Microwave magnetoelectric effect via skyrmion resonance modes in a helimagnetic multiferroic

Optimizing skyrmionium movement and stability via stray magnetic fields in trilayer nanowire constructs

Skyrmioniums, known for their unique transport and regulatory properties, are emerging as potential cornerstones for future data storage systems. However, the stability of skyrmionium movement faces considerable challenges due to the skyrmion Hall effect, which is induced by deformation. In response, our research introduces an innovative solution: we utilized micro-magnetic simulations to create a sandwiched trilayer nanowire structure augmented with a stray magnetic field. This combination effectively guides the skyrmionium within the ferromagnetic (FM) layer. Our empirical investigations reveal that the use of a stray magnetic field not only reduces the size of the skyrmionium but also amplifies its stability. This dual-effect proficiently mitigates the deformation of skyrmionium movement and boosts their thermal stability. We find these positive outcomes are most pronounced at a particular intensity of the stray magnetic field. Importantly, the required stray magnetic field can be generated using a heavy metal (HM1) layer of suitable thickness, rendering the practical application of this approach plausible in real-world experiments. Additionally, we analyze the functioning mechanism based on the Landau-Lifshitz-Gilbert (LLG) equation and energy variation. We also develop a deep spiking neural network (DSNN), which achieves a remarkable recognition accuracy of 97%. This achievement is realized through supervised learning via the spike timing dependent plasticity rule (STDP), considering the nanostructure as an artificial synapse device that corresponds to the electrical properties of the nanostructure. In conclusion, our study provides invaluable insights for the design of innovative information storage devices utilizing skyrmionium technology. By tackling the issues presented by the skyrmion Hall effect, we outline a feasible route for the practical application of this advanced technology. Our research, therefore, serves as a robust platform for continued investigations in this field.

Berry-Curvature Engineering for Nonreciprocal Directional Dichroism in Two-Dimensional Antiferromagnets

In two-dimensional antiferromagnets, we find that the mixed Berry curvature can be attributed as the geometrical origin of the nonreciprocal directional dichroism (NDD), which refers to the difference in light absorption between opposite propagation directions. This Berry curvature is closely related to the uniaxial strain in accordance with the symmetry constraint, leading to a highly tunable NDD, whose sign and strength can be tuned via strain direction. We choose the lattice model of MnBi_{2}Te_{4} as a concrete example. The coupling between mixed Berry curvature and strain also suggests the magnetic quadrupole of the Bloch wave packet as the macroscopic order parameter probed by the NDD in two dimensions, which is distinct from the multiferroic order P×M or the spin toroidal and quadrupole order within a unit cell in previous studies. Our work paves the way for the Berry-curvature engineering for optical nonreciprocity in two-dimensional antiferromagnets.

Instability of skyrmion lattice under microwave magnetic field due to single-qhelimagnetic excitation mode

Composed of the three spiral magnetic vectors, the structure of skyrmion lattice (SkL) can be destructed by spin excitations in possibly two ways: one is to make decoherence of all the helices through the phase change of a certain spiral magnetic vector, and the other is to inhibit one or two spiral components while enhancing the others so that it becomes a magnetic structure of single or double magnetic vectors. Here, we present a micromagnetic study on the spin excitations of a two-dimensional SkL under the in-plane microwave magnetic field. By calculating the parameters describing the in-plane spin excitations mode, we find that the spin configuration tends to be an enhanced single-vector spiral magnetic structure due to the excitation modes under some specific frequencies so that the SkL will collapse to the topologically trivial state. Our results help to form a deeper understanding of the spin excitation in SkL under an ac magnetic field.

Topological magnon band structure of emergent Landau levels in a skyrmion lattice

The motion of a spin excitation across topologically nontrivial magnetic order exhibits a deflection that is analogous to the effect of the Lorentz force on an electrically charged particle in an orbital magnetic field. We used polarized inelastic neutron scattering to investigate the propagation of magnons (i.e., bosonic collective spin excitations) in a lattice of skyrmion tubes in manganese silicide. For wave vectors perpendicular to the skyrmion tubes, the magnon spectra are consistent with the formation of finely spaced emergent Landau levels that are characteristic of the fictitious magnetic field used to account for the nontrivial topological winding of the skyrmion lattice. This provides evidence of a topological magnon band structure in reciprocal space, which is borne out of the nontrivial real-space topology of a magnetic order.

