Using the ab initio local force method, we investigate the formation mechanism of the helical spin structure in GdRu$_2$Si$_2$ and Gd$_2$PdSi$_3$. We calculate the paramagnetic spin susceptibility and find that the Fermi surface nesting is not the origin of the incommensurate modulation, in contrast to the naive scenario based on the Ruderman-Kittel-Kasuya-Yosida mechanism. We then decompose the exchange interactions between the Gd spins into each orbital component, and show that spin-density-wave type interaction between the Gd-5$d$ orbitals is ferromagnetic, but the interaction between the Gd-4$f$ orbitals is antiferromagnetic. We conclude that the competition of these two interactions, namely, the inter-orbital frustration, stabilizes the finite-Q structure.
We present long-wavelength neutron diffraction data measured on both single crystal and polycrystalline samples of the skyrmion host material Cu$_{2}$OSeO$_{3}$. We observe magnetic satellites around the $(0\bar{1}1)$ diffraction peak not accessible to other techniques, and distinguish helical from conical spin textures in reciprocal space. We confirm successive transitions from helical to conical to field polarised ordered spin textures as the external magnetic field is increased. The formation of a skyrmion lattice with propagation vectors perpendicular to the field direction is observed in …
We investigate the existence and stability of skyrmions in a frustrated chiral ferromagnet by considering the competition between ferromagnetic (FM) nearest-neighbour (NN) interaction ($J_1$) and antiferromagnetic (AFM) next-nearest-neighbour (NNN) interaction ($J_2$). Contrary to the general wisdom that long-range ferromagnetic order is not energy preferable under frustration, the skyrmion lattice not only exists but is even stable for a large field range when $J_2 \leq J_1$ compared with frustration-free systems. We defend that the enlargement of stability window of skyrmions is a consequenc…
Magnetic skyrmion textures are realized mainly in non-centrosymmetric, e.g. chiral or polar, magnets. Extending the field to centrosymmetric bulk materials is a rewarding challenge, where the released helicity / vorticity degree of freedom and higher skyrmion density result in intriguing new properties and enhanced functionality. We report here on the experimental observation of a skyrmion lattice (SkL) phase with large topological Hall effect and an incommensurate helical pitch as small as 2.8 nm in metallic Gd3Ru4Al12, which materializes a breathing kagomé lattice of Gadolinium moments. The …
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 charac…
The experimental realization of magnetic skyrmions in centrosymmetric materials has been driven by theoretical understanding of how a delicate balance of anisotropy and frustration can stabilize topological spin structures in applied magnetic fields. Recently, the centrosymmetric material Gd$_{2}$PdSi$_{3}$ was shown to host a field-induced skyrmion phase, but the skyrmion stabilization mechanism remains unclear. Here, we employ neutron-scattering measurements on an isotopically-enriched polycrystalline Gd$_{2}$PdSi$_{3}$ sample to quantify the interactions that drive skyrmion formation. Our a…
Magnetic skyrmions are nanoscale spin whirlpools that promise breakthroughs in future spintronic applications. Controlled generation of magnetic skyrmions by electric current is crucial for this purpose. While previous studies have demonstrated this operation, the topological charge of the generated skyrmions is determined by the direction of the external magnetic fields, thus is fixed. Here, we report the current-induced skyrmions creation in a chiral magnet FeGe nanostructure by using the \emph{in-situ} Lorentz transmission electron microscopy. We show that magnetic skyrmions or antiskyrmion…
Spin waves are the low-energy excitations of magnetically ordered materials. They are key elements in the stability analysis of the ordered phase and have a wealth of technological applications. Recently, we showed that spin waves of a magnetic nanowire may carry a definite amount of orbital angular momentum components along the propagation direction. This helical, in addition to the chiral, character of the spin waves is related to the spatial modulations of the spin wave phase across the wire. It, however, remains a challenge to generate and control such modes with conventional magnetic fiel…
By employing magnetization and small angle neutron scattering (SANS) measurements, we have investigated the behavior of the skyrmion lattice (SKL) and the helical order in MnSi0.992Ga0.008. Our results indicate that the order of the SKL is sensitive to the orientation of an applied magnetic field with respect to the crystal lattice and small variations in the sequence of temperature and applied magnetic field changes. The disorder caused by the substitution of the heavier element Ga for Si is sufficient to reduce the pinning of the SKL to the underlying crystalline lattice. This reduces the pr…
