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Skyrmions are excellent candidates for racetrack memory and synaptic devices&lt;sup&gt;1,2&lt;/sup&gt;. However, their movement in ferromagnets (FM) is hindered by their transverse movement (skyrmions Hall effect, SkHE) and pinning at defects&lt;sup&gt;3&lt;/sup&gt;. Ferrimagnetic (FiM) systems are proposed to overcome the transverse movement, while amorphous ferromagnets systems such as CoFeB have already shown significant reduction in pinning&lt;sup&gt;4,5&lt;/sup&gt; but yield skyrmions with larger diameters. Therefore, we propose a robust amorphous-ferrimagnetic system to bring forth the best of the two. So far, skyrmions have been generated in amorphous ferrimagnetic systems such as Pt/GdFeCo/MgO&lt;sup&gt;5&lt;/sup&gt; and Pt/CoGd/TaO&lt;sup&gt;6&lt;/sup&gt; where SkHE and pinning were considerably mitigated. However, these systems lack a certain robustness owing to the rapidly diminishing DMI at the FiM/Heavy metal (HM) interface with increase in rare-earth (RE) content. This hinders the concurrent attainment of small size, desired density, room temperature (RT) stability and high–mobility in skyrmions. To overcome this we followed a strategy previously used to generate dense, small skyrmions in FM&lt;sup&gt;7&lt;/sup&gt;- employing two DMI generating interfaces of Ir/Fe-FiM and Co-FiM/Pt. The two DMIs at the interfaces being additive, strengthens the total DMI and provides a robust, tunable FiM system capable of addressing the above-mentioned challenges.&lt;br/&gt;Figure 1 shows the schematic, hysteresis loops and MFM images of a few of these multilayers. By tuning the rare-earth/3d transition magnetic material ratio and thicknesses in both the FiM layers, along with systematic change in the Tb/Gd ratio (tunes anisotropy) we were able to achieve a robust multilayer FiM system, with small (~50 nm), high-density skyrmions, and up to 88% reduction in the necessary energy to nucleate them. For instance, in 1c we show a considerably high-density of skyrmions, around ~72 nm in diameter, while the magnetization and nucleation fields are reduced by 70% and 88% respectively. Our multilayer system serves as a suitable template for designing desired skyrmion densities, sizes and reduced SkHE along with lower energy requirements for nucleation and possibly movement.

![](https://assets.underline.io/uploads/markdown_image/1/image/5bae4b2d492d8e480f3947ee0e9a336e.jpg)

Figure 1: Schematic, hysteresis loops, MFM (same scale in all images) of a) FM and b)-c) FiM

2022 Joint MMM-INTERMAG

Robust and tunable rare-earth ferrimagnetic systems for dense, small and high-mobility skyrmions at room temperature

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INTERMAG 2021

Skyrmions are excellent candidates for racetrack memory and synaptic devices1,2. However, their movement in ferromagnets (FM) is hindered by their transverse movement (skyrmions Hall effect, SkHE) and pinning at defects3. Ferrimagnetic (FiM) systems are proposed to overcome the transverse movement, while amorphous ferromagnets systems such as CoFeB have already shown significant reduction in pinning4,5 but yield skyrmions with larger diameters. Therefore, we propose a robust amorphous-ferrimagnetic system to bring forth the best of the two. So far, skyrmions have been generated in amorphous ferrimagnetic systems such as Pt/GdFeCo/MgO5 and Pt/CoGd/TaO6 where SkHE and pinning were considerably mitigated. However, these systems lack a certain robustness owing to the rapidly diminishing DMI at the FiM/Heavy metal (HM) interface with increase in rare-earth (RE) content. This hinders the concurrent attainment of small size, desired density, room temperature (RT) stability and high–mobility in skyrmions. To overcome this we followed a strategy previously used to generate dense, small skyrmions in FM7- employing two DMI generating interfaces of Ir/Fe-FiM and Co-FiM/Pt. The two DMIs at the interfaces being additive, strengthens the total DMI and provides a robust, tunable FiM system capable of addressing the above-mentioned challenges. Figure 1 shows the schematic, hysteresis loops and MFM images of a few of these multilayers. By tuning the rare-earth/3d transition magnetic material ratio and thicknesses in both the FiM layers, along with systematic change in the Tb/Gd ratio (tunes anisotropy) we were able to achieve a robust multilayer FiM system, with small (~50 nm), high-density skyrmions, and up to 88% reduction in the necessary energy to nucleate them. For instance, in 1c we show a considerably high-density of skyrmions, around ~72 nm in diameter, while the magnetization and nucleation fields are reduced by 70% and 88% respectively. Our multilayer system serves as a suitable template for designing desired skyrmion densities, sizes and reduced SkHE along with lower energy requirements for nucleation and possibly movement.

