Magnetic control of ferroelectric polarization

Dynamical magnetoelectric phenomena of skyrmions in multiferroics

Magnetic skyrmions, nanoscopic spin vortices carrying a quantized topological number in chiral-lattice magnets, are recently attracting great research interest. Although magnetic skyrmions had been observed only in metallic chiral-lattice magnets such as B20 alloys in the early stage of the research, their realization was discovered in 2012 also in an insulating chiral-lattice magnet Cu 2 OSeO 3 $\textrm{Cu}_2\textrm{OSeO}_3$ . A characteristic of the insulating skyrmions is that they can host multiferroicity, that is, the noncollinear magnetization alignment of skyrmion induces electric polarizations in insulators with a help of the relativistic spin-orbit interaction. It was experimentally confirmed that the skyrmion phase in Cu 2 OSeO 3 $\textrm{Cu}_2\textrm{OSeO}_3$ is indeed accompanied by the spin-induced ferroelectricity. The resulting strong magnetoelectric coupling between magnetizations and electric polarizations can provide us with a means to manipulate and activate magnetic skyrmions by application of electric fields. This is in sharp contrast to skyrmions in metallic systems, which are driven through injection of electric currents. The magnetoelectric phenomena specific to the skyrmion-based multiferroics are attracting intensive research interest, and, in particular, those in dynamical regime are widely recognized as an issue of vital importance because their understanding is crucial both for fundamental science and for technical applications. In this article, we review recent studies on multiferroic properties and dynamical magnetoelectric phenomena of magnetic skyrmions in insulating chiral-lattice magnet Cu 2 OSeO 3 $\textrm{Cu}_2\textrm{OSeO}_3$ . It is argued that the multiferroic skyrmions show unique resonant excitation modes of coupled magnetizations and polarizations, so-called electromagnon excitations, which can be activated both magnetically with a microwave magnetic field and electrically with a microwave electric field. The interference between these two activation processes gives rise to peculiar phenomena in the gigahertz regime. As its representative example, we discuss a recent theoretical prediction of unprecedentedly large nonreciprocal directional dichroism of microwaves in the skyrmion phase of Cu 2 OSeO 3 $\textrm{Cu}_2\textrm{OSeO}_3$ . This phenomenon can be regarded as a one-way window effect on microwaves, that is, the extent of microwave absorption changes significantly when its incident direction is reversed. This dramatic effect was indeed observed by subsequent experiments. These studies demonstrated that the multiferroic skyrmions can be a promising building block for microwave devices.

Tunable physical properties in BiAl1-x Mn x O3 thin films with novel layered supercell structures

Morphological control in oxide nanocomposites presents enormous opportunities for tailoring the physical properties. Here, we demonstrate the strong tunability of the magnetic and optical properties of Bi-based layered supercell (LSC) multiferroic structures, i.e., BiAl_1-x Mn _x O_3, by varying the Al : Mn molar ratio. The microstructure of the LSC structure evolves from a supercell structure to Al-rich pillars in the supercell structure as the Al molar ratio increases. The LSC structures present excellent multiferroic properties with preferred in-plane magnetic anisotropy, a tunable band gap and anisotropic dielectric permittivity, all attributed to the microstructure evolution and their anisotropic microstructure. Three different strain relaxation mechanisms are identified that are active during thin film growth. This study provides opportunities for microstructure and physical property tuning which can also be explored in other Bi-based LSC materials with tailorable multiferroic and optical properties.

Multiferroics beyond electric-field control of magnetism

Multiferroic materials, with their combined and coupled magnetism and ferroelectricity, provide a playground for studying new physics and chemistry as well as a platform for the development of novel devices and technologies. Based on my July 2017 Royal Society Inaugural Lecture, I review recent progress and propose future directions in the fundamentals and applications of multiferroics, with a focus on initially unanticipated developments outside of the core activity of electric-field control of magnetism.

Detection of 3,4-diaminotoluene based on Sr0.3Pb0.7TiO3/CoFe2O4 core/shell nanocomposite via an electrochemical approach

We reported a scalable sol–gel method for the preparation of Sr_0.3Pb_0.7TiO₃/CoFe₂O₄ core–shell magnetic nanocomposite with a finely controlled shell and evaluated its efficiency as an electrochemical sensor for the selective detection of 3,4-diaminotoluene.

Orthorhombic GdMnO3 Epitaxial Thin Film Grown onto SrTiO3 (110)

GdMnO3 epitaxial thin films were deposited onto (110)-oriented SrTiO3 substrates by RF magnetron sputtering. The structure, microstructure, dielectric and magnetic properties were investigated in detail. The XRD results revealed that the GdMnO3 thin films exhibit an epitaxial strained orthorhombic symmetry and grow preferably in off-plane (001) orientation, wherein the basal lattice parameters are strained by the substrate lattice. A dielectric relaxation process was ascertained, whose activation energy is sensitive to the magnetic phase transitions, occurring at 41 K and at 20 K, respectively. The canted nature of the low temperature magnetic phase is discussed.

Structural, electronic and magnetic properties of Sc3+ doped CoCr2O4 nanoparticles

Experimental and theoretical analyses were combined to reveal the major properties of Co_1−xSc_xCr₂O₄ nanoparticles – a putative candidate for magnetic applications.