The lack of inversion symmetry in the crystal lattice of magnetic materials gives rise to complex non-collinear spin orders through interactions of relativistic nature, resulting in interesting physical phenomena, such as emergent electromagnetism. Studies of cubic chiral magnets revealed a universal magnetic phase diagram, composed of helical spiral, conical spiral and skyrmion crystal phases. Here, we report a remarkable deviation from this universal behavior. By combining neutron diffraction with magnetization measurements we observe a new multi-domain state in Cu2OSeO3. Just below the uppe…
The chiral spin textures of a two-dimensional (2D) triangular system, where both antiferromagnetic (AF) Heisenberg exchange and chiral Dzyaloshinsky-Moriya interactions co-exist, are investigated numerically with an optimized quantum Monte Carlo method based on mean-field theory. We find that: helical, skyrmionic and vortical AF crystals can be formed when an external magnetic field is applied perpendicular to the 2D monolayer; the sizes of these skyrmions and vortices change abruptly at several critical points of the external magnetic field; each of these AF crystals can be decomposed into th…
Analytic properties of the multiple spin density waves showing vortex structures, which have recently been found in the fcc Hubbard model using the generalized Hartree-Fock (GHF) approximation, have been investigated. It is shown that the 2Q multiple helical spin density waves (SDW) consist of two types of half-skyrmion vortices and two types of antivortices. In the 3Q multiple helical SDW, the half-skyrmion vortex structures with the "westerlies" are shown to be twisted along the axis perpendicular to the vortex plane. The 12Q multiple SDW (12QMSDW) are analyzed as a superposition of the 2-4Q…
We present a comprehensive theory of the magnetic phases in monolayer nickel-based Janus dihalides (NiIBr, NiICl, NiBrCl) through a combination of first-principles calculations and atomistic simulations. Phonon band structure calculations and finite temperature molecular dynamics simulations show that Ni-dihalide Janus monolayers are stable. The parameters of the interacting spin Hamiltonian extracted from ab initio calculations show that nickel-dihalide Janus monolayers exhibit varying degrees of magnetic frustration together with a large Dzyaloshinskii-Moriya interaction due to their inheren…
Magneto-transport properties have been investigated for epitaxial thin films of B20-type MnSi grown on Si(111) substrates. Both Lorentz transmission electron microscopy (TEM) images and topological Hall effect (THE) clearly point to the robust formation of skyrmions over a wide temperature-magnetic field region. New features distinct from those of bulk MnSi are observed for epitaxial MnSi films: a shorter (nearly half) period of the spin helix and skyrmions, and an opposite sign of THE. These observations suggest versatile features of skyrmion-induced THE beyond the current understanding.
In this manuscript we demonstrate the skyrmion formation in ultrathin nanodots using magnetic force microscopy tip. Submicron-size dots based on Pt/Co/Au multilayers hosting interfacial Dzyaloshiskii-Morya interaction were used in the experiments. We have found that the tip field generated by the magnetic tip significantly affects the magnetization state of the nanodots and leads to the formation of skyrmions. Micromagnetic simulations explain the evolution of the magnetic state during magnetic force microscopy scans and confirm the possibility of the skyrmion formation. The key transition in …
Skyrmion stabilization in novel magnetic systems with the B20 crystal structure is reported here, primarily based on theoretical results. The focus is on the effect of alloying on the 3d sublattice of the B20 structure by substitution of heavier 4d and 5d elements, with the ambition to tune the spin-orbit coupling and its influence on magnetic interactions. State-of-the-art methods based on density functional theory are used to calculate both isotropic and anisotropic exchange interactions. Significant enhancement of the Dzyaloshinskii-Moriya interaction is reported for 5d-doped FeSi and CoSi,…
We show from first-principles that barrel-shaped structures within the Fermi surface of the centrosymmetric intermetallic compounds GdRu$_2$Si$_2$ and Gd$_2$PdSi$_3$ give rise to Fermi surface nesting, which determines the strength and sign of quasi-two-dimensional Ruderman-Kittel-Kasuya-Yosida pairwise exchange interactions between the Gd moments. This is the principal mechanism leading to their helical single-$q$ spin-spiral ground states, providing transition temperatures and magnetic periods in good agreement with experiment. Using atomistic spin-dynamic simulations, we draw a direct line …