![](https://assets.underline.io/uploads/markdown_image/1/image/5bae4b2d492d8e480f3947ee0e9a336e.jpg)

Figure 1: Schematic, hysteresis loops, MFM (same scale in all images) of a) FM and b)-c) FiM

technical paper

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Research into magnetic skyrmions and their spintronics applications has revealed complex chiral spin textures. However, direct characterizations of the structure of skyrmion and related spin textures pose an experimental challenge. To better understand their structure, we use Lorentz transmission electron microscopy (LTEM) to track their evolution from well-studied domain walls (DWs) into skyrmion and biskyrmion phases. Magnetic skyrmions were first predicted as a result of the Dzyaloshinskii-Moriya interaction (DMI) found in materials with broken inversion symmetry1. However, topologically equivalent chiral bubbles, or dipole skyrmions, can be stabilized in achiral thin films by competing long-range dipole and short-range DW energies2. Recently, a novel skyrmion phase consisting of bound skyrmion pairs with opposite helicities was reported in achiral Fe/Gd multilayers3 (Fig. 1). However, the primary magnetic imaging techniques for thin films are LTEM, which yields projected in-plane magnetic field, and resonant X-ray techniques, which yield projected out-of-plane magnetization. This complicates identification of complex magnetic spin textures, as multiple spin textures can yield qualitatively similar projected magnetic fields, and there has been subsequent debate over the structure of the reported skyrmion phases4,5. By tracking the field-dependent evolution of magnetic spin textures from the well-studied magnetic stripes to the novel skyrmion phases, we can identify key components of these spin textures. First, by applying an out-of-plane magnetic field with a small in-plane component, stripe DWs form, alternatingly aligned and anti-aligned with the in-plane component, matching previous results2. As the field is further increased, the stripe DWs split, and the aligned DWs form the center of the novel texture, while the anti-aligned form closure loops (Fig. 2), supporting that the magnetization is a pair of contour-rotating vortices. Fully understanding these textures will require knowledge of the 3D structure, so surface sensitive techniques like SEMPA, SPLEEM, and MFM will be vital moving forward.

![](https://assets.underline.io/uploads/markdown_image/1/image/26875a594ef774ade1f7585132522bfd.jpg)

Fig. 1. The projected in-plane field of the novel texture.

![](https://assets.underline.io/uploads/markdown_image/1/image/c339839e8a22aef9d6e717998b111ef8.jpg)

Fig. 2. Stripe domains breaking into the novel phase.

Evolution of Novel Chiral Spin Textures in Fe/Gd Based Multilayers

Anti-symmetric exchange, or the Dzyaloshinskii–Moriya interaction (DMI), is responsible for non-collinear spin textures such as canting, helices and skyrmions in bulk systems or films with asymmetric structure [1]. Analogously, thin films without DMI can have competing anisotropies which stabilise non-collinear magnetic textures. Using resonant soft x-ray scattering, we study the rigid stripe rotation in an Fe/Gd multilayer which accompanies the transition from the stripe phase to the six-fold dipole skyrmion lattice. The sample was measured in transmission and the small-angle diffraction gave the average period and in-plane orientation, Φ, of the perpendicular stripes. By changing the sample tilt, ω, we control the resultant field vector which changes the threshold, Honset, and abruptness of the observed rotation (Fig. 1a). We used micromagnetic simulation software MuMax3 [2] to model the system using similar parameters to previous work [3]. By carefully setting the initial state and polarity of the Bloch center of the helical domain wall we reproduce the rotational behaviour observed experimentally (Fig. 1a(inset), 1b). We show on inspection of the simulated 3D spin structure that as the magnetic field is increased the helical domain wall region tries to unwind before rotation and then reverts back to a more wound structure in the rotated state before transitioning into the skyrmion/bubble lattice and finally saturating.

