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

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

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.

/pdf/multiferroics-a-magnetic-twist-for-ferroelectricity-40nmxke8g8.pdf

Multiferroics: a magnetic twist for ferroelectricity

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

The response of the worldwide scientific community to the discovery in 2008 of superconductivity at T c = 26 K in the Fe-based compound LaFeAsO1−x F x has been very enthusiastic. In short order, ot...

The puzzle of high temperature superconductivity in layered iron pnictides and chalcogenides

We analyze antiferromagnetism and superconductivity in novel Fe-based superconductors within the itinerant model of small electron and hole pockets near 0,0 and ,. We argue that the effective interactions in both channels logarithmically flow toward the same values at low energies; i.e., antiferromagnetism and superconductivity must be treated on equal footing. The magnetic instability comes first for equal sizes of the two pockets, but loses to superconductivity upon doping. The superconducting gap has no nodes, but changes sign between the two Fermi surfaces extended s-wave symmetry. We argue that the T dependencies of the spin susceptibility and NMR relaxation rate for such a state are exponential only at very low T, and can be well fitted by power laws over a wide T range below Tc.

https://www.pks.mpg.de/~ieremin/Pub/PhysRevB_78_134512.pdf

Magnetism, superconductivity, and pairing symmetry in iron-based superconductors

Transition metal oxides with a perovskite-type structure constitute a large group of compounds with interesting properties. Among them are materials such as the prototypical ferroelectric system BaTiO(3), colossal magnetoresistance manganites and the high-T(c) superconductors. Hundreds of these compounds are magnetic, and hundreds of others are ferroelectric, but these properties very seldom coexist. Compounds with an interdependence of magnetism and ferroelectricity could be very useful: they would open up a plethora of new applications, such as switching of magnetic memory elements by electric fields. Here, we report on a possible way to avoid this incompatibility, and show that in charge-ordered and orbitally ordered perovskites it is possible to make use of the coupling between magnetic and charge ordering to obtain ferroelectric magnets. In particular, in manganites that are less than half doped there is a type of charge ordering that is intermediate between site-centred and bond-centred. Such a state breaks inversion symmetry and is predicted to be magnetic and ferroelectric.

Bond-versus site-centred ordering and possible ferroelectricity in manganites

Iron selenide is an appealingly clean system for understanding the origin of superconductivity in iron pnictides. A detailed NMR study shows that the nematic order preceding the superconducting phase is driven by orbital degrees of freedom.

Orbital-driven nematicity in FeSe

A very fundamental and unconventional characteristic of superconductivity in iron-based materials is that it occurs in the vicinity of {\it two} other instabilities. Apart from a tendency towards magnetic order, these Fe-based systems have a propensity for nematic ordering: a lowering of the rotational symmetry while time-reversal invariance is preserved. Setting the stage for superconductivity, it is heavily debated whether the nematic symmetry breaking is driven by lattice, orbital or spin degrees of freedom. Here we report a very clear splitting of NMR resonance lines in FeSe at $T_{nem}$ = 91K, far above superconducting $T_c$ of 9.3 K. The splitting occurs for magnetic fields perpendicular to the Fe-planes and has the temperature dependence of a Landau-type order-parameter. Spin-lattice relaxation rates are not affected at $T_{nem}$, which unequivocally establishes orbital degrees of freedom as driving the nematic order. We demonstrate that superconductivity competes with the emerging nematicity.

Two-dimensional second-order topological superconductors (SOTSCs) have gapped bulk and edge states with zero-energy Majorana bound states localized at corners. The authors propose to construct a tunable SOTSC in a two-dimensional Majorana nanowire array by using superconducting phase differences to modify interwire couplings. The system, which is characterized within the framework of scattering theory, is robust against disorder that can actually increase the extent of the topological phase in parameter space. As such, it realizes a higher-order topological Anderson phase.

Dmitry V. Efremov

Papers

Magnetism, superconductivity, and pairing symmetry in iron-based superconductors

Bond-versus site-centred ordering and possible ferroelectricity in manganites

Orbital-driven nematicity in FeSe

Orbital-driven nematicity in FeSe

Phase-tunable second-order topological superconductor