Magnetic skyrmions have attracted broad attention during recent years because they are regarded as promising candidates as bits of information in novel data storage devices. A broad range of theoretical and experimental investigations have been conducted with the consideration of rotational symmetric skyrmions in isotropic environments. However, one naturally observes a huge variety of anisotropic behavior in many experimentally relevant materials. In the present work, we investigate the influence of anisotropic environments onto the formation and behavior of the non-collinear spin states of s…
By performing density functional calculations, we investigate the origin of the skyrmion state and ferroelectricity in Cu2OSeO3. We find that the Dzyaloshinskii-Moriya interactions between the two different kinds of Cu ions are extremely strong and induce the helical ground state and the skyrmion state in the absence and presence of magnetic field, respectively. On the basis of the general model for the spin-order induced polarization, we propose that the ferroelectric polarization of Cu2OSeO3 in the collinear ferrimagnetic state arises from an unusual mechanism, i.e., the single-spin-site con…
We demonstrate the formation of metastable Néel-type skyrmion arrays in Pt/Co/Ni/Ir multi-layers at zero-field following \textit{ex situ} application of an in-plane magnetic field using Lorentz transmission electron microscopy. The resultant skyrmion texture is found to depend on both the strength and misorientation of the applied field as well as the interfacial Dzyaloshinskii-Moriya interaction. To demonstrate the importance of the applied field angle, we leverage bend contours in the specimens which coincide with transition regions between skyrmion and labyrinth patterns. Subsequent applica…
Real-space topological magnetic structures such as skyrmions and merons are promising candidates for information storage and transport. However, the microscopic mechanisms that control their formation and evolution are still not clear. Here, using in-situ Lorentz transmission electron microscopy, we demonstrate that skyrmion crystals (SkXs) can nucleate, grow, and evolve from the conical phase in the same ways that real nanocrystals form from vapors or solutions. More intriguingly, individual skyrmions can also "reproduce" by division in a mitosis-like process that allows them to annihilate Sk…
Synthesis of new materials that can host magnetic skyrmions and their thorough experimental and theoretical characterization are essential for future technological applications. The $β$-Mn-type compound FePtMo$_3$N is one such novel material that belongs to the chiral space group $P4_132$, where the antisymmetric Dzyaloshinkii-Moriya interaction is allowed due to the absence of inversion symmetry. We report the results of small-angle neutron scattering (SANS) measurements of FePtMo$_3$N and demonstrate that its magnetic ground state is a long-period spin helix with a Curie temperature of 222~K…
Robust topological surface states in skyrmion-host magnets Eu(Ga,Al)4: evidence for dual topology
Tohoku University（东北大学）；Advanced Institute for Materials Research (WPI-AIMR), Tohoku University（东北大学先进材料研究所）；Okinawa Institute of Science and Technology (OIST)（冲绳科学技术大学院大学）；Center for Science and Innovation in Spintronics (CSIS), Tohoku University（东北大学自旋电子学科学与创新中心）；Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构物质结构科学研究所）；UVSOR Synchrotron Facility, Institute for Molecular Science（分子科学研究所UVSOR同步辐射设施）；School of Physical Sciences, The Graduate University for Advanced Studies (SOKENDAI)（综合研究大学院大学自然科学研究科）
Magnetic skyrmions form in chiral multilayers from the shrinking or fission of elongated stripe textures. Here we report an experimental and theoretical study of the temperature dependence of this stripe-to-skyrmion transition in Co/Pt-based multilayers. Field-reversal magnetometry and Lorentz microscopy experiments over 100 - 350 K establish the increased efficacy of stripe-to-skyrmion fission at higher temperatures - driven primarily by the thermal evolution of key magnetic interactions - thereby enhancing skyrmion density. Atomistic calculations elucidate that the energy barrier to fission …
Helical multishell gold nanowire is studied theoretically for the formation mechanism of helical domain boundary. Nanowires with the wire length of more than 10 nm are relaxed by quantum mechanical molecular dynamics simulation with tight-binding form Hamiltonian. In results, non-helical nanowires are transformed into helical ones with the formation of atom pair defects at domain boundary, where the defective atom pair is moved from an inner shell. Analysis of local electronic structure shows a competitive feature of the energy gain of reconstruction on wire surface and the energy loss of the …
B20 phase magnetic materials, such as FeGe, have been of significant interests in recent years because they enable magnetic skyrmions, which can potentially lead to low energy cost spintronic applications. One major effort in this emerging field is the stabilization of skyrmions at room temperature and zero external magnetic field. We report the growth of phase-pure FeGe epitaxial thin films on Si(111) substrates by ultrahigh vacuum off-axis sputtering. The high crystalline quality of the FeGe films was confirmed by x-ray diffraction and scanning transmission electron microscopy. Hall effect m…
