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

We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other.

Band parameters for III–V compound semiconductors and their alloys

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.

/pdf/epitaxial-bifeo3-multiferroic-thin-film-heterostructures-2ns67gte2l.pdf

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

Recent advances in the field of nonlinear optical phenomena are reviewed with particular empphasis placed on such topics as parametric oscillation self-focusing and trapping of laser beams, and stimulated Raman, Rayleigh, and Brillouin scattering. The optical frequency radiation is treated classically in terms of the amplitudes and phases of the electromagnetic fields. The interactions of light waves in a mterial are then formulated in terms of Maxwell's equations and the electric dipole approximation. In this method, non-linear susceptibility tensors are introdueed which relate the induced dipole moment to a power series expansion in field strengths. The tensor nature and the frequency dependence of the nonlinearity coefficients are considered. The various experimental, observations are described and interpreted in terms of this formalism.

https://ieeexplore.ieee.org/iel5/5/31089/01447053.pdf

Nonlinear optics

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

Optical second harmonic spectroscopy is introduced as a powerful supplement for the determination of complex magnetic structures. Experimental efforts are simplified and new degrees of freedom are opened. Thereby, some principal or technical restrictions of neutron or magnetic x-ray diffraction experiments are overcome. High spatial resolution leads to additional information about magnetically ordered matter. As an example, the noncollinear magnetic structure of the hexagonal manganites $R{\mathrm{MnO}}_{3}$ ( $R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{Sc}$, Y, Ho, Er, Tm, Yb, Lu) is analyzed. The results show that some earlier conclusions on their magnetic symmetry and properties should be revised.

Determination of the Magnetic Symmetry of Hexagonal Manganites by Second Harmonic Generation

Rydberg excitons (condensed-matter analogues of hydrogen atoms) are shown to exist in single-crystal copper oxide with principal quantum numbers as large as n = 25 and giant wavefunctions with extensions of around two micrometres; this has implications for research in condensed-matter optics. Excitons, electron–hole pairs that play an essential role in the optical properties of semiconductors, can be viewed as condensed-matter analogues of hydrogen atoms, with a similar excitation spectrum. Dietmar Frohlich and colleagues extend the series of excitations from the previous record of principal quantum number n = 12, to n = 25 for excitons in single crystal cuprous oxide. At such high quantum numbers, the wave function of the excitons becomes giant, around 2 micrometres, and it is expected that these giant excitons (also called Rydberg excitons) strongly interact with each other. The authors observe evidence for a blockade effect where the presence of an exciton prevents excitation of another exciton in its vicinity. This work opens new research directions for optics in condensed matter. A highly excited atom having an electron that has moved into a level with large principal quantum number is a hydrogen-like object, termed a Rydberg atom. The giant size of Rydberg atoms1 leads to huge interaction effects. Monitoring these interactions has provided insights into atomic and molecular physics on the single-quantum level. Excitons—the fundamental optical excitations in semiconductors2, consisting of an electron and a positively charged hole—are the condensed-matter analogues of hydrogen. Highly excited excitons with extensions similar to those of Rydberg atoms are of interest because they can be placed and moved in a crystal with high precision using microscopic energy potential landscapes. The interaction of such Rydberg excitons may allow the formation of ordered exciton phases or the sensing of elementary excitations in their surroundings on a quantum level. Here we demonstrate the existence of Rydberg excitons in the copper oxide Cu2O, with principal quantum numbers as large as n = 25. These states have giant wavefunction extensions (that is, the average distance between the electron and the hole) of more than two micrometres, compared to about a nanometre for the ground state. The strong dipole–dipole interaction between such excitons is indicated by a blockade effect in which the presence of one exciton prevents the excitation of another in its vicinity.

Giant Rydberg excitons in the copper oxide Cu2O.

The second harmonic spectrum of ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ is studied in the 1.7-2.9 eV spectral range as a function of temperature. Below the N\'eel temperature ${T}_{N}=307.5$ K a nonlinear electric susceptibility ${\ensuremath{\chi}}_{\mathrm{ijk}}^{e}(c)$ appears, which changes sign under the time-reversal operation. The interference of this susceptibility with the time-invariant magnetic susceptibility ${\ensuremath{\chi}}_{\mathrm{ijk}}^{m}(i)$ leads to a pronounced polarization dependence for circularly polarized light propagating along the optical axis. This gives a novel tool to study antiferromagnetic domains with opposite orientation of the order parameter.

Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3.

Coherent propagation of quadrupole polaritons in ${\mathrm{Cu}}_{2}$O is demonstrated by time-resolved spectroscopy. This manifests itself in a strong distortion of the temporal shape of a picosecond optical pulse which is in resonance with the 1S exciton polariton. Oscillations with time-dependent period in the transmitted light intensity are quantitatively explained as resulting from quantum beats between the two branches of the exciton polariton. The analysis yields the homogeneous linewidth and oscillator strength.

Dietmar Fröhlich

Papers

Observation of coupled magnetic and electric domains

Determination of the Magnetic Symmetry of Hexagonal Manganites by Second Harmonic Generation

Giant Rydberg excitons in the copper oxide Cu2O.

Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3.

Coherent propagation and quantum beats of quadrupole polaritons in Cu2O.