Electric field control of the skyrmion lattice in Cu2OSeO3

Demonstration of Controlled Skyrmion Injection Across a Thickness Step

Spintronic devices incorporating magnetic skyrmions have attracted significant interest recently. Such devices traditionally focus on controlling magnetic textures in 2D thin films. However, enhanced performance of spintronic properties through the exploitation of higher dimensionalities motivates the investigation of variable-thickness skyrmion devices. We report the demonstration of a skyrmion injection mechanism that utilizes charge currents to drive skyrmions across a thickness step and, consequently, a metastability barrier. Our measurements show that under certain temperature and field conditions skyrmions can be reversibly injected from a thin region of an FeGe lamella, where they exist as an equilibrium state, into a thicker region, where they can only persist as a metastable state. This injection is achieved with a current density of 3 × 108 A m-2, nearly 3 orders of magnitude lower than required to move magnetic domain walls. This highlights the possibility to use such an element as a skyrmion source/drain within future spintronic devices.

The influence of antiferromagnetic spin cantings on the magnetic helix pitch in cubic helimagnets

In cubic helimagnets MnSi and Cu2OSeO3with their nearly isotropic magnetic properties, the magnetic structure undergoes helical deformation, which is almost completely determined by the helicoid wavenumberk=D/J, where magnetization field stiffnessJis associated with isotropic spin exchange, andDis a pseudoscalar value characterizing the antisymmetric Dzyaloshinskii-Moriya (DM) interaction. Another magnetic feature of these crystals, also caused by the DM interactions, are antiferromagnetic spin cantings, similar to the ferromagnetic cantings responsible for the phenomenon of weak ferromagnetism. Here we show that cantings can strongly influence the helical order through the value of the parameterD. Changing the cantings in a strong magnetic field is predicted to affect the magnon spectrum of the crystals.

Hysteretic Responses of Skyrmion Lattices to Electric Fields in Magnetoelectric Cu2OSeO3

Electric field control of topologically nontrivial magnetic textures, such as skyrmions, provides a paradigm shift for future spintronics beyond the current silicon-based technology. While significant progress has been made by X-ray and neutron scattering studies, direct observation of such nanoscale spin structures and their dynamics driven by external electric fields remains a challenge in understanding the underlying mechanisms and harness functionalities. Here, using Lorentz transmission electron microscopy combined with in situ electric and magnetic fields at liquid helium temperatures, we report the crystallographic orientation-dependent skyrmion responses to electric fields in thin slabs of magnetoelectric Cu2OSeO3. We show that electric fields not only stabilize the hexagonally packed skyrmion lattices in the entire sample in a hysteretic manner but also induce the rotation of their reciprocal vector discretely by 30°. The nonvolatile and energy-efficient skyrmion lattice control by electric fields demonstrated in this work provides an important foundation for designing skyrmion-based qubits and memory devices.

Chiral surface spin textures in Cu2OSeO3 unveiled by soft X-ray scattering in specular reflection geometry

Resonant elastic soft X-ray magnetic scattering (XRMS) is a powerful tool to explore long-periodic spin textures in single crystals. However, due to the limited momentum transfer range imposed by long wavelengths of photons in the soft x-ray region, Bragg diffraction is restricted to crystals with the large lattice parameters. Alternatively, small-angle X-ray scattering has been involved in the soft energy X-ray range which, however, brings in difficulties with the sample preparation that involves focused ion beam milling to thin down the crystal to below a few hundred nm thickness. We show how to circumvent these restrictions using XRMS in specular reflection from a sub-nanometer smooth crystal surface. The method allows observing diffraction peaks from the helical and conical spin modulations at the surface of a Cu   2 OSeO   3 single crystal and probing their corresponding chirality as contributions to the dichroic scattered intensity. The results suggest a promising way to carry out XRMS studies on a plethora of noncentrosymmetric systems hitherto unexplored with soft X-rays due to the absence of the commensurate Bragg peaks in the available momentum transfer range.

