Skyrmion pinning energetics in thin film systems

Creation of Independently Controllable and Long Lifetime Polar Skyrmion Textures in Ferroelectric-Metallic Heterostructures

Topological textures like vortices, labyrinths, and skyrmions formed in ferroic materials have attracted extensive interest during the past decade for their fundamental physics, intriguing topology, and technological prospects. So far, polar skyrmions remain scarce in ferroelectrics as they require a delicate balance between various dipolar interactions. Here, it is reported that PbTiO3 thin films in a metallic contact undergo a topological phase transition and hold a broad family of skyrmion-like textures including Q = ±1 skyrmions, multiple π-twist target skyrmions, and skyrmion bags, with independent controllability, analogous to those reported in magnetic systems. Weakly-interacted skyrmion arrays with a density over 300 Gbit/inch2 are successfully written, erased, and read out by local electrical and mechanical stimuli of a scanning probe. Interestingly, in contrast to the relatively short lifetime (<20 hours) of the normal skyrmions, the multiple π-twist target skyrmions and skyrmion bags show topology-enhanced stability with a lifetime of over two weeks. Experimental and theoretical analysis implies the heterostructures carry electric Dzyaloshinskii-Moriya interaction mediated by oxygen octahedral tiltings. The results demonstrate ferroelectric-metallic heterostructures as fertile playgrounds for topological states and emergent phenomena.

The role of magnetic dipolar interactions in skyrmion lattices

Magnetic skyrmions are topological two-dimensional (2D) spin textures that can be stabilized at room temperature and low magnetic fields in magnetic multilayer stacks. Besides their envisioned applications in data storage and processing, these 2D quasiparticles constitute an ideal model system to study 2D particle properties. More precisely, the role of inter-particle dipolar interactions in 2D ensembles can be fully captured in skyrmion lattices. We engineer a multilayer stack hosting skyrmion lattices and increase the relevance of the dipolar coupling by increasing the number of repetitions n from n = 1 to n = 30 . To ascertain the impact on the spin structure, we carry out a series of imaging experiments and find a drastic change of the skyrmion size. We develop an analytical description for the skyrmion radius in the whole multilayer regime, from thin to thick film limits, identifying the key impact of the nucleation process leading to the skyrmion lattice. Our work provides a detailed understanding of the skyrmion-skyrmion interaction, clarifying the role of dipolar interactions as the multilayer stack is expanded in the z direction.

Realizing Quantitative Quasiparticle Modeling of Skyrmion Dynamics in Arbitrary Potentials

We demonstrate fully quantitative Thiele model simulations of magnetic skyrmion dynamics on previously unattainable experimentally relevant large length and time scales by ascertaining the key missing parameters needed to calibrate the experimental and simulation timescales and current-induced forces. Our work allows us to determine complete spatial pinning energy landscapes that enable quantification of experimental studies of diffusion in arbitrary potentials within the Lifson-Jackson framework. Our method enables us to ascertain the timescales, and by isolating the effect of ultralow current density (order 10^{6}  A/m^{2}) generated torques we directly infer the total force acting on the skyrmion for a quantitative modeling.

Room Temperature Magnetic Skyrmions in Gradient-Composition Engineered CoPt Single Layers

Topologically protected magnetic skyrmions in magnetic materials are stabilized by an interfacial or bulk Dzyaloshinskii-Moriya interaction (DMI). Interfacial DMI decays with an increase of the magnetic layer thickness in just a few nanometers, and bulk DMI typically stabilizes magnetic skyrmions at low temperatures. Consequently, more flexibility in the manipulation of DMI is required for utilizing nanoscale skyrmions in energy-efficient memory and logic devices at room temperature (RT). Here, we demonstrate the observation of RT skyrmions stabilized by gradient DMI (g-DMI) in composition gradient-engineered CoPt single-layer films by employing the topological Hall effect, magnetic force microscopy, and nitrogen-vacancy scanning magnetometry. Skyrmions remain stable over a wide range of applied magnetic fields and are confirmed to be nearly Bloch-type from micromagnetic simulation and analytical magnetization reconstruction. Furthermore, we observe skyrmion pairs, which may be explained by skyrmion-antiskyrmion interactions. Our findings expand the family of magnetic materials hosting RT magnetic skyrmions by tuning g-DMI via gradient polarity and a choice of magnetic elements.

Enhancing the Thermal Stability of Skyrmion in Magnetic Nanowires for Nanoscale Data Storage

Magnetic skyrmion random switching and structural stability are critical limitations for storage data applications. Enhancing skyrmions' magnetic properties could improve their thermal structural stability. Hence, micromagnetic calculation was carried out to explore the thermal nucleation and stability of skyrmions in magnetic nanodevices. Different magnetic properties such as uniaxial magnetic anisotropy energy (Ku), saturation magnetization (Ms) and Dzyaloshinskii-Moriya interaction (DMI) were used to assess the thermal stability of skyrmions in magnetic nanowires. For some values of Ms and Ku, the results verified that the skyrmion structure is stable at temperatures above 800 K, which is higher than room temperature. Additionally, manipulating the nanowire geometry was found to have a substantial effect on the thermal structural stability of the skyrmion in storage nanodevices. Increasing the nanowire dimensions, such as length or width, enhanced skyrmions' structural stability against temperature fluctuations in nanodevices. Furthermore, the random nucleation of the skyrmions due to the device temperature was examined. It was shown that random skyrmion nucleation occurs at temperature values greater than 700 K. These findings make skyrmion devices suitable for storage applications.

Skyrmion flow in periodically modulated channels

Magnetic skyrmions, topologically stabilized chiral magnetic textures with particlelike properties, have so far primarily been studied statically. Here, we experimentally investigate the dynamics of skyrmion ensembles in metallic thin film conduits where they behave as quasiparticle fluids. By exploiting our access to the full trajectories of all fluid particles by means of time-resolved magneto-optical Kerr microscopy, we demonstrate that boundary conditions of skyrmion fluids can be tuned by modulation of the channel geometry. We observe as a function of channel width deviations from classical flow profiles even into the no- or partial-slip regime. Unlike conventional colloids, the skyrmion Hall effect can also introduce transversal flow asymmetries and even local motion of single skyrmions against the driving force which we explore with particle-based simulations, demonstrating the unique properties of skyrmion liquid flow that uniquely deviates from previously known behavior of other quasiparticles.

Gesture recognition with Brownian reservoir computing using geometrically confined skyrmion dynamics

Physical reservoir computing leverages the dynamical properties of complex physical systems to process information efficiently, significantly reducing training efforts and energy consumption. Magnetic skyrmions, topological spin textures, are promising candidates for reservoir computing systems due to their enhanced stability, non-linear interactions and low-power manipulation. Traditional spin-based reservoir computing has been limited to quasi-static detection or real-world data must be rescaled to the intrinsic timescale of the reservoir. We address this challenge by time-multiplexed skyrmion reservoir computing, that allows for aligning the reservoir's intrinsic timescales to real-world temporal patterns. Using millisecond-scale hand gestures recorded with Range-Doppler radar, we feed voltage excitations directly into our device and detect the skyrmion trajectory evolution. This method scales down to the nanometer level and demonstrates competitive or superior performance compared to energy-intensive software-based neural networks. Our hardware approach's key advantage is its ability to integrate sensor data in real-time without temporal rescaling, enabling numerous applications.

Realization of skyrmion shift register

The big data explosion demands novel data storage technology. Among many different approaches, solitonic racetrack memory devices hold great promise for accommodating nonvolatile and low-power functionalities. As representative topological solitons, magnetic skyrmions are envisioned as potential information carriers for efficient information processing. While their advantages as memory and logic elements have been vastly exploited from theoretical perspectives, the corresponding experimental efforts are rather limited. These challenges, which are key to versatile skyrmionic devices, will be studied in this work. Through patterning concaved surface topography with designed arrays of indentations on standard Si/SiO2 substrates, we demonstrate that the resultant non-flat energy landscape could lead to the formation of hexagonal and square skyrmion lattices in Ta/CoFeB/MgO multilayers. Based on these films, one-dimensional racetrack devices are subsequently fabricated, in which a long-distance deterministic shifting of skyrmions between neighboring indentations is achieved at room temperature. Through separating the word line and the bit line, a prototype shift register device, which can sequentially generate and precisely shift complex skyrmionic data strings, is presented. The deterministic writing and long-distance shifting of skyrmionic bits can find potential applications in transformative skyrmionic memory, logic as well as the in-memory computing devices.

Emergent Mechanics of Magnetic Skyrmions Deformed by Defects

While magnetic skyrmions are often modeled as rigid particles, both experiments and micromagnetic simulations indicate their easy-to-deform characteristic, especially when their motion is restricted by defects. Here we establish a theoretical framework for the dynamics of magnetic skyrmions by incorporating the degrees of freedom related to deformation and predict well the current-driven dynamics of deformable skyrmions in the presence of line defects without any parameter fitting, where classical theories based on rigid-particle assumption deviate significantly. Further, we define an emergent property of magnetic skyrmions-flexibility and show that this property strongly modulates the depinning dynamics of skyrmions along a line defect with breaches. Our work explores the emergent mechanics of magnetic skyrmions and extends the current understanding on the dynamics of skyrmions interacted with defects.

Survival of skyrmions along granular racetracks at room temperature

Skyrmions can be envisioned as bits of information that can be transported along nanoracetracks. However, temperature, defects, and/or granularity can produce diffusion, pinning, and, in general, modification in their dynamics. These effects may cause undesired errors in information transport. We present simulations of a realistic system where both the (room) temperature and sample granularity are taken into account. Key feasibility magnitudes, such as the success probability of a skyrmion traveling a given distance along the racetrack, are calculated. The results are evaluated in terms of the eventual loss of skyrmions by pinning, destruction at the edges, or excessive delay due to granularity. The model proposed is based on the Fokker-Planck equation resulting from Thiele's rigid model for skyrmions. The results could serve to establish error detection criteria and, in general, to discern the dynamics of skyrmions in realistic situations.

Enhanced thermally-activated skyrmion diffusion with tunable effective gyrotropic force

Magnetic skyrmions, topologically-stabilized spin textures that emerge in magnetic systems, have garnered considerable interest due to a variety of electromagnetic responses that are governed by the topology. The topology that creates a microscopic gyrotropic force also causes detrimental effects, such as the skyrmion Hall effect, which is a well-studied phenomenon highlighting the influence of topology on the deterministic dynamics and drift motion. Furthermore, the gyrotropic force is anticipated to have a substantial impact on stochastic diffusive motion; however, the predicted repercussions have yet to be demonstrated, even qualitatively. Here we demonstrate enhanced thermally-activated diffusive motion of skyrmions in a specifically designed synthetic antiferromagnet. Suppressing the effective gyrotropic force by tuning the angular momentum compensation leads to a more than 10 times enhanced diffusion coefficient compared to that of ferromagnetic skyrmions. Consequently, our findings not only demonstrate the gyro-force dependence of the diffusion coefficient but also enable ultimately energy-efficient unconventional stochastic computing.

Ordering of room-temperature magnetic skyrmions in a polar van der Waals magnet

Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the μm scale, showing control over this order-disorder transition on scales relevant for device applications.

300-Times-Increased Diffusive Skyrmion Dynamics and Effective Pinning Reduction by Periodic Field Excitation

Thermally induced skyrmion dynamics, as well as skyrmion pinning effects, in thin films have attracted significant interest. While pinning poses challenges in deterministic skyrmion devices and slows down skyrmion diffusion, for applications in non-conventional computing, both pinning of an appropriate strength and skyrmion diffusion speed are key. Here, periodic field excitations are employed to realize an increase of the skyrmion diffusion by more than two orders of magnitude. Amplifying the excitation, a drastic reduction of the effective skyrmion pinning, is reported, and a transition from pinning-dominated diffusive hopping to dynamics approaching free diffusion is observed. By tailoring the field oscillation frequency and amplitude, a continuous tuning of the effective pinning and skyrmion dynamics is demonstrated, which is a key asset and enabler for non-conventional computing applications. It is found that the periodic excitations additionally allow stabilization of skyrmions at different sizes for field values that are inaccessible in static systems, opening up new approaches to ultrafast skyrmion motion by transiently exciting moving skyrmions.

Brownian reservoir computing realized using geometrically confined skyrmion dynamics

Reservoir computing (RC) has been considered as one of the key computational principles beyond von-Neumann computing. Magnetic skyrmions, topological particle-like spin textures in magnetic films are particularly promising for implementing RC, since they respond strongly nonlinearly to external stimuli and feature inherent multiscale dynamics. However, despite several theoretical proposals that exist for skyrmion reservoir computing, experimental realizations have been elusive until now. Here, we propose and experimentally demonstrate a conceptually new approach to skyrmion RC that leverages the thermally activated diffusive motion of skyrmions. By confining the electrically gated and thermal skyrmion motion, we find that already a single skyrmion in a confined geometry suffices to realize nonlinearly separable functions, which we demonstrate for the XOR gate along with all other Boolean logic gate operations. Besides this universality, the reservoir computing concept ensures low training costs and ultra-low power operation with current densities orders of magnitude smaller than those used in existing spintronic reservoir computing demonstrations. Our proposed concept is robust against device imperfections and can be readily extended by linking multiple confined geometries and/or by including more skyrmions in the reservoir, suggesting high potential for scalable and low-energy reservoir computing.