Introduction

Magnetic skyrmions are stable nanoscale whirls of magnetic spin textures1,2,3,4,5,6. Due to their topological stability, small size at the nanometer scale and controlled mobility under low current densities, skyrmions hold the promise to impact significantly next-generation information storage technology7,8,9,10,11,12,13,14,15,16. Initially introduced in nuclear physics as soliton solutions of non-linear field equations1,17, they hold now a distinct place in solid state physics as well, following their theoretical prediction18 and experimental observation19. Broken inversion symmetry that is characteristic to certain crystal structures induces a non-collinear coupling mechanism that contributes as an asymmetric term in the Hamiltonian describing the resulting magnetically chiral ground states20. Under certain conditions, these chiral states concur in forming magnetic skyrmions as observed in archetypal cubic chiral crystals that exhibit a bulk Dzyaloshinskii-Moriya interaction (DMI)19,21,22,23,24,25. Moreover, symmetry breaking along with spin-orbit coupling present at magnetic interfaces lead to a weak interfacial DMI that contributes to the stabilisation of skyrmions observed in thin films26,27,28,29,30 and multilayers31,32,33,34,35,36.

Skyrmion lattices that occur in single crystals fill a small pocket in the phase diagram for temperatures that typically extends over few Kelvin19,37. This is detrimental to applications which require stability over a broad range around room temperature. The temperature pocket can be eventually extended by reducing the dimensionality of the structures or by engineering the interfacial DMI of ferromagnetic thin films and multilayers38. Yet, caused by the skyrmion Hall effect39,40, the trajectories of these ferromagnetic topological units in devices are not straight, being deflected away by the Lorentz forces. To overcome this limitation, ferrimagnetic materials are offering an advantage due to a versatile tunability of their magnetic properties.

Rare earth transition metals (RE-TM) ferrimagnetic (FiM) alloys consist of two anitferromagnetically coupled sublattices. At the compensation temperature (Tcomp), the magnetizations of both sub-lattices are equal, leading to a vanishing net magnetization, just as for an antiferromagnet. By the choice of the elemental composition and through temperature variation, their magnetic properties, including Tcomp, net magnetization and magnetic anisotropy, can be easily engineered, which makes FiM materials advantageous for spintronics devices41,42,43. By selecting the RE element, two classes of FiM can be distinguished, namely Gd-base FiM alloys that exhibit a weak perpendicular magnetic anisotropy (PMA) due to the vanishing orbital moment of the RE, and Dy, Tb, Ho-based FiM alloys which have a stronger PMA due to the large orbital moment of the RE. The latter category has the potential to offer a higher stability of stored information, but the reports on skyrmions in these systems are scarce44.

By contrast, for weak PMA FiM alloys, like FeGdCo, magnetic skyrmions have been recently observed45 and they can be controlled in microstructured devices46,47. Since then, much research has been carried out to enable control and fuctionalization of ferrimagnetic skyrmions: they have been observed in ferrimagnetic confined nanostructures48; topological spin memory is reported for Co/Gd multilayers exhibiting skyrmion stability in fully compensated antiferromagnetically coupled heterostructure49; observation of spin spirals and individual skyrmions in synthetic Pt/CoGd/Pt ferrimagnetic multilayers at room-temperature has been achieved without the assistance of external magnetic fields50; magneto-transport measurements have revealed a topological contribution resulting from the occurrence of an interfacial DMI in Ho/CoFeGd/β-W multilayers51; evidence for chiral ferrimagnetism in an ultrathin GdCo layer has been demonstrated through a combination of high-resolution Lorentz microscopy and XMCD52; Néel-type homochirality has been observed over a large temperature range in Ta/Ir/Fe/GdFeCo/Pt multilayers using scanning electron microscopy with polarization analysis53; and information on Néel versus Bloch DWs can be inferred by a tilt geometry with Lorentz transmission microscopy as shown for a Mn3Sn topological antiferromagnet54. However, a direct determination of the type of the spin structures, namely Néel-type versus Bloch-type, was not experimentally reported, for neither of the two FiM classes.