Tunable gigahertz dynamics of low-temperature skyrmion lattice in a chiral magnet

Recently, it has been shown that the chiral magnetic insulator Cu₂OSeO₃hosts skyrmions in two separated pockets in temperature and magnetic field phase space. It has also been shown that the predominant stabilization mechanism for the low-temperature skyrmion (LTS) phase is via the crystalline anisotropy, opposed to temperature fluctuations that stabilize the well-established high-temperature skyrmion (HTS) phase. Here, we report on a detailed study of LTS generation by field cycling, probed by GHz spin dynamics in Cu₂OSeO₃. LTSs are populated via a field cycling protocol with the static magnetic field applied parallel to the ⟨100⟩ crystalline direction of plate and cuboid-shaped bulk crystals. By analyzing temperature-dependent broadband spectroscopy data, clear evidence of LTS excitations with clockwise (CW), counterclockwise (CCW), and breathing mode (BR) character at temperatures belowT= 40 K are shown. We find that the mode intensities can be tuned with the number of field-cycles below the saturation field. By tracking the resonance frequencies, we are able to map out the field-cycle-generated LTS phase diagram, from which we conclude that the LTS phase is distinctly separated from the high-temperature counterpart. We also study the mode hybridization between the dark CW and the BR modes as a function of temperature. By using two Cu₂OSeO₃crystals with different shapes and therefore different demagnetization factors, together with numerical calculations, we unambiguously show that the magnetocrystalline anisotropy plays a central role for the mode hybridization.

Topological spin crystals by itinerant frustration

Spin textures with nontrivial topology, such as vortices and skyrmions, have attracted attention as a source of unconventional magnetic, transport, and optical phenomena. Recently, a new generation of topological spin textures has been extensively studied in itinerant magnets; in contrast to the conventional ones induced, e.g., by the Dzyaloshinskii-Moriya interaction in noncentrosymmetric systems, they are characterized by extremely short magnetic periods and stable even in centrosymmetric systems. Here we review such new types of topological spin textures with particular emphasis on their stabilization mechanism. Focusing on the interplay between charge and spin degrees of freedom in itinerant electron systems, we show that itinerant frustration, which is the competition among electron-mediated interactions, plays a central role in stabilizing a variety of topological spin crystals including a skyrmion crystal with unconventional high skyrmion number, meron crystals, and hedgehog crystals. We also show that the essential ingredients in the itinerant frustration are represented by bilinear and biquadratic spin interactions in momentum space. This perspective not only provides a unified understanding of the unconventional topological spin crystals but also stimulates further exploration of exotic topological phenomena in itinerant magnets.

Skyrmion Qubits: A New Class of Quantum Logic Elements Based on Nanoscale Magnetization

We introduce a new class of primitive building blocks for realizing quantum logic elements based on nanoscale magnetization textures called skyrmions. In a skyrmion qubit, information is stored in the quantum degree of helicity, and the logical states can be adjusted by electric and magnetic fields, offering a rich operation regime with high anharmonicity. By exploring a large parameter space, we propose two skyrmion qubit variants depending on their quantized state. We discuss appropriate microwave pulses required to generate single-qubit gates for quantum computing, and skyrmion multiqubit schemes for a scalable architecture with tailored couplings. Scalability, controllability by microwave fields, operation time scales, and readout by nonvolatile techniques converge to make the skyrmion qubit highly attractive as a logical element of a quantum processor.

Microwave resonances of magnetic skyrmions in thin film multilayers

Non-collinear magnets exhibit a rich array of dynamic properties at microwave frequencies. They can host nanometre-scale topological textures known as skyrmions, whose spin resonances are expected to be highly sensitive to their local magnetic environment. Here, we report a magnetic resonance study of an [Ir/Fe/Co/Pt] multilayer hosting Néel skyrmions at room temperature. Experiments reveal two distinct resonances of the skyrmion phase during in-plane ac excitation, with frequencies between 6-12 GHz. Complementary micromagnetic simulations indicate that the net magnetic dipole moment rotates counterclockwise (CCW) during both resonances. The magnon probability distribution for the lower-frequency resonance is localised within isolated skyrmions, unlike the higher-frequency mode which principally originates from areas between skyrmions. However, the properties of both modes depend sensitively on the out-of-plane dipolar coupling, which is controlled via the ferromagnetic layer spacing in our heterostructures. The gyrations of stable isolated skyrmions reported in this room temperature study encourage the development of new material platforms and applications based on skyrmion resonances. Moreover, our material architecture enables the resonance spectra to be tuned, thus extending the functionality of such applications over a broadband frequency range.

