Multidomain Skyrmion Lattice State in Cu2OSeO3

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.

Axially Bound Magnetic Skyrmions: Glueing Topological Strings Across an Interface

A major challenge in topological magnetism lies in the three-dimensional (3D) exploration of their magnetic textures. A recent focus has been the question of how 2D skyrmion sheets vertically stack to form distinct types of 3D topological strings. Being able to manipulate the vertical coupling should therefore provide a route to the engineering of topological states. Here, we present a new type of axially bound magnetic skyrmion string state in which the strings in two distinct materials are glued together across their interface. With quasi-tomographic resonant elastic X-ray scattering, the 3D skyrmion profiles before and after their binding across the interface were unambiguously determined and compared. Their attractive binding is accompanied by repulsive twisting; i.e., the coupled skyrmions mutually affect each other via a compensating twisting. This state exists in chiral magnet-magnetic thin film heterostructures, providing a new arena for the engineering of 3D topological phases.

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.

Superposition of Emergent Monopole and Antimonopole in CoTb Thin Films

A three-dimensional singular point that consists of two oppositely aligned emergent monopoles is identified in continuous CoTb thin films, as confirmed by complementary techniques of resonant elastic x-ray scattering, Lorentz transmission electron microscopy, and scanning transmission x-ray microscopy. This new type of topological defect can be regarded as a superposition of an emergent magnetic monopole and an antimonopole, around which the source and drain of the magnetic flux overlap in space. We experimentally prove that the observed spin twist seen in Lorentz transmission electron microscopy reveals the cross section of the superimposed three-dimensional structure, providing a straightforward strategy for the observation of magnetic singularities. Such a quasiparticle provides an excellent platform for studying the rich physics of emergent electromagnetism.

Magnetic Topological Insulator Heterostructures: A Review

Topological insulators (TIs) provide intriguing prospects for the future of spintronics due to their large spin-orbit coupling and dissipationless, counter-propagating conduction channels in the surface state. The combination of topological properties and magnetic order can lead to new quantum states including the quantum anomalous Hall effect that was first experimentally realized in Cr-doped (Bi,Sb)₂ Te₃ films. Since magnetic doping can introduce detrimental effects, requiring very low operational temperatures, alternative approaches are explored. Proximity coupling to magnetically ordered systems is an obvious option, with the prospect to raise the temperature for observing the various quantum effects. Here, an overview of proximity coupling and interfacial effects in TI heterostructures is presented, which provides a versatile materials platform for tuning the magnetic and topological properties of these exciting materials. An introduction is first given to the heterostructure growth by molecular beam epitaxy and suitable structural, electronic, and magnetic characterization techniques. Going beyond transition-metal-doped and undoped TI heterostructures, examples of heterostructures are discussed, including rare-earth-doped TIs, magnetic insulators, and antiferromagnets, which lead to exotic phenomena such as skyrmions and exchange bias. Finally, an outlook on novel heterostructures such as intrinsic magnetic TIs and systems including 2D materials is given.

Creation of a Chiral Bobber Lattice in Helimagnet-Multilayer Heterostructures

A chiral bobber is a localized three-dimensional magnetization configuration, terminated by a singularity. Chiral bobbers coexist with magnetic skyrmions in chiral magnets, lending themselves to new types of skyrmion-complementary bits of information. However, the on-demand creation of bobbers, as well as their direct observation remained elusive. Here, we introduce a new mechanism for creating a stable chiral bobber lattice state via the proximity of two skyrmion species with comparable size. This effect is experimentally demonstrated in a Cu_{2}OSeO_{3}/[Ta/CoFeB/MgO]_{4} heterostructure in which an exotic bobber lattice state emerges in the phase diagram of Cu_{2}OSeO_{3}. To unambiguously reveal the existence of the chiral bobber lattice state, we have developed a novel characterization technique, magnetic truncation rod analysis, which is based on resonant elastic x-ray scattering.

