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

Multiferroic magnetoelectric materials, which simultaneously exhibit ferroelectricity and ferromagnetism, have recently stimulated a sharply increasing number of research activities for their scientific interest and significant technological promise in the novel multifunctional devices. Natural multiferroic single-phase compounds are rare, and their magnetoelectric responses are either relatively weak or occurs at temperatures too low for practical applications. In contrast, multiferroic composites, which incorporate both ferroelectric and ferri-/ferromagnetic phases, typically yield giant magnetoelectric coupling response above room temperature, which makes them ready for technological applications. This review of mostly recent activities begins with a brief summary of the historical perspective of the multiferroic magnetoelectric composites since its appearance in 1972. In such composites the magnetoelectric effect is generated as a product property of a magnetostrictive and a piezoelectric substance. A...

Multiferroic magnetoelectric composites: Historical perspective, status, and future directions

In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic, and thermodynamic quantities in these systems are reviewed here. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and nonequilibrium statistical physics, and time-dependent phenomena is also discussed. This review additionally considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by the DMRG.

http://www.physics.udel.edu/~bnikolic/QTTG/NOTES/DMRG/SCHOLLWOCK=RMP_dmrg.pdf

The density-matrix renormalization group

A number of image processing techniques IPTs have been implemented for detecting civil infrastructure defects to partially replace human-conducted onsite inspections. These IPTs are primarily used to manipulate images to extract defect features, such as cracks in concrete and steel surfaces. However, the extensively varying real-world situations e.g., lighting and shadow changes can lead to challenges to the wide adoption of IPTs. To overcome these challenges, this article proposes a vision-based method using a deep architecture of convolutional neural networks CNNs for detecting concrete cracks without calculating the defect features. As CNNs are capable of learning image features automatically, the proposed method works without the conjugation of IPTs for extracting features. The designed CNN is trained on 40 K images of 256 × 256 pixel resolutions and, consequently, records with about 98% accuracy. The trained CNN is combined with a sliding window technique to scan any image size larger than 256 × 256 pixel resolutions. The robustness and adaptability of the proposed approach are tested on 55 images of 5,888 × 3,584 pixel resolutions taken from a different structure which is not used for training and validation processes under various conditions e.g., strong light spot, shadows, and very thin cracks. Comparative studies are conducted to examine the performance of the proposed CNN using traditional Canny and Sobel edge detection methods. The results show that the proposed method shows quite better performances and can indeed find concrete cracks in realistic situations.

/pdf/deep-learning-based-crack-damage-detection-using-1cucavd1rf.pdf

Deep Learning-Based Crack Damage Detection Using Convolutional Neural Networks

A unified method based on the inclusion formulation is proposed to determine the magnetic, electric, and elastic fields in a composite with piezoelectric and piezomagnetic phases. The composite reinforcements are treated as ellipsoidal inclusions that enable the reinforcement geometries ranging from thin flakes to continuous fibers. Utilizing the proposed method, the magneto-electro-elastic tensors analogous to Eshelby tensors for elastic ellipsoidal inclusions are obtained. With these tensors, the magnetic, electric, and elastic fields around the inclusion as well as concentration factors are determined. Furthermore, based upon the Mori–Tanaka mean-field theory [Acta Metall. 21, 571 (1973)] to account for the interaction between inclusions and matrix, the effective magneto-electro-elastic constants (elastic moduli, piezoelectric coefficients, dielectric constants, piezomagnetic coefficients, magnetoelectric, and magnetic permeability) of the composites are expressed explicitly in terms of phase propertie...

The analysis of piezoelectric/piezomagnetic composite materials containing ellipsoidal inclusions

In this paper, a number of problems of fundamental importance in a piezoelectric-piezomagnetic composite material are solved. The problems covered range from the derivation of the analytical expressions for the magneto-electro-elastic Eshelby tensors to the analysis of the magnetoelectric coupling effect which is a new property exhibited in the piezoelectric-piezomagnetic composite. In particular, when both the matrix and the inclusions of the composite are transversely isotropic with different magneto-electro-elastic moduli, and shapes of inclusions are of elliptic cylinder, circular cylinder, disk, and ribbon, closed-form solutions for the magnetoelectric coupling coefficientS are presented compactly. The resulting solutions are a function of the shape of inclusion, phase properties, and volume fraction of the inclusions. These results could provide us with insight into how a piezoelectric-piezomagnetic composite material consisting of inclusions will perform and would be helpful in understanding the magneto-electric-elastic behavior of the composite.

Analytical predictions for the magnetoelectric coupling in piezomagnetic materials reinforced by piezoelectric ellipsoidal inclusions

Closed-form solutions for the magnetoelectric coupling coefficients in fibrous composites with piezoelectric and piezomagnetic phases

Coupled magnetic-mechanical-electric effects involving linearly and nonlinearly coupling interactions in ferroic composites are investigated using a Green's function technique. We use the theory to suggest a possible giant magnetoelectric effect in a ferroelectric poly(vinylidene fluoride-trifluorethylene) copolymer filled by giant magnetostrictive rare-earth--iron alloy particles, which is markedly larger than that in the best known magnetoelectric materials. The flexible composite is expected to exhibit large magnetostriction. Our results show how to design such flexible polymer-matrix magnetoelectric composites with better performance and may stimulate further interest in the areas of coupled multifield effects and magnetoelectric materials for practical applications.

Jin H. Huang

Papers

The analysis of piezoelectric/piezomagnetic composite materials containing ellipsoidal inclusions

Analytical predictions for the magnetoelectric coupling in piezomagnetic materials reinforced by piezoelectric ellipsoidal inclusions

Closed-form solutions for the magnetoelectric coupling coefficients in fibrous composites with piezoelectric and piezomagnetic phases

Calculations of giant magnetoelectric effects in ferroic composites of rare-earth–iron alloys and ferroelectric polymers

Detection of cracks using neural networks and computational mechanics