The ultrathin limit of improper ferroelectricity

The secondary nature of polarization in improper ferroelectrics promotes functional properties beyond those of conventional ferroelectrics. In technologically relevant ultrathin films, however, the improper ferroelectric behavior remains largely unexplored. Here, we probe the emergence of the coupled improper polarization and primary distortive order parameter in thin films of hexagonal YMnO₃. Combining state-of-the-art in situ characterization techniques separately addressing the improper ferroelectric state and its distortive driving force, we reveal a pronounced thickness dependence of the improper polarization, which we show to originate from the strong modification of the primary order at epitaxial interfaces. Nanoscale confinement effects on the primary order parameter reduce the temperature of the phase transition, which we exploit to visualize its order-disorder character with atomic resolution. Our results advance the understanding of the evolution of improper ferroelectricity within the confinement of ultrathin films, which is essential for their successful implementation in nanoscale applications.

Evolution of improper ferroelectricity within the confinement of ultrathin films is essential for their successful implementation in nanoscale applications. Here, the authors show thickness dependence of the improper polarization originating from the strong modification of the primary order at epitaxial interfaces.

Spin-Glass Magnetic Properties of A-Site Columnar-Ordered Quadruple Perovskites Y2MnGa(Mn4-xGax)O12 with 0 ≤ x ≤ 3

Y₂MnGa(Mn_4-xGa_x)O₁₂ solid solutions were synthesized at high pressure of ∼6 GPa and high temperature of ∼1570 K for the 0 ≤ x ≤ 3 compositional range. Synchrotron X-ray and neutron powder diffraction were used to study the crystal structures and cation distributions. These solutions adopt the parent structure of the A-site columnar-ordered quadruple perovskite family with space group P4₂/nmc (No. 137). They have lattice parameters of a = 7.36095 Å and c = 7.753 84 Å (x = 0), a = 7.361 68 Å and c = 7.716 16 Å (x = 1), a = 7.360 34 Å and c = 7.67142 Å (x = 2), and a = 7.363 93 Å and c = 7.616 85 Å (x = 3) at room temperature. The x = 0 sample has a cation distribution of [Y³⁺₂]_A[Mn³⁺]_A'[Ga³⁺_0.68Mn²⁺_0.32]_A″[Mn_3.68Ga_0.32]_BO₁₂ with a preferred localization of Ga³⁺ in the tetrahedral A″ site and with a small amount of Ga³⁺ in the octahedral B site. A complete triple A-site order, [Y³⁺₂]_A[Mn³⁺]_A'[Ga³⁺]_A″[Mn³⁺_4-xGa³⁺_x]_BO₁₂, is realized for x ≥ 1. All samples demonstrate spin-glass-like magnetic properties, and the absence of a long-range magnetic order at the ground state at 1.5 K was confirmed by neutron diffraction for the x = 1 sample. First-principles calculations indicated the spin-glass-like magnetic ordering is derived from the Ga substitution to the B sites and gave evidence that the ideal cation distribution could produce robust ferromagnetism in this family of perovskites.

Destruction of multiferroicity in Tb2BaNiO5 by Sr-doping and its implication to magnetodielectric coupling

The Haldane spin-chain compound, Tb₂BaNiO₅, with two antiferromagnetic transitions, one at T ₁  =  63 K and the other at T ₂  =  25 K, has been recently shown to be an exotic multiferroic below T ₂. Here, we report the results of our investigation of Sr doping at the Ba site by magnetization, heat-capacity, magnetodielectric (MDE) and pyrocurrent measurements. An intriguing finding, which we stress, is that the ferroelectricity is lost even for a doping level of ten atomic percent, though magnetic ordering prevails. The doped specimens however retain significant MDE behaviour, but with reduced magnitudes and qualitative changes with respect to the behaviour of the parent compound. This implies that ferroelectric order is also crucial for the anomalously large MDE in the parent compound, in addition to the role of 4f single-ion anisotropy.

Ferroelectric polarization in multiferroics

Multiferroic materials, showing ordering of both electrical and magnetic degrees of freedom, are promising candidates enabling the design of novel electronic devices. Various mechanisms ranging from geometrically or spin-driven improper ferroelectricity via lone-pairs, charge-order or -transfer support multiferroicity in single-phase or composite compounds. The search for materials showing these effects constitutes one of the most important research fields in solid-state physics during the last years, but scientific interest even traces back to the middle of the past century. Especially, a potentially strong coupling between spin and electric dipoles captured the interest to control via an electric field the magnetization or via a magnetic field the electric polarization. This would imply a promising route for novel electronics. Here, we provide a review about the dielectric and ferroelectric properties of various multiferroic systems ranging from type I multiferroics, in which magnetic and ferroelectric order develop almost independently of each other, to type II multiferroics, which exhibit strong coupling of magnetic and ferroelectric ordering. We thoroughly discuss the dielectric signatures of the ferroelectric polarization for BiFeO3, Fe3O4, DyMnO3 and an organic charge-transfer salt as well as show electric-field poling studies for the hexagonal manganites and a spin-spiral system LiCuVO4.

