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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.

The deterministic nucleation of single skyrmions at a controlled position along multilayered magnetic racetracks is demonstrated by exploiting spin-orbit torques without the need of in-plane magnetic fields. Magnetic skyrmions are stabilized by a combination of external magnetic fields, stray field energies, higher-order exchange interactions and the Dzyaloshinskii–Moriya interaction (DMI) 1 , 2 , 3 , 4 , 5 , 6 . The last favours homochiral skyrmions, whose motion is driven by spin–orbit torques and is deterministic, which makes systems with a large DMI relevant for applications. Asymmetric multilayers of non-magnetic heavy metals with strong spin–orbit interactions and transition-metal ferromagnetic layers provide a large and tunable DMI 4 , 5 , 6 , 7 , 8 . Also, the non-magnetic heavy metal layer can inject a vertical spin current with transverse spin polarization into the ferromagnetic layer via the spin Hall effect 9 . This leads to torques 10 that can be used to switch the magnetization completely in out-of-plane magnetized ferromagnetic elements, but the switching is deterministic only in the presence of a symmetry-breaking in-plane field 11 , 12 , 13 . Although spin–orbit torques led to domain nucleation in continuous films 14 and to stochastic nucleation of skyrmions in magnetic tracks 15 , no practical means to create individual skyrmions controllably in an integrated device design at a selected position has been reported yet. Here we demonstrate that sub-nanosecond spin–orbit torque pulses can generate single skyrmions at custom-defined positions in a magnetic racetrack deterministically using the same current path as used for the shifting operation. The effect of the DMI implies that no external in-plane magnetic fields are needed for this aim. This implementation exploits a defect, such as a constriction in the magnetic track, that can serve as a skyrmion generator. The concept is applicable to any track geometry, including three-dimensional designs 16 .

Magnetic skyrmions are topologically stabilized nanoscale spin structures that could be of use in the development of future spintronic devices. When a skyrmion is driven by an electric current it propagates at an angle relative to the flow of current—known as the skyrmion Hall angle (SkHA)—that is a function of the drive current. This drive dependence, as well as thermal effects due to Joule heating, could be used to tailor skyrmion trajectories, but are not well understood. Here we report a study of skyrmion dynamics as a function of temperature and drive amplitude. We find that the skyrmion velocity depends strongly on temperature, while the SkHA does not and instead evolves differently in the low- and high-drive regimes. In particular, the maximum skyrmion velocity in ferromagnetic devices is limited by a mechanism based on skyrmion surface tension and deformation (where the skyrmion transitions into a stripe). Our mechanism provides a complete description of the SkHA in ferromagnetic multilayers across the full range of drive strengths, illustrating that skyrmion trajectories can be engineered for device applications. An analysis of skyrmion dynamics at different temperatures and electric drive currents is used to develop a complete description of the skyrmion Hall angle in ferromagnetic multilayers from the creep to the flow regime and illustrates that skyrmion trajectories can be engineered for device applications.

Generation of stable skyrmion lattices and displacement of trains of individual skyrmions along a magnetic racetrack by short current pulses are demonstrated at room temperature in ultrathin metallic ferromagnets. Magnetic skyrmions 1 , 2 are topologically protected spin textures that exhibit fascinating physical behaviours 1 , 2 , 3 , 4 , 5 , 6 and large potential in highly energy-efficient spintronic device applications 7 , 8 , 9 , 10 , 11 , 12 , 13 . The main obstacles so far are that skyrmions have been observed in only a few exotic materials and at low temperatures 1 , 2 , 3 , 4 , 6 , 7 , 8 , and fast current-driven motion of individual skyrmions has not yet been achieved. Here, we report the observation of stable magnetic skyrmions at room temperature in ultrathin transition metal ferromagnets with magnetic transmission soft X-ray microscopy. We demonstrate the ability to generate stable skyrmion lattices and drive trains of individual skyrmions by short current pulses along a magnetic racetrack at speeds exceeding 100 m s −1 as required for applications. Our findings provide experimental evidence of recent predictions 10 , 11 , 12 , 13 and open the door to room-temperature skyrmion spintronics in robust thin-film heterostructures.

Magnetic skyrmions are promising candidates for future spintronic applications such as skyrmion racetrack memories and logic devices. They exhibit exotic and complex dynamics governed by topology and are less influenced by defects, such as edge roughness, than conventionally used domain walls. In particular, their non-zero topological charge leads to a predicted ‘skyrmion Hall effect’, in which current-driven skyrmions acquire a transverse velocity component analogous to charged particles in the conventional Hall effect. Here, we use nanoscale pump–probe imaging to reveal the real-time dynamics of skyrmions driven by current-induced spin–orbit torques. We find that skyrmions move at a well-defined angle Θ SkH that can exceed 30° with respect to the current flow, but in contrast to conventional theoretical expectations, Θ SkH increases linearly with velocity up to at least 100 ms −1 . We qualitatively explain our observation based on internal mode excitations in combination with a field-like spin–orbit torque, showing that one must go beyond the usual rigid skyrmion description to understand the dynamics. Experiments show that when driven by electric currents, magnetic skyrmions experience transverse motion due to their topological charge — similar to the conventional Hall effect experienced by charged particles in a perpendicular magnetic field.

Topological states of matter exhibit fascinating physics combined with an intrinsic stability. A key challenge is the fast creation of topological phases, which requires massive reorientation of charge or spin degrees of freedom. Here we report the picosecond emergence of an extended topological phase that comprises many magnetic skyrmions. The nucleation of this phase, followed in real time via single-shot soft X-ray scattering after infrared laser excitation, is mediated by a transient topological fluctuation state. This state is enabled by the presence of a time-reversal symmetry-breaking perpendicular magnetic field and exists for less than 300 ps. Atomistic simulations indicate that the fluctuation state largely reduces the topological energy barrier and thereby enables the observed rapid and homogeneous nucleation of the skyrmion phase. These observations provide fundamental insights into the nature of topological phase transitions, and suggest a path towards ultrafast topological switching in a wide variety of materials through intermediate fluctuating states. Time-resolved X-ray scattering is utilized to demonstrate an ultrafast 300 ps topological phase transition to a skyrmionic phase. This transition is enabled by the formation of a transient topological fluctuation state.

Fluctuations and stochastic transitions are ubiquitous in nanometre-scale systems, especially in the presence of disorder. However, their direct observation has so far been impeded by a seemingly fundamental, signal-limited compromise between spatial and temporal resolution. Here we develop coherent correlation imaging (CCI) to overcome this dilemma. Our method begins by classifying recorded camera frames in Fourier space. Contrast and spatial resolution emerge by averaging selectively over same-state frames. Temporal resolution down to the acquisition time of a single frame arises independently from an exceptionally low misclassification rate, which we achieve by combining a correlation-based similarity metric 1 , 2 with a modified, iterative hierarchical clustering algorithm 3 , 4 . We apply CCI to study previously inaccessible magnetic fluctuations in a highly degenerate magnetic stripe domain state with nanometre-scale resolution. We uncover an intricate network of transitions between more than 30 discrete states. Our spatiotemporal data enable us to reconstruct the pinning energy landscape and to thereby explain the dynamics observed on a microscopic level. CCI massively expands the potential of emerging high-coherence X-ray sources and paves the way for addressing large fundamental questions such as the contribution of pinning 5 – 8 and topology 9 – 12 in phase transitions and the role of spin and charge order fluctuations in high-temperature superconductivity 13 , 14 . Nanoscale magnetic fluctuations are spatiotemporally resolved beyond conventional resolution limits using coherent correlation imaging, in which frames in Fourier space are recorded and analysed using an iterative hierarchical clustering algorithm.

Current-induced dynamics of twisted domain walls and skyrmions in ferromagnetic perpendicularly magnetized multilayers is studied through three-dimensional micromagnetic simulations and analytical modeling. It is shown that such systems generally exhibit a Walker breakdown-like phenomenon in the presence of current-induced damping-like spin-orbit torque. Above a critical current threshold, corresponding to typical velocities of the order tens of m/s, domain walls in some layers start to precess with frequencies in the gigahertz regime, which leads to oscillatory motion and a significant drop in mobility. This phenomenon originates from complex stray field interactions and occurs for a wide range of multilayer materials and structures that include at least three ferromagnetic layers and finite Dzyaloshinskii-Moriya interaction. An analytical model is developed to describe the precessional dynamics in multilayers with surface-volume stray field interactions, yielding qualitative agreement with micromagnetic simulations.

We present an analytical theory to describe three-dimensional magnetic textures in perpendicularly magnetized magnetic multilayers that arise in the presence of magnetostatic interactions and the Dzyaloshinskii-Moriya interaction (DMI). We demonstrate that domain walls in multilayers develop a complex twisted structure, which persists even for films with strong DMI. The origin of this twist is surface-volume stray field interactions that manifest as a depth-dependent effective field whose form mimics the DMI effective field. We find that the wall twist has a minor impact on the equilibrium skyrmion or domain size, but can significantly affect current-driven dynamics. Our conclusions are based on the derived analytical expressions for the magnetostatic energy and confirmed by micromagnetic simulations.