Stability of single skyrmionic bits

Disorder-Induced Topological State Transition in the Optical Skyrmion Family

Skyrmions endowed with topological protection have been extensively investigated in various platforms including magnetics, ferroelectrics, and liquid crystals, stimulating applications such as memories, logic devices, and neuromorphic computing. While the optical counterpart has been proposed and realized recently, the study of optical skyrmions is still in its infancy. Among the unexplored questions, the investigation of the topology induced robustness against disorder is of substantial importance on both fundamental and practical sides but remains elusive. In this Letter, we manage to generate optical skyrmions numerically in real space with different topological features at will, providing a unique platform to investigate the robustness of various optical skyrmions. A disorder-induced topological state transition is observed for the first time in a family of optical skyrmions composed of six classes with different skyrmion numbers. Intriguingly, the optical skyrmions produced from a vectorial hologram are exceptionally robust against scattering from a random medium, shedding light on topological photonic devices for the generation and manipulation of robust states for applications including imaging and communication.

A micromagnetic theory of skyrmion lifetime in ultrathin ferromagnetic films

We use the continuum micromagnetic framework to derive the formulas for compact skyrmion lifetime due to thermal noise in ultrathin ferromagnetic films with relatively weak interfacial Dzyaloshinskii-Moriya interaction. In the absence of a saddle point connecting the skyrmion solution to the ferromagnetic state, we interpret the skyrmion collapse event as "capture by an absorber" at microscale. This yields an explicit Arrhenius collapse rate with both the barrier height and the prefactor as functions of all the material parameters, as well as the dynamical paths to collapse.

Unveiling the Emergent Traits of Chiral Spin Textures in Magnetic Multilayers

Magnetic skyrmions are topologically wound nanoscale textures of spins whose ambient stability and electrical manipulation in multilayer films have led to an explosion of research activities. While past efforts focused predominantly on isolated skyrmions, recently ensembles of chiral spin textures, consisting of skyrmions and magnetic stripes, are shown to possess rich interactions with potential for device applications. However, several fundamental aspects of chiral spin texture phenomenology remain to be elucidated, including their domain wall (DW) structure, thermodynamic stability, and morphological transitions. Here the evolution of these textural characteristics are unveiled on a tunable multilayer platform-wherein chiral interactions governing spin texture energetics can be widely varied-using a combination of full-field electron and soft X-ray microscopies with numerical simulations. With increasing chiral interactions, the emergence of Néel helicity, followed by a marked reduction in domain compressibility, and finally a transformation in the skyrmion formation mechanism are demonstrated. Together with an analytical model, these experiments establish a comprehensive microscopic framework for investigating and tailoring chiral spin texture character in multilayer films.

Rashba-Type Dzyaloshinskii-Moriya Interaction, Perpendicular Magnetic Anisotropy, and Skyrmion States at 2D Materials/Co Interfaces

We report a significant Dzyaloshinskii-Moriya interaction (DMI) and perpendicular magnetic anisotropy (PMA) at interfaces comprising hexagonal boron nitride (h-BN) and Co. By comparing the behavior of these phenomena at graphene/Co and h-BN/Co interfaces, it is found that the DMI in the latter increases as a function of Co thickness and beyond three monolayers stabilizes with 1 order of magnitude larger values compared to those at graphene/Co, where the DMI shows opposite decreasing behavior. Meanwhile, the PMA for both systems shows similar trends with larger values for graphene/Co and no significant variations for all thickness ranges of Co. Furthermore, using micromagnetic simulations we demonstrate that such significant DMI and PMA values remaining stable over a large range of Co thickness give rise to the formation of skyrmions with small applied external fields. These findings open up further possibilities toward integrating two-dimensional (2D) materials in spin-orbitronics devices.

Kinetics of Magnetic Skyrmion Crystal Formation from the Conical Phase

The particle-like magnetic skyrmion or skyrmion lattice (SkX) formation has promoted strong application and fundamental science interests. Despite extensive research, the kinetic of the SkX development is much less understood because of the ultrafast spin rotation and high sensitivity to external perturbations. Here, using in situ Lorentz transmission electron microscopy, we successfully measured the dynamics of SkX formation from the conical phase with precise control of both the temperature and the magnetic field. We discovered that the Avrami equation can accurately describe the transition process with an initial Avrami constant around 1, suggesting that the rate-limiting step for the quasiparticle lattice formation is one-dimensional heterogeneous nucleation of individual skyrmions. A modified Arrhenius rate law is established, with an energy barrier that has a square-root dependence on temperature and a quadratic dependence on the magnetic field. This study paves the way toward precise and predictable manipulation of topological spin structures.