![](https://assets.underline.io/uploads/markdown_image/1/image/1fa3e6fa70435914350d7a2a9c56d6db.jpg)

(a) The Φ angle of the diffracted peaks is plotted for different values of ω as a function of the modulus of applied field where solid symbols are Hz and open symbols are -Hz. Increasing Φ shows clockwise (CW) motion for ω<1 and counter clockwise (CCW) motion for ω>1 . (Inset) The experimental in-plane (IP) component of Honset along with the corresponding values from the simulations. (b) Micromagnetically simulated rotation of the stripe domains for combined IP and OOP magnetic field. H is indicated at the bottom and is in the z direction for all panels except the bottom row where it denotes an in-plane field along the x direction. Simulated area was 2x2 μm2, color wheel indicates direction of in-plane magnetisation and white and black are up and down perpendicular magnetisation, respectively.

Frustration of coupled helices in weakly perpendicular magnetic thin films

Magnetic racetrack memories offer the possibility of increasing the density and speed of data storage. Yet, achieving fast current-induced motion of domain walls (DWs) and skyrmions at room temperature remains a challenge. We study nearly compensated ferrimagnetic CoGd alloys inserted between two heavy metals for which we have already demonstrated the optimization of spin-orbit torques (SOTs)1 and interfacial Dzyaloshinskii-Moriya interactions2. Ferrimagnets are attractive materials for their low stray field and fast spin dynamics which has been theoretically predicted to enable formation of ultrasmall3 and fast skyrmions. However, so far, the reported skyrmion velocities4 are much lower than of DWs3. Here, we investigate the nucleation and dynamics of chiral magnetic textures induced by current pulses in Pt/CoGd(5 nm)/(W or Ta) films. First, we demonstrate fast motion of DWs driven by SOTs at room temperature. We observe a maximum DW velocity of about 460 m s-1 (Fig. 1). Hence, we confirm that our ferrimagnetic materials have a very low DW pinning and density of defects, which is ideal for fast current-induced motion of DWs and skyrmions. Most literature studies focus on materials with a skyrmionic ground state. Here, our CoGd films have a sharp magnetic hysteresis loop and skyrmions are metastable. In Fig. 2a, we show that we can achieve field free nucleation of skyrmion bubbles with a single 5-ns current pulse and with a density of 2.7 x1012 A m-2. In addition, sequential magneto-optical Kerr (MOKE) imaging (Fig. 2b-f) after applying a single 5-ns current pulse with a density of 1.5 x1012 A m-2 reveals fast skyrmion motion with a velocity of about 400 m s-1. A small out-of-plane magnetic field of -5.7 mT is applied to stabilize the skyrmion bubble. In this study, we demonstrate that our low pinning ferrimagnetic films enable one of the fastest skyrmion motion thus far reported5. Our results could pave the way for ultrafast racetrack memory operations. This research was supported by DARPA award No. D18AP00009.

![](https://assets.underline.io/uploads/markdown_image/1/image/675f52758a6a530350f50604ed06cb0b.jpg)

Average DW velocity driven by SOTs in Pt/CoGd/(W or Ta).

![](https://assets.underline.io/uploads/markdown_image/1/image/c0bb1144e41d0a2de9c390f652bdf62b.jpg)

Field free current-induced nucleation (a) and motion (b-f) of skyrmion bubbles by a single 5-ns current pulse.

Fast current-induced domain wall and skyrmion motion in a nearly compensated amorphous ferrimagnetic alloy

Skyrmions are typically manipulated by driving them with an electrical current in a racetrack and have been proven to be advantageous, due to their high mobility, energy efficient drivability and potential in overcoming edge roughness-related pinning occurring in domain wall (DW)- based racetrack devices [1]-[3]. However, to have high density skyrmion based memory devices, it is essential to create and manipulate skyrmions in magnetic tunnel junctions (MTJs). Previously, it has been shown with micromagnetic simulations that voltage-controlled magnetic anisotropy (VCMA) can be used in perpendicular MTJs to create an intermediate skyrmion starting from a ferromagnetic up/down state and subsequently annihilating it to form a ferromagnetic down/up state [4] and thus energy efficient electrical field switching robust to defects and thermal noise can be achieved. Towards the experimental realization of this switching strategy, skyrmions have to be created and manipulated with VCMA in a confined geometry where the skyrmion lateral dimension equals the lateral dimension of a nanodot. However, so far creation and annihilation of fixed magnetic skyrmions using VCMA has only been experimentally observed through magnetic force microscopy (MFM) imaging in thin ferromagnetic films where the skyrmions are much smaller in lateral dimension compared to the thin films and the imaging was performed after withdrawal of the applied electric field (Fig.1) [5]. Here, we will study experimental creation and annihilation of skyrmions using VCMA in a confined geometry of &lt;1μm lateral dimension with in-situ application of voltage while imaging. This will enable visualization of the skyrmion/ferromagnet state as a function of the applied electric field and the mechanism through which skyrmions can be manipulated with VCMA induced change in PMA in the presence of interactions with the boundary of the patterned nanodot. Fig. 2 shows an example of a nanostructure in which such experiments will be carried out. Acknowledgement: NSF grant CCF #1909030

