# Direct observation of Néel-type skyrmions and domain walls in a
ferrimagnetic thin film via scanning transmission X-ray microscopy

Chen Luo  Helmholtz-Zentrum-Berlin für Materialen und Energie, Albert-
Einstein-Straße 15, 12489 Berlin, Germany  Institute of Experimental Physics
of Functional Spin Systems, Technical University Munich, James-Franck-Straße
1, 85748 Garching b. München, Germany  Kai Chen<EMAIL_ADDRESS>Helmholtz-Zentrum-Berlin für Materialen und Energie, Albert-Einstein-Straße
15, 12489 Berlin, Germany  National Synchrotron Radiation Laboratory,
University of Science and Technology of China, Hefei, Anhui 230029, China
Victor Ukleev  Helmholtz-Zentrum-Berlin für Materialen und Energie, Albert-
Einstein-Straße 15, 12489 Berlin, Germany  Sebastian Wintz  Helmholtz-Zentrum-
Berlin für Materialen und Energie, Albert-Einstein-Straße 15, 12489 Berlin,
Germany  Max-Planck-Institut für Intelligente Systeme, 70569 Stuttgart,
Germany  Markus Weigand  Helmholtz-Zentrum-Berlin für Materialen und Energie,
Albert-Einstein-Straße 15, 12489 Berlin, Germany  Max-Planck-Institut für
Intelligente Systeme, 70569 Stuttgart, Germany  Karel Prokeš  Helmholtz-
Zentrum-Berlin für Materialen und Energie, Hahn-Meitner Platz 1, D-14109
Berlin, Germany  Florin Radu<EMAIL_ADDRESS>Helmholtz-
Zentrum-Berlin für Materialen und Energie, Albert-Einstein-Straße 15, 12489
Berlin, Germany

###### Abstract

Isolated magnetic skyrmions are stable, topologically protected spin textures
that are at the forefront of research interests today due to their potential
applications in information technology. A distinct class of skyrmion hosts are
rare earth - transition metal (RE-TM) ferrimagnetic materials. To date, the
nature and the control of basic traits of skyrmions in these materials are not
fully understood. We show that for an archetypal ferrimagnetic material that
exhibits strong perpendicular anisotropy, the ferrimagnetic skyrmion size can
be tuned by external magnetic fields. Moreover, by taking advantage of the
high spatial resolution of scanning transmission X-ray microscopy (STXM) and
utilizing a large x-ray magnetic linear dichroism (XMLD) contrast that occurs
naturally at the RE resonant edges, we resolve the nature of the magnetic
domain walls of ferrimagnetic skyrmions. We demonstrate that through this
method one can easily discriminate between Bloch and Néel type domain walls
for each individual skyrmion. For all isolated ferrimagnetic skyrmions, we
observe that the domain walls are of Néel-type. This key information is
corroborated with results of micromagnetic simulations and allows us to
conclude on the nature of the Dzyaloshinskii–Moriya interaction (DMI) which
concurs to the stabilisation of skyrmions in ferrimagnetic systems.
Establishing that an intrinsic DMI occurs in RE-TM materials will also be
beneficial towards a deeper understanding of chiral spin texture control in
ferrimagnetic materials.