We experimentally demonstrate the formation of room-temperature skyrmions with radii of about 25\,nm in easy-plane anisotropy multilayers with interfacial Dzyaloshinskii-Moriya interaction (DMI). We detect the formation of individual magnetic skyrmions by magnetic force microscopy and find that the skyrmions are stable in out-of-plane fields up to about 200 mT. We determine the interlayer exchange coupling as well as the strength of the interfacial DMI. Additionally, we investigate the dynamic microwave spin excitations by broadband magnetic resonance spectroscopy. From the uniform Kittel mode…
We perform an extensive study of the spin-configurations in a PdFe bilayer on Ir(111) in terms of ab initio and spin-model calculations. We use the spin-cluster expansion technique to obtain spin model parameters, and solve the Landau-Lifshitz-Gilbert equations at zero temperature. In particular, we focus on effects of layer relaxations and the evolution of the magnetic ground state in external magnetic field. In the absence of magnetic field, we find a spin-spiral ground state, while applying external magnetic field skyrmions are generated in the system. Based on energy calculations of frozen…
FeGe in the B20 phase is an experimentally well-studied prototypical chiral magnet exhibiting helical spirals, skyrmion lattices and individual skyrmions with a robust length of 70~nm. While the helical spiral ground state can be verified by first-principles calculations based on density functional theory, this feature size could not be reproduced even approximately. To develop a coherent picture of the discrepancy between experiment and theory, we investigate in this work the magnetic properties of FeGe from first-principles using different electronic-structure methods. We study atomistic as …
We observe metastable localized spin configurations with topological charges ranging from $Q=-3$ to $Q=2$ in a (Pt$_{0.95}$Ir$_{0.05}$)/Fe bilayer on Pd$(111)$ surface by performing spin dynamics simulations, using a classical Hamiltonian parametrized by ab initio calculations. We demonstrate that the frustration of the isotropic exchange interactions is responsible for the creation of these various types of skyrmionic structures. The Dzyaloshinsky--Moriya interaction present due to the breaking of inversion symmetry at the surface energetically favors skyrmions with $Q=-1$, distorts the shape…
This work studies the resonance excitations of the three-dimensional skyrmions lattice in the finite thickness plate of an isotropic chiral magnet using spin dynamics simulations. We found that the absorption spectra and resonance modes differ from those predicted by the two-dimensional model and the model of the unconfined bulk crystal. The features observed on the spectra can be explained by the formation of chiral standing spin waves, which, contrary to conventional standing spin waves, are characterized by the helical profile of dynamic magnetization of fixed chirality defined by the Dzyal…
The insulating ferrimagnet Cu2OSeO3 shows a rich variety of phases such as skyrmion lattice and helical magnetism controlled by interplay of different exchange interactions which can be tuned by external pressure. In this work we have investigated pressure-induced phase transitions at room temperature using synchrotron based x- ray diffraction and Raman scattering measurements. With first-principles theoretical analysis, we show that spin-spin exchange couplings in the ambient cubic phase are affected notably by hydrostatic pressure. The ambient cubic phase transforms to a monoclinic phase abo…
We study the evolution of helical magnetism in MnGe chiral magnet upon partial substitution of Mn for non magnetic 3d-Co and 4d-Rh ions. At high doping levels, we observe spin helices with very long periods -more than ten times larger than in the pure compound- and sizable ordered moments. This behavior calls for a change in the energy balance of interactions leading to the stabilization of the observed magnetic structures. Strikingly, neutron scattering unambiguously shows a double periodicity in the observed spectra at $x \gtrsim 0.45$ and $\gtrsim 0.25$ for Co- and Rh-doping, respectively. …
Skyrmions in chiral magnetic materials are topologically stable and energetically balanced spin configurations appearing under the presence of ferromagnetic interaction (FMI) and Dzyaloshinskii-Moriya interaction (DMI). Much of the current interest has focused on the effects of magneto-elastic coupling on these interactions under mechanical stimuli, such as uniaxial stresses for future applications in spintronics devices. Recent studies suggest that skyrmion shape deformations in thin films are attributed to an anisotropy in the coefficient of DMI, such that $D_{x}\!\not=\!D_{y}$, which makes …