Origin of metamagnetism in skyrmion host Cu[Formula: see text]OSeO[Formula: see text]

Skyrmion host chiral Cu[Formula: see text]OSeO[Formula: see text] has attracted researchers due to several intriguing properties. Observation of metamagnetism in low-temperature and low-field makes the magnetic properties of Cu[Formula: see text]OSeO[Formula: see text] more complex. Here, we present an investigation on metamagnetism in Cu[Formula: see text]OSeO[Formula: see text] by analyzing its structural and magnetic properties. Study of magnetic properties reveal spin-flip of one of the Cu[Formula: see text] ions, embedded in square pyramidal CuO[Formula: see text] polyhedra, due to the development of strain in low-temperature and low-field regime. The spin-flip is found to be the main reason for field-induced first-order metamagnetic transition. Magnetic phase diagram of Cu[Formula: see text]OSeO[Formula: see text] has been constructed with the help of magnetization analyses. It is argued that the metamagnetic hysteretic field region may be low-temperature skyrmion phase with additional spiral and tilted-conical phases. A tricritical point has been observed in the phase diagram at which first-order metamagnetic hysteretic field range ceases to exist.

Different Critical Exponents on Two Sides of a Transition: Observation of Crossover from Ising to Heisenberg Exchange in Skyrmion Host Cu_{2}OSeO_{3}

We present experimental investigation on critical phenomena in Cu_{2}OSeO_{3} by analyzing the critical behavior of magnetization using a new method. This is necessary as a crossover from 3D Ising to 3D Heisenberg has been observed in Cu_{2}OSeO_{3}. The proposed method is applicable to explore the physics for a wide range of materials showing trivial or nontrivial critical behavior on two sides of the transition. A magnetic phase diagram has been constructed from the critical analysis. Multiple critical points due to multiple phases and transition between them have been observed in the phase diagram of Cu_{2}OSeO_{3}.

Real-space observations of 60-nm skyrmion dynamics in an insulating magnet under low heat flow

Thermal-current induced electron and spin dynamics in solids –dubbed “caloritronics”– have generated widespread interest in both fundamental physics and spintronics applications. Here, we examine the dynamics of nanometric topological spin textures, skyrmions driven by a temperature gradient ∇T or heat flow, that are evaluated through in-situ real-space observations in an insulating helimagnet Cu₂OSeO₃. We observe increases of the skyrmion velocity and the Hall angle with increasing ∇T above a critical value of ~ 13 mK/mm, which is two orders of magnitude lower than the ∇T required to drive ferromagnetic domain walls. A comparable magnitude of ∇T is also observed to move the domain walls between a skyrmion domain and the non-topological conical-spin domain from cold to hot regions. Our results demonstrate the efficient manipulation of skyrmions by temperature gradients, a promising step towards energy-efficient “green” spintronics.

Skyrmions are a type of topological spin texture that great potential across a wide variety of technological applications. Here, Yu et al. study the thermally driven motion of Skyrmions and find a minimum temperature gradient for the motion of skyrmions two orders of magnitude smaller than for domain walls.

Characterization of a Disordered above Room Temperature Skyrmion Material Co8Zn8Mn4

Topologically nontrivial spin textures host great promise for future spintronic applications. Skyrmions in particular are of burgeoning interest owing to their nanometric size, topological protection, and high mobility via ultra-low current densities. It has been previously reported through magnetic susceptibility, microscopy, and scattering techniques that Co8Zn8Mn4 forms an above room temperature triangular skyrmion lattice. Here, we report the synthesis procedure and characterization of a polycrystalline Co8Zn8Mn4 disordered bulk sample. We employ powder X-ray diffraction and backscatter Laue diffraction as characterization tools of the crystallinity of the samples, while magnetic susceptibility and Small Angle Neutron Scattering (SANS) measurements are performed to study the skyrmion phase. Magnetic susceptibility measurements show a dip anomaly in the magnetization curves, which persists over a range of approximately 305 K-315 K. SANS measurements reveal a rotationally disordered polydomain skyrmion lattice. Applying a symmetry-breaking magnetic field sequence, we were able to orient and order the previously jammed state to yield the prototypical hexagonal diffraction patterns with secondary diffraction rings. This emergence of the skyrmion order serves as a unique demonstration of the fundamental interplay of structural disorder and anisotropy in stabilizing the thermal equilibrium phase.

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.