Directional locking and the influence of obstacle density on skyrmion dynamics in triangular and honeycomb arrays

We numerically examine the dynamics of a single skyrmion driven over triangular and honeycomb obstacle arrays at zero temperature. The skyrmion Hall angleθ_sk, defined as the angle between the applied external drive and the direction of the skyrmion motion, increases in quantized steps or continuously as a function of the applied drive. For the obstacle arrays studied in this work, the skyrmion exhibits two main directional locking angles ofθ_sk= -30° and -60°. We show that these directions are privileged due to the obstacle landscape symmetry, and coincide with channels along which the skyrmion may move with few or no obstacle collisions. Here we investigate how changes in the obstacle density can modify the skyrmion Hall angles and cause some dynamic phases to appear or grow while other phases vanish. This interesting behavior can be used to guide skyrmions along designated trajectories via regions with different obstacle densities. For fixed obstacle densities, we investigate the evolution of the lockedθ_sk= -30° and -60° phases as a function of the Magnus force, and discuss possibilities for switching between these phases using topological selection.

Nano-to-micro spatiotemporal imaging of magnetic skyrmion's life cycle

Magnetic skyrmions are self-organized topological spin textures that behave like particles. Because of their fast creation and typically long lifetime, experimental verification of skyrmion's creation/annihilation processes has been challenging. Here, we successfully track skyrmion dynamics in defect-introduced Co₉Zn₉Mn₂ by using pump-probe Lorentz transmission electron microscope. Following the nanosecond photothermal excitation, we resolve 160-nm skyrmion's proliferation at <1 ns, contraction at 5 ns, drift from 10 ns to 4 μs, and coalescence at ~5 μs. These motions relay the multiscale arrangement and relaxation of skyrmion clusters in a repeatable cycle of 20 kHz. Such repeatable dynamics of skyrmions, arising from the weakened but still persistent topological protection around defects, enables us to visualize the whole life of the skyrmions and demonstrates the possible high-frequency manipulations of topological charges brought by skyrmions.

Motion-induced inertial effects and topological phase transitions in skyrmion transport

When the skyrmion dynamics beyond the particle-like description is considered, this topological structure can deform due to a self-induced field. In this work, we perform Monte Carlo simulations to characterize the skyrmion deformation during its steady movement. In the low-velocity regime, the deformation in the skyrmion shape is quantified by an effective inertial mass, which is related to the dissipative force. When skyrmions move faster, the large self-induced deformation triggers topological transitions. These transitions are characterized by the proliferation of skyrmions and a different total topological charge, which is obtained as a function of the skyrmion velocity. Our findings provide an alternative way to describe the dynamics of a skyrmion that accounts for the deformations of its structure. Furthermore, such motion-induced topological phase transitions make it possible to control the number of ferromagnetic skyrmions through velocity effects.

Role of higher-order exchange interactions for skyrmion stability

Transition-metal interfaces and multilayers are a promising class of systems to realize nanometer-sized, stable magnetic skyrmions for future spintronic devices. For room temperature applications, it is crucial to understand the interactions which control the stability of isolated skyrmions. Typically, skyrmion properties are explained by the interplay of pair-wise exchange interactions, the Dzyaloshinskii-Moriya interaction and the magnetocrystalline anisotropy energy. Here, we demonstrate that higher-order exchange interactions - which have so far been neglected - can play a key role for the stability of skyrmions. We use an atomistic spin model parametrized from first-principles and compare three different ultrathin film systems. We consider all fourth-order exchange interactions and show that, in particular, the four-site four spin interaction has a large effect on the energy barrier preventing skyrmion and antiskyrmion collapse into the ferromagnetic state. Our work opens perspectives to stabilize topological spin structures even in the absence of Dzyaloshinskii-Moriya interaction.