An unambiguous determination of the skyrmion type is crucial for understanding the stabilization mechanism of skyrmions in these materials. Indeed, one would expect stabilization of Néel-type skyrmions in a thin film system with an interfacial DMI induced by engineering of the spin–orbit coupling of the ferrimagnetic layer with neighboring heavy-metal (HM) layers8. However, this approach usually requires stacking ultrathin magnetic and HM layers into an asymmetric periodic multilayer in order to achieve a sizeable magnitude of DMI and, consequently, a small enough (~100 nm) skyrmion size32. On the other hand, “bulk" DMI stabilizing chiral Bloch-type skyrmions requires an intrinsic lack of inversion symmetry within the material20. Alternatively, skyrmion bubbles having the same topological charge, but degenerate chirality can also be stabilized by dipolar interactions55. Furthermore, dipolar interaction can compete with an interfacial DMI and change the spin rotation sense from Néel to Bloch type, or give rise to hybrid spin textures56. Therefore, unveiling the skyrmion type in FiM will shed light onto the microscopic spin Hamiltonian in this class of thin-film FiM alloys.

In this study, we report real space imaging of the magnetic structures in a FiM DyCo3 thin film by means of scanning transmission x-ray microscopy (STXM), utilizing both x-ray magnetic circular dichroism (XMCD) and x-ray magnetic linear dichroism (XMLD) contrast57,58,59,60,61. Using XMCD-STXM, we directly observe well-isolated FiM skyrmions and their transformation to maze-like domains as a function of an out-of-plane external field. With XMLD-STXM, we demonstrate that these FiM skyrmions are Néel-type and the maze-like domains also show a preference of Néel-type domain walls. We confirm our experimental results to be consistent with micromagnetic simulations. Please note that the experiments reported here are performed at low temperatures (26 K) which correspond to a non-fully compensated magnetization state. The fully compensated magnetization for this ferrimagnet occurs at a temperature that is well above the room temperature, therefore a vanishing skyrmion Hall effect is not addressed (see Supplementary Note 1.2).

Results and discussion

Field dependence of Skyrmion size

In Fig. 1a, we show the hysteresis loop in perpendicular geometry which was measured by SQUID magnetometry. The magnetic reversal of the DyCo3 film as a function of applied field was investigated at 26 K using STXM. Because the maximum magnetic field for the STXM experiments is limited to 260 mT, which is not enough to saturate the sample at low temperatures, we saturated the sample out-of-plane at room temperature prior to the STXM measurements. After cooling down the sample (in a perpendicular magnetic field of +260 mT) to 26 K, the STXM images were obtained with the magnetic field sweeping from +260 to −260 mT. Figure 1b shows selected examples of XMCD-STXM areal images of the FiM skyrmions acquired at different perpendicular magnetic fields. One can distinguish the evolution of well-isolated FiM skyrmions as a function of the magnetic field, ranging from 260 to 140 mT (within the field range that is marked by a gray rectangle in Fig. 1a). The average density and radius of the skyrmions extracted from the STXM images as a function of field are shown in Fig. 1c, d, respectively. It increases from 2.5 to 9.6 skyrmions per square micrometer when the field is decreased from 260 to 140 mT, indicating that the skyrmions can be created and annihilated by varying the field. At the same time, the average skyrmion radius R increases from 45 to 65 nm, demonstrating that the skyrmion size can be reduced and inflated with the external field. When the magnetic field decreases further, the skyrmions will merge into worm- and maze-like domain structures, as shown in the insets of Fig. 1a.

Fig. 1: Hysteresis loop (measured by superconducting quantum interference device (SQUID) magnetometry) and scanning transmission x-ray microscopy (STXM) images of ferrimagnetic (FiM) skyrmions at 26 K.
figure 1

a Out-of-plane magnetic hysteresis loop measured at 26 K by SQUID magnetometry. The external magnetic field μ0H is expressed in units and sub-units of Tesla (T), with μ0 being the vacuum magnetic permeability and H denoting the magnetic field strength. b STXM images showing the FiM skyrmions at different perpendicular magnetic fields recorded at the Dy M5 edge and 26 K. The average density (c) and radius (d) of the skyrmions as a function of external magnetic fields, were extracted from the STXM images. The gray rectangle box in (a) represents the magnetic field range where the FiM skyrmions are probed. The arrow represents the field sweeping direction. The insets of (a) show the transition into maze-like domains.

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Lateral imaging of skyrmions with XMCD contrast

To resolve the details of the FiM skyrmions, high resolution XMCD-STXM images were recorded at the Co L3 and the Dy M5 edges at an external field of 140 mT, as shown in Fig. 2. The left panels display the images of several single skyrmions, whereas in the right panels we show their line profiles along the X and Y axes, which represent the normalized perpendicular magnetic moment of Dy (MDy) and Co (MCo) elements. One can easily observe that the magnetic profiles of MDy and MCo overlap nicely, which clearly demonstrate the formation of FiM skyrmions with an antiparallel alignment of the Dy and Co moments. At this field, the radius (FWHM) of the respective skyrmion is about 65 nm.