Particle-size dependent structural transformation of skyrmion lattice

Magnetic skyrmion is a topologically protected particle-like object in magnetic materials, appearing as a nanometric swirling spin texture. The size and shape of skyrmion particles can be flexibly controlled by external stimuli, which suggests unique features of their crystallization and lattice transformation process. Here, we investigated the detailed mechanism of structural transition of skyrmion lattice (SkL) in a prototype chiral cubic magnet Cu₂OSeO₃, by combining resonant soft X-ray scattering (RSXS) experiment and micromagnetic simulation. This compound is found to undergo a triangular-to-square lattice transformation of metastable skyrmions by sweeping magnetic field (B). Our simulation suggests that the symmetry change of metastable SkL is mainly triggered by the B-induced modification of skyrmion core diameter and associated energy cost at the skyrmion-skyrmion interface region. Such internal deformation of skyrmion particle has further been confirmed by probing the higher harmonics in the RSXS pattern. These results demonstrate that the size/shape degree of freedom of skyrmion particle is an important factor to determine their stable lattice form, revealing the exotic manner of phase transition process for topological soliton ensembles in the non-equilibrium condition.

Skyrmions are topological spin textures and are of great interest due to their impressive stability. Here, by sweeping an applied magnetic field, the authors observe a change in the skyrmion lattice structure, shedding light on the relation between skyrmion size and stability.

Room-temperature skyrmion phase in bulk Cu2OSeO3 under high pressures

A skyrmion state in a noncentrosymmetric helimagnet displays topologically protected spin textures with profound technological implications for high-density information storage, ultrafast spintronics, and effective microwave devices. Usually, its equilibrium state in a bulk helimagnet occurs only over a very restricted magnetic field-temperature phase space and often in the low-temperature region near the magnetic transition temperature T_c We have expanded and enhanced the skyrmion phase region from the small range of 55 to 58.5 K to 5 to 300 K in single-crystalline Cu₂OSeO₃ by pressures up to 42.1 GPa through a series of phase transitions from the cubic P2₁3, through orthorhombic P2₁2₁2₁ and monoclinic P2₁, and finally to the triclinic P1 phase, using our newly developed ultrasensitive high-pressure magnetization technique. The results are in agreement with our Ginzburg-Landau free energy analyses, showing that pressures tend to stabilize the skyrmion states and at higher temperatures. The observations also indicate that the skyrmion state can be achieved at higher temperatures in various crystal symmetries, suggesting the insensitivity of skyrmions to the underlying crystal lattices and thus the possible more ubiquitous presence of skyrmions in helimagnets.

Robust Perpendicular Skyrmions and Their Surface Confinement

Magnetic skyrmions are two-dimensional magnetization swirls that stack in the form of tubes in the third dimension and which are proposed as prospective information carriers for nonvolatile memory devices due to their unique topological properties. From resonant elastic X-ray scattering measurements on Cu₂OSeO₃ with an in-plane magnetic field, we find that a state of perpendicularly ordered skyrmions forms, in stark contrast to the well-studied bulk state. The surface state is stable over a wide temperature range, unlike the bulk state in out-of-plane fields which is confined to a narrow region of the temperature-field phase diagram. In contrast to ordinary skyrmions found in the bulk, the surface state skyrmions result from the presence of magnetic interactions unique to the surface which stabilize them against external perturbations. The surface guiding makes the robust state particular interesting for racetracklike devices, ultimately allowing for much higher storage densities due to the smaller lateral footprint of the perpendicular skyrmions.