Spiral spin structures and skyrmions in multiferroics

In this article, we focus on (1) type-II multiferroics driven by spiral spin orderings and (2) magnetoelectric couplings in multiferroic skyrmion-hosting materials. We present both phenomenological understanding and microscopic mechanisms for spiral spin state, which is one of the essential starting points for type-II multiferroics and magnetic skyrmions. Two distinct mechanisms of spiral spin states (frustration and Dzyaloshinskii–Moriya [DM] interaction) are discussed in the context of the lattice symmetry. We also discuss the spin-induced ferroelectricity on the basis of the symmetry and microscopic atomic configurations. We compare two well-known microscopic models: the generalized inverse DM mechanism and the metal-ligand d-p hybridization mechanism. As a test for these models, we summarize the multiferroic properties of a family of triangular-lattice antiferromagnets. We also give a brief review of the magnetic skyrmions. Three types of known skyrmion-hosting materials with multiferroicity are discussed from the view point of crystal structure, magnetism, and origins of the magnetoelectric couplings. For exploration of new skyrmion-hosting materials, we also discuss the theoretical models for stabilizing skyrmions by magnetic frustration in centrosymmetric system. Several basic ideas for material design are given, which are successfully demonstrated by the recent experimental evidences for the skyrmion formation in centrosymmetric frustrated magnets.

Design and Manipulation of Ferroic Domains in Complex Oxide Heterostructures

The current burst of device concepts based on nanoscale domain-control in magnetically and electrically ordered systems motivates us to review the recent development in the design of domain engineered oxide heterostructures. The improved ability to design and control advanced ferroic domain architectures came hand in hand with major advances in investigation capacity of nanoscale ferroic states. The new avenues offered by prototypical multiferroic materials, in which electric and magnetic orders coexist, are expanding beyond the canonical low-energy-consuming electrical control of a net magnetization. Domain pattern inversion, for instance, holds promises of increased functionalities. In this review, we first describe the recent development in the creation of controlled ferroelectric and multiferroic domain architectures in thin films and multilayers. We then present techniques for probing the domain state with a particular focus on non-invasive tools allowing the determination of buried ferroic states. Finally, we discuss the switching events and their domain analysis, providing critical insight into the evolution of device concepts involving multiferroic thin films and heterostructures.

Dynamical Magnetic Field Accompanying the Motion of Ferroelectric Domain Walls

The recently proposed dynamical multiferroic effect describes the generation of magnetization from temporally varying electric polarization. Here, we show that the effect can lead to a magnetic field at moving ferroelectric domain walls, where the rearrangement of ions corresponds to a rotation of ferroelectric polarization in time. We develop an expression for the dynamical magnetic field, and calculate the relevant parameters for the example of 90° and 180° domain walls, as well as for polar skyrmions, in BaTiO_{3}, using a combination of density functional theory and phenomenological modeling. We find that the magnetic field reaches the order of several μT at the center of the wall, and we propose two experiments to measure the effect with nitrogen-vacancy center magnetometry.

The growth and improved magnetoelectric response of strain-modified Aurivillius SrBi4.25La0.75Ti4FeO18 thin films

In this study, we grew 5-layered SrBi4.25La0.75Ti4FeO18 (SBLFT) polycrystalline thin films (80-330 nm thick) via pulsed-laser deposition to study their ferroelectric and magnetoelectric response. Structural/microstructural analysis confirmed the formation of orthorhombic SBLFT with good crystallinity and randomly oriented Aurivillius phases. Detailed scanning transmission electron microscopy analysis of 120 nm film revealed a predominantly five-layered structure with the coexistence of four-layer stacking. Such stacking defects are found to be pertinent to the high structural flexibility of Bi-rich Aurivillius phases, alleviated by lattice strain. Raman spectral features at ambient temperatures depict the signature of the orthorhombic-tetragonal phase transition. SBLFT films have a strong ferroelectric nature (remanent polarization 2Pr of 35 μC cm-2) with a fatigue endurance up to 1010 cycles and strongly improved, switchable magnetization as opposed to its antiferromagnetic bulk counterpart. The scaling behavior of dynamic hysteresis reveals that ferroelectric domain reversal has good stability and low energy consumption. We observed the presence of SBLFT nanoregions (1-5 nm), distributed across the film, with Bi and Fe-rich compositions and oxygen vacancies that contribute to the weak ferromagnetic behavior mediated by the Dzyaloshinskii-Moriya interactions. Subtle changes in the structural strain and lattice distortions of thin films with varied thicknesses led to distinct ferroic properties. Stronger ferroelectric polarization of 80 nm and 120 nm films compared to that of thicker ones can be due to structural strain and the possible rearrangement of BO6 octahedra. The observation of the improved magnetoelectric coefficient of 50 mV cm-1 Oe-1 for 120 nm film, as compared to that of several Aurivillius oxides, indicates that the structural strain modification in SBLFT is beneficial for the fatigue-free magnetic field switching of ferroelectric polarization. The structural strain of the unit cell as well as the presence of Bi- and ferromagnetic Fe-rich nanoregions was found to be responsible for the improved multiferroic behaviour of the SBLFT films.

Spin Injection and Transport in Organic Materials

This review introduces some important spin phenomena of organic molecules and solids and their devices: Organic spin injection and transport, organic spin valves, organic magnetic field effects, organic excited ferromagnetism, organic spin currents, etc. We summarize the experimental and theoretical progress of organic spintronics in recent years and give prospects.

Ripple State in the Frustrated Honeycomb-Lattice Antiferromagnet

We discover a new type of multiple-q state, a "ripple state," in a frustrated honeycomb-lattice Heisenberg antiferromagnet under magnetic fields. The ground state has an infinite ringlike degeneracy in the wave vector space, exhibiting a cooperative paramagnetic state, a "ring-liquid" state. We elucidate that the system exhibits the ripple state as a new low-temperature thermodynamic phase via a second-order phase transition from the ring-liquid state, keeping the ringlike spin structure factor. The spin texture in real space looks like a "water ripple" and can induce a giant electric polarization vortex. A possible relationship to the honeycomb-lattice compound, Bi_{3}Mn_{4}O_{12}(NO_{3}), is discussed.

Pressure-dependent X-ray diffraction of the multiferroics RMn2O5

The room-temperature structural properties of the RMn₂O₅ multiferroics have been investigated under pressure, using powder X-ray scattering and density functional theory (DFT) calculations. It was possible to determine the lattice parameters and the main atomic positions as a function of pressure. Good agreement was observed between the X-ray and DFT results for most of the determined crystallographic data. From the DFT calculations, it was possible to infer the pressure evolution of the exchange interactions, and this analysis led to the conclusion that the onset of the q = (½, 0, ½) magnetic structure under pressure is related to the increase in the J₁ super-exchange terms (due to the reduction in the Mn-O distances) compared with the Mn-R exchange interactions. In addition, the 1D antiferromagnetic character of the compounds should be reinforced under pressure.

Lattice Dynamics Coupled to Charge and Spin Degrees of Freedom in the Molecular Dimer-Mott Insulator κ-(BEDT-TTF)_{2}Cu[N(CN)_{2}]Cl

Inelastic neutron scattering measurements on the molecular dimer-Mott insulator κ-(BEDT-TTF)_{2}Cu[N(CN)_{2}]Cl reveal a phonon anomaly in a wide temperature range. Starting from T_{ins}∼50-60  K where the charge gap opens, the low-lying optical phonon modes become overdamped upon cooling towards the antiferromagnetic ordering temperature T_{N}=27  K, where also a ferroelectric ordering at T_{FE}≈T_{N} occurs. Conversely, the phonon damping becomes small again when spins and charges are ordered below T_{N}, while no change of the lattice symmetry is observed across T_{N} in neutron diffraction measurements. We assign the phonon anomalies to structural fluctuations coupled to charge and spin degrees of freedom in the BEDT-TTF molecules.

Single-phase multiferroics: new materials, phenomena, and physics

Multiferroics, where multiple ferroic orders coexist and are intimately coupled, promise novel applications in conceptually new devices on one hand, and on the other hand provide fascinating physics that is distinctly different from the physics of high-T_C superconductors and colossal magnetoresistance manganites. In this mini-review, we highlight the recent progress of single-phase multiferroics in the exploration of new materials, efficient roadmaps for functionality enhancement, new phenomena beyond magnetoelectric coupling, and underlying novel physics. In the meantime, a slightly more detailed description is given of several multiferroics with ferrimagnetic orders and double-layered perovskite structure and also of recently emerging 2D multiferroics. Some emergent phenomena such as topological vortex domain structure, non-reciprocal response, and hybrid mechanisms for multiferroicity engineering and magnetoelectric coupling in various types of multiferroics will be briefly reviewed.

Hydrogen/Deuterium Dynamics in Hydroxyl Salts Co2(OH)3Br/Co2(OD)3Br Revealed by Muon Spin Relaxation

The temperature-dependent dynamics of the hydrogen/deuterium atoms in geometrically frustrated magnets Co₂(OH)₃Br and its deuterated form Co₂(OD)₃Br were investigated by muon spin relaxation (μSR). The deuterium atoms in Co₂(OD)₃Br were found to be rapidly fluctuating at high temperatures, which should be arising as a quantum atomic effect due to the small mass of deuterium, then they drastically slowed down toward T_c = 250 K where a broad anomaly appeared in the dielectric response, and finally became quasi-static at around 180 K. Meanwhile, the hydrogen atoms in Co₂(OH)₃Br also exhibited a two-step slowing at ~240 K and ~180 K, respectively. The revealed properties in Co₂(OH)₃Br/Co₂(OD)₃Br are reminiscent of relaxor-type ferroelectrics. The present study suggested the effectiveness of the μSR technique on revealing the hydrogen/deuterium (H/D) dynamics in Co₂(OH)₃Br/Co₂(OD)₃Br. Furthermore, magnetic coupling was found to be existing at high temperatures in this system. This work provides clear evidence to the mechanism of ferroelectric responses in the hydroxyl salts, i.e., the slowing of protons (deuterium ions) is directly related to the newly revealed ferroelectricity.