Effect of chemical substitution on the skyrmion phase in Cu2OSeO3

Magnetic skyrmions have been the focus of intense research due to their unique qualities which result from their topological protections. Previous work on Cu2OSeO3, the only known insulating multiferroic skyrmion material, has shown that chemical substitution alters the skyrmion phase. We chemically substitute Zn, Ag, and S into powdered Cu2OSeO3 to study the effect on the magnetic phase diagram. In both the Ag and the S substitutions, we find that the skyrmion phase is stabilized over a larger temperature range, as determined via magnetometry and small-angle neutron scattering (SANS). Meanwhile, while previous magnetometry characterization suggests two high temperature skyrmion phases in the Zn-substituted sample, SANS reveals the high temperature phase to be skyrmionic while we are unable to distinguish the other from helical order. Overall, chemical substitution weakens helical and skyrmion order as inferred from neutron scattering of the q ≈ 0.01 Å - 1 magnetic peak.

MnSnTeO6: A Chiral Antiferromagnet Prepared by a Two-Step Topotactic Transformation

MnSnTeO₆, a new chiral antiferromagnet, was prepared both by topotactic transformation of the metastable rosiaite-type polymorph and by direct synthesis from coprecipitated hydroxides. Its structure and its static and dynamic magnetic properties were studied comprehensively both experimentally (through X-ray and neutron powder diffraction, magnetization, specific heat, dielectric permittivity, and ESR techniques) and theoretically (by means of ab initio density functional theory (DFT) calculations within the spin-polarized generalized gradient approximation). MnSnTeO₆ is isostructural with MnSb₂O₆ (space group P321) and does not show any structural transition between 3 and 300 K. The magnetic susceptibility and specific heat exhibit an antiferromagnetic ordering at T_N ≈ 9.8 K, which is confirmed by low-temperature neutron data. At the same time, the thermodynamic parameters demonstrate an additional anomaly on the temperature dependences of magnetic susceptibility χ(T), specific heat C_p(T) and dielectric permittivity ε(T) at T* ≈ 4.9 K, which is characterized by significant temperature hysteresis. Clear enhancement of the dielectric permittivity at T* is most likely to reflect the coupling of dielectric and magnetic subsystems leading to development of electric polarization. It was established that the ground state of MnSnTeO₆ is stabilized by seven exchange parameters, and neutron diffraction revealed incommensurate magnetic structure with propagation vector k = (0, 0, 0.183) analogous to that of MnSb₂O₆. Ab initio DFT calculations demonstrate that the strongest exchange coupling occurs between planes along diagonals. All exchange parameters are antiferromagnetic and reveal moderate frustration.

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.

Functional Ferroic Domain Walls for Nanoelectronics

A prominent challenge towards novel nanoelectronic technologies is to understand and control materials functionalities down to the smallest scale. Topological defects in ordered solid-state (multi-)ferroic materials, e.g., domain walls, are a promising gateway towards alternative sustainable technologies. In this article, we review advances in the field of domain walls in ferroic materials with a focus on ferroelectric and multiferroic systems and recent developments in prototype nanoelectronic devices.

Direct electric field control of the skyrmion phase in a magnetoelectric insulator

Magnetic skyrmions are topologically protected spin-whirls currently considered as promising for use in ultra-dense memory devices. Towards achieving this goal, exploration of the skyrmion phase response and under external stimuli is urgently required. Here we show experimentally, and explain theoretically, that in the magnetoelectric insulator Cu2OSeO3 the skyrmion phase can expand and shrink significantly depending on the polarity of a moderate applied electric field (few V/μm). The theory we develop incorporates fluctuations around the mean-field that clarifies precisely how the electric field provides direct control over the free energy difference between the skyrmion and the surrounding conical phase. The quantitative agreement between theory and experiment provides a solid foundation for the development of skyrmionic applications based on magnetoelectric coupling.

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.

Laser-Induced Skyrmion Writing and Erasing in an Ultrafast Cryo-Lorentz Transmission Electron Microscope

We demonstrate that light-induced heat pulses of different duration and energy can write Skyrmions in a broad range of temperatures and magnetic field in FeGe. Using a combination of camera-rate and pump-probe cryo-Lorentz transmission electron microscopy, we directly resolve the spatiotemporal evolution of the magnetization ensuing optical excitation. The Skyrmion lattice was found to maintain its structural properties during the laser-induced demagnetization, and its recovery to the initial state happened in the sub-μs to μs range, depending on the cooling rate of the system.

