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

Ferroelectromagnets are an interesting group of compounds that complement purely (anti-)ferroelectric or (anti-)ferromagnetic materials--they display simultaneous electric and magnetic order. With this coexistence they supplement materials in which magnetization can be induced by an electric field and electrical polarization by a magnetic field, a property which is termed the magnetoelectric effect. Aside from its fundamental importance, the mutual control of electric and magnetic properties is of significant interest for applications in magnetic storage media and 'spintronics'. The coupled electric and magnetic ordering in ferroelectromagnets is accompanied by the formation of domains and domain walls. However, such a cross-correlation between magnetic and electric domains has so far not been observed. Here we report spatial maps of coupled antiferromagnetic and ferroelectric domains in YMnO3, obtained by imaging with optical second harmonic generation. The coupling originates from an interaction between magnetic and electric domain walls, which leads to a configuration that is dominated by the ferroelectromagnetic product of the order parameters.

Observation of coupled magnetic and electric domains

We analyze the coupling between the ferroelectric and magnetic order parameters in the magnetoelectric multiferroic $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ using density functional theory within the local spin density approximation (LSDA) and the $\mathrm{LSDA}+\mathrm{U}$ method. We show that weak ferromagnetism of the Dzyaloshinskii-Moriya type occurs in this material, and we analyze the coupling between the resulting magnetization and the structural distortions. We explore the possibility of electric-field-induced magnetization reversal and show that, although it is unlikely to be realized in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$, it is not in general impossible. Finally, we outline the conditions that must be fulfilled to achieve switching of the magnetization using an electric field.

/pdf/weak-ferromagnetism-and-magnetoelectric-coupling-in-bismuth-acptbzeohy.pdf

Weak ferromagnetism and magnetoelectric coupling in bismuth ferrite

Domain aspects of multi-ferroics are reviewed, i.e. of materials, in which two or all three of the properties ‘ferroelectricity.’ ‘ferromagnetism’ and ‘ferroelasticity’ occur simultaneously in the same phase, and in which the magnetic point group has been reliably established by magnetoelectric, optical, dielectric, magnetic and related studies on single crystals and single domains. Nearly only members of the boracite crystal family are concerned, whereas for the perovskite family and other classes of material there is great paucity of data on single crystals. Polarized light microscopy is shown to be an indispensable tool for the study of multi-ferroics, in particular when ferroelasticity is involved. Potential multi-ferroic magnetoelectrics, so far only known in ceramic form, are excluded from the survey.

/pdf/multi-ferroic-magnetoelectrics-4zi47flck9.pdf

Multi-ferroic magnetoelectrics

Domains in ferroelectrics were considered to be well understood by the middle of the last century: They were generally rectilinear, and their walls were Ising-like. Their simplicity stood in stark contrast to the more complex Bloch walls or N\'eel walls in magnets. Only within the past decade and with the introduction of atomic-resolution studies via transmission electron microscopy, electron holography, and atomic force microscopy with polarization sensitivity has their real complexity been revealed. Additional phenomena appear in recent studies, especially of magnetoelectric materials, where functional properties inside domain walls are being directly measured. In this paper these studies are reviewed, focusing attention on ferroelectrics and multiferroics but making comparisons where possible with magnetic domains and domain walls. An important part of this review will concern device applications, with the spotlight on a new paradigm of ferroic devices where the domain walls, rather than the domains, are the active element. Here magnetic wall microelectronics is already in full swing, owing largely to the work of Cowburn and of Parkin and their colleagues. These devices exploit the high domain wall mobilities in magnets and their resulting high velocities, which can be supersonic, as shown by Kreines' and co-workers 30 years ago. By comparison, nanoelectronic devices employing ferroelectric domain walls often have slower domain wall speeds, but may exploit their smaller size as well as their different functional properties. These include domain wall conductivity (metallic or even superconducting in bulk insulating or semiconducting oxides) and the fact that domain walls can be ferromagnetic while the surrounding domains are not.

/pdf/domain-wall-nanoelectronics-3iwxoy7x89.pdf

Domain wall nanoelectronics

A ferromagnetic, ferroelectric, or ferroelastic crystal is called full or partial, according to whether all or not all but some of its orientation states are different in spontaneous magnetization vector, spontaneous polarization vector, or spontaneous strain tensor. In previous theories \char22{} for nonmagnetic crystals \char22{} the concept of "species" was introduced, a determination was made of all possible species of full ferroelectrics and of full ferroelastics, and those species were found in which ferroelectricity and ferroelasticity coexist and completely couple with each other. These theories are now extended to cover magnetic crystals in addition to nonmagnetic crystals and to cover the partial in addition to the full. A determination is made of all possible species of full ferromagnetics, partial ferromagnetics, full ferroelectrics, partial ferroelectrics, full ferroelastics, and partial ferroelastics, and it is found out in which of these species two or all of ferromagnetism, ferroelectricity, and ferroelasticity should couple completely or incompletely with each other.

Possible Species of Ferromagnetic, Ferroelectric, and Ferroelastic Crystals

It is convenient to grasp crystals of a kind as “ferroelastic” crystals. They are defined analogously to “ferroelectric” crystals, mechanical strain and stress in the former corresponding to electric polarization and field in the latter respectively. The order of magnitude of the coercive stress for ferroelastic state-shifts which corresponds to the coercive field for ferroelectric state-shifts is expected, on the average, to be 10 2 newt·cm -2 . A determination is made of all theoretically possible species of ferroelastic crystals and the number of states and ferroelectricity or nonferroelctricity in each of these species. It is found that there are 94 of these ferroelastic species and that 42 of them are simultaneously ferroelectric. Incidentally, an alteration is made of the hitherto used symbols for the 88 species of ferroeletric crystals.

Possible Species of “Ferroelastic” Crystals and of Simultaneously Ferroelectric and Ferroelastic Crystals

For a crystal which can become ferroelastic , it is important to know those elements of those linear combinations of elements of mechanical strain tensor each of which, at null stress, is not equal in all the orientation states of the ferroelastic phase and is zero over the whole temperature range in the prototypic phase. These quantities are a kind of state parameters . Also, it is convenient to introduce “spontaneous strain” as a total measure for the `degree' of ferroelasticity. Spontaneous strain should be independent of choice of the rectangular coordinate system, be the same in all the orientation states of the ferroelastic phase, and be zero over the whole temperature range in the prototypic phase. For each of the 94 species of ferroelastics, the set of state parameters is found, its way of changing with each state shift is determined, and the spontaneous strain (satisfying the above conditions) is formulated.

Determination of the State Parameters and Formulation of Spontaneous Strain for Ferroelastics

Simultaneous Ferroelectricity and Ferroelasticity of Gd 2 (MoO 4 ) 3

The ferroic state shifts higher by one order than the ferroelectric state shifts and the ferroelastic ones are considered. (Nonmagnetism is assumed.) The styles and directions of mechanical, electrical or combined forces effective on these second-order state shifts are expounded with simple examples. The orders of magnitude of the “coercive forces” for these state shifts are estimated. The optical discernibility between domains connected by such a state shift is discussed.

Kêitsiro Aizu

Papers

Possible Species of Ferromagnetic, Ferroelectric, and Ferroelastic Crystals

Possible Species of “Ferroelastic” Crystals and of Simultaneously Ferroelectric and Ferroelastic Crystals

Determination of the State Parameters and Formulation of Spontaneous Strain for Ferroelastics

Simultaneous Ferroelectricity and Ferroelasticity of Gd 2 (MoO 4 ) 3

Second-Order Ferroic State Shifts