Dynamics of chiral state transitions and relaxations in an FeGe thin plate via in situ Lorentz microscopy

Studying the magnetic transition between different topological spin textures in noncentrosymmetric magnets under external stimuli is an important topic in chiral magnetism. Here, using in situ Lorentz transmission electron microscopy (LTEM) we directly visualize the thermal-driven magnetic transitions and dynamic characteristics in FeGe thin plates. A novel protocol-dependent phase diagram of FeGe thin plates was obtained via pulsed laser excitation. Moreover, by setting the appropriate specimen temperature, the relaxation of chiral magnetic states in FeGe specimens was recorded and analyzed with an Arrhenius-type relaxation mechanism. We present the field-dependent activation energy barriers for chiral state transitions and the magnetic transition pathways of these spin textures for FeGe thin plates. Our results unveil the effects of thermal excitation on the topological spin texture transitions and provide useful information about magnetic dynamics of chiral magnetic state relaxation.

Topology-Dependent Brownian Gyromotion of a Single Skyrmion

Noninteracting particles exhibiting Brownian motion have been observed in many occasions of sciences, such as molecules suspended in liquids, optically trapped microbeads, and spin textures in magnetic materials. In particular, a detailed examination of Brownian motion of spin textures is important for designing thermally stable spintronic devices, which motivates the present study. In this Letter, through using temporally and spatially resolved polar magneto-optic Kerr effect microscopy, we have experimentally observed the thermal fluctuation-induced random walk of a single isolated Néel-type magnetic skyrmion in an interfacially asymmetric Ta/CoFeB/TaO_{x} multilayer. An intriguing topology-dependent Brownian gyromotion behavior of skyrmions has been identified. The onset of Brownian gyromotion of a single skyrmion induced by thermal effects, including a nonlinear temperature-dependent diffusion coefficient and topology-dependent gyromotion are further formulated based on the stochastic Thiele equation. The experimental and numerical demonstration of topology-dependent Brownian gyromotion of skyrmions can be useful for understanding the nonequilibrium magnetization dynamics and implementing spintronic devices.

Direct Demonstration of Topological Stability of Magnetic Skyrmions via Topology Manipulation

Topological protection precludes a continuous deformation between topologically inequivalent configurations in a continuum. Motivated by this concept, magnetic skyrmions, topologically nontrivial spin textures, are expected to exhibit topological stability, thereby offering a prospect as a nanometer-scale nonvolatile information carrier. In real materials, however, atomic spins are configured as not continuous but discrete distributions, which raises a fundamental question if the topological stability is indeed preserved for real magnetic skyrmions. Answering this question necessitates a direct comparison between topologically nontrivial and trivial spin textures, but the direct comparison in one sample under the same magnetic fields has been challenging. Here we report how to selectively achieve either a skyrmion state or a topologically trivial bubble state in a single specimen and thereby experimentally show how robust the skyrmion structure is in comparison with the bubbles. We demonstrate that topologically nontrivial magnetic skyrmions show longer lifetimes than trivial bubble structures, evidencing the topological stability in a real discrete system. Our work corroborates the physical importance of the topology in the magnetic materials, which has hitherto been suggested by mathematical arguments, providing an important step toward ever-dense and more-stable magnetic devices.

A model for individual quantal nano-skyrmions

A quantal model description of a discrete localized skyrmion singularity embedded in a ferromagnetic environment is proposed. It allows discussing the importance of various parameters in the appearance of a quantal skyrmion singularity. Analysis of the skyrmion reveals a few specific quantal properties: presence of a whole series of skyrmion states, non-classical nature of the local spins, presence of superposition states and presence of extra-skyrmion states due to the quantization of the central spin of the singularity. The interaction of an electron, tunneling or substrate, with the skyrmion is also described allowing a new view at the origin of the skyrmion stability as well as the possibility to discriminate between ferromagnetic and skyrmion phase in an inelastic electron tunneling spectroscopy experiment, based on the skyrmion quantal properties.

Interlayer Dzyaloshinskii-Moriya Interactions

The interfacial Dzyaloshinkii-Moriya interaction defines a rotational sense for the spin structure in two-dimensional magnetic films and can be used to create chiral magnetic structures like spin spirals and skyrmions in those films. Here, we show by means of atomistic calculations that in heterostructures an interlayer coupling of the Dzyaloshinskii-Moriya type across a spacer can emerge. We quantify this interaction in the framework of the Lévy-Fert model for trilayers consisting of two ferromagnets separated by a nonmagnetic spacer and show that such an interlayer Dzyaloshinkii-Moriya interaction yields nontrivial three-dimensional spin textures across the entire trilayer, which evolve within as well as between the planes and, hence, combine intraplane and interplane chiralities. This analysis opens new perspectives for three-dimensional tailoring of magnetic chirality in multilayers.