##  I INTRODUCTION

Magnetic skyrmions are stable nanoscale whirls of magnetic spin textures
Skyrme (1962, 1962); Roessler  _et al._ (2006); Yu  _et al._ (2010); Münzer
_et al._ (2010); Sampaio  _et al._ (2013); Fert  _et al._ (2017). 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 technology Parkin  _et al._
(2008); Fert  _et al._ (2013); Parkin and Yang (2015); Zhang  _et al._ (2015);
Tomasello  _et al._ (2014); Kang  _et al._ (2016); Tomasello  _et al._ (2017);
Zhang  _et al._ (2020); Hoffmann  _et al._ (2021); One  _et al._ (2022).
Initially introduced in nuclear physics as soliton solutions of non-linear
field equations Skyrme (1961, 1962), they hold now a distinct place in solid
state physics as well, following their theoretical prediction Bogdanov and
Yablonskii (1989) and experimental observation Mühlbauer  _et al._ (2009).
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
states Bogdanov and Hubert (1994). 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)
Mühlbauer  _et al._ (2009); Seki  _et al._ (2012); Neubauer  _et al._ (2009);
Onose  _et al._ (2012); Pöllath  _et al._ (2019); Ukleev  _et al._ (2022).
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 films Yu  _et al._ (2011); Heinze
_et al._ (2011); Bode  _et al._ (2007); Yu  _et al._ (2016); Jiang  _et al._
(2015) and multilayers Romming  _et al._ (2013); Moreau-Luchaire  _et al._
(2016); Woo  _et al._ (2016, 2017); Hrabec  _et al._ (2017); Boulle  _et al._
(2016).

Skyrmion lattices that occur in single crystals fill a small pocket in the
phase diagram for temperatures that typically extends over few Kelvin
Mühlbauer  _et al._ (2009); Buhrandt and Fritz (2013). 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 multilayers Ma  _et al._ (2022). Yet, caused by
the skyrmion Hall effect Jiang  _et al._ (2017); Litzius  _et al._ (2017), 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 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
devices Radu and Sánchez-Barriga (2018); Kim  _et al._ (2022); Sala and
Gambardella (2022). 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 scarce Chen  _et al._ (2020).

By contrast, for weak PMA FiM alloys, like FeGdCo, magnetic skyrmions have
been recently observed Kim  _et al._ (2019) and they can be controlled in
microstructured devices Woo  _et al._ (2018); Wu  _et al._ (2020). Since then
much research has been carried out to enable control and fuctionalization of
ferrimagnetic skyrmions: they have been observed in ferrimagnetic confined
nanostructures Brandão  _et al._ (2019); topological spin memory is reported
for Co/Gd multilayers exhibiting skyrmion stability in fully compensated
antiferromagnetically coupled heterostructure Wang  _et al._
(2022);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 fields Brandão  _et al._ (2022);
magneto-transport measurements have revealed a topological contribution
resulting from the occurrence of an interfacial DMI in Ho/CoFeGd/$\beta-$W
multilayers Budhani  _et al._ (2022); evidence for chiral ferrimagnetism in an
ultrathin GdCo layer has been demonstrated through a combination of high-
resolution Lorentz microscopy and XMCD Streubel  _et al._ (2018); Néel-type
homochirality has been observed over a large temperature range in
Ta/Ir/Fe/GdFeCo/Pt multilayers using scanning electron microscopy with
polarisation analysis Seng  _et al._ (2021); and information on Néel versus
Bloch DWs can be inferred by a tilt geometry with Lorentz transmission
microscopy as shown for a Mn3Sn topological antiferromagnet Xu  _et al._
(2021). 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) layers Fert  _et al._
(2013). 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 ($\sim 100$ nm)
skyrmion size Moreau-Luchaire  _et al._ (2016). On the other hand, "bulk" DMI
stabilizing chiral Bloch-type skyrmions requires an intrinsic lack of
inversion symmetry within the material Bogdanov and Hubert (1994).
Alternatively, skyrmion bubbles having the same topological charge, but
degenerate chirality can also be stabilized by dipolar interactions Büttner
_et al._ (2018). 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 textures Legrand  _et al._ (2018). 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) contrast Thole  _et al._ (1985); Kuiper  _et al._
(1993); Kortright  _et al._ (2000); Schütz  _et al._ (1987); Luo  _et al._
(2019). Using XMCD-STXM, we directly observe well-isolated FiM skyrmions and
their transformation to maze-like domains as a function of the 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.

##  II Results and discussion

###  II.1 Field dependence of Skyrmion size

Figure 1:  Hysteresis loop (measured by SQUID) and STXM images of FiM
skyrmions at 26 K. (a) Out-of-plane magnetic hysteresis loop measured at 26 K
by SQUID magnetometry. (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 grey rectangle box in panel
(a) represents the magnetic field range where the FiM skyrmions are probed.
The arrow represents the field sweeping direction. The insets of panel (a)
show the transition into maze-like domains.