Fig. 2: X-ray magnetic circular dichroism imaging of isolated skyrmions.
figure 2

a Scanning transmission x-ray microscopy (STXM) images at the Co L3 edge and the Dy M5 edge (b), respectively. The color bar represents the normalized sublattice magnetization (Mz) along the magnetic field (and the x-ray beam) direction. c, d Line profiles across a skyrmion along the X and Y axes (see the dashed lines in (a)), representing the normalized perpendicular magnetic moment for Dy and Co elements.

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Lateral imaging of skyrmion domain walls with XMLD contrast

To identify the spin structure of the domain walls of the FiM skyrmions, XMLD was utilized by taking advantage of the strong linear dichroism of Dy at the M5 absorption edge. Figure 3a presents the demonstration of x-ray absorption spectroscopy (XAS) at the Dy M5 edge for circular left (CL), circular right (CR), linear vertical (LV) and linear horizontal (LH) polarizations, respectively. The XMCD spectrum was obtained by taking the difference of (CR-CL), and the XMLD spectrum was obtained by taking the difference of (LV-LH). One can see that the maximum XMLD signal appears enhanced at the second peak of the Dy M5 edge whereas the maximum XMCD signal is located at the third peak. The intensity of the XMLD spectra at the Dy edge is sufficiently large to be exploited for the STXM measurements61. Unlike XMCD which is sensitive to the magnetic moments collinear to the x-ray propagation direction, XMLD is sensitive to the magnetic moments collinear to the \(\vec{E}\) vector of linearly polarized x-rays, which lies in the plane of the sample surface for our experimental geometry. To distinguish Néel-type and Bloch-type skyrmions from each other, we made simulations on how the two different types of skyrmions should look like in the presence of circular and linearly polarized x-rays, which are shown in Fig. 3b, c. By comparison, one can see that our experimental data match very well with the Néel-type contrast, indicating that the FiM skyrmions in our DyCo3 thin film are Néel-type skyrmions.

Fig. 3: Resolve of the magnetic domain wall type using x-ray magnetic linear dichroism.
figure 3

a X-ray absorption spectra (XAS) measured by circular left (CL), circular right (CR), linear horizontal (LH) and linear vertical (LV) polarized x-rays, as well as x-ray magnetic linear dichroism (XMLD) and x-ray magnetic circular dichroism(XMCD) spectra at the Dy M5 edge at 4 K. The three peaks of the Dy M5 edge are marked by dashed lines. Expected magnetic image contrast when using circular, LH and LV polarized x-rays for Bloch-type (b) and Néel-type (c) skyrmions. d Experimental Scanning transmission x-ray microscopy (STXM) results. Here the STXM images for LV and LH x-ray polarizations were obtained at the middle peak of the Dy M5 edge, and the STXM image for circular polarized x-rays was measured at the third peak of the Dy M5 edge.

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Lateral imaging of domain walls of a maze domain state with XMLD contrast

After successfully identifying Néel-type skyrmions utilizing the advantage of XMLD, we also investigated the domain walls for maze-like domains using the same technique, as shown in Fig. 4a–c. One can easily observe that the domain walls at the top/bottom sides are more pronounced for LV, and that the domain walls at the left/right sides show more intensity for LH, similar to the domain walls in skyrmions shown in Fig. 3d. Note that, one still can see a weak contrast for some domain walls which do not follow this rule. This result indicates that the majority of the domain walls for maze-like domains are Néel-type with a low mixing of Bloch-type. We also applied Fast Fourier Transform (FFT) to the STXM images, which show different patterns for different polarizations (see Fig. 4d–f. The FFT shows a ring pattern for circular polarization. For linear polarization, however, it shows an ellipse with long vertical axis for LV and an ellipse with long horizontal axis for LH, which represent the preference of Néel-type domain walls (compare also to the results of micromagnetic simulations shown in the Supplementary Notes 3 and 4).

Fig. 4: Imaging of the magnetic domains and domain walls in a maze domain state and their corresponding Fast Fourier Transform.
figure 4

a–c Scanning transmission x-ray microscopy (STXM) images of the maze domains at −260 mT for circular right (CR), linear horizontal (LH) and linear vertical (LV) polarized x-rays, respectively. d–f Fast Fourier Transform (FFT) of the top STXM images, with the dashed circles and ellipses as guide to the eye.