![](https://assets.underline.io/uploads/markdown_image/1/image/8ddae612ae2d0e4ae2fc5e04ca640dfb.jpg)

Fig. 1. Magnetization state before application of any electric field (a) and after application of negative (b), positive (c) voltage pulse [5]

![](https://assets.underline.io/uploads/markdown_image/1/image/a01a9085cbf4c95176982da23375450e.jpg)

Fig. 2. Skyrmions to be studied in confined geometries

Creation and Annihilation of Magnetic Skyrmions in Confined Geometry using Voltage Control of Magnetic Anisotropy

In magnetic trilayers composed of heavy-metal/ferromagnet/oxide (HM/FM/MOx), the structural inversion asymmetry gives rise to the so-called interfacial Dzyaloshinskii-Moriya interaction (iDMI) [1]. This antisymmetric exchange interaction is at the origin of non-collinear spin textures, such as spin spirals or magnetic skyrmions [2] with chiral Néel domain-walls (DWs). Their dynamics is directly related to their chirality, imposed by the iDMI sign [3]. Thus, controlling their current-induced motion (CIM) driven by spin-orbit torques can be achieved by controlling the iDMI. In this study, we propose techniques to control the skyrmion motion in a Ta/FeCoB/TaOx trilayer, through the control of the iDMI sign and amplitude. The skyrmion motion can be controlled, or even reversed, either by modulation of deposition parameters or dynamically by applying a gate voltage. We have found that modulation of the oxidation state at the FeCoB/TaOx interface (Fig. 1(a-b)) leads to an inversion of the iDMI sign, as measured by Brillouin light scattering. This iDMI sign crossover is accompanied by an inversion of the skyrmion CIM direction. Skyrmion motion reversal can also be triggered by a gate voltage through the control of iDMI sign (Fig. 1(c-d)). Moreover, our micromagnetic simulations show that a fine control of the iDMI amplitude and sign is feasible on individual nanometer-size magnetic skyrmion without annihilating it (Fig. 2(a-c)). The dipolar energy prevents the spin texture from annihilation when iDMI is close to zero, leading to a stable Bloch skyrmion (Fig 2b). The angle of the moments inside the DWs (Fig. 2d) evolves continuously from 0° to 180° when varying the iDMI value. This allows a fine tuning of the skyrmion CIM direction (Fig. 2e), allowing to suppress the skyrmion Hall angle, otherwise detrimental for device applications.

![](https://assets.underline.io/uploads/markdown_image/1/image/0d5c24338e22f487f485d4062d620b55.jpg)

Figure 1: Control of iDMI sign : (a-b) Modulation of the FeCoB/TaOx interface oxidation and (c) Gate-controlled skyrmion motion (Magneto-Optical Kerr Effect images)

![](https://assets.underline.io/uploads/markdown_image/1/image/9276aafb08d714e75ddb64319fe097bf.jpg)

Figure 2: (a-c) Micromagnetic simulations : Adiabatic iDMI reversal on a nm-size magnetic skyrmion leading to (d) continuous transformation from CW (D<0) to CCW chirality (D>0). (e) Skyrmion's trajectory controlled by iDMI value

Get skyrmions back on track : Suppressing skyrmion Hall angle by material engineering or gate voltage

