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

Enhancement of polarization and related properties in heteroepitaxially constrained thin films of the ferroelectromagnet, BiFeO3, is reported. Structure analysis indicates that the crystal structure of film is monoclinic in contrast to bulk, which is rhombohedral. The films display a room-temperature spontaneous polarization (50 to 60 microcoulombs per square centimeter) almost an order of magnitude higher than that of the bulk (6.1 microcoulombs per square centimeter). The observed enhancement is corroborated by first-principles calculations and found to originate from a high sensitivity of the polarization to small changes in lattice parameters. The films also exhibit enhanced thickness-dependent magnetism compared with the bulk. These enhanced and combined functional responses in thin film form present an opportunity to create and implement thin film devices that actively couple the magnetic and ferroelectric order parameters.

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Epitaxial BiFeO3 multiferroic thin film heterostructures.

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 piezoelectric properties of relaxor based ferroelectric single crystals, such as Pb(Zn1/3Nb2/3)O3–PbTiO3 and Pb(Mg1/3Nb2/3)O3–PbTiO3 were investigated for electromechanical actuators. In contrast to polycrystalline materials such as Pb(Zr,Ti)O3, morphotropic phase boundary compositions were not essential for high piezoelectric strain. Piezoelectric coefficients (d33’s)>2500 pC/N and subsequent strain levels up to >0.6% with minimal hysteresis were observed. Crystallographically, high strains are achieved for 〈001〉 oriented rhombohedral crystals, although 〈111〉 is the polar direction. Ultrahigh strain levels up to 1.7%, an order of magnitude larger than those available from conventional piezoelectric and electrostrictive ceramics, could be achieved being related to an E-field induced phase transformation. High electromechanical coupling (k33)>90% and low dielectric loss <1%, along with large strain make these crystals promising candidates for high performance solid state actuators.

Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals

BiFeO3 is perhaps the only material that is both magnetic and a strong ferroelectric at room temperature. As a result, it has had an impact on the field of multiferroics that is comparable to that of yttrium barium copper oxide (YBCO) on superconductors, with hundreds of publications devoted to it in the past few years. In this Review, we try to summarize both the basic physics and unresolved aspects of BiFeO3 (which are still being discovered with several new phase transitions reported in the past few months) and device applications, which center on spintronics and memory devices that can be addressed both electrically and magnetically.

Physics and Applications of Bismuth Ferrite

This article reports the fabrication of thick films of lead zirconate titanate (PZT) on platinum‐buffered silicon substrates by screen printing. Crack‐free films, up to 12 μm on a single pass, show a dielectric permittivity of 200, tangent losses of 0.05, remanent polarization of 2.5 μC/cm2, and coercive field of 40 kV/cm. The field‐induced longitudinal piezoelectric coefficient d33 at 40 kV/cm dc bias and 4 kV/cm alternating field corresponded to 50 pC/N. The magnitude of the piezoelectric voltage coefficient g33, computed from the strain coefficient and dielectric permittivity, under the same conditions, was found to be 36×10−3 V m/N, higher than that of a poled PZT bulk ceramic in comparison. These results are promising for a broad variety of sensor applications.

Dielectric, ferroelectric, and piezoelectric properties of lead zirconate titanate thick films on silicon substrates

Grain size effects in polycrystalline BaTiO3 are reviewed in terms of the “internal stress model”. By considering polarization dependent terms in the Devonshire free energy expression, the dielectric constant may be calculated for the whole ferroelectric temperature region, under various stress systems. Encouraging comparisons with measured values may be made.

The effect of grain size on the permittivity of BaTiO3

The elastic Gibbs function for BaTiO3 introduced by Buessem, Goswami and Cross1 has been modified by including the last symmetry permitted sixth order term HP12P22P32 with a coefficient H = 4.91 × 109 Vm9 C-5. The function predicts the correct high electric field behavior of the low temperature ferroelectric: ferroelectric phase changes in the single crystal and suggests an interesting change of sign of the pyroelectric effect at high field levels in the induced tetragonal ferroelectric phase.

A phenomenological gibbs function for BaTiO3 giving correct e field dependence of all ferroelectric phase changes

The domain configuration of rhombohedral PZN-8%PT single crystals has been observed as a function of electric-field and crystallographic orientation using polarizing microscope. Although a single domain state could be achieved by applying an E-field along the rhombohedral polar direction [111], a multidomain state was observed with the removal of the E-field. This domain instability was associated with large hysteresis of the strain vs. E-field behavior. In contrast, an engineered domain configuration of [001] oriented rhombohedral crystals was found to be stable with no domain motion detectable under DC-bias, resulting in hysteresis minimized strain vs. E-field behavior. The stable engineered domain configuration under bias in multidomain [001] oriented crystals was suggested as an evidence of macroscopic symmetry 4mm out of 3m rhombohedral crystals.

Engineered domain configuration in rhombohedral PZN-PT single crystals and their ferroelectric related properties

The ADAGE computer graphics system has been used to develop a modified Devonshire form for the elastic Gibbs function to describe the simple proper ferroelectric phases in the PbZrO3:PbTiO3 family of crystalline solid solutions The unusual morphotropic phase boundary between tetragonal and rhombohedral forms has been used to help delineate the coefficients in the function at that composition For the Devonshire formulation, spontaneous strain in the ferroelectric phases is assumed to be electrostrictive in origin and an x-ray determination of the strains as function of composition and temperature has been used to derive the composition and temperature dependence of the higher order stiffness coefficients The Gibbs function which has been derived permits for the first time the calculation of the full family of thermal, elastic, dielectric, and piezoelectric parameters for the ferroelectric single domain states and an evaluation of the manner in which these parameters change under different elastic and el

L. E. Cross

Papers

Dielectric, ferroelectric, and piezoelectric properties of lead zirconate titanate thick films on silicon substrates

The effect of grain size on the permittivity of BaTiO3

A phenomenological gibbs function for BaTiO3 giving correct e field dependence of all ferroelectric phase changes

Engineered domain configuration in rhombohedral PZN-PT single crystals and their ferroelectric related properties

A phenomenological Gibbs function for the single cell region of the PbZrO3:PbTiO3 solid solution system