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 mT 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 mT to 140 mT (within the field range that is
marked by a grey 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. The average density increases from 2.5 to 9.6 skyrmions per square
micrometer when the field is decreased from 260 mT 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 nm to 65 nm,
demonstrating 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.

Figure 2: (a) STXM images at the Co L3 edge and the Dy M5 edge (b),
respectively. (c, d) Line profiles across a skyrmion along the X and Y axes
(see the dashed lines in panel a), representing the normalized perpendicular
magnetic moment for Dy and Co elements.

###  II.2 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
($M_{\textrm{Dy}}$) and Co ($M_{\textrm{Co}}$) elements. One can easily
observe that the magnetic profiles of $M_{\textrm{Dy}}$ and $M_{\textrm{Co}}$
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.

###  II.3 Lateral imaging of skyrmion domain walls with XMLD contrast

Figure 3: (a) XAS, XMLD and 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 STXM results. Here the STXM
images for LV and LH 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.

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 measurements Luo  _et al._ (2019). 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
$\overrightarrow{E}$ 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 and 3c. 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.

Figure 4: (a-c) STXM images of the maze domains at -260 mT for CR, LH and LV
polarized X-rays, respectively, as well as their Fast Fourier Transform (FFT)
(d-f) with the dashed circle and ellipses as a guide for the eye.

###  II.4 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. 4. 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.

###  II.5 Micromagnetic simulations

Figure 5: Micromagnetic simulations of relaxed spin configurations for the
DyCo3 film as a function of out-of-plane magnetic field. The white and black
represent the magnetization being parallel and antiparallel to the $z$-axis,
respectively. The color code represents the orientation of the in-plane
component of the magnetization within each cell as shown in the color wheel in
panel (d). Bottom panels show the magnetization component along the $x$-axis,
with the color code of the intensity of $M_{\textrm{x}}$ being given in the
bottom panel (d).

Micromagnetic simulations were performed using the MuMax3 package
Vansteenkiste  _et al._ (2014) using magnetic parameters for a DyCo3 thin film
deduced in a previous study Chen  _et al._ (2020) and in the present
magnetometry measurements that can be found in the Supplementary Information
file.

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 $M_{x}$. 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
$\mu_{0}H=530$ 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 Figs. 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 polarisation-dependent STXM contrast. Circular and elliptic shapes
of FFT patterns in Figs. 4d,e,f correspond very well to the ones calculated
from the simulation (see Supplementary Figure S6).

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 Figure S10), being consistent with the theory
reported for magnetic multilayers Lemesh and Beach (2018). 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 Figure S8). 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. For a
discussion on the possible origin of a "bulk" DMI in this system see Ref. Chen
_et al._ (2020) and the afferent section S6 in the Supplementary Information
file. 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 textures
Birch  _et al._ (2022).

##  III Conclusions

We presented 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 ferrimagntic skyrmions
are observed between +260 mT and +140 mT, and the density as well as the
radius of the skyrmions can be controlled by the external field. When the
external 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 wall. Hence, we are able to unambiguously
conclude the interfacial-type symmetry Buhl (2019) 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.

##  IV Methods

###  IV.1 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
$1.5\times 10^{-3}$ mbar with a base pressure of $5\times 10^{-9}$ 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 are
described in the Supplementary Information file.

###  IV.2 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 Energie Nolle  _et al._ (2012).
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 Figure S1, in Ref Luo  _et al._ (2019)). 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 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 Soleil Ohresser  _et al._ (2014) 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.

