Skyrmion Diameter Research Articles

Size and density control of skyrmions with picometer CoFeB thickness variations—observation of zero-field skyrmions and skyrmion merging

The controlled formation and adjustment of size and density of magnetic skyrmions in Ta/CoFeB/MgO trilayers with low Dzyaloshinskii–Moriya interaction is demonstrated. Close to the out-of-plane to in-plane magnetic spin reorientation transition, we find that small energy contributions enable skyrmion formation in a narrow window of 20 pm in CoFeB thickness. Zero-field stable skyrmions are established with proper magnetic field initialization within a 10 pm CoFeB thickness range. Using magneto-optical imaging with quantitative image processing, variations in skyrmion distribution and diameter are analyzed quantitatively, the latter for sizes well below the optical resolution limit. We demonstrate the controlled merging of individual skyrmions. The overall demonstrated degree of comprehension of skyrmion control aids to the development of envisioned skyrmion based magnetic memory devices.

Study of skyrmions stability in strained VTe2 monolayer using DFT calculations and Monte-Carlo simulations

The structural, electronic, and magnetic properties of the H-VTe2 monolayer under external strain have been studied by first-principles approaches with Hubbard U corrections combined with Monte Carlo (MC) simulation. We investigated the magnetic spin textures in the VTe2 monolayer using the Heisenberg Hamiltonian, which includes the ferromagnetic interaction J, magnetic anisotropy K, Dzyaloshinskii–Moriya interaction DMI, and the applied magnetic field B. We have numerically verified that the skyrmion can be created by the competition between these different interactions. At T = 0 K, the ground state (GS) is determined by minimizing the interaction energy and showing that the transition phase occurs at about Tc= 555 K. Also, we have demonstrated that if a magnetic field, has a direction opposite to the magnetic moment of the skyrmion center, attains a critical value Bc, the core of the skyrmion inverses the direction of its magnetization in order to recover the FM ground state. Moreover, we have studied the phase diagram in the plane (B,DMI). We have deduced that for a certain range of the DMI a skyrmion crystal can be stabilized within a certain range of the magnetic fields. Finally, we investigated the effect of the external magnetic field on the properties of the skyrmions, such as the skyrmion number (Nsky) and diameter (d).

Quantum oscillations in the centrosymmetric skyrmion-hosting magnetGdRu2Si2

The skyrmion formation mechanism in centrosymmetric systems remains to be understood, partially because of the lack of fundamental understanding of the electronic structure. The authors observe de Haas--van Alphen and Shubnikov--de Haas oscillations in high magnetic fields up to 58 $T$ on GdRu${}_{2}$Si${}_{2}$, which is one of such centrosymmetric skyrmion-hosting magnets with the shortest skyrmion diameter ever found. Combined with first-principles calculations, the authors now reveal the electronic structure of GdRu${}_{2}$Si${}_{2}$ and its reconstruction at the magnetic phase boundary.

Analysis of Skyrmion Shuffling Chamber Stochasticity for Neuromorphic Computing Applications

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.

Enhancement of skyrmion density via interface engineering

Magnetic skyrmions are promising candidates for computing and memory applications. The static and dynamic behaviors of skyrmions are tunable by altering the interfacial magnetic properties. These interfacial magnetic properties are alterable by modifying the interface structure of thin films. However, the relationship between the structural properties of the interface and the skyrmions properties is not straightforward, and a comprehensive insight is required to facilitate better controllability of the skyrmions’ behaviors. Here, we comprehensively understand the relationship between atomic displacements at the interface and skyrmions’ static behavior. In this study, we used ion irradiation to achieve inter-atomic displacements. We observed that the inter-atomic displacements could tailor the physical properties of skyrmions. We noticed a peculiar increase in the magnetization, Dzyaloshinskii–Moriya interaction, and exchange stiffness. The modifications in magnetic properties reduced the domain wall energy, which enhanced the skyrmion density (by six-folds) and reduced the average skyrmion diameter (by 50%). Furthermore, we compared the observed results of ion irradiation with those from the annealing process (a well-studied method for modifying magnetic properties) to better understand the effect of atomic displacements. Our study provides a route to achieve a highly-dense skyrmion state, and it can be explored further to suppress the skyrmion Hall effect for skyrmion-based applications.