Magnetic Skyrmions are topologically protected swirling structures induced by chiral interactions in non-centrosymmetric magnetic compounds or thin films with broken inversion symmetry [1]. The spintronic devices based on these textures promise increased density and energy efficient data storage due to small nanometric size and topological protection [2][3]. In this work we present the effect of DMI, surface anisotropy, magnetic field and spin orbit torque (SOT) on the creation and annihilation of the skyrmions. Fig.1 (a) shows that the skyrmion density is increased as we increase the magnitude of DMI coefficient from 1mJ/m2 to 3mJ/m2. But with increasing the surface anisotropy the density is reduced and skyrmions are annihilated at some threshold anisotropy Kth which is proportional to the magnitude of the DMI coefficient. Furthermore, the size of skyrmion decreases with increasing anisotropy as shown in Fig. 1(b). In Fig. 1 (c-d) we study the effect of external magnetic field on the skyrmions. Fig. 1 (c) shows the MOKE images of the fabricated sample depicting the transition of magnetic texture from Labriynth domains to skyrmions around 8 Oe. The skyrmion density increases proportionally with field till 20 Oe and begins to roll off after 20 Oe. These results are supported by MuMax simulations as shown in Fig. 1(d). These results suggest that by proper optimization of material parameters and stack geometry we can tweak the skyrmion density for its application in memory and logic. In Fig. 2(a) we show MTJ with skyrmions in the free layer, using SOT control we propose this device for its application in neuromorphic computing. The SOT manipulation of skyrmion size, density and motion is shown in Fig. 2 (b). Increasing current Ic via the heavy metal increases the skyrmion density from 21µm-2 (at 2×1011 A/m2) to 40 21µm-2 (at 8×1011 A/m2). Further increase in Ic results in decrease of the skyrmion density. Finally, we implement a simple neuromorphic circuit using the proposed device.

![](https://assets.underline.io/uploads/markdown_image/1/image/0451b4c2cb6a4b63949ea900b0511b43.jpg)

Fig. 1: (a) Skyrmion density vs anisotropy and DMI coefficient. (b) Density and size of skyrmion vs anisotropy. (c) MOKE images (d) MuMax simulations.

![](https://assets.underline.io/uploads/markdown_image/1/image/363eb0a3db7cbc306cb4f2f3e42c459d.jpg)

(a) Skyrmion-MTJ neuromorphic device. (b) Skyrmion density vs current density

Creation and Annihilation of Skyrmions for Neuromorphic Computing Applications

Skyrmion-based devices have been proposed as candidates for future low-power, ultra-dense nanocomputing and neuromorphic systems enabled by the characteristic properties (nanoscale size, non-volatility, robustness, low current density of propagation) of magnetic skyrmions, arising from their topology [1-2]. This is more pressing especially since the recent experimental demonstrations at room temperature (e.g., in technologically relevant magnetic multilayers (MMLs) [3-4]). At the same time, skyrmions have attracted extensive interest in CMOS-compatible nanodevices that can emulate biological synapses. Specifically, a multi-bit storage device using skyrmions as information carriers (bits) has been proposed in ideal conditions [5-6]. However, room temperature operation is required to integrate skyrmionic synapses in practical future devices. In our recent work [7], we propose a nanoscale skyrmionic synapse composed of MMLs that enables room temperature device operation (Fig. 1). We demonstrate that when embedding such MML skyrmionic synapses in a simple spiking neural network (SNN) with the spike-timing-dependent plasticity (STDP) learning rule, we can achieve only a ~75% classification accuracy in the MNIST handwritten data set. We propose that this performance can be significantly improved to ~98.61% by using a deep SNN with supervised learning rules. Our results illustrate that the proposed skyrmionic synapse can be a competitive candidate for future energy-efficient neuromorphic computing and edge computing.

![](https://assets.underline.io/uploads/markdown_image/1/image/ab5e21eb72c5f492aa06ba6e24bb2d6f.jpg)

Fig. 1. Schematic of biological neurons connected with a synapse, and the proposed nanoscale multilayer skyrmionic synapse device. The multilayer structure enables room-temperature operations.

Nanoscale room-temperature skyrmionic synapse for deep spiking neural networks

Skyrmionic devices show potential for low-power-low-heat nanocomputing with multiple information carriers, enabled by quasi-particles with a topological charge N, including skyrmions (N=±1) [1] and skyrmioniums (N=0) [2-3]. This is more pressing since the co-existence of stable and high-degree skyrmionic configurations with arbitrary value and sign of N has been experimentally demonstrated in liquid crystals and numerically predicted in ferromagnetic systems [4-5]. Hitherto, skyrmionic on-site memory, nanocomputing, and neuromorphic components have increasingly been investigated [6-7]. However, the “missing component” in skyrmionics so far has been an all-magnetic skyrmion-based interconnect, which may be relevant to future spintronic neuromorphic computing and quantum computing hardware. Our recent work investigates the dynamics of magnetic skyrmionic quasi-particles for a new concept for skyrmionic nanodevices, i.e., skyrmionic interconnect device [8]. We propose encoding sequences of information by using distinct skyrmionic quasi-particles as information carriers in a single device, such that we exploit topological filtering in order to enable automatic signal multiplexing (Fig. 1), circumventing the need for control signals. This results in saving signal routing by 50%, a major benefit compared to modern CMOS devices. We then propose to strategically etch notches in the device to introduce pipelining, which significantly boosts the signal throughput of the device. Our proposal widens the possibilities for spintronics-based nanocomputing.