###  IV.3 Magnetic simulations

Micromagnetic simulations were performed using MuMax3 Vansteenkiste  _et al._
(2014). The simulation was performed on a three-dimensional grid $512\times
512\times 25$ voxels with the size of $2\times 2\times 2$ 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
$1024\times 1024\times 25$ 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
$A_{\textrm{ex}}=6$ pJm-1, saturation magnetization $M_{s}$ = 600 kAm-1, and
uniaxial anisotropy K${}^{\textrm{u}}$ = 130 kJm-3. The interfacial-type DMI
constant $D_{\textrm{int}}$ 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
$D_{\textrm{int}}$=0.0015 J/m2. It is remarkable that this value amounts about
8% of the exchange energy of DyCo$3$ Yakinthos and Mentzafos (1975), in
agreement with the suggestion of up to $\sim$20% of the isotropic exchange
expected for DMI in disordered systems Fert and Levy (1980); Fert (1990) (see
section S6 in the Supplementary Information file).

##  V Acknowledgments

We thank the Helmholtz-Zentrum Berlin für Materialien und Energie for the
allocation of synchrotron radiation beamtime. F. R. acknowledges financial
support by the German Research Foundation via Project No. SPP2137/RA 3570. We
acknowledge the use of the Physical properties laboratory, which is part of
the CoreLab "Quantum Materials" operated by HZB. F. R. acknowledges insightful
information provided by Dr. Eugen Weschke on the UE46 undulator operation.

##  VI Contributions

C.L., K.C. and F.R. conceived and designed the experiments. K.C. prepared the
samples. C.L. and F.R. performed the STXM experiments with the help of S.W.
and M.W., C.L. and K.C. analyzed the STXM data and prepared the figures. V.U.
performed the micromagnetic simulations. K.P. performed the magnetic
characterization by SQUID. C.L., V.U. and F.R. wrote the manuscript draft. All
authors discussed the results and contributed to the manuscript.

## Supplementary Information

##  S1 Magnetic Characterization

The magnetic properties of the sample have been measured by SQUID
magnetometry. The sample has been cooled down to 2 K in a magnetic field of 2
Tesla and magnetic hysteresis loops have been measured as a function of
temperature, on warming. They are shown in the Figure S1. The left axis
displays the magnetization in kA/m as a function of an external magnetic field
which was applied in a direction perpendicular to the sample surface. At each
temperature a field dependent magnetization was measured without the sample to
correct for the eventual contributions from the sample holder itself. The
absolute value of the magnetization is obtained by dividing the corrected
SQUID raw response (emu) on the volume of the layer which is area $\times$
thickness, where the measured surface area was measured to be $6.53\times
10^{-6}\textrm{m}^{2}$ and the thickness of the film is $50\times
10^{-9}\textrm{m}$. The hysteresis loops exhibit a typical characteristic
shape for films with perpendicular magnetic anisotropy, showing the onset of
the magnetization reversal at the nucleation field (the magnetic field where
the global remagnetization initiates), followed by magnetic domains formation
down to the annihilation field where the magnetization is fully reversed.

The nucleation field is extracted for each temperature and is shown in Figure
S2. It exhibits a peculiar behavior: it has negative values at room
temperature, changes sign at an intermediate temperature of about 230 K,
increases in absolute values up to about 50 K and decreases again, even to
negative values, towards lower temperatures. This type of behavior is expected
for ferrimagnetic alloys due to the interplay between the anisotropy and the
demagnetization energies.

in Figure S3 the saturation net magnetization extracted at the highest applied
field is shown together with the magnetization at the nucleation field. The
net magnetization increases from room temperature towards lower temperatures
in a monotonic way. Interestingly, the net magnetization at the nucleation
field begins to deviate significantly from the saturation magnetization at a
temperature of about 150 K. This temperature range (150 K to 2 K) can be
considered as the phase diagram for the skyrmions formation.

With the magnetic parameters determined from the hysteresis loops, one can
extract the uniaxial magnetic anisotropy of the film as Aharoni (2000); Carcia
_et al._ (1985):

$K^{u}=\frac{1}{2}\mu M_{net}(-H_{n}+4\pi M_{net})$ (1)

where $H_{N}$ is the nucleation field, $M_{net}$ is the net magnetization at
the nucleation field. The results are shown in Figure S4. We observe that the
magnetic anisotropy changes as function of temperature in an expected fashion.
For ferrimagnetic films, it is dominated by the single ion anisotropy which
further follows the character of the orbital magnetic moment of the rare
earth. The orbital magnetic moment was measured previously by soft x-ray
spectroscopy Chen  _et al._ (2015). It exhibits a non-monotonic increase below
200 K which correlates well with the temperature dependence of the anisotropy
determined from the SQUID data.