Magnetic Skyrmions and Skyrmion Clusters in the Helical Phase of Cu_{2}OSeO_{3}

Skyrmions are nanometric spin whirls that can be stabilized in magnets lacking inversion symmetry. The properties of isolated Skyrmions embedded in a ferromagnetic background have been intensively studied. We show that single Skyrmions and clusters of Skyrmions can also form in the helical phase and investigate theoretically their energetics and dynamics. The helical background provides natural one-dimensional channels along which a Skyrmion can move rapidly. In contrast to Skyrmions in ferromagnets, the Skyrmion-Skyrmion interaction has a strong attractive component and thus Skyrmions tend to form clusters with characteristic shapes. These clusters are directly observed in transmission electron microscopy measurements in thin films of Cu_{2}OSeO_{3}. Topological quantization, high mobility, and the confinement of Skyrmions in channels provided by the helical background may be useful for future spintronics devices.

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.

Antiferromagnetic spin cantings as a driving force of ferroelectricity in multiferroic Cu2OSeO3

Ferroelectric properties of cubic chiral magnet Cu₂OSeO₃ can emerge due to the spin noncollinearity induced by antiferromagnetic cantings. The cantings are the result of the Dzyaloshinskii-Moriya interaction and in many ways similar to the ferromagnetic cantings in weak ferromagnets. An expression for the local electric polarization is derived, including terms with gradients of magnetization [Formula: see text]. When averaged over the crystal the electric polarization has a non-vanishing part associated with the anisotropy of the crystal point group 23. In the framework of the microscopic theory, it is shown that both scalar and vector products of spins, [Formula: see text] and [Formula: see text], can give contributions of the same order of magnitude into the electric polarization.

Heuristic Description of Magnetoelectricity of Cu2OSeO3

CuO2SeO3 is an insulating material that hosts topologically nontrivial spin whirls, so-called skyrmions, and exhibits magnetoelectric coupling allowing to manipulate these skyrmions by means of electric fields. We report magnetic force microscopy imaging of the real-space spin structure on the surface of a bulk single crystal of CuO2SeO3. Based on measurements of the electric polarization using Kelvin-probe force microscopy, we develop a heuristic description of the magnetoelectric properties in CuO2SeO3. The model successfully describes the dependency of the electric polarization on the magnetization in all magnetically modulated phases.

Multidomain Skyrmion Lattice State in Cu2OSeO3

Magnetic skyrmions in chiral magnets are nanoscale, topologically protected magnetization swirls that are promising candidates for spintronics memory carriers. Therefore, observing and manipulating the skyrmion state on the surface level of the materials are of great importance for future applications. Here, we report a controlled way of creating a multidomain skyrmion state near the surface of a Cu2OSeO3 single crystal, observed by soft resonant elastic X-ray scattering. This technique is an ideal tool to probe the magnetic order at the L3 edge of 3d metal compounds giving an average depth sensitivity of ∼50 nm. The single-domain 6-fold-symmetric skyrmion lattice can be broken up into domains, overcoming the propagation directions imposed by the cubic anisotropy by applying the magnetic field in directions deviating from the major cubic axes. Our findings open the door to a new way to manipulate and engineer the skyrmion state locally on the surface or on the level of individual skyrmions, which will enable applications in the future.

Magnon spectrum of the helimagnetic insulator Cu2OSeO3

Complex low-temperature-ordered states in chiral magnets are typically governed by a competition between multiple magnetic interactions. The chiral-lattice multiferroic Cu2OSeO3 became the first insulating helimagnetic material in which a long-range order of topologically stable spin vortices known as skyrmions was established. Here we employ state-of-the-art inelastic neutron scattering to comprehend the full three-dimensional spin-excitation spectrum of Cu2OSeO3 over a broad range of energies. Distinct types of high- and low-energy dispersive magnon modes separated by an extensive energy gap are observed in excellent agreement with the previously suggested microscopic theory based on a model of entangled Cu4 tetrahedra. The comparison of our neutron spectroscopy data with model spin-dynamical calculations based on these theoretical proposals enables an accurate quantitative verification of the fundamental magnetic interactions in Cu2OSeO3 that are essential for understanding its abundant low-temperature magnetically ordered phases.

Dramatic pressure-driven enhancement of bulk skyrmion stability

The recent discovery of magnetic skyrmion lattices initiated a surge of interest in the scientific community. Several novel phenomena have been shown to emerge from the interaction of conducting electrons with the skyrmion lattice, such as a topological Hall-effect and a spin-transfer torque at ultra-low current densities. In the insulating compound Cu2OSeO3, magneto-electric coupling enables control of the skyrmion lattice via electric fields, promising a dissipation-less route towards novel spintronic devices. One of the outstanding fundamental issues is related to the thermodynamic stability of the skyrmion lattice. To date, the skyrmion lattice in bulk materials has been found only in a narrow temperature region just below the order-disorder transition. If this narrow stability is unavoidable, it would severely limit applications. Here we present the discovery that applying just moderate pressure on Cu2OSeO3 substantially increases the absolute size of the skyrmion pocket. This insight demonstrates directly that tuning the electronic structure can lead to a significant enhancement of the skyrmion lattice stability. We interpret the discovery by extending the previously employed Ginzburg-Landau approach and conclude that change in the anisotropy is the main driver for control of the size of the skyrmion pocket.

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.

Multiferroicity and skyrmions carrying electric polarization in GaV4S8

Skyrmions are whirl-like topological spin objects with high potential for future magnetic data storage. A fundamental question that is relevant to both basic research and application is whether ferroelectric (FE) polarization can be associated with skyrmions' magnetic texture and whether these objects can be manipulated by electric fields. We study the interplay between magnetism and electric polarization in the lacunar spinel GaV4S8, which undergoes a structural transition associated with orbital ordering at 44 K and reveals a complex magnetic phase diagram below 13 K, including ferromagnetic, cycloidal, and Néel-type skyrmion lattice (SkL) phases. We found that the orbitally ordered phase of GaV4S8 is FE with a sizable polarization of ~1 μC/cm(2). Moreover, we observed spin-driven excess polarizations in all magnetic phases; hence, GaV4S8 hosts three different multiferroic phases with coexisting polar and magnetic order. These include the SkL phase, where we predict a strong spatial modulation of FE polarization close to the skyrmion cores. By taking into account the crystal symmetry and spin patterns of the magnetically ordered phases, we identify exchange striction as the main microscopic mechanism behind the spin-driven FE polarization in each multiferroic phase. Because GaV4S8 is unique among known SkL host materials owing to its polar crystal structure and the observed strong magnetoelectric effect, this study is an important step toward the nondissipative electric field control of skyrmions.

Magnetoelectric effects in the skyrmion host material Cu2OSeO3

Insulating helimagnetic Cu₂OSeO₃ shows sizeable magnetoelectric effects in its skyrmion phase. Using magnetization measurements, magneto-current analysis and dielectric spectroscopy, we provide a thorough investigation of magnetoelectric coupling, polarization and dielectric constants of the ordered magnetic and polar phases of single-crystalline Cu₂OSeO₃ in external magnetic fields up to 150 mT and at temperatures below 60 K. From these measurements we construct a detailed phase diagram. Especially, the skyrmion phase and the metamagnetic transition of helical to conical spin order are characterized in detail. Finally we address the question if there is any signature of polar order that can be switched by an external electric field, which would imply multiferroic behaviour of Cu₂OSeO₃.

Large anisotropic deformation of skyrmions in strained crystal

Mechanical control of magnetism is an important and promising approach in spintronics. To date, strain control has mostly been demonstrated in ferromagnetic structures by exploiting a change in magnetocrystalline anisotropy. It would be desirable to achieve large strain effects on magnetic nanostructures. Here, using in situ Lorentz transmission electron microscopy, we demonstrate that anisotropic strain as small as 0.3% in a chiral magnet of FeGe induces very large deformations in magnetic skyrmions, as well as distortions of the skyrmion crystal lattice on the order of 20%. Skyrmions are stabilized by the Dzyaloshinskii-Moriya interaction, originating from a chiral crystal structure. Our results show that the change in the modulation of the strength of this interaction is amplified by two orders of magnitude with respect to changes in the crystal lattice due to an applied strain. Our findings may provide a mechanism to achieve strain control of topological magnetic structures based on the Dzyaloshinskii-Moriya interaction.