![](https://assets.underline.io/uploads/markdown_image/1/image/28d051e7ad5fe9607f48995d96d5c5e1.jpg)

Fig. 1. Schematic drawing of the proposed skyrmionic interconnect device, and spin texture of a Néel skyrmion and a skyrmionium.

Skyrmionic Interconnect Device

Inversion symmetry breaking (ISB) is of great significance in governing many interesting physics. For example, the interfacial Dzyaloshinskii-Moriya interaction (DMI) exists at the heavy metal/ferromagnet (HM/FM) interface with the ISB along the sample normal direction, which holds promises for design and control of chiral spin textures in low-dimensional magnets with efficient current-driven dynamics [1,2]. In this talk, we discuss about a synthetic antiferromagnet (SAF) with built-in planar asymmetry which is attributed to both variable ferromagnetic-layer thickness and the spacer thickness. First we show how the sign and strength of the interlayer exchange coupling (IEC) and magnetic configurations depend on the ferromagnetic-layer thicknesses and the spacer thickness [3]. Interestingly, the IEC can be efficiently modified via changing the ferromagnetic-layer thickness which is essential to advancing magnetic memory and sensing [4] applications with efficient controls. Furthermore, we show the demonstration of the existence of interlayer DMI in our SAF with the built-in planar asymmetry, which supports a chiral magnetization across the SAF. We present the study of current-induced spin-orbit torque (SOT) switching of the chiral magnetization across the SAF and analyse the interlayer DMI’s effects on magnetization and its switching through a combination of experimental and numerical studies [5]. Based on our studies, we will give an outlook of potential applications of our findings in future SOT and domain wall-based devices.

Synthetic antiferromagnet with built-in planar asymmetry

Magnetic skyrmions are topological spin textures that can be stabilized by the Dzyaloshinskii-Moriya interaction [1,2]. There are particularly suitable for next generation spintronics devices, like the skyrmion-based racetrack memory [3]. Recent studies confirmed their current-driven skyrmion dynamics in ultrathin ferromagnets via spin-orbit torques [4], where the chirality and spin texture of the skyrmions are key. However, the topological Magnus effect leads to a transverse motion of ferromagnetic skyrmions due to their non-zero topological charge [5], which is disadvantageous for devices. Antiferromagnetically exchange-coupled skyrmions or compensated ferrimagnets could suppress this effect owing to an overall zero topological charge [6]. Here we explore a GdFeCo-based ferrimagnet system with perpendicular magnetic anisotropy. We demonstrate that in this system the chirality of worm domains as well as a magnetic skyrmionium can be observed using scanning electron microscopy with polarization analysis (SEMPA) (Figure) [7]. The high spatial resolution magnetic imaging technique reveals the domain wall (DW) spin structure as a function of temperature, with the observed structures found to be pure Néel-type spin textures, which is promising for devices. From the images we extract the DW width as a function of the temperature and we calculate the exchange stiffness for the system. Figure: Determination of the magnetization direction inside the DW of different ferrimagnetic chiral spin textures. a) The direction of the in-plane magnetization in the DW is displayed, as defined by the color wheel in the bottom left corner of the image. Scale bar in a): 1 µm. b) Distribution of the direction of the in-plane magnetization in the DW with respect to the local tangent at RT: angle Ψ (see inset where a clockwise angle is defined as negative following the usual convention). A Gaussian fit indicates a central value around −90°. c) Absolute in-plane magnetization intensity with the DW skeleton displayed in white and d) direction of the in-plane magnetization in the DW of a ferrimagnetic skyrmionium at 320 K. Scale bars in c,d): 500 nm. Extracted from [7].

![](https://assets.underline.io/uploads/markdown_image/1/image/92e18cd0f6b430b4b7a16c0928992f0f.jpg)

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