Magnetoelectricity in multiferroics: a theoretical perspective

The key physical property of multiferroic materials is the existence of coupling between magnetism and polarization, i.e. magnetoelectricity. The origin and manifestations of magnetoelectricity can be very different in the available plethora of multiferroic systems, with multiple possible mechanisms hidden behind the phenomena. In this review, we describe the fundamental physics that causes magnetoelectricity from a theoretical viewpoint. The present review will focus on mainstream physical mechanisms in both single-phase multiferroics and magnetoelectric heterostructures. The most recent tendencies addressing possible new magnetoelectric mechanisms will also be briefly outlined.

Lattice and spin dynamics in multiferroic BiFeO3 and RMnO3

The multiferroic materials BiFeO₃ and RMnO₃ exhibit coexisting magnetic order and ferroelectricity, and provide exciting platforms for new physics and potentially novel devices, where intriguing interplay between phonons and magnons exists. In this review, we paint a complete picture of bulk BiFeO₃ together with orthorhombic and hexagonal RMnO₃ (R includes rare-earth elements and yttrium) by summarizing the dynamics of spin and lattice and their magnetoelectric coupling, as well as the methods of controlling these characteristics under non-equilibrium conditions, from experimental and simulation perspectives.

Electric-Field Control of Magnetization, Jahn-Teller Distortion, and Orbital Ordering in Ferroelectric Ferromagnets

Controlling the direction of the magnetization by an electric field in multiferroics that are both ferroelectric and strongly ferromagnetic will open the door to the design of the next generation of spintronics and memory devices. Using first-principles simulations, we report that the discovery that the PbTiO_{3}/LaTiO_{3} (PTO/LTO) superlattice possesses such highly desired control, as evidenced by the electric-field-induced rotation of 90° and even a possible full reversal of its magnetization in some cases. Moreover, such systems also exhibit Jahn-Teller distortions, as well as orbital orderings, that are switchable by the electric field, therefore making PTO/LTO of importance for the tuning of electronic properties too. The origin for such striking electric-field controls of magnetization, Jahn-Teller deformations, and orbital orderings resides in the existence of three different types of energetic coupling: one coupling polarization with antiphase and in-phase oxygen octahedral tiltings, a second one coupling polarization with antiphase oxygen octahedra tilting and Jahn-Teller distortions, and finally a biquadratic coupling between antiphase oxygen octahedral tilting and magnetization.

Multiferroicity in atomic van der Waals heterostructures

Materials that are simultaneously ferromagnetic and ferroelectric - multiferroics - promise the control of disparate ferroic orders, leading to technological advances in microwave magnetoelectric applications and next generation of spintronics. Single-phase multiferroics are challenged by the opposite d-orbital occupations imposed by the two ferroics, and heterogeneous nanocomposite multiferroics demand ingredients' structural compatibility with the resultant multiferroicity exclusively at inter-materials boundaries. Here we propose the two-dimensional heterostructure multiferroics by stacking up atomic layers of ferromagnetic Cr2Ge2Te6 and ferroelectric In2Se3, thereby leading to all-atomic multiferroicity. Through first-principles density functional theory calculations, we find as In2Se3 reverses its polarization, the magnetism of Cr2Ge2Te6 is switched, and correspondingly In2Se3 becomes a switchable magnetic semiconductor due to proximity effect. This unprecedented multiferroic duality (i.e., switchable ferromagnet and switchable magnetic semiconductor) enables both layers for logic applications. Van der Waals heterostructure multiferroics open the door for exploring the low-dimensional magnetoelectric physics and spintronic applications based on artificial superlattices.

Spin-charge-lattice coupling in quasi-one-dimensional Ising spin chain CoNb2O6

Magnetization, magnetostriction and dielectric constant measurements are performed on single crystals of quasi-one-dimensional Ising spin chain CoNb₂O₆ at temperatures below and above the antiferromagnetic phase transition. Field-induced magnetic transitions are clearly reflected in magnetodielectric and magnetostriction data. Sharp anomalies are observed around the critical fields of antiferromagnetic to ferrimagnetic and ferrimagnetic to saturated-paramagnetic transition in both magnetodielectric and magnetostriction experiments. Detailed analysis of temperature and field dependence of dielectric constant and magnetostriction suggests that spins are coupled with lattice as well as charges in CoNb₂O₆. Below the antiferromagnetic transition temperature, the overall resemblance in anomalies, observed in various physical parameters such as magnetization, dielectric constant, magnetostriction and magnetic entropy change gives a deeper insight about the influence of spin configuration on these parameters in CoNb₂O₆.

The phenomenon of conversion polymorphism in Bi-containing metastable perovskites

A post-synthesis thermal treatment of metastable phases in the high-pressure stabilised perovskite BiFe1-yScyO3 system results in the irreversible formation of polymorphs which represent novel polar and antipolar structures with interesting magnetic properties. Such annealing-stimulated polymorphism is believed to be a general phenomenon which can be found in other systems.