Skyrmion-containing devices have been proposed as a promising solution for low energy data storage. These devices include racetrack or logic structures and require skyrmions to be confined in regions with dimensions comparable to the size of a single skyrmion. Here we examine Bloch skyrmions in FeGe device shapes using Lorentz transmission electron microscopy (LTEM) to reveal the consequences of skyrmion confinement in a device-like structure. Dumbbell-shaped elements were created by focused ion beam (FIB) milling to provide regions where single skyrmions are confined adjacent to areas contain…
Skyrmion Lattice Domain Formation in a Non-Flat Energy Landscape
Institute of Physics, Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学物理研究所）；Singulus Technologies AG（辛古卢斯技术有限公司）；Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology（挪威科技大学物理系量子自旋电子学中心）
Self-organisation into spatially modulated structures has different nature from phase transition into uniform states. Skyrmions and half-skyrmions (merons) are representatives of such structures and are utilised in designing magnetoelectric, optical, and mechanoresponsive materials by controlling topological phases. However, skyrmions and half-skyrmions in molecular solids are rarely studied, though there is a universality in theoretical descriptions between magnetic and molecular systems with chiral interactions. Here we develop a simple physical system for controlling topological phases in a…
Magnetic skyrmions are topologically stable spin swirls with particle-like character and potentially suitable for the design of high-density information bits. While most known skyrmion systems arise in noncentrosymmetric systems with Dzyaloshinskii-Moriya interaction, also centrosymmetric magnets with a triangular lattice can give rise to skyrmion formation, with geometrically-frustrated lattice being considered essential in this case. Until today, it remains an open question if skyrmions can also exist in the absence of both geometrically-frustrated lattice and inversion symmetry breaking. He…
The controllable phase transition and nanopatterning of topological states in a ferroelectric system under external stimuli are critical for realizing the potential applications in nanoelectronic devices such as logic, memory, race-track, etc. Herein, using the phase-field simulations, we demonstrate the mechanical manipulation of polar skyrmions in ferroelectric superlattices by applying external local compressive stress through an atomic force microscopy (AFM) tip. Different switching pathways are observed: under small to moderate force (<1 uN), the skyrmions coalesce to form a long stripe; …
Underlying disorder in skyrmion materials may both inhibit and facilitate skyrmion reorientations and changes in topology. The identification of these disorder-induced topologically active regimes is critical to realizing robust skyrmion spintronic implementations, yet few studies exist for disordered bulk samples. Here, we employ small-angle neutron scattering (SANS) and micromagnetic simulations to examine the influence of skyrmion order on skyrmion lattice formation, transition, and reorientation dynamics across the phase space of a disordered polycrystalline Co$_{8}$Zn$_{8}$Mn$_{4}$ bulk s…
A model for formation of helical multishell gold nanowires is proposed and is confirmed with the quantum mechanical molecular dynamics simulations. The model can explain the magic number of the helical gold nanowires in the multishell structure. The reconstruction from ideal non-helical to realistic helical nanowires consists of two stages: dissociations of atoms on the outermost shell from atoms on the inner shell and slip deformations of atom rows generating (111)-like structure on the outermost shell. The elementary processes are governed by competition between energy loss and gain by s- an…
We have studied the effects of electrical current pulses on skyrmion formation in a series of Co/Ni/Pt-based multilayers. Transmission X-ray microscopy reveals that by applying electrical current pulses of duration and current density on the order of $τ$=50 $μ$s and j=1.7x10$^1$$^0$ A/m$^2$, respectively, in an applied magnetic field of $μ$$_0$Hz=50 mT, stripe-to-skyrmion transformations are attained. The skyrmions remain stable across a wide range of magnetic fields, including zero field. The skyrmions then remain stable across a wide range of magnetic fields, including zero field. We primari…
Skyrmions, topologically protected vortex-like nanometric spin textures in magnets, have been attracting increasing attention for emergent electromagnetic responses and possible technological applications for spintronics. In particular, metallic magnets with chiral and cubic/tetragonal crystal structure may have high potential to host skyrmions that can be driven by low electrical current excitation. However, experimental observations of skyrmions have so far been limited to below room temperature for the metallic chiral magnets, specifically for the MnSi-type B20 compounds. Toward technologic…