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.

Establishing the fundamental magnetic interactions in the chiral Skyrmionic Mott insulator Cu(2)OSeO(3) by terahertz electron spin resonance

The recent discovery of Skyrmions in Cu(2)OSeO(3) has established a new platform to create and manipulate Skyrmionic spin textures. We use high-field electron spin resonance with a terahertz free-electron laser and pulsed magnetic fields up to 64 T to probe and quantify its microscopic spin-spin interactions. In addition to the previously observed long-wavelength Goldstone mode, this technique probes also the high-energy part of the excitation spectrum which is inaccessible by standard low-frequency electron spin resonance. Fitting the behavior of the observed modes in magnetic field to a theoretical framework establishes experimentally that the fundamental magnetic building blocks of this Skyrmionic magnet are rigid, highly entangled and weakly coupled tetrahedra.

Electric-field-induced Skyrmion distortion and giant lattice rotation in the magnetoelectric insulator Cu2OSeO3

Uniquely in Cu2OSeO3, the Skyrmions, which are topologically protected magnetic spin vortexlike objects, display a magnetoelectric coupling and can be manipulated by externally applied electric (E) fields. Here, we explore the E-field coupling to the magnetoelectric Skyrmion lattice phase, and study the response using neutron scattering. Giant E-field induced rotations of the Skyrmion lattice are achieved that span a range of ∼25°. Supporting calculations show that an E-field-induced Skyrmion distortion lies behind the lattice rotation. Overall, we present a new approach to Skyrmion control that makes no use of spin-transfer torques due to currents of either electrons or magnons.

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.

ac current generation in chiral magnetic insulators and Skyrmion motion induced by the spin Seebeck effect

We show that a temperature gradient induces an ac electric current in multiferroic insulators when the sample is embedded in a circuit. We also show that a thermal gradient can be used to move magnetic Skyrmions in insulating chiral magnets: the induced magnon flow from the hot to the cold region drives the Skyrmions in the opposite direction via a magnonic spin transfer torque. Both results are combined to compute the effect of Skyrmion motion on the ac current generation and demonstrate that Skyrmions in insulators are a promising route for spin caloritronics applications.

Coupled Skyrmion sublattices in Cu(2)OSeO(3)

We report the observation of a Skyrmion lattice in the chiral multiferroic insulator Cu2OSeO3 using Cu L3-edge resonant soft x-ray diffraction. We observe the unexpected existence of two distinct Skyrmion sublattices that arise from inequivalent Cu sites with chemically identical coordination numbers but different magnetically active orbitals. The Skyrmion sublattices are rotated with respect to each other, implying a long wavelength modulation of the lattice. The modulation vector is controlled with an applied magnetic field, associating this moirélike phase with a continuous phase transition. Our findings will open up a new class of science involving manipulation of quantum topological states.

Review and prospects of magnonic crystals and devices with reprogrammable band structure

Research efforts addressing spin waves (magnons) in microand nanostructured ferromagnetic materials have increased tremendously in recent years. Corresponding experimental and theoretical work in magnonics faces significant challenges in that spinwave dispersion relations are highly anisotropic and different magnetic states might be realized via, for example, the magnetic field history. At the same time, these features offer novel opportunities for wave control in solids going beyond photonics and plasmonics. In this topical review we address materials with a periodic modulation of magnetic parameters that give rise to artificially tailored band structures and allow unprecedented control of spin waves. In particular, we discuss recent achievements and perspectives of reconfigurable magnonic devices for which band structures can be reprogrammed during operation. Such characteristics might be useful for multifunctional microwave and logic devices operating over a broad frequency regime on either the macroor nanoscale.

Note: versatile sample stick for neutron scattering experiments in high electric fields

We present a versatile high voltage sample stick that fits into all cryomagnets and standard cryostats at the Swiss Spallation Neutron Source, Paul Scherrer Institut, and which provides a low effort route to neutron scattering experiments that combine electric field with low temperature and magnetic field. The stick allows for voltages up to 5 kV and can be easily adapted for different scattering geometries. We discuss the design consideration and thermal behavior of the stick, and give one example to showcase the abilities of the device.

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.