Strong magnetoelectric coupling in mixed ferrimagnetic-multiferroic phases of a double perovskite

Exploring new magnetic materials is essential for finding advantageous functional properties such as magnetoresistance, magnetocaloric effect, spintronic functionality, and multiferroicity. Versatile classes of double perovskite compounds have been recently investigated because of intriguing physical properties arising from the proper combination of several magnetic ions. In this study, it is observed that the dominant ferrimagnetic phase is coexisted with a minor multiferroic phase in single-crystalline double-perovskite Er₂CoMnO₆. The majority portion of the ferrimagnetic order is activated by the long-range order of Er³⁺ moments below T_Er = 10 K in addition to the ferromagnetic order of Co²⁺ and Mn⁴⁺ moments arising at T_C = 67 K, characterized by compensated magnetization at T_Comp = 3.15 K. The inverted magnetic hysteresis loop observed below T_Comp can be described by an extended Stoner-Wohlfarth model. The additional multiferroic phase is identified by the ferroelectric polarization of ~0.9 μC/m² at 2 K. The coexisting ferrimagnetic and multiferroic phases appear to be strongly correlated in that metamagnetic and ferroelectric transitions occur simultaneously. The results based on intricate magnetic correlations and phases in Er₂CoMnO₆ enrich fundamental and applied research on magnetic materials through the scope of distinct magnetic characteristics in double perovskites.

Realizing Magnetoelectric Coupling with Hydrogen Intercalation

Materials with a coexistence of magnetic and ferroelectric order (i.e., multiferroics) provide an efficient route for the control of magnetism by electric fields. Unfortunately, a long-sought room temperature multiferroic with strongly coupled ferroelectric and ferromagnetic (or ferrimagnetic) orderings is still lacking. Here, we propose that hydrogen intercalation in antiferromagnetic transition-metal oxides is a promising way to realize multiferroics with strong magnetoelectric coupling. Taking brownmillerite SrCoO_{2.5} as an example, we show that hydrogen intercalated SrCoO_{2.5} displays strong ferrimagnetism and large electric polarization in which the hydroxide acts as a new knob to simultaneously control the magnetization and polarization at room temperature. We expect that ion intercalation will become a general way to design magnetoelectric and spintronic functional materials.

Magnetization-polarization cross-control near room temperature in hexaferrite single crystals

Mutual control of the electricity and magnetism in terms of magnetic (H) and electric (E) fields, the magnetoelectric (ME) effect, offers versatile low power consumption alternatives to current data storage, logic gate, and spintronic devices. Despite its importance, E-field control over magnetization (M) with significant magnitude was observed only at low temperatures. Here we have successfully stabilized a simultaneously ferrimagnetic and ferroelectric phase in a Y-type hexaferrite single crystal up to 450 K, and demonstrated the reversal of large non-volatile M by E field close to room temperature. Manipulation of the magnetic domains by E field is directly visualized at room temperature by using magnetic force microscopy. The present achievement provides an important step towards the application of ME multiferroics.

Mutual control of the electric polarization and magnetization promises for low power consumption spintronic devices but remains challenging. Here the authors show reversal of non-volatile magnetization by electric field as well as the polarization switching by magnetic field in a single-component material, close to room temperature.

Multiferroic quantum criticality

The zero-temperature limit of a continuous phase transition is marked by a quantum critical point, which can generate physical effects that extend to elevated temperatures. Magnetic quantum criticality is now well established, and has been explored in systems ranging from heavy fermion metals to quantum Ising materials. Ferroelectric quantum critical behaviour has also been recently demonstrated, motivating a flurry of research investigating its consequences. Here, we introduce the concept of multiferroic quantum criticality, in which both magnetic and ferroelectric quantum criticality occur in the same system. We develop the phenomenology of multiferroic quantum criticality and describe the associated experimental signatures, such as phase stability and modified scaling relations of observables. We propose several material systems that could be tuned to multiferroic quantum criticality utilizing alloying and strain as control parameters. We hope that these results stimulate exploration of the interplay between different kinds of quantum critical behaviours.

Structural, Dielectric and Magnetic Studies of Perovskite [Gd1−xMxCrO3 (M = La, Co, Bi)] Nanoparticles: Photocatalytic Degradation of Dyes

Nanoparticles (NPs) of Gd1−xMxCrO3 (M = La, Co, Bi) were synthesized by microemulsion techniques, involving simultaneous single ion substitution philosophy. Structural, magnetic, dielectric properties, morphology, elemental analysis and distribution size of fabricated nano-crystalline were determined. The techniques employed for investigation are X-ray diffraction (XRD), vibrating sample magnetometer (VSM), dielectric measurement and scanning electron microscopy (SEM), energy dispersive X-ray (EDX), photoluminescence (PL) and atomic force microscopy (AFM), respectively. XRD pattern confirm that all the as-synthesized NPs have orthorhombic structure and successfully substituted of different metal ions into the regular crystal structure of GdCrO3. The lattice parameters X-ray density, bulk density, porosity and grain size were calculated from XRD pattern of Gd1−xMxCrO3 (M = La, Co, Bi) substituted and un-substituted GdCrO3. The magnetic hysteresis loop of fabricated product confirmed that the entire sample exhibits ferromagnetic behavior at room temperature. It was also found that the fabricated NPs show excellent photocatalytic activity (PCA) against Congo-red, about 78.24% after 55 min of incubation.