The magnetic compensation temperature of the film is about 380 K Chen  _et
al._ (2015).

Figure S1: Hysteresis loops measured by SQUID at different temperatures with
field applied perpendicular to the sample’s surface. Figure S2: Temperature
dependence of the nucleation field determined from data shown in Fig. S1

Figure S3: Top panel: Saturation net magnetization extracted from the
hysteresis loops at 2 Tesla (black down-triangles) and the magnetization at
the nucleation field(blue up-triangles). Bottom panel: The difference between
the saturation net magnetization and the magnetization at the nucleation
field. This panel can be considered at a phase diagram for temperature range
(0-150K) of skyrmions formation. Figure S4: Temperature dependence of the
magnetic anisotropy calculated according to Eq. 1.

##  S2 STXM images for a 45 degrees orientation of the linear polarization

A 45∘ rotation of the linear X-ray polarization was implemented to investigate
the skyrmions for larger areas, as demonstratively shown in Figure S5. By
comparing such a STXM image to those with LH and LV polarization, it can be
seen that the contrast of the domain walls also rotates by 45 degrees, which
further confirms that the skyrmions are Néel-type.

Note that in spite of a clear Néel character, the the skyrmion and domain
walls shape exhibit distortions. Given that the atomic arrangements in
amorphous alloys are not well-defined, local variation of magnetic anisotropy
and stiffness may impact on the homogeneity of the magnetic ground states.
Also, local pinning at eventual defect sites may contribute to complex
skyrmion shape distortions Gruber  _et al._ (2022).

Figure S5:  XMLD-STXM images of skyrmions at 140 mT and 30 K for LH and LV,
and 45∘ linear x-ray polarization.

##  S3 Micromagnetic simulations: Fast Fourier Transform of the maze-domain
state with Néel walls

The $M_{z}$, $M_{x}$, and $M_{y}$ magnetization components of the maze domain
pattern resulting from the micromagnetic simulations are shown in Figure S6,
together with their Fast Fourier transform (FFT) patterns. The FFTs correspond
well to the experimental data shown in Figure 4d of the main text. While the
FFT of the $M_{z}$ component, which corresponds to the contrast mechanism to
the circular light, results in a ring of intensity (Figure S6a), the FFT
patterns for the square of $M_{x}$, $M_{y}$ show arcs of intensity aligned in
horizontal and vertical directions, respectively (Figure S6b,c). On the other
hand, the FFTs of the experimental data measured with linear horizontal and
vertical light polarizations (Figure 4e,f) appear as elongated ellipses
because of a broader width distribution of the maze domains in the real
sample, which is further convoluted with the finite resolution of STXM images.

Figure S6:  Micromagnetic simulations of the zero-field maze domain pattern
for the DyCo3 film. Magnetization components (a) $M_{z}$, (b) $M_{x}$, and (c)
$M_{y}$ are shown, respectively. First (from the left) bottom panel shows the
Fast Fourier transform (FFT) of the $M_{z}$ component while the other two
bottom panels show the FFT of the square of the corresponding upper $M_{x}$
and $M_{y}$ patterns.

##  S4 Micromagnetic simulations: Fourier Transform of the maze-domain state
with Bloch walls

FFT of $M_{z}$, $M_{x}$, $M_{y}$ components were also calculated for the
micromagnetic simulations results without taking a DMI into account (Figure
S7). While the ring-like intensity is clearly observed in the FFT of the
$M_{z}$ component, FFTs for $M_{x}$ and $M_{y}$ are clearly rotated by 90∘
compared to the previous case (Figure S6). This clearly indicates the Bloch
type character of the maze domain walls for a vanishing DMI in contrast to the
Néel type case when the DMI is present.