Size-dependent mobility of skyrmions beyond pinning in ferrimagnetic GdCo thin films

Magnetic skyrmions are swirling magnetic textures that can be efficiently driven with spin-orbit torques with a deflected trajectory. However, pinning slows skyrmions down and alters their trajectory, which prevents a quantitative comparison to analytical models. Here, we study skyrmions driven by spin-orbit torques at room temperature in ferrimagnetic GdCo thin films, an amorphous material with low pinning. Above a sharp current depinning threshold, we observe a clearly linear velocity increase with current that extrapolates to zero and a constant deflection angle, reaching high velocities up to 200 m/s. The mobility increases and the depinning threshold current decreases with the skyrmion diameter, which we vary using an external magnetic field. An analytical model based on the Thiele equation quantitatively reproduces these findings with a single fitting parameter. This validates the linear flow regime description and shows, in particular, the important role of skyrmion size in its dynamics.

Collective skyrmion motion under the influence of an additional interfacial spin-transfer torque

Here we study the effect of an additional interfacial spin-transfer torque, as well as the well-established spin–orbit torque and bulk spin-transfer torque, on skyrmion collections—group of skyrmions dense enough that they are not isolated from one another—in ultrathin heavy metal/ferromagnetic multilayers, by comparing modelling with experimental results. Using a skyrmion collection with a range of skyrmion diameters and landscape disorder, we study the dependence of the skyrmion Hall angle on diameter and velocity, as well as the velocity as a function of diameter. We show that inclusion of the interfacial spin-transfer torque results in reduced skyrmion Hall angles, with values close to experimental results. We also show that for skyrmion collections the velocity is approximately independent of diameter, in marked contrast to the motion of isolated skyrmions, as the group of skyrmions move together at an average group velocity. Moreover, the calculated skyrmion velocities are comparable to those obtained in experiments when the interfacial spin-transfer torque is included. Our results thus show the significance of the interfacial spin-transfer torque in ultrathin magnetic multilayers, which helps to explain the low skyrmion Hall angles and velocities observed in experiment. We conclude that the interfacial spin-transfer torque should be considered in numerical modelling for reproduction of experimental results.

Scaling of voltage controlled magnetic anisotropy based skyrmion memory and its neuromorphic application

Voltage controlled skyrmion memory requires less energy compared to current controlled method where voltage changes magnetic anisotropy (VCMA) and Dzyaloshinskii-Moriya interaction (DMI). Ferromagnetic (FM) and synthetic antiferromagnetic (SAFM) memory devices are simulated using electric field control method where gate and gap width are chosen as smaller than skyrmion size so that skyrmion can feel the change in voltage polarity in the neighbouring gate and moves accordingly. Scaling of memory device is performed which shows SAFM memory can be made much narrower compared to FM memory as skyrmion diameter also depends on width of the structure. Effects of device structure and skyrmion-skyrmion repulsion force on skyrmion diameter variation are shown in cylindrical structure considering effect of demagnetizing field. Apart from these, neuromorphic application is considered where skyrmion moves from central square neuron region to surrounding synapse region or vice versa by the application of voltage. Switching time, voltage range, energy and scaling of device dimensions are shown for synapse-neuron having different number of skyrmions where multiple skyrmions represent different weight in the neuromorphic circuit.

Thermal motion of skyrmion arrays in granular films

Magnetic skyrmions are topologically distinct swirls of magnetic moments which display particlelike behavior, including the ability to undergo thermally driven diffusion. In this paper we study the thermally activated motion of arrays of skyrmions using temperature dependent micromagnetic simulations where the skyrmions form spontaneously. In particular, we study the interaction of skyrmions with grain boundaries, which are a typical feature of sputtered ultrathin films used in experimental devices. We find the interactions lead to two distinct regimes. For longer lag times the grains lead to a reduction in the diffusion coefficient, which is strongest for grain sizes similar to the skyrmion diameter. At shorter lag times the presence of grains enhances the effective diffusion coefficient due to the gyrotropic motion of the skyrmions induced by their interactions with grain boundaries. For grain sizes significantly larger than the skyrmion diameter clustering of the skyrmions occurs in grains with lower magnetic anisotropy.

Zero-field skyrmions in FeGe thin films stabilized through attaching a perpendicularly magnetized single-domain Ni layer* *Project supported by the National Natural Science Foundation of China (Grant No. 11774045), the Joint Research Fund Liaoning-Shenyang National Laboratory for Materials Science (Grant No. 20180510008), and the Fundamental Research Funds for Central Universities, China (Grant No. N182410008-1).

A numerical study reports that the zero-field skyrmions in FeGe thin films are stabilized when a FeGe layer is exchange coupled to a single-domain Ni layer, which has been magnetized perpendicularly. Due to the small thickness, an easy-plane anisotropy in the FeGe layer is taken into account, and the skyrmion-crystal state is favored to appear for low anisotropies and intermediate FeGe/Ni interlayer exchange couplings, and finally transformed from a labyrinth-like and into an out-of-plane uniform state for the large couplings or into an in-plane state for the high anisotropies. Furthermore, the maximum skyrmion charge number is bigger for the periodic and fixed boundary conditions with an out-of-plane magnetization; on the contrary, the Bloch-type skyrmions can be frozen and stabilized for the larger couplings on the fixed boundary with an in-plane magnetization, similar to the experimental results of the magnetic-field-induced skyrmions. Finally, the skyrmion charge number and diameter both decrease if the nonmagnetic defects exist, and the skyrmion centers are prone to being captured by defect sites. This work evidences that the ensembles of homochiral skyrmions stabilized in the multilayers fabricated by well-established technologies present a roadmap to design new classes of the materials that can host skyrmions.

Néel Skyrmionic States and Chiral Stripes in the Magnetic Bilayer with Transverse Easy Axis

Chiral spin structures, such as skyrmions, are topologically nontrivial magnetization configurations, which have potential applications in magnetic recording media. In particular, an antiferromagnetically coupled system that hosts skyrmions is of great interest because of high-speed skyrmion motion and reduced skyrmion Hall effect. Here, we consider TbCo/GdFe-based amorphous ferrimagnetic system showing chiral stripe domains and Neel-type skyrmions. It is observed that skyrmionic configurations are stabilized with the help of dipolar interactions that exist in the system. Optimized thicknesses of TbCo (30 nm) and GdFe (6 nm) show isolated skyrmions in both the layers with average skyrmion diameter of 40 ± 5 nm. We have also investigated a phase diagram in a wide range of layer thickness, which represents the presence of the mixture of either vortex, chiral stripes, or/and Neel-type skyrmions. To understand the underlying phenomena which help chiral ferrimagnetism in this kind of amorphous system, we perform layer-resolved micromagnetic modeling. We found variety of chiral textures in a wide thickness range of ferrimagnetic bilayer systems, which may be useful for fundamental understanding of formation of skyrmion and their application in spintronic devices.

Role of an additional interfacial spin-transfer torque for current-driven skyrmion dynamics in chiral magnetic layers

Skyrmions can be driven by spin-orbit torques as a result of the spin Hall effect. Here we model an additional contribution in ultra-thin multilayers, arising from the spin accumulation at heavy metal / ferromagnetic interfaces and observe the effects on a large range of skyrmion diameters. The combination of the interfacial spin-transfer torque and the spin-orbit torque results in skyrmion motion which helps to explain the observation of small skyrmion Hall angles for skyrmion diameters less than 100 nm. We show that this additional term has a significant effect on the skyrmion dynamics and leads to rapidly decreasing skyrmion Hall angles for small skyrmion diameters, as well as a skyrmion Hall angle versus skyrmion velocity dependence nearly independent of the surface roughness characteristics. Also, the effect of various disordered energy landscapes, in the form of surface roughness, on the skyrmion Hall angle and velocity is shown to be largely drive-dependent. Our results show good agreement with those found in experiments thus concluding that the interfacial spin-transfer torque should be included in micromagnetics simulations for the reproduction of experimental results.

Statistical Properties and Configurational Entropy of a Two-Dimensional Néel Magnetic Skyrmions Population

The study of the thermodynamic properties of topological defects is important not only for understanding their magnetic properties but also for suggesting novel applications. In this paper, the statistical and statistical thermodynamic properties of a population of Néel magnetic skyrmion diameters hosted in an ultrathin cylindrical dot is determined within a two-dimensional analytical approach. The statistical properties such as the skyrmion size are calculated in the region of skyrmion metastability and are compared with the ones obtained using a recent three-dimensional analytical approach based on the analogy with the Maxwell–Boltzmann distribution of dilute gas molecules. The investigation of the statistical thermodynamic properties focus on the calculation of the configurational entropy at thermodynamic equilibrium determined in the continuous limit from the Boltzmann order function. While the statistical properties are quantitatively similar passing from the two-dimensional to the three-dimensional approach, the configurational entropy calculated from the two-dimensional skyrmions distribution is considerably lower than the one obtained from the three-dimensional skyrmions distribution. Because of the strong resemblance between the statistical configurational entropy and Jaynes’s information entropy, it is suggested to use magnetic skyrmions as temperature and external field dependent information entropy carriers for a future potential technological application in the field of low-dimensional magnetic systems and skyrmionics.

Statistical Thermodynamics of Chiral Skyrmions in a Ferromagnetic Material.

Solitons are a challenging topic in condensed matter physics and materials science because of the interplay between their topological and physical properties and for the crucial role they play in topological phase transitions. Among them, chiral skyrmions hosted in ferromagnetic systems are axisymmetric solitonic states attracting a lot of attention for their dazzling physical properties and technological applications. In this paper, the equilibrium statistical thermodynamics of chiral magnetic skyrmions developing in a ferromagnetic material having the shape of an ultrathin cylindrical dot is investigated. This is accomplished by determining via analytical calculations for both Néel and Bloch skyrmions: (1) the internal energy of a single chiral skyrmion; (2) the partition function; (3) the free energy; (4) the pressure; and (5) the equation of state of a skyrmion diameters population. To calculate the thermodynamic functions for points (2)–(5), the derivation of the average internal energy and of the configurational entropy is crucial. Numerical calculations of the thermodynamic functions for points (1)–(5) are applied to Néel skyrmions. These results could advance the field of materials science with special regard to low-dimensional magnetic systems.

Skyrmion motion induced by voltage-controlled in-plane strain gradients

Micromagnetic simulations are used to investigate the motion of magnetic skyrmions in an in-plane strain gradient. The skyrmion diameter and energy are found to depend on the strain, which leads to a force that moves the skyrmion toward regions with higher strain. An analytical expression for the skyrmion velocity as a function of the strain gradient is derived assuming a rigid profile for the skyrmion, and good agreement with simulations is obtained. Furthermore, electromechanical simulations of a hybrid ferromagnetic/piezoelectric device show that the in-plane strain gradients needed to move skyrmions can be achieved by applying moderate voltages in the piezoelectric substrate, which offers an original way to control skyrmion motion efficiently.

Experimental Observation of Single Skyrmion Signatures in a Magnetic Tunnel Junction.

We have deterministically created a stable topological spin texture in magnetic tunnel junctions (MTJ) by using pulsed or microwave currents. The spin texture is characterized by a field-dependent intermediate resistance state and a new magnetic resonance. Micromagnetic simulations show that the observations are consistent with the nucleation of a single skyrmion, facilitated by a spatially nonuniform stray field. The unique resonance spectrum is identified as the skyrmion breathing mode and a skyrmion diameter of 75nm is estimated. This work shows the possibility to create skyrmions in MTJs without the Dzyaloshinskii-Moriya interaction and could lead to noninvasive, on-chip skyrmion measurement.