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Micromagnetic simulations

Micromagnetic simulations were performed using the MuMax3 package62 using magnetic parameters for a DyCo3 thin film deduced in a previous study44 and in the present magnetometry measurements that can be found in the Supplementary Information file (see Supplementary Note 1.1).

Figure 5 shows simulated magnetic structures as a function of the magnetic field applied perpendicular to the sample plane. The top row shows the color-coded three-dimensional orientation of the magnetization, and the bottom row shows the in-plane component Mx. A maze domain pattern shows up upon a relaxation of the random magnetization state at zero field (Fig. 5a), featuring also some Néel-type skyrmions with opposite polarities. Skyrmions with core magnetization parallel to the applied magnetic field collapse and disappear upon increasing the field (Fig. 5b). Finally, at a higher field of μ0H = 530 mT the maze domain pattern evolves into a isolated skyrmion phase (Fig. 5c). This phase persists up to 810 mT when the skyrmions collapse and the sample gets fully magnetized along the field. Bottom panels of Fig. 5a–d show the in-plane magnetization component within each cell of the simulation. The contrast inversion from blue (left) to red (right) of each stable Néel-type skyrmion represents the chirality of the system given by the sign of the DMI constant, which is not picked up by the STXM experiment. Importantly, the simulation captures accurately the impact of the domain wall type on the polarization-dependent STXM contrast. Circular and elliptic shapes of FFT patterns in Fig. 4d–f correspond very well to the ones calculated from the simulations (compare to Supplementary Fig. 7) described in the Supplementary Note 3.

Fig. 5: Micromagnetic simulations demonstrating Néel-type skyrmion formation in the presence of a finite Dzyaloshinskii–Moriya interaction.
figure 5

Top row of (a–d): Micromagnetic simulations of relaxed spin configurations for the DyCo3 film as a function of out-of-plane magnetic field. The external magnetic field μ0H is expressed in sub-units of Tesla (T), with μ0 being the vacuum magnetic permeability and H denoting the magnetic field strength. The white and black colors represent the net normalized magnetization being parallel and antiparallel to the z-axis, respectively. The other colors represents the orientation of the in-plane component of the net magnetization within each cell as shown in the color wheel in top panel (d). Bottom row of (a–d): the magnetization component along the x-axis. The color bar shown in the bottom panel (d) represents the normalized net magnetization Mx.

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Interestingly, the simulated skyrmion size is very tunable and can be changed by the external magnetic field by a factor of three from R = 32 nm at 530 mT to R = 9 nm at 810 mT. While the skyrmion size differs from the experimental value quite significantly, lower DMI parameters do not allow to stabilize purely Néel-type skyrmions but rather hybrid ones that carry Bloch caps at the surface (see Supplementary Note 5.2), being consistent with the theory reported for magnetic multilayers63. If no DMI is assumed, the interplay between PMA and the stray field results in the formation of a bubble lattice with dominantly Bloch-type domain walls (see Supplementary Note 5.1). Once a DMI term of sufficient strength is introduced, the stability of the skyrmions is increased towards higher fields, and the unique rotation sense of the domain walls gets defined. Note also that besides the DMI strength, the saturation net magnetization and the magnetic anisotropy parameters play an important role for the skyrmion formation in this material (see Supplementary Fig. 3).

For a discussion on the possible origin of a “bulk" DMI in this system, see ref. 44 and the afferent Supplementary Note 6. Similar observations have recently been reported in Fe3GeTe2 flakes of various thickness where an interplay between dipolar and DM interactions results in a complex history-dependent magnetic phase diagram of spin textures64.

Conclusions

We presented an experimental resolve of skyrmion traits in a ferrimagnetic DyCo3 thin film at 26 K using STXM imaging, utilizing both XMCD and XMLD contrast. With XMCD-STXM, the magnetic structures in real space are revealed as a function of decreasing external field. Well-isolated ferrimagnetic skyrmions are observed between +260 and +140 mT, and the density as well as the radius of the skyrmions can be controlled by the external magnetic field. When the magnetic field is further reduced, these skyrmions will merge into maze-like domains, which matches very well with the results of magnetic simulations. Utilizing XMLD-STXM at the Dy M5 edge, we successfully identify the domain wall type of ferrimagnetic skyrmions to be of Néel-type. Moreover, the domain walls for the maze-like domains are also investigated, revealing also a majority of Néel-type domain walls. Hence, we are able to unambiguously conclude the interfacial-type symmetry65 of DMI in DyCo3 thin film. Nevertheless, the origin of the strong DMI of this type remains an open question. The technique of using XMLD contrast in the STXM measurements at the rare earth M edges provides a promising way to study complex spin textures in real-space, which is highly useful for the characterization of skyrmions, chiral domain walls and various non-collinear magnetic systems.

Methods

Sample preparation and characterization

The ferrimagnetic DyCo3 film of 50 nm thickness was prepared by magnetron sputtering chamber (MAGSSY) at room temperature and in an argon atmosphere of 1.5 × 10−3 mbar with a base pressure of 5 × 10−9 mbar. The stoichiometry of the DyCo3 alloy was controlled by varying the deposition rates of the Co and the Dy targets in a co-sputtering scheme. A Si3N4 membrane with a thickness of 100 nm was used as substrate for the soft x-ray transmission measurements. A capping layer of 3 nm-thick Ta was deposited on top of the sample surface to prevent surface oxidation. The magnetic properties of the sample have been measured by SQUID magnetometry and by anomalous Hall effect (Tensormeter RTM1, HZDR Innovation, Germany), and they are described in the Supplementary Information file.

X-ray measurements

Scanning transmission x-ray microscopy (STXM) measurements were performed at the MAXYMUS endstation at the Bessy II electron storage ring operated by the Helmholtz-Zentrum Berlin für Materialien und Energie66. The x-ray beam was focused with a zone plate and an order selecting aperture on the transmissive sample in the presence of an applied out-of-plane magnetic field which was controlled by varying the arrangement of four permanent magnets. The STXM images were collected pixel by pixel using a piezoelectric sample stage at the Co L3 edge and the Dy M5 edge by exploiting the effects of x-ray magnetic circular dichroism (XMCD) and x-ray magnetic linear dichroism (XMLD). The XMLD contrast represents an intensity map for LV (vertical axis in real space, parallel to the sample surface) and LH (horizontal axis in real space, parallel to the sample surface) orientations of the linear polarization axes. When the linear polarization is perpendicular to the spin axis, the XAS intensity measured at the middle resonance peak of the M5 edge is low (high in transmission), whereas for a parallel orientation of the linear polarization axis with respect to the spin axis, the intensity is high (low in transmission) (see for instance Fig. S1, in ref. 61). This makes the XMLD contrast easy to comprehend for the present transmission geometry of films with perpendicular magnetic anisotropy: a change of intensity along the linear direction shown on the LV, LH and L45 maps (see Supplementary Note 2) can be given only by Néel walls, whereas a change of intensity towards a direction perpendicular to the linear polarization direction can be given only by Bloch walls. Note that the experimental XMLD maps shown in the manuscript are all logarithm of the raw data images.

The XAS, XMLD and XMCD spectra for the Dy M5 edge (Fig. 3a) were performed at the Deimos beamline at synchrotron Soleil67 in transmission mode using the same 50 nm-thick DyCo3 sample grown on a Si3N4 membrane. The magnetic field of 2 T, which is much higher than the saturation field, was applied along the beam during the XMCD measurements using circular polarized x-rays and perpendicular to the beam during the XMLD measurements using linear horizontal and linear vertical polarized x-rays.

Magnetic simulations

Micromagnetic simulations were performed using MuMax362. The simulations were performed on a three-dimensional grid 512 × 512 × 25 voxels with the size of 2 × 2 × 2 nm3. The material parameters used for the simulation are given further below and can be found in the Supplementary Information file. A larger scale simulation with a grid of 1024 × 1024 × 25 voxels was carried out for the simulation without DMI, in order to account for the larger domain size. The computation was performed using a graphics processing unit (GPU) NVIDIA GeForce RTX 3080 Ti. The following material parameters were used: exchange stiffness Aex = 6 pJ m−1, saturation magnetization Ms = 600 kA m−1, and uniaxial anisotropy Ku = 130 kJ m−3. The interfacial-type DMI constant Dint was tuned to obtain the isolated field-induced Néel-type skyrmion phase without admixtures of maze domains. The minimal value of DMI required for the purely Néel-type skyrmion stability was found to be Dint = 0.0015 J m−2. It is remarkable that this value amounts about 8% of the exchange energy of DyCo368, in agreement with the suggestion of up to ~20% of the isotropic exchange expected for DMI in disordered systems69,70 (see Supplementary Note 6).