $R\mathrm{Fe}\mathrm{Co}{\mathrm{O}}_{4}$, $R\mathrm{Fe}\mathrm{Cu}{\mathrm{O}}_{4}$, and $R\mathrm{Ga}\mathrm{Cu}{\mathrm{O}}_{4}$. From the analysis of the dielectric dispersion, the distribution of the fluctuation time of polar regions is wider in $R\mathrm{Fe}\mathrm{Co}{\mathrm{O}}_{4}$, $R\mathrm{Fe}\mathrm{Cu}{\mathrm{O}}_{4}$, and $R\mathrm{Ga}\mathrm{Cu}{\mathrm{O}}_{4}$ than in $R{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$; a coherent motion of polar regions is suppressed in the substituted systems. By comparison to the results from the magnetic measurements, the dielectric properties are discussed in connection with a charge transfer between the transition-metal $3d$ orbitals, consistently with the proposed mechanism of the ferroelectricity in $R{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$.

Kenji Yoshii

Papers

Ferroelectricity from iron valence ordering in the charge-frustrated system LuFe2O4.

Magnetic Properties of Perovskite GdCrO3

Positive exchange bias from magnetization reversal in La1−xPrxCrO3 (x ∼ 0.7–0.85)

Magnetic and dielectric properties of RFe2O4, RFeMO4, and RGaCuO4 (R=Yb and Lu, M=Co and Cu)

Magnetic Properties of La1−xPrxCrO3