Figure S7:  Micromagnetic simulations of the zero-field maze domain pattern
for the DyCo3 film without taking DMI into account. Magnetization components
(a) $M_{z}$, (b) $M_{x}$, and (c) $M_{y}$ are shown, respectively. First (from
the left) bottom panel shows the Fast Fourier transform (FFT) of the $M_{z}$
component while the other two bottom panels show the FFT of the square of the
corresponding upper $M_{x}$ and $M_{y}$ patterns.

##  S5 Micromagnetic simulations: Few more relevant showcases

###  S5.1 Case 1: Simulations for magnetic parameters corresponding to 26 K,
without DMI

The magnetic field dependence of the maze domain pattern has been calculated
also for the case of a vanishing DMI, where the magnetic ground state is
determined by the interplay between dipolar interaction and uniaxial
anisotropy only. Except for the DMI constant, all the other parameters in the
simulation are similar to the ones in the main text. Figure S8 shows the
simulated magnetization distributions at zero applied magnetic field, 230 mT,
340 mT and 450 mT. Relatively large ($\sim$100 nm) magnetic domains are
observed at zero field, that evolve into worm-like stripes and, finally, into
skyrmion bubbles as higher out-of-plane magnetic field is applied. The size of
the bubbles originally formed at 340 mT decreases to 45 nm at 450 mT and then
the skyrmion state collapses into a homogeneous one as the field is further
increased. As a result, in the absence of DMI, maze domain walls and field-
induced skyrmions are clearly identified as Bloch-type, which can be easily
seen in the bottom panels of Figure S8, where the intensity of the $M_{x}$
component changes from positive to negative at the top and bottom edges of the
skyrmions. This is in contrast to the case of Néel type domain walls and
skyrmions where the intensity of these maps is rotated by 90 degrees (see main
text).

Figure S8:  Micromagnetic simulations of the spin configurations for the DyCo3
film as a function of magnetic field without taking any DMI into account.The
white and black represent the magnetization parallel and anti-parallel to the
$z$-axis. The color code represents the orientation of the in-plane component
of the magnetization within each cell as shown in the color wheel in the panel
(d). The bottom panels show the magnetization component along the $x$-axis.
The color code of the intensity of $M_{\textrm{x}}$ is given in the bottom
panel (d).

###  S5.2 Case 2: Simulations for the magnetic parameters corresponding to 200
K with DMI

Micromagnetic simulations for a saturation magnetization of $M_{s}=358.5$
kA/m, an uniaxial anisotropy of $K^{\textrm{u}}=69.8$ kJm-3 and DMI equal to
$D_{int}=0.0015$ Jm-2 were carried out to mimic the sample behavior at 200 K.
The saturation net magnetization and magnetic anisotropy parameters were
extracted from the magnetometry measurements. Here, large magnetic domains (of
the order of hundreds of nm) with Néel-type walls take place, evolving into a
very sparse skyrmion state ($\sim 1$ per 1 $\mu$m2) at higher applied fields
(Figure S9). The simulation matches well with the STXM results which show
similar large-scale textures at 200 K Chen  _et al._ (2020) and absence of the
skyrmion phase. We speculate that tuning the DyCo composition in order to
increase the anisotropy and saturation magnetization towards room temperature
can pave a way to stabilize technologically promising ferrimagnetic
topological spin textures in DyCo at 300 K.

Interestingly, a single anti-skyrmion has been spotted at an intermediate
field range of 150-180 mT in the simulations (Figure S9c), which is unexpected
in the system with this type of DMI. Confirmation of this observation requires
further computational and experimental studies.

Figure S9:  Micromagnetic simulations of the spin configurations for the DyCo3
film as a function of magnetic field with the $M_{s}$ and $K^{\textrm{u}}$
parameters corresponding to 200 K. The black and white contrast indicates the
magnetization being parallel and anti-parallel to the $z$-axis. The color code
represents the orientation of the in-plane component of the magnetization
within each cell as shