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Skyrmion lattice defects a Visualisation of an edge dislocation in a skyrmion crystal. This dislocation manifests itself as a topological defect, which can be thought of as one skyrmion gaining a nearest neighbour from an adjacent skyrmion; the Voronoi cells surrounding the skyrmions with 5 and 7 nearest neighbours are coloured yellow and green, respectively. This so-called 5–7 defect can glide along its Burgers vector, indicated by b, costing very little energy. The Burgers vector of a 5–7 defect must lie along a real lattice basis vector²⁸. Were the lattice sheared vertically, strain could be efficiently relieved by propagation of the pictured 5–7 defect along its Burgers vector. b Idealized visualization of the diffraction pattern from a strained 2D crystal with a 5–7 defect. Strain in the vicinity of the defect elongates four of the peaks anisotropically: the Burgers vector specifies a unique direction and its corresponding defect breaks the six-fold symmetry of the hexagonal lattice³⁴.
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Magnetic skyrmions are topologically non-trivial, swirling magnetization textures that form lattices in helimagnetic materials. These magnetic nanoparticles show promise as high efficiency next-generation information carriers, with dynamics that are governed by their topology. Among the many unusual properties of skyrmions is the tendency of their...
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Magnetic skyrmions are nanoscale spin textures touted as next-generation computing elements. When subjected to lateral currents, skyrmions move at considerable speeds. Their topological charge results in an additional transverse deflection known as the skyrmion Hall effect (SkHE). While promising, their dynamic phenomenology with current, skyrmion...
Magnetic skyrmions are attracting much attention due to their nontrivial topology and high mobility to electric current. Nevertheless, suppression of the skyrmion Hall effect and maintaining high velocity of skyrmions with low energy cost are two major challenges concerning skyrmion-based spintronic devices. Here we show theoretically that in a nan...
Topological charge Q classifies non-trivial spin textures and determines many of their characteristics. Most abundant are topological textures with |Q| ≤ 1, such as (anti)skyrmions, (anti)merons or (anti)vortices. In this study we created and imaged in real space magnetic skyrmion bundles, that is, multi-Q three-dimensional skyrmionic textures. The...
Magnetic skyrmions have gained unprecedented attention for their potential applications in spintronic devices, such as non-volatile memory, energy-efficient, and non-von Neumann devices. In particular, skyrmions in synthetic antiferromagnets (SAF) are believed to overcome the fundamental limitations of the widely studied ferromagnetic skyrmions in...
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... The magnitude of this Hall angle increases linearly with , escalating by a factor of 40 as progresses from 0.1 to 1, while the skyrmion's velocity experiences only a slight rise from 280 to 300 m/s (see Fig. 7(b)). Our investigation affirms the theoretical projections [25,[72][73][74], that skyrmions of opposing polarities present Hall angles that are equal in magnitude yet opposite in sign. Thus replacing a skyrmion with opposite polarity but the same chirality results in Hall angles at different values that are equal in size but opposite in direction. ...
Magnetic skyrmions have garnered attention for their potential roles in spintronic applications, such as information carriers in computation, data storage, and nano-oscillators due to their small size, topological stability, and the requirement of small electric currents to manipulate them. Two key challenges in harnessing skyrmions are the stabilization requirement through a strong out-of-plane field, and the skyrmion Hall effect (SkHE). Here, we present a systematic model study of skyrmions in FM/AFM multi-layer structures by employing both atomistic Monte Carlo and atomistic spin dynamics simulations. We demonstrate that skyrmions stabilized by exchange bias have superior stability than field-stabilized skyrmions due to the formation of a magnetic imprint within the AFM layer. Additionally, stacking two skyrmion hosting FM layers between two antiferromagnetic (AFM) layers suppresses the SkHE and enables the transport of AFM-coupled skyrmions with high velocity in the order of a few Km/s. This proposed multi-layer configuration could serve as a pathway to overcome existing limitations in the development of skyrmion-based devices, and the insights obtained through this study contribute significantly to the broader understanding of topological spin textures in magnetic materials.
... One of the key differences between skyrmions and superconducting vortices is that skyrmions have a strong Magnus force that creates velocities that are perpendicular to the forces experienced by the skyrmions. As a result, under a drive skyrmions move at an angle with respect to the driving direction, called the skyrmion Hall angle [35,37,59,67,[69][70][71][72][73]. Additionally, the Magnus force affects the fluctuations skyrmions experi-033221-2 ence from moving over the pinning landscape [74]. ...
We investigate the topological defect populations for superconducting vortices and magnetic skyrmions on random pinning substrates under driving amplitudes that are swept at different rates or suddenly quenched. When the substrate pinning is sufficiently strong, the system exhibits a nonequilibrium phase transition at a critical drive into a more topologically ordered state where there are few non-sixfold coordinated particles. We examine the number of topological defects that remain as we cross the ordering transition at different rates. In the vortex case, the system dynamically orders into a moving smectic, and the Kibble-Zurek scaling hypothesis gives exponents consistent with directed percolation. Due to their strong Magnus force, the skyrmions dynamically order into an isotropic crystal, producing different Kibble-Zurek scaling exponents that are more consistent with coarsening. We argue that, in the skyrmion crystal, the topological defects can both climb and glide, facilitating coarsening, whereas in the vortex smectic state, the defects cannot climb and coarsening is suppressed. We also examine pulsed driving across the ordering transition and find that the defect population on the ordered side of the transition decreases with time as a power law, indicating that coarsening can occur across nonequilibrium phase transitions. Our results should be general to a wide class of nonequilibrium systems driven over random disorder where there are well-defined topological defects.
... In many magnetic systems, this stems from broken inversion symmetry in the crystal, resulting in a Dzyaloshinskii-Moriya interaction (DMI), or at interfaces, leading to the Rashba effect, that can stabilize such topologically nontrivial spin configurations 2,6 . Due to the topological protection from weak fluctuations and the ability to manipulate them with a magnetic field or charge current, magnetic skyrmions are of significant interest for next generation information technologies [7][8][9][10][11] . Neuromorphic computing architectures based on skyrmions have been proposed, using the diffusion of skyrmions and the resulting magnetoresistance to carry out probabilistic computing [12][13][14] . ...
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.
... In this study, as illustrated in Fig. 2, it was observed that at high current densities, skyrmions move with high velocities and can drift away from the track direction due to the Hall angle [Brearton 2021]. To address this issue, high anisotropy constant materials have been proposed to be added at the edges of the racetrack, as discussed in reference [Lai 2017]. ...
In this study, micromagnetic simulations of a magnetic skyrmion reshuffling chamber for probabilistic computing applications are performed. The skyrmion shuffling chamber is modeled with a custom current density masking technique to capture current density variation, grain boundary variations, and anisotropy changes. The results show that the skyrmion oscillatory dynamics contribute to the system's stochasticity, allowing uncorrelated signals to be achieved with a single chamber. Our findings indicate that uncorrelated signals are generally achieved at all temperatures simulated, with the skyrmion diameter playing a role in the resulting stochasticity. Furthermore, we find that local temperature control has the benefit of not affecting the overall skyrmion diameter, while still perturbing the skyrmion trajectory. The results from varying chamber size, global temperature, and local temperature are analyzed using Pearson correlation coefficient (PCC) and p-value. This research contributes to the development of tunable probabilistic computing devices and artificial synapses using magnetic skyrmions.
... Due to its topological stability in nature, it is easy to control electrically in the device architecture. The origin of chiral spin textures of skyrmion is due to the competition among several energies like magnetic anisotropy energy, exchange energy, demagnetization energy, Zeeman energy and Dzyaloshinskii-Moriya interaction (DMI), which is observed in magnetic systems lacking inversion symmetry [10][11][12][13][14][15][16]. Skyrmion based logic also possess these qualities to be as key player in this emerging domain [17][18][19] and also serves as an excellent [20][21][22] platform for developing new logic and memory architectures [23][24][25][26][27]. Skyrmions are a potential prospects for beyond-Moore systems because of their nanoscale dimension, room temperature stability, despite the skyrmion Hall effect's nonlinear motion posing certain obstacles [16,[20][21][22][28][29][30][31][32][33][34]. ...
In this study, we introduce the area efficient low complex runtime reconfigurable architecture design methodology based on Skyrmion logic for universal logic gate (ULG) i.e., NOR / NAND implementation using micromagnetic simulations. We have modelled the two input 3D device structure using bilayer ferromagnet/heavy metal where the magnetic tunnel junctions (MTJs) inject and detect the input and output skyrmions by exploiting the input reversal mechanism. The implementation of NOR and NAND is performed using this same device where it is reconfigured runtime with enhanced tunability by the ON and OFF state of current passing through a nonmagnetic metallic gate respectively. This gate acts as a barrier for skyrmion motion (additional control mechanism) to realize the required Skyrmion logic output states. To the best of authors's knowledge the boolean optimizations and the mapping logic have been presented for the first time to demonstrate the functionalities of the NOR / NAND implementation. This proposed architecture design methodology of ULG leads to reduced device footprint with regard to the number of thin film structures proposed, low complexity in terms of fabrication and also providing runtime reconfigurability to reduce the number of physical designs to achieve all truth table entries (∼75 % device footprint reduction). The proposed 3D ULG architecture design benefits from the miniaturization resulting in opening up a new perspective for magneto-logic devices.
... In this letter, as illustrated in Fig. 2, it was observed that at high current densities, skyrmions move with high velocities and can drift away from the track direction due to the Hall angle [Brearton 2021]. To address this issue, high anisotropy constant materials have been developed to be added at the edges of the racetrack, as discussed in Lai [2017]. ...
In this study, micromagnetic simulations of a magnetic skyrmion reshuffling chamber for probabilistic computing applications are performed. The skyrmion shuffling chamber is modeled with a custom current density masking technique to capture current density variation, grain boundary variations, and anisotropy changes. The results show that the skyrmion oscillatory dynamics contribute to the system's stochasticity, allowing uncorrelated signals to be achieved with a single chamber. Our findings indicate that uncorrelated signals are generally achieved at all temperatures simulated, with the skyrmion diameter playing a role in the resulting stochasticity. Furthermore, we find that local temperature control has the benefit of not affecting the overall skyrmion diameter, while still perturbing the skyrmion trajectory. The results from varying chamber size, global temperature, and local temperature are analyzed using Pearson correlation coefficient (PCC) and p-value. This research contributes to the development of tunable probabilistic computing devices and artificial synapses using magnetic skyrmions.
... magnetic anisotropy [35]. It is known that the damping constant is correlated to the skyrmion Hall effect [36][37][38]. The skyrmion has a motion perpendicular to the direction of the current flow considered along the nanowire. ...
Skyrmions are the smallest stable magnetic textures and they could be considered ideal elements for ultra-dense magnetic memories. The size and the speed of the skyrmions are crucial characteristics for their proper functionality. In this study, the modified Landau–Lifshitz–Gilbert formalism is carried out to understand the correlation between the physical properties and skyrmion performances such as stability, size and motion speed. The magnetic anisotropy, Dzyaloshinskii–Moriya interaction, exchange coupling and saturation magnetization are varied and magnetization dynamics is evaluated. It is found that all parameters mentioned can affect the speed and dimension of the skyrmion. The calculations are conducted using nanosecond pulsed current. In summary, a phase diagram combining several parameters is established, which could define the optimal conditions for achieving small-sized skyrmions that can be displaced with high velocity.
... Describing the motion of particles in lossy environments (such as colloids in water) and quasiparticles such as topological defects often involves a mobility matrix µ, such thatẋ = µ ·F ≡ F , whereF = −∇V is potential. Such an equation of motion arises, for example, in collections of fast-spinning, pinned gyroscopes connected by springs (215,216,217,218,219,206,220,221,222,223), skyrmions (224,225,226,227,228,229) and vortices in superfluids (230,231,232,233,234,235,236,237,238) 10 , see Fig. 6E-G. ...
Elasticity typically refers to a material's ability to store energy, while viscosity refers to a material's tendency to dissipate it. In this review, we discuss fluids and solids for which this is not the case. These materials display additional linear response coefficients known as odd viscosity and odd elasticity. We first introduce odd elasticity and odd viscosity from a continuum perspective, with an emphasis on their rich phenomenology, including transverse responses, modified dislocation dynamics, and topological waves. We then provide an overview of systems that display odd viscosity and odd elasticity. These systems range from quantum fluids, to astrophysical gasses, to active and driven matter. Finally, we comment on microscopic mechanisms by which odd elasticity and odd viscosity arise.
... In this geometry, the coexistence between various states is easily observed, since the states are remarkably similar in free energy [23]. This coexistence is easily achieved in real samples and has the potential to be utilised within skyrmionic devices, as these states occupy local minima within the magnetic Hamiltonian, and as such have repulsive interactions [27]. ...
... In our simulations, an isolated skyrmion is driven downstream towards the two possible exits, guided by edge states [41]. A number of mechanisms have been proposed to induce isolated skyrmion motion, including thermal and magnetic field gradients [27,42,43]. However, despite Cu 2 OSeO 3 ...
Magnetic skyrmions are vortex-like, swirls of magnetisation whose topological protection and particle-like nature have suggested them to be suitable for a number of novel spintronic devices. One such application is skyrmionic computing, which has the advantage over conventional schemes due to the amalgamation of logic calculations and data storage. Using small-angle neutron scattering from Cu2OSeO3, and applying electric and magnetic fields, we find that the direction of the skyrmion-coexisting conical states can be manipulated by varying the electric field, and explain this using a free energy approach. Our findings unlock the prospect of creating a number of skyrmion devices which may constitute part of a skyrmion computer, as the direction of a skyrmion within a nanosized racetrack can be manipulated into different channels by controllably changing the direction of the localised conical state. We provide time-dependant micromagnetic simulations to demonstrate such a device: a skyrmion double transistor.
... Experimental detection.-The meron lattice phase can be measured by directly imaging the magnetization pattern in real space through Lorentz transmission electron microscopy [26,67] and nitrogen vacancy magnetometry [68] or in reciprocal space via X-ray diffraction [22,[69][70][71][72][73][74]. The spontaneous magnetization can also be measured through magneto-optical measurements such as the magneto-optical Kerr effect (MOKE) [75,76] and reflective magnetic circular dichroism (RMDC) [77]. ...
We present a promising new route to realize spontaneous magnetic order on the surface of a 3D topological insulator by applying a superlattice potential. The superlattice potential creates tunable van Hove singularities, which, when combined with strong spin-orbit coupling and Coulomb repulsion give rise to a topological meron lattice spin texture. The periodicity of this designer meron lattice can be tuned by varying the periodicity of the superlattice potential. We characterize the magnetic order using Ginzburg-Landau theory and show that the magnetic transition temperature reaches experimentally accessible values. Our work introduces a new direction to realize exotic quantum order by engineering interacting Dirac electrons in a superlattice potential, with promising applications to spintronics.