Chiral asymmetry detected in a 2D array of permalloy square nanomagnets using circularly polarized x-ray resonant magnetic scattering

The sensitivity of circularly polarized x-ray resonant magnetic scattering (CXRMS) to chiral asymmetry has been demonstrated. The study was performed on a 2D array of Permalloy (Py) square nanomagnets of 700 nm lateral size arranged in a chess pattern, in a square lattice of 1000 nm lattice parameter. Previous x-ray magnetic circular dichroism photoemission electron microscopy (XMCD-PEEM) images on this sample showed the formation of vortices at remanence and a preference in their chiral state. The magnetic hysteresis loops of the array along the diagonal axis of the squares indicate a non-negligible and anisotropic interaction between vortices. The intensity of the magnetic scattering using circularly polarized light along one of the diagonal axes of the square magnets becomes asymmetric in intensity in the direction transversal to the incident plane at fields where the vortex states are formed. The asymmetry sign is inverted when the direction of the applied magnetic field is inverted. The result is the expected in the presence of an unbalanced chiral distribution. The effect is observed by CXRMS due to the interference between the charge scattering and the magnetic scattering.

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.

Response of the Skyrmion Lattice in MnSi to Cubic Magnetocrystalline Anisotropies

We report high-precision small-angle neutron scattering of the orientation of the Skyrmion lattice in a spherical sample of MnSi under systematic changes of the magnetic field direction. For all field directions the Skyrmion lattice may be accurately described as a triple-Q[over →] state, where the modulus |Q[over →]| is constant and the wave vectors enclose rigid angles of 120°. Along a great circle across ⟨100⟩, ⟨110⟩, and ⟨111⟩ the normal to the Skyrmion-lattice plane varies systematically by ±3° with respect to the field direction, while the in-plane alignment displays a reorientation by 15° for magnetic field along ⟨100⟩. Our observations are qualitatively and quantitatively in excellent agreement with an effective potential, which is determined by the symmetries of the tetrahedral point group T and includes contributions up to sixth order in spin-orbit coupling, providing a full account of the effect of cubic magnetocrystalline anisotropies on the Skyrmion lattice in MnSi.

Stabilization and Reversal of Skyrmion Lattice in Ta/CoFeB/MgO Multilayers

Recently, magnetic skyrmion has attracted much attention due to its potential application in racetrack memory and other nanodevices. In bulk chiral magnets with non-centrosymmetric crystal structures, skyrmion lattice phase has been extensively observed. However, in film or multilayers with interfacial Dzyaloshinskii-Moriya interaction, individual skyrmion is often observed. Here, we report a short-ordered skyrmion lattice observed in [Ta(5.0 nm)/CoFeB(1.5 nm)/MgO(1.0 nm)]₁₅ multilayer in a remnant state. The structure, stabilization, and reversal of these skyrmions are discussed. Applying a slightly tilted in-plane magnetic field caused reversal of the skyrmion lattice. This reversal came from disappearance of skyrmions and nucleation of new skyrmions in the interstitial regions of the lattice. Also, we investigated how the skyrmion lattice depended on the CoFeB thickness. Our findings provide a pathway to stabilize and reverse the skyrmions in multilayers films.

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.

Direct Observation of Twisted Surface skyrmions in Bulk Crystals

Magnetic skyrmions in noncentrosymmetric helimagnets with D_{n} symmetry are Bloch-type magnetization swirls with a helicity angle of ±90°. At the surface of helimagnetic thin films below a critical thickness, a twisted skyrmion state with an arbitrary helicity angle has been proposed; however, its direct experimental observation has remained elusive. Here, we show that circularly polarized resonant elastic x-ray scattering is able to unambiguously measure the helicity angle of surface skyrmions, providing direct experimental evidence that a twisted skyrmion surface state also exists in bulk systems. The exact surface helicity angles of twisted skyrmions for both left- and right-handed chiral bulk Cu_{2}OSeO_{3}, in the single as well as in the multidomain skyrmion lattice state, are determined, revealing their detailed internal structure. Our findings suggest that a skyrmion surface reconstruction is a universal phenomenon, stemming from the breaking of translational symmetry at the interface.