A sum rule of uniaxial anisotropy and external magnetic field for formation of Néel-type skyrmion lattices in two-dimensional ferromagnets

It is generally believed that the perpendicular magnetic anisotropy (PMA) plays an important role in stabilizing skyrmion lattices (SkL) in two-dimensional (2D) magnetic systems in which both Heisenberg exchange and Dzyaloshinskii-Moriya interactions co-exist, and the skyrmion sizes in SkLs are mainly determined by the strengths of these two intrinsic interactions. To investigate the details, we employ here a quantum computational approach we develop in recent years to simulate the Néel-type skyrmion lattices formed on a 2D PdFe/Ir(1 1 1)-like film. From our simulated results, we find that: within an external magnetic field applied normal to the film plane, the PMA is indeed able to help induce Néel-type SkLs in a wider field range; however, to stabilize the SkLs, the PMA cannot be too strong, the strengths of the external magnetic field and the maximal PMA must satisfy a sum rule since the effective perpendicular magnetic field generated by these two interactions cannot exceed a largest value. We also notice that the periodical boundary condition imposed on the FM system in simulations is able to facilitate SkL formations, and it can also modify the skyrmion size in a certain extend.

Relaxation Dynamics of Zero-Field Skyrmions over a Wide Temperature Range

The promise of magnetic skyrmions in future spintronic devices hinges on their topologically enhanced stability and the ability to be manipulated by external fields. The technological advantages of nonvolatile zero-field skyrmion lattice (SkL) are significant if their stability and reliability can be demonstrated over a broad temperature range. Here, we study the relaxation dynamics including the evolution and lifetime of zero-field skyrmions generated from field cooling (FC) in an FeGe single-crystal plate via in situ Lorentz transmission electron microscopy (L-TEM). Three types of dynamic switching between zero-field skyrmions and stripes are identified and distinguished. Moreover, the generation and annihilation of these metastable skyrmions can be tailored during and after FC by varying the magnetic fields and the temperature. This dynamic relaxation behavior under the external fields provides a new understanding of zero-field skyrmions for their stability and reliability in spintronic applications and also raises new questions for theoretical models of skyrmion systems.

Ferroelectrically tunable magnetic skyrmions in ultrathin oxide heterostructures

Magnetic skyrmions are topologically protected whirling spin texture. Their nanoscale dimensions, topologically protected stability and solitonic nature, together are promising for future spintronics applications. To translate these compelling features into practical spintronic devices, a key challenge lies in achieving effective control of skyrmion properties, such as size, density and thermodynamic stability. Here, we report the discovery of ferroelectrically tunable skyrmions in ultrathin BaTiO₃/SrRuO₃ bilayer heterostructures. The ferroelectric proximity effect at the BaTiO₃/SrRuO₃ heterointerface triggers a sizeable Dzyaloshinskii-Moriya interaction, thus stabilizing robust skyrmions with diameters less than a hundred nanometres. Moreover, by manipulating the ferroelectric polarization of the BaTiO₃ layer, we achieve local, switchable and nonvolatile control of both skyrmion density and thermodynamic stability. This ferroelectrically tunable skyrmion system can simultaneously enhance the integratability and addressability of skyrmion-based functional devices.

Theory of isolated magnetic skyrmions: From fundamentals to room temperature applications

Magnetic skyrmions are topological quasiparticles of great interest for data storage applications because of their small size, high stability, and ease of manipulation via electric current. However, although models exist for some limiting cases, there is no universal theory capable of accurately describing the structure and energetics of all skyrmions. The main barrier is the complexity of non-local stray field interactions, which are usually included through crude approximations. Here we present an accurate analytical framework to treat isolated skyrmions in any material, assuming only a circularly-symmetric 360° domain wall profile and a homogeneous magnetization profile in the out-of-plane direction. We establish the first rigorous criteria to distinguish stray field from DMI skyrmions, resolving a major dispute in the community. We discover new phases, such as bi-stability, a phenomenon unknown in magnetism so far. We predict materials for sub-10 nm zero field room temperature stable skyrmions suitable for applications. Finally, we derive analytical equations to describe current-driven dynamics, find a topological damping, and show how to engineer materials in which compact skyrmions can be driven at velocities >1000 m/s.

Lifetime of racetrack skyrmions

The skyrmion racetrack is a promising concept for future information technology. There, binary bits are carried by nanoscale spin swirls-skyrmions-driven along magnetic strips. Stability of the skyrmions is a critical issue for realising this technology. Here we demonstrate that the racetrack skyrmion lifetime can be calculated from first principles as a function of temperature, magnetic field and track width. Our method combines harmonic transition state theory extended to include Goldstone modes, with an atomistic spin Hamiltonian parametrized from density functional theory calculations. We demonstrate that two annihilation mechanisms contribute to the skyrmion stability: At low external magnetic field, escape through the track boundary prevails, but a crossover field exists, above which the collapse in the interior becomes dominant. Considering a Pd/Fe bilayer on an Ir(111) substrate as a well-established model system, the calculated skyrmion lifetime is found to be consistent with reported experimental measurements. Our simulations also show that the Arrhenius pre-exponential factor of escape depends only weakly on the external magnetic field, whereas the pre-exponential factor for collapse is strongly field dependent. Our results open the door for predictive simulations, free from empirical parameters, to aid the design of skyrmion-based information technology.

A nontrivial crossover in topological Hall effect regimes

We propose a new theory of the topological Hall effect (THE) in systems with non-collinear magnetization textures such as magnetic skyrmions. We solve the problem of electron scattering on a magnetic skyrmion exactly, for an arbitrary strength of exchange interaction and the skyrmion size. We report the existence of different regimes of THE and resolve the apparent contradiction between the adiabatic Berry phase theoretical approach and the perturbation theory for THE. We traced how the topological charge Hall effect transforms into the spin Hall effect upon varying the exchange interaction strength or the skyrmion size. This transformation has a nontrivial character: it is accompanied by an oscillating behavior of both charge and spin Hall currents. This hallmark of THE allows one to identify the chirality driven contribution to Hall response in the experiments.

Real-Space Observation of Nonvolatile Zero-Field Biskyrmion Lattice Generation in MnNiGa Magnet

Magnetic skyrmions, particular those without the support of external magnetic fields over a wide temperature region, are promising as alternative spintronic units to overcome the fundamental size limitation of conventional magnetic bits. In this study, we use in situ Lorentz microscope to directly demonstrate the generation and sustainability of robust biskyrmion lattice at zero magnetic field over a wide temperature range of 16-338 K in MnNiGa alloy. This procedure includes a simple field-cooling manipulation from 360 K (higher than Curie temperature T_C ∼ 350 K), where topological transition easily occurs by adapting the short-range magnetic clusters under a certain magnetic field. The biskyrmion phase is favored upon cooling below T_C. Once they are generated, the robust high-density biskyrmions persist even after removing the external magnetic field due to the topological protection and the increased energy barrier.

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.

Enhanced skyrmion stability due to exchange frustration

Skyrmions are localized, topologically non-trivial spin structures which have raised high hopes for future spintronic applications. A key issue is skyrmion stability with respect to annihilation into the ferromagnetic state. Energy barriers for this collapse have been calculated taking only nearest neighbor exchange interactions into account. Here, we demonstrate that exchange frustration can greatly enhance skyrmion stability. We focus on the prototypical film system Pd/Fe/Ir(111) and use an atomistic spin model parametrized from first-principles calculations. We show that energy barriers and critical fields of skyrmion collapse as well as skyrmion lifetimes are drastically enhanced due to frustrated exchange and that antiskyrmions are metastable. In contrast an effective nearest-neighbor exchange model can only account for equilibrium properties of skyrmions such as their magnetic field dependent profile or the zero temperature phase diagram. Our work shows that frustration of long range exchange interactions - a typical feature in itinerant electron magnets - is a route towards enhanced skyrmion stability even in systems with a ferromagnetic ground state.

Entropy-limited topological protection of skyrmions

Magnetic skyrmions are topologically protected whirls that decay through singular magnetic configurations known as Bloch points. We used Lorentz transmission electron microscopy to infer the energetics associated with the topological decay of magnetic skyrmions far from equilibrium in the chiral magnet Fe_1-x Co _x Si. We observed that the lifetime τ of the skyrmions depends exponentially on temperature, [Formula: see text]. The prefactor τ₀ of this Arrhenius law changes by more than 30 orders of magnitude for small changes of the magnetic field, reflecting a substantial reduction of the lifetime of skyrmions by entropic effects and, thus, an extreme case of enthalpy-entropy compensation. Such compensation effects, being well known across many different scientific disciplines, affect topological transitions and, thus, topological protection on an unprecedented level.

Tunable room-temperature magnetic skyrmions in Ir/Fe/Co/Pt multilayers

Magnetic skyrmions are nanoscale topological spin structures offering great promise for next-generation information storage technologies. The recent discovery of sub-100-nm room-temperature (RT) skyrmions in several multilayer films has triggered vigorous efforts to modulate their physical properties for their use in devices. Here we present a tunable RT skyrmion platform based on multilayer stacks of Ir/Fe/Co/Pt, which we study using X-ray microscopy, magnetic force microscopy and Hall transport techniques. By varying the ferromagnetic layer composition, we can tailor the magnetic interactions governing skyrmion properties, thereby tuning their thermodynamic stability parameter by an order of magnitude. The skyrmions exhibit a smooth crossover between isolated (metastable) and disordered lattice configurations across samples, while their size and density can be tuned by factors of two and ten, respectively. We thus establish a platform for investigating functional sub-50-nm RT skyrmions, pointing towards the development of skyrmion-based memory devices.

Skyrmion-Anti-Skyrmion Pair Creation by in-Plane Currents

Magnetic Skyrmions can be considered as localized vortexlike spin textures which are topologically protected in continuous systems. Because of their stability, their small size, and the possibility to move them by low electric currents, they are promising candidates for spintronic devices. Without changing the topological charge, it is possible to create Skyrmion-anti-Skyrmion pairs. We derive a Skyrmion equation of motion which reveals how spin-polarized charge currents create Skyrmion-anti-Skyrmion pairs. It allows us to identify general prerequisites for the pair creation process. We corroborate these general principles by numerical simulations. On a lattice, where the concept of topological protection has to be replaced by that of a finite energy barrier, the anti-Skyrmion partner of the pairs is annihilated and only the Skyrmion survives. This eventually changes the total Skyrmion number and yields a new way of creating and controlling Skyrmions.

Self-consistent mean field theory studies of the thermodynamics and quantum spin dynamics of magnetic Skyrmions

A self-consistent mean field theory is introduced and used to investigate the thermodynamics and spin dynamics of an S  =  1 quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. In addition, the spin dynamics of a magnetic Skyrmion is described by solving the time dependent Schrödinger equation with additional damping term. The Skyrmion annihilation process driven by an electric field is used to compare the trajectories of the quantum mechanical simulation with a semi-classical description for the spin expectation values using a differential equation similar to the classical Landau-Lifshitz-Gilbert equation.

Skyrmions with Attractive Interactions in an Ultrathin Magnetic Film

We determined the parameters of a classical spin Hamiltonian describing an Fe monolayer on Pd(111) surface with a Pt_{1-x}Ir_{x} alloy overlayer from ab initio calculations. While the ground state of the system is ferromagnetic for x=0.00, it becomes a spin spiral state as Ir is intermixed into the overlayer. Although the Dzyaloshinsky-Moriya interaction is present in the system, we will demonstrate that the frustrated isotropic exchange interactions play a prominent role in creating the spin spiral state, and these frustrated couplings lead to an attractive interaction between Skyrmions at short distances. Using spin dynamics simulations, we show that under these conditions the individual Skyrmions form clusters, and that these clusters remain stable at finite temperature.

Switching the Magnetic Vortex Core in a Single Nanoparticle

Imaging and manipulating the spin structure of nano- and mesoscale magnetic systems is a challenging topic in magnetism, yielding a wide range of spin phenomena such as skyrmions, hedgehog-like spin structures, or vortices. A key example has been provided by the vortex spin texture, which can be addressed in four independent states of magnetization, enabling the development of multibit magnetic storage media. Most of the works devoted to the study of the magnetization reversal mechanisms of the magnetic vortices have been focused on micrometer-size magnetic platelets. Here we report the experimental observation of the vortex state formation and annihilation in individual 25 nm molecular-based magnetic nanoparticles measured by low-temperature variable-field magnetic force microscopy. Interestingly, in these nanoparticles the switching of the vortex core can be induced with very small values of the applied static magnetic field.