Impact of interlayer coupling on magnetic skyrmion size

Abstract We study the magnetic skyrmion formation in thin-film stacks, consist of two magnetic layers separated by a non-magnetic spacer. The Landau-Lifshitz-Gilbert equation, comprising the spin precession term and the damping term with all relevant contributions, is numerically solved within the micromagnetic framework. Through extensive systematic calculations, we find that skyrmion size can be controlled by the interlayer exchange coupling, as well as the external magnetic field. z-component of the magnetization of the layers, which can be tailored by the coupling, strongly affects the skyrmion diameter. The skyrmion phase coexists with the helical phase for both types of coupling, being antiferromagnetic or ferromagnetic, in the absence of the magnetic field. The size of the skyrmions at zero field can also be controlled by the interaction. We anticipate that our predictions not only expand our fundamental understanding of the physical mechanisms responsible for skyrmion formation but also provide rational basis for the next-generation logic/memory device applications.

Configurational entropy of magnetic skyrmions as an ideal gas

The study of thermodynamics of topological defects is an important challenge to understand their underlying physics. Among them, magnetic skyrmions have a leading role for their physical properties and potential applications in storage and neuromorphic computing. In this paper, the thermodynamic statistics of magnetic skyrmions is derived. It is shown that the skyrmion free energy can be modelled via a parabolic function and the diameters statistics obeys the Maxwell-Boltzmann distribution. This allows for making an analogy between the behavior of the distribution of skyrmion diameters statistics and the diluted gas Maxwell-Boltzmann molecules distribution at thermodynamical equilibrium. The calculation of the skyrmion configurational entropy, due to thermally-induced changes of size and shape of the skyrmion, is essential for the determination of thermal fluctuations of the skyrmion energy around its average value. These results can be employed to advance the field of skyrmionics.

Quantifying chiral exchange interaction for Néel-type skyrmions via Lorentz transmission electron microscopy

Magnetic skyrmions are topological spin textures that have been observed in bulk magnets and magnetic multilayers. For bulk magnetic materials, their noncollinear spin profiles have often been studied by using Lorentz transmission electron microscopy (TEM). We experimentally utilized Lorentz TEM imaging to study an inversion asymmetric ${[\mathrm{Pt}(1.5\phantom{\rule{0.16em}{0ex}}\mathrm{nm})/\mathrm{Co}(1\phantom{\rule{0.16em}{0ex}}\mathrm{nm})/\mathrm{W}(1\phantom{\rule{0.16em}{0ex}}\mathrm{nm})]}_{8}$ heterostructure that exhibits N\'eel-type skyrmions at zero field. By tracking the evolution of skyrmion diameters as a function of magnetic fields, we determined the strength of the interfacial Dzyaloshinskii-Moriya interaction (DMI). Our results suggest that in situ Lorentz TEM imaging combined with simulations can provide valuable quantitative information about the interfacial DMI strengths, which can be helpful for optimizing skyrmion materials. Furthermore, we show that in theory, Lorentz TEM can identify the spin chirality of N\'eel-type skyrmions, although an experimental verification is challenging due to the relatively low signal-to-noise ratio.

Building traps for skyrmions by the incorporation of magnetic defects into nanomagnets: Pinning and scattering traps by magnetic properties engineering

In this work we have used micromagnetic simulations to report four ways to build traps for magnetic skyrmions. Magnetic defects have been modeled as local variations in the material parameters, such as the exchange stiffness, saturation magnetization, magnetocrystalline anisotropy and Dzyaloshinskii-Moriya constant. We observe both pinning (potential well) and scattering (potential barrier) traps when tuning either a local increase or a local reduction for each one of these magnetic properties. It is found that the skyrmion-defect aspect ratio is a crucial parameter to build traps for skyrmions. In particular, the efficiency of the trap is compromised if the defect size is smaller than the skyrmion size, because they interact weakly. On the other hand, if the defect size is larger than the skyrmion diameter, the skyrmion-defect interaction becomes evident. Thus, the strength of the skyrmion-defect interaction can be tuned by the modification of the magnetic properties within a region with suitable size. Furthermore, the basic physics behind the mechanisms for pinning and for scattering is discussed. In particular, we discover that skyrmions move towards the magnetic region which tends to maximize its diameter; it enables the magnetic system to minimize its energy. Thus, we are able to explain why skyrmions are either attracted or repelled by a region with modified magnetic properties. Results here presented are of utmost significance for the development and realization of future spintronic devices, in which skyrmions will work as information carriers.