A First-Principles Study on the Multiferroic Property of Two-Dimensional BaTiO₃ (001) Ultrathin Film with Surface Ba Vacancy

In this work, the multiferroic property of Ba-deficient BaTiO₃ (001) ultrathin film is studied employing the first-principles approach. The BaTiO₃ (001) ultrathin film is more energetically stable and behaves as a semiconductor relative to the (111) and (101) configurations, confirmed from the surface grand potential and electronic density of states. The electronic structures show that the O vacancy can switch the (001) film from a semi-conductor into a metal, while the Ba defect has a slight influence on the band gap, at a concentration of ~2.13%. In Ba-deficient (001) film, the spontaneous polarization pattern is changed and a spontaneous polarization parallel to the surface is observed. Furthermore, a magnetic moment is induced, and it is found to be originated from the O atoms in the supercell. Our results suggest that a strong magnetoelectric coupling occurs because the magnetic moment exhibits a 43.66% drop when the spontaneous polarization increases from 12.84 µC/cm² to 23.99 µC/cm² in the deficient BaTiO₃ with m = 2 under the bi-axial compress stress field.

Electronic structure of multiferroic BiFeO3: Electron energy-loss spectroscopy and first-principles study

The electronic structure of BiFeO₃ has been investigated by using electron energy loss spectrum and first-principle calculations. Assignments of the individual interband transitions have been accomplished by comparing the interband transition energy with the calculated PDOS. The DOS is mainly divided into two regions, the hybridized region of O 2p with Fe 3p in the valence band and that of O 2p hybridized with Bi 6p in the conduction band. From the simulation of high energy-loss near-edge structure, the core-hole effect is believed to be more significant. The feature groups for the experimental spectra of O K-edge and Fe L_2,3-edge are consistent with simulation results.

Valley polarization and ferroelectricity in a two-dimensional GaAsC6 monolayer

Valley polarization and ferroelectricity are the two basic concepts in electronic device applications. However, the coexistence of these two scenarios in one material has not been reported. Here, using first-principles calculations, we demonstrated that the two-dimensional GaAsC6 monolayer which is a hybrid structure of GaAs and graphene has a pair of inequivalent valleys with opposite Berry curvatures and an intrinsic out-of-plane spontaneous electric polarization. It also has a direct band gap of about 1.937 eV and a high carrier mobility of about 1.80 × 105 cm2 V-1 s-1, which are promising for electronic device applications. The integration of valley polarization and ferroelectricity in a single material offers a promising platform for the design of electronic devices.

Microwave Directional Dichroism Resonant with Spin Excitations in the Polar Ferromagnet GaV_{4}S_{8}

We have investigated the directional dichroism of magnetic resonance spectra in the polar ferromagnet GaV_{4}S_{8}. While four types of structural domains are energetically degenerated under a zero field, the magnetic resonance for each domain is well separated by applying magnetic fields due to uniaxial magnetic anisotropy. Consequently, a directional dichroism as large as 20% is clearly observed without domain cancellation. The present observation therefore demonstrates that not only magnetoelectric monodomain crystals but also magnetoelectric multidomain specimens can be used to realize microwave (optical) diodes owing to the lack of inversion domains.

Recent developments in single-molecule toroics

An update overview of emerging single-molecule toroics (SMTs) is expounded to elucidate the strategy to design SMTs and ultimately inspire the seeking of SMTs with enhanced toroidal moment.

First-principles study of the electric, magnetic, and orbital structure in perovskite ScMnO3

Perovskite ScMnO₃ has been synthesized under high temperature and high pressure. The magnetic ordering of this compound was proposed to be in the E-AFM state in previous theoretical research. Such magnetic ordering would lead the Mn³⁺ ions to be off-centered in the MnO₆ octahedra; however, this is not detected experimentally. To address this issue, we systematically investigate the magnetic, orbital, and electric structures of perovskite ScMnO₃ with first-principles calculations. It is found that its magnetic ground state is G-AFM and the magnetic ordering can explain the puzzle very well. Moreover, there is an unreported three-dimensional alternating cooperative orbital ordering in perovskite ScMnO₃. The antiferromagnetic coupling between the nearest-neighbor Mn³⁺ ions is stabilized by the strong octahedral distortions that decrease the ferromagnetic interaction between the e_g orbitals of the Mn³⁺ ions. In addition, we find that perovskite ScMnO₃ is a bipolar antiferromagnetic semiconductor in which completely spin-polarized currents with reversible spin polarization can be tuned simply by applying a gate voltage. Such controllability of the spin polarization of the current opens up new avenues for future spintronic devices. Our results not only suggest that the G-AFM phase is the ground magnetic state for perovskite ScMnO₃, but also enrich research in orbital ordering in rare-earth manganites.

The crystal structure and three-dimensional alternating complementary orbital ordering of perovskite ScMnO₃.

Spin–orbit coupling in magnetoelectric Ba3(Zn1−xCox)2Fe24O41 hexaferrites

Z-type hexaferrites Ba₃(Zn_1−xCo_x)₂Fe₂₄O₄₁ (x = 0.2, 0.4, 0.6, 0.8, defined as Z1–Z4) were synthesized by a sol–gel method.