Manipulation of skyrmion motion by magnetic field gradients

Magnetic skyrmions are particle-like, topologically protected magnetisation entities that are promising candidates as information carriers in racetrack memory. The transport of skyrmions in a shift-register-like fashion is crucial for their embodiment in practical devices. Here, we demonstrate that chiral skyrmions in Cu2OSeO3 can be effectively manipulated under the influence of a magnetic field gradient. In a radial field gradient, skyrmions were found to rotate collectively, following a given velocity-radius relationship. As a result of this relationship, and in competition with the elastic properties of the skyrmion lattice, the rotating ensemble disintegrates into a shell-like structure of discrete circular racetracks. Upon reversing the field direction, the rotation sense reverses. Field gradients therefore offer an effective handle for the fine control of skyrmion motion, which is inherently driven by magnon currents. In this scheme, no local electric currents are needed, thus presenting a different approach to shift-register-type operations based on spin transfer torque.

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.

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.

Dynamical Defects in Rotating Magnetic Skyrmion Lattices

The chiral magnet Cu_{2}OSeO_{3} hosts a Skyrmion lattice that may be equivalently described as a superposition of plane waves or a lattice of particlelike topological objects. A thermal gradient may break up the Skyrmion lattice and induce rotating domains, raising the question of which of these scenarios better describes the violent dynamics at the domain boundaries. Here, we show that in an inhomogeneous temperature gradient caused by illumination in a Lorentz transmission electron microscope different parts of the Skyrmion lattice can be set into motion with different angular velocities. Tracking the time dependence, we show that the constant rearrangement of domain walls is governed by dynamic 5-7 defects arranging into lines. An analysis of the associated defect density is described by Frank's equation and agrees well with classical 2D Monte Carlo simulations. Fluctuations of boundaries show a surgelike rearrangement of Skyrmion clusters driven by defect rearrangement consistent with simulations treating Skyrmions as point particles. Our findings underline the particle character of the Skyrmion.

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.

Direct experimental determination of the topological winding number of skyrmions in Cu2OSeO3

The mathematical concept of topology has brought about significant advantages that allow for a fundamental understanding of the underlying physics of a system. In magnetism, the topology of spin order manifests itself in the topological winding number which plays a pivotal role for the determination of the emergent properties of a system. However, the direct experimental determination of the topological winding number of a magnetically ordered system remains elusive. Here, we present a direct relationship between the topological winding number of the spin texture and the polarized resonant X-ray scattering process. This relationship provides a one-to-one correspondence between the measured scattering signal and the winding number. We demonstrate that the exact topological quantities of the skyrmion material Cu₂OSeO₃ can be directly experimentally determined this way. This technique has the potential to be applicable to a wide range of materials, allowing for a direct determination of their topological properties.

Experimental demonstrations of topologically nontrivial states in magnetic films currently rely on indirect comparisons of theoretical models with microscopic images. Here the authors show that resonant X-ray scattering provides direct information on the topology of magnetic textures.

Jointed magnetic skyrmion lattices at a small-angle grain boundary directly visualized by advanced electron microscopy

The interactions between magnetic skyrmions and structural defects, such as edges, dislocations, and grain boundaries (GBs), which are all considered as topological defects, will be important issues when magnetic skyrmions are utilized for future memory device applications. To investigate such interactions, simultaneous visualization of magnetic skyrmions and structural defects at high spatial resolution, which is not feasible by conventional techniques, is essential. Here, taking advantages of aberration-corrected differential phase-contrast scanning transmission electron microscopy, we investigate the interaction of magnetic skyrmions with a small-angle GB in a thin film of FeGe_1−xSi_x. We found that the magnetic skyrmions and the small-angle GB can coexist each other, but a domain boundary (DB) was formed in the skyrmion lattice along the small-angle GB. At the core of the DB, unexpectedly deformed magnetic skrymions, which appear to be created by joining two portions of magnetic skyrmions in the adjacent lattices, were formed to effectively compensate misorientations between the two adjacent magnetic skyrmion lattices. These observations strongly suggest the flexible nature of individual magnetic skyrmions, and also the significance of defect engineering for future device applications.

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.