Magnetic Skyrmion Materials

Skyrmion, a concept originally proposed in particle physics half a century ago, can now find the most fertile field for its applicability, that is, the magnetic skyrmion realized in helimagnetic materials. The spin swirling vortex-like texture of the magnetic skyrmion can define the particle nature by topology; that is, all the constituent spin moments within the two-dimensional sheet wrap the sphere just one time. Such a topological nature of the magnetic skyrmion can lead to extraordinary metastability via topological protection and the driven motion with low electric-current excitation, which may promise future application to spintronics. The skyrmions in the magnetic materials frequently show up as the crystal lattice form, e.g., hexagonal lattice, but sometimes as isolated or independent particles. These skyrmions in magnets were initially found in acentric magnets, such as chiral, polar, and bilayered magnets endowed with antisymmetric spin exchange interaction, while the skyrmion host materials have been explored in a broader family of compounds including centrosymmetric magnets. This review describes the materials science and materials chemistry of magnetic skyrmions using the classification scheme of the skyrmion forming microscopic mechanisms. The emergent phenomena and functions mediated by skyrmions are described, including the generation of emergent magnetic and electric field by statics and dynamics of skrymions and the inherent magnetoelectric effect. The other important magnetic topological defects in two or three dimensions, such as biskyrmions, antiskyrmions, merons, and hedgehogs, are also reviewed in light of their interplay with the skyrmions.

Nonreciprocity of spin waves in the conical helix state

Nonreciprocity emerges in nature and in artificial objects from various physical origins, being widely utilized in contemporary technologies as exemplified by diode elements in electronics. While most of the nonreciprocal phenomena are realized by employing interfaces where the inversion symmetry is trivially lifted, nonreciprocal transport of photons, electrons, magnons, and possibly phonons also emerge in bulk crystals with broken space inversion and time reversal symmetries. Among them, directional propagation of bulk magnons (i.e., quanta of spin wave excitation) is attracting much attention nowadays for its potentially large nonreciprocity suitable for spintronic and spin-caloritronic applications. Here, we demonstrate nonreciprocal propagation of spin waves for the conical spin helix state in Cu₂OSeO₃ due to a combination of dipole and Dzyaloshinskii-Moriya interactions. The observed nonreciprocal spin dispersion smoothly connects to the hitherto known magnetochiral nonreciprocity in the field-induced collinear spin state; thus, all the spin phases show diode characteristics in this chiral insulator.

Nonreciprocal charge transport up to room temperature in bulk Rashba semiconductor α-GeTe

Nonmagnetic Rashba systems with broken inversion symmetry are expected to exhibit nonreciprocal charge transport, a new paradigm of unidirectional magnetoresistance in the absence of ferromagnetic layer. So far, most work on nonreciprocal transport has been solely limited to cryogenic temperatures, which is a major obstacle for exploiting the room-temperature two-terminal devices based on such a nonreciprocal response. Here, we report a nonreciprocal charge transport behavior up to room temperature in semiconductor α-GeTe with coexisting the surface and bulk Rashba states. The combination of the band structure measurements and theoretical calculations strongly suggest that the nonreciprocal response is ascribed to the giant bulk Rashba spin splitting rather than the surface Rashba states. Remarkably, we find that the magnitude of the nonreciprocal response shows an unexpected non-monotonical dependence on temperature. The extended theoretical model based on the second-order spin-orbit coupled magnetotransport enables us to establish the correlation between the nonlinear magnetoresistance and the spin textures in the Rashba system. Our findings offer significant fundamental insight into the physics underlying the nonreciprocity and may pave a route for future rectification devices.

A short history of multiferroics

The realization that materials with coexisting magnetic and ferroelectric order open up efficient ways to control magnetism by electric fields unites scientists from different communities in the effort to explore the phenomenon of multiferroics. Following a tremendous development, the field has now gained some maturity. In this article, we give a succinct review of the history of this exciting class of materials and its evolution from “ferroelectromagnets” to “multiferroics” and beyond.

Spin Wave Radiation by a Topological Charge Dipole

The use of spin waves (SWs) as data carriers in spintronic and magnonic logic devices offers operation at low power consumption, free of Joule heating. Nevertheless, the controlled emission and propagation of SWs in magnetic materials remains a significant challenge. Here, we propose that skyrmion-antiskyrmion bilayers form topological charge dipoles and act as efficient sub-100 nm SW emitters when excited by in-plane ac magnetic fields. The propagating SWs have a preferred radiation direction, with clear dipole signatures in their radiation pattern, suggesting that the bilayer forms a SW antenna. Bilayers with the same topological charge radiate SWs with spiral and antispiral spatial profiles, enlarging the class of SW patterns. We demonstrate that the characteristics of the emitted SWs are linked to the topology of the source, allowing for full control of the SW features, including their amplitude, preferred direction of propagation, and wavelength.

Giant magnetoelectric coupling observed at high frequency in NiFe2O4-BaTiO3 particulate composite

A giant magnetoelectric voltage coupling coefficient without direct current magnetic field observed in NiFe₂O₄-BaTiO₃ particulate composite is reported. The particulate composite was obtained by combining hydrothermal and sol-gel method, and was studied for their crystallographic structure, morphology, magnetic, dielectric and magnetoelectric properties. Results of Mössbauer spectra demonstrated the presence of interface phase in particulate composite, where the changes of the magnetic properties in composite compared to the pure NiFe₂O₄ also confirmed this. The particulate composite exhibits remarkable magnetoelectric effect through both static measurement and dynamic measurement. The special magnetoelectric property of the particulate composite is beneficial for applications in high frequency devices.

Tunable magnetic textures and excitation modes in FePt multilayer films

Micromagnetic simulations have been performed to investigate the magnetic textures and dynamic properties of FePt-based multilayer films. The uniform state, Neel skyrmion and Bloch skyrmion can be obtained using variable magnetic parameters. A microwave field is applied to induce spin precession along the out-plane and in-plane axes. For the perpendicular resonance modes, low-frequency peaks are identified as domain-wall modes. It is shown that radial-like and azimuthal-like resonance modes appear with increase in frequency. The excited modes are qualitatively different when the microwave field is applied along the in-plane axis. For the uniform state, the phase responds to the excitation with waves that spread out in a circle, which is a characteristic feature of the azimuthal mode in the spin wave. Because of the nonuniform effective field in Neel and Bloch skyrmions, the dynamic response localizes at the center and the edge spreads into the adjacent domains. These observations are important for tunable and abundant high-frequency magnetic properties in skyrmion-based devices.

Micromagnetic simulations have been performed to investigate the magnetic textures and dynamic properties of FePt-based multilayer films.

Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications

The field of magnetic skyrmions has been actively investigated across a wide range of topics during the last decades. In this topical review, we mainly review and discuss key results and findings in skyrmion research since the first experimental observation of magnetic skyrmions in 2009. We particularly focus on the theoretical, computational and experimental findings and advances that are directly relevant to the spintronic applications based on magnetic skyrmions, i.e. their writing, deleting, reading and processing driven by magnetic field, electric current and thermal energy. We then review several potential applications including information storage, logic computing gates and non-conventional devices such as neuromorphic computing devices. Finally, we discuss possible future research directions on magnetic skyrmions, which also cover rich topics on other topological textures such as antiskyrmions and bimerons in antiferromagnets and frustrated magnets.

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.

Ferromagnetic Resonance with Magnetic Phase Selectivity by Means of Resonant Elastic X-Ray Scattering on a Chiral Magnet

Cubic chiral magnets, such as Cu_{2}OSeO_{3}, exhibit a variety of noncollinear spin textures, including a trigonal lattice of spin whirls, the so-called skyrmions. Using magnetic resonant elastic x-ray scattering (REXS) on a crystalline Bragg peak and its magnetic satellites while exciting the sample with magnetic fields at gigahertz frequencies, we probe the ferromagnetic resonance (FMR) modes of these spin textures by means of the scattered intensity. Most notably, the three eigenmodes of the skyrmion lattice are detected with large sensitivity. As this novel technique, which we label REXS FMR, is carried out at distinct positions in reciprocal space, it allows us to distinguish contributions originating from different magnetic states, providing information on the precise character, weight, and mode mixing as a prerequisite of tailored excitations for applications.

Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole

We identify the quantum metric dipole as the geometric origin of the nonreciprocal directional dichroism which describes the change in the refractive index upon reversing the light propagation direction. Specifically, we find that the static limit of the nonreciprocal directional dichroism corresponds to a quadrupolar transport current from the quantum metric dipole, in response to a quadrupolar electric field. Moreover, at a finite frequency, we demonstrate that the steepest slope of the averaged quantum metric dipole gives rise to a peak in the differential refractive index between counterpropagating lights. Finally, we illustrate both features in a low-energy model.

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.

Skyrmions Driven by Intrinsic Magnons

We study the dynamics of a Skyrmion in a magnetic insulating nanowire in the presence of time-dependent oscillating magnetic field gradients. These ac fields act as a net driving force on the Skyrmion via its own intrinsic magnetic excitations. In a microscopic quantum field theory approach, we include the unavoidable coupling of the external field to the magnons, which gives rise to time-dependent dissipation for the Skyrmion. We demonstrate that the magnetic ac field induces a super-Ohmic to Ohmic crossover behavior for the Skyrmion dissipation kernels with time-dependent Ohmic terms. The ac driving of the magnon bath at resonance results in a unidirectional helical propagation of the Skyrmion in addition to the otherwise periodic bounded motion.