Emergent electromagnetism in condensed matter

Electrons in solids constitute quantum many-body systems showing a variety of phenomena. It often happens that the eigen states of the Hamiltonian are classified into subgroups separated by energy gaps. Band structures in solids and spin polarization in Mott insulators are two representative examples. The subspace spanned by these wavefunctions belonging to each of this subgroup can be regarded as a manifold in Hilbert space, and concepts concerning differential geometry become relevant. Connection and curvature are two key quantities, which correspond to the vector potential and field strength of electromagnetism, respectively. Therefore, one can construct an effective electromagnetic field from the structure of the Hilbert space, which is called an "emergent electromagnetic field". In this article, we review the physics related to this emergent electromagnetic field in solids, including the gauge theory of strongly correlated electrons, various Hall effects, multiferroics, topological matter, magnetic texture such as skyrmions, and the shift current in noncentrosymmetric materials.

Scalable energy-efficient magnetoelectric spin-orbit logic

Since the early 1980s, most electronics have relied on the use of complementary metal-oxide-semiconductor (CMOS) transistors. However, the principles of CMOS operation, involving a switchable semiconductor conductance controlled by an insulating gate, have remained largely unchanged, even as transistors are miniaturized to sizes of 10 nanometres. We investigated what dimensionally scalable logic technology beyond CMOS could provide improvements in efficiency and performance for von Neumann architectures and enable growth in emerging computing such as artifical intelligence. Such a computing technology needs to allow progressive miniaturization, reduce switching energy, improve device interconnection and provide a complete logic and memory family. Here we propose a scalable spintronic logic device that operates via spin-orbit transduction (the coupling of an electron's angular momentum with its linear momentum) combined with magnetoelectric switching. The device uses advanced quantum materials, especially correlated oxides and topological states of matter, for collective switching and detection. We describe progress in magnetoelectric switching and spin-orbit detection of state, and show that in comparison with CMOS technology our device has superior switching energy (by a factor of 10 to 30), lower switching voltage (by a factor of 5) and enhanced logic density (by a factor of 5). In addition, its non-volatility enables ultralow standby power, which is critical to modern computing. The properties of our device indicate that the proposed technology could enable the development of multi-generational computing.

Comprehensive inelastic neutron scattering study of the multiferroic M n 1 - x C o x W O 4

Using high-resolution inelastic neutron scattering, we examine the spin dynamics ofM n 1 - x C o x W O 4 in the collinear AF1, the a c - b spiral AF2, and the a c cycloidal AF5 phases. The spin wave excitations are well described by a Heisenberg model with competing long-range exchange interactions (J i up to 12th nearest neighbors) and the single-ion anisotropy K induced by the spin-orbit interaction. While the exchange constants are relatively unchanged, the dominant effect of doping is to change the single-ion anisotropy from easy axis ( K > 0 ) in the collinear AF1 phase to easy plane ( K < 0 ) in the two multiferroic phases.

Crystal and Magnetic Structures and Properties of (Lu1- xMn x)MnO3 Solid Solutions

(Lu_{1- x}Mn _x)MnO₃ solid solutions, having the perovskite-type structure and Pnma space group, with 0 ≤ x ≤ 0.4 were synthesized by a high-pressure, high-temperature method at 6 GPa and about 1670 K from Lu₂O₃ and Mn₂O₃. Their crystal and magnetic structures were studied by neutron powder diffraction. The degree of octahedral MnO₆ tilting decreases in (Lu_{1- x}Mn _x)MnO₃ with increasing x. Only the incommensurate (IC) spin structure with a propagation vector of k = ( k₀, 0, 0) and k₀ ≈ 0.44 remains in (Lu_0.9Mn_0.1)MnO₃ in the whole temperature range below the Neel temperature T_N = 36 K, and the commensurate noncollinear E-type structure that has been reported in the literature for undoped o-LuMnO₃ is not observed. (Lu_{1- x}Mn _x)MnO₃ samples with 0.2 ≤ x ≤ 0.4 have a ferrimagnetic structure with a propagation vector of k = (0, 0, 0) and ferromagnetic (FM) ordering of Mn³⁺ and Mn⁴⁺ cations at the B site, which are antiferromagnetically coupled to a noncollinear predominantly FM arrangement of Mn²⁺ at the A site. The ferrimagnetic Curie temperature, T_C, increases monotonically from 67 K for x = 0.2 to 118 K for x = 0.4. Magnetic and dielectric properties of (Lu_{1- x}Mn _x)MnO₃ and a composition-temperature phase diagram are also reported.

A new mathematical approach to finding global solutions of the magnetic structure determination problem

Determination of magnetic structure is an important analytical procedure utilized in various fields ranging from fundamental condensed-matter physics and chemistry to advanced manufacturing. It is typically performed using a neutron diffraction technique; however, finding global solutions of the magnetic structure optimization problem represents a significant challenge. Generally, it is not possible to mathematically prove that the obtained magnetic structure is a truly global solution and that no solution exists when no acceptable structure is found. In this study, the global optimization technique called semidefinite relaxation of quadratic optimization, which has attracted much interest in the field of applied mathematics, is proposed to use as a new analytical method for the determination of magnetic structure, followed by the application of polarized neutron diffraction data. This mathematical approach allows avoiding spurious local solutions, decreasing the amount of time required to find a tentative solution and finding multiple solutions when they exist.