Reciprocal space tomography of 3D skyrmion lattice order in a chiral magnet

It is commonly assumed that surfaces modify the properties of stable materials within the top few atomic layers of a bulk specimen only. Exploiting the polarization dependence of resonant elastic X-ray scattering to go beyond conventional diffraction and imaging techniques, we have determined the depth dependence of the full 3D spin structure of skyrmions-that is, topologically nontrivial whirls of the magnetization-below the surface of a bulk sample of Cu₂OSeO₃ We found that the skyrmions change exponentially from pure Néel- to pure Bloch-twisting over a distance of several hundred nanometers between the surface and the bulk, respectively. Though qualitatively consistent with theory, the strength of the Néel-twisting at the surface and the length scale of the variation observed experimentally exceed material-specific modeling substantially. In view of the exceptionally complete quantitative theoretical account of the magnetic rigidities and associated static and dynamic properties of skyrmions in Cu₂OSeO₃ and related materials, we conclude that subtle changes of the materials properties must exist at distances up to several hundred atomic layers into the bulk, which originate in the presence of the surface. This has far-reaching implications for the creation of skyrmions in surface-dominated systems and identifies, more generally, surface-induced gradual variations deep within a bulk material and their impact on tailored functionalities as an unchartered scientific territory.

Spectroscopic features of ultrahigh-pressure impact glasses of the Kara astrobleme

The state of substances under ultrahigh pressures and temperatures (UHPHT) now raises a special interest as a matter existing under extreme conditions and as potential new material. Under laboratory conditions only small amounts of micrometer-sized matter are produced at a pressure up to 100 GPa and at room temperature. Simultaneous combination of ultrahigh pressures and temperatures in a lab still requires serious technological effort. Here we describe the composition and structure of the UHPHT vein-like impact glass discovered by us in 2015 on the territory of the Kara astrobleme (Russia) and compare its properties with impact glass from the Ries crater (Germany). A complex of structural and spectroscopic methods presents unusual high pressure marks of structural elements in 8-fold co-ordination that had been described earlier neither in synthetic nor natural glasses. The Kara natural UHPHT glasses being about 70 Ma old have well preserved initial structure, presenting some heterogeneity as a result of partial liquation and crystallization differentiation where an amorphous component is proposed to originate from low level polymerization. Homogeneous parts of the UHPHT glasses can be used to deepened fundamental investigation of a substance under extreme PT conditions and to technological studies for novel material creations.

Helimagnon Resonances in an Intrinsic Chiral Magnonic Crystal

We experimentally study magnetic resonances in the helical and conical magnetic phases of the chiral magnetic insulator Cu_{2}OSeO_{3} at the temperature T=5  K. Using a broadband microwave spectroscopy technique based on vector network analysis, we identify three distinct sets of helimagnon resonances in the frequency range 2  GHz≤f≤20  GHz with low magnetic damping α≤0.003. The extracted resonance frequencies are in accordance with calculations of the helimagnon band structure found in an intrinsic chiral magnonic crystal. The periodic modulation of the equilibrium spin direction that leads to the formation of the magnonic crystal is a direct consequence of the chiral magnetic ordering caused by the Dzyaloshinskii-Moriya interaction. The mode coupling in the magnonic crystal allows excitation of helimagnons with wave vectors that are multiples of the spiral wave vector.

Linearly polarized GHz magnetization dynamics of spin helix modes in the ferrimagnetic insulator Cu2OSeO3

Linear dichroism - the polarization dependent absorption of electromagnetic waves- is routinely exploited in applications as diverse as structure determination of DNA or polarization filters in optical technologies. Here filamentary absorbers with a large length-to-width ratio are a prerequisite. For magnetization dynamics in the few GHz frequency regime strictly linear dichroism was not observed for more than eight decades. Here, we show that the bulk chiral magnet Cu₂OSeO₃ exhibits linearly polarized magnetization dynamics at an unexpectedly small frequency of about 2 GHz at zero magnetic field. Unlike optical filters that are assembled from filamentary absorbers, the magnet is shown to provide linear polarization as a bulk material for an extremely wide range of length-to-width ratios. In addition, the polarization plane of a given mode can be switched by 90° via a small variation in width. Our findings shed a new light on magnetization dynamics in that ferrimagnetic ordering combined with antisymmetric exchange interaction offers strictly linear polarization and cross-polarized modes for a broad spectrum of sample shapes at zero field. The discovery allows for novel design rules and optimization of microwave-to-magnon transduction in emerging microwave technologies.

Noncentrosymmetric Magnets Hosting Magnetic Skyrmions

The concept of a skyrmion, which was first introduced by Tony Skyrme in the field of particle physics, has become widespread in condensed matter physics to describe various topological orders. Skyrmions in magnetic materials have recently received particular attention; they represent vortex-like spin structures with the character of nanometric particles and produce fascinating physical properties rooted in their topological nature. Here, a series of noncentrosymmetric ferromagnets hosting skyrmions is reviewed: B20 metals, Cu₂ OSeO₃ , Co-Zn-Mn alloys, and GaV₄ S₈ , where Dzyaloshinskii-Moriya interaction plays a key role in the stabilization of skyrmion spin texture. Their topological spin arrangements and consequent emergent electromagnetic fields give rise to striking features in transport and magnetoelectric properties in metals and insulators, such as the topological Hall effect, efficient electric-drive of skyrmions, and multiferroic behavior. Such electric controllability and nanometric particle natures highlight magnetic skyrmions as a potential information carrier for high-density magnetic storage devices with excellent energy efficiency.

Magnetoelectrical control of nonreciprocal microwave response in a multiferroic helimagnet

The control of physical properties by external fields is essential in many contemporary technologies. For example, conductance can be controlled by a gate electric field in a field effect transistor, which is a main component of integrated circuits. Optical phenomena induced by an electric field such as electroluminescence and electrochromism are useful for display and other technologies. Control of microwave propagation is also important for future wireless communication technology. Microwave properties in solids are dominated mostly by magnetic excitations, which cannot be easily controlled by an electric field. One solution to this problem is to use magnetically induced ferroelectrics (multiferroics). Here we show that microwave nonreciprocity, that is, different refractive indices for microwaves propagating in opposite directions, could be reversed by an external electric field in a multiferroic helimagnet Ba₂Mg₂Fe₁₂O₂₂. This approach offers an avenue for the electrical control of microwave properties.

Control of microwave propagation is important for future communication technology. Here, Iguchi et al. report the reversal of microwave nonreciprocity by an external electric field in a multiferroic helimagnet Ba₂Mg₂Fe₁₂O₂₂.

Room-temperature helimagnetism in FeGe thin films

Chiral magnets are promising materials for the realisation of high-density and low-power spintronic memory devices. For these future applications, a key requirement is the synthesis of appropriate materials in the form of thin films ordering well above room temperature. Driven by the Dzyaloshinskii-Moriya interaction, the cubic compound FeGe exhibits helimagnetism with a relatively high transition temperature of 278 K in bulk crystals. We demonstrate that this temperature can be enhanced significantly in thin films. Using x-ray scattering and ferromagnetic resonance techniques, we provide unambiguous experimental evidence for long-wavelength helimagnetic order at room temperature and magnetic properties similar to the bulk material. We obtain α_intr = 0.0036 ± 0.0003 at 310 K for the intrinsic damping parameter. We probe the dynamics of the system by means of muon-spin rotation, indicating that the ground state is reached via a freezing out of slow dynamics. Our work paves the way towards the fabrication of thin films of chiral magnets that host certain spin whirls, so-called skyrmions, at room temperature and potentially offer integrability into modern electronics.

Tailoring Spin Textures in Complex Oxide Micromagnets

Engineered topological spin textures with submicron dimensions in magnetic materials have emerged in recent years as the building blocks for various spin-based memory devices. Examples of these magnetic configurations include magnetic skyrmions, vortices, and domain walls. Here, we show the ability to control and characterize the evolution of spin textures in complex oxide micromagnets as a function of temperature through the delicate balance of fundamental materials parameters, micromagnet geometries, and epitaxial strain. These results demonstrate that in order to fully describe the observed spin textures, it is necessary to account for the spatial variation of the magnetic parameters within the micromagnet. This study provides the framework to accurately characterize such structures, leading to efficient design of spin-based memory devices based on complex oxide thin films.

One-Way Transparency of Light in Multiferroic CuB(2)O(4)

We experimentally demonstrate one-way transparency of light in multiferroic CuB(2)O(4). The material is rendered transparent for light propagating in one direction, while opaque for light propagating in the opposite direction. The novel transparency results from a destructive interference of the electric dipole and magnetic dipole transitions. The realization of the effect has been accomplished by the application of a high magnetic field and the proper selection of the propagation direction of light in agreement with our quantum mechanical formulation of nonreciprocal directional dichroism.

Dynamical magnetoelectric phenomena of multiferroic skyrmions

Magnetic skyrmions, vortex-like swirling spin textures characterized by a quantized topological invariant, realized in chiral-lattice magnets are currently attracting intense research interest. In particular, their dynamics under external fields is an issue of vital importance both for fundamental science and for technical application. Whereas observations of magnetic skyrmions has been limited to metallic magnets so far, their realization was also discovered in a chiral-lattice insulating magnet Cu2OSeO3 in 2012. Skyrmions in the insulator turned out to exhibit multiferroic nature with spin-induced ferroelectricity. Strong magnetoelectric coupling between noncollinear skyrmion spins and electric polarizations mediated by relativistic spin-orbit interaction enables us to drive motion and oscillation of magnetic skyrmions by application of electric fields instead of injection of electric currents. Insulating materials also provide an environment suitable for detection of pure spin dynamics through spectroscopic measurements owing to the absence of appreciable charge excitations. In this article, we review recent theoretical and experimental studies on multiferroic properties and dynamical magnetoelectric phenomena of magnetic skyrmions in insulators. We argue that multiferroic skyrmions show unique coupled oscillation modes of magnetizations and polarizations, so-called electromagnon excitations, which are both magnetically and electrically active, and interference between the electric and magnetic activation processes leads to peculiar magnetoelectric effects in a microwave frequency regime.

Nickel Ferrite Nanoparticles Anchored onto Silica Nanofibers for Designing Magnetic and Flexible Nanofibrous Membranes

Many applications proposed for magnetic silica nanofibers require their assembly into a cellular membrane structure. The feature to keep structure stable upon large deformation is crucial for a macroscopic porous material which functions reliably. However, it remains a key issue to realize robust flexibility in two-dimensional (2D) magnetic silica nanofibrous networks. Here, we report that the combination of electrospun silica nanofibers with zein dip-coating can lead to the formation of flexible, magnetic, and hierarchical porous silica nanofibrous membranes (SNM). The 290 nm diameter silica nanofibers act as templates for the uniform anchoring of nickel ferrite nanoparticles (size of 50 nm). Benefiting from the homogeneous and stable nanofiber-nanoparticle composite structure, the resulting magnetic SNM can maintain their structure integrity under repeated bending as high as 180° and can facilely recover. The unique hierarchical structure also provides this new class of silica membrane with integrated properties of ultralow density, high porosity, large surface area, good magnetic responsiveness, robust dye adsorption capacity, and effective emulsion separation performance. Significantly, the synthesis of such fascinating membranes may provide new insight for further application of silica in a self-supporting, structurally adaptive, and 2D membrane form.

Microwave Magnetochiral Dichroism in the Chiral-Lattice Magnet Cu_{2}OSeO_{3}

Through broadband microwave spectroscopy in Faraday geometry, we observe distinct absorption spectra accompanying magnetoelectric (ME) resonance for oppositely propagating microwaves, i.e., directional dichroism, in the multiferroic chiral-lattice magnet Cu_{2}OSeO_{3}. The magnitude of the directional dichroism critically depends on the magnetic-field direction. Such behavior is well accounted for by considering the relative direction of the oscillating electric polarizations induced via the ME effect with respect to microwave electric fields. Directional dichroism in a system with an arbitrary form of ME coupling can be also discussed in the same manner.

Microwave Magnetochiral Effect in Cu_{2}OSeO_{3}

We theoretically find that in the multiferroic chiral magnet Cu_{2}OSeO_{3} resonant magnetic excitations are coupled to the collective oscillation of the electric polarization, and thereby attain simultaneous activity to the ac magnetic field and ac electric field. Because of the interference between these magnetic and electric activation processes, this material hosts a gigantic magnetochiral dichroism for microwaves, that is, a directional dichroism at gigahertz frequencies in the Faraday geometry. The absorption intensity of a microwave differs by as much as ~30% depending on whether its propagation direction is parallel or antiparallel to the external magnetic field.

Universal helimagnon and skyrmion excitations in metallic, semiconducting and insulating chiral magnets

Nearly seven decades of research on microwave excitations of magnetic materials have led to a wide range of applications in electronics. The recent discovery of topological spin solitons in chiral magnets, so-called skyrmions, promises high-frequency devices that exploit the exceptional emergent electrodynamics of these compounds. Therefore, an accurate and unified quantitative account of their resonant response is key. Here, we report all-electrical spectroscopy of the collective spin excitations in the metallic, semiconducting and insulating chiral magnets MnSi, Fe1-xCoxSi and Cu2OSeO3, respectively, using broadband coplanar waveguides. By taking into account dipolar interactions, we achieve a precise quantitative modelling across the entire magnetic phase diagrams using two material-specific parameters that quantify the chiral and the critical field energy. The universal behaviour sets the stage for purpose-designed applications based on the resonant response of chiral magnets with tailored electric conductivity and an unprecedented freedom for an integration with electronics.

Ultrafast optical excitation of magnetic skyrmions

Magnetic skyrmions in an insulating chiral magnet Cu2OSeO3 were studied by all-optical spin wave spectroscopy. The spins in the conical and skyrmion phases were excited by the impulsive magnetic field from the inverse-Faraday effect, and resultant spin dynamics were detected by using time-resolved magneto-optics. Clear dispersions of the helimagnon were observed, which is accompanied by a distinct transition into the skyrmion phase, by sweeping temperature and magnetic field. In addition to the collective excitations of skyrmions, i.e., rotation and breathing modes, several spin precession modes were identified, which would be specific to optical excitation. The ultrafast, nonthermal, and local excitation of the spin systems by photons would lead to the efficient manipulation of nano-magnetic structures.

Real-space anisotropic dielectric response in a multiferroic skyrmion lattice

A magnetic skyrmion lattice is a microstructure consisting of hexagonally aligned skyrmions. While a skyrmion as a topologically protected carrier of information promises a number of applications, an easily accessible probe of the skyrmion and skyrmion lattice at mesoscopic scale is of significance. It is known that neutron scattering, Lorentz transmission electron microscopy, and spin-resolved STM as effective probes of skyrmions have been established. In this work, we propose that the spatial contour of dielectric permittivity in a skyrmion lattice with ferromagnetic interaction and in-plane (xy) Dzyaloshinskii-Moriya (DM) interaction can be used to characterize the skyrmion lattice. The phase field and Monte Carlo simulations are employed to develop the one-to-one correspondence between the magnetic skyrmion lattice and dielectric dipole lattice, both exhibiting the hexagonal symmetry. Under excitation of in-plane electric field in the microwave range, the dielectric permittivity shows the dumbbell-like pattern with the axis perpendicular to the electric field, while it is circle-like for the electric field along the z-axis. The dependences of the spatial contour of dielectric permittivity on external magnetic field along the z-axis and dielectric frequency dispersion are discussed.

Flower-like dynamics of coupled Skyrmions with dual resonant modes by a single-frequency microwave magnetic field

Resonant excitations of confined systems have aroused much attention because of their potential application in future microwave devices and spintronics. Under resonant excitations, the motion of topo-logical objects exhibits circular, elliptical or even stadium-like dynamics. However, more complex non-linear resonant excitations of topological objects in confined systems have seldom been reported and the associated physical mechanism remains unclear. Here, we present an observation of flower-like resonant excitations for coupled skyrmions in Co/Ru/Co nanodisks activated by a single-frequency microwave magnetic field by means of numerical simulation. We find that flower-like dynamics of coupled skyrmions is always accompanied by an excitation of an eigenfrequency near 1.15 GHz, which is strongly associated with the large non-local deformation of the topological density distribution of coupled skyrmions. These results distinguish a skyrmion from other topological objects in dynamics and will be instrumental to the manipulation of skyrmions for applications.

Multiferroics of spin origin

Multiferroics, compounds with both magnetic and ferroelectric orders, are believed to be a key material system to achieve cross-control between magnetism and electricity in a solid with minute energy dissipation. Such a colossal magnetoelectric (ME) effect has been an issue of keen interest for a long time in condensed matter physics as well as a most desired function in the emerging spin-related electronics. Here we begin with the basic mechanisms to realize multiferroicity or spin-driven ferroelectricity in magnetic materials, which have recently been clarified and proved both theoretically and experimentally. According to the proposed mechanisms, many families of multiferroics have been explored, found (re-discovered), and newly developed, realizing a variety of colossal ME controls. We overview versatile multiferroics from the viewpoints of their multiferroicity mechanisms and their fundamental ME characteristics on the basis of the recent advances in exploratory materials. One of the new directions in multiferroic science is the dynamical ME effect, namely the dynamical and/or fast cross-control between electric and magnetic dipoles in a solid. We argue here that the dynamics of multiferroic domain walls significantly contributes to the amplification of ME response, which has been revealed through the dielectric spectroscopy. Another related issue is the electric-dipole-active magnetic resonance, called electromagnons. The electromagnons can provide a new stage of ME optics via resonant coupling with the external electromagnetic wave (light). Finally, we give concluding remarks on multiferroics physics in the light of a broader perspective from the emergent electromagnetism in a solid as well as from the possible application toward future dissipationless electronics.

Dual-frequency microwave-driven resonant excitations of skyrmions in nanoscale magnets

The polygon-like resonant excitation of coupled skyrmions can be controlled in nanoscale magnets by a dual-frequency microwave field.

Topological properties and dynamics of magnetic skyrmions

Magnetic skyrmions are particle-like nanometre-sized spin textures of topological origin found in several magnetic materials, and are characterized by a long lifetime. Skyrmions have been observed both by means of neutron scattering in momentum space and microscopy techniques in real space, and their properties include novel Hall effects, current-driven motion with ultralow current density and multiferroic behaviour. These properties can be understood from a unified viewpoint, namely the emergent electromagnetism associated with the non-coplanar spin structure of skyrmions. From this description, potential applications of skyrmions as information carriers in magnetic information storage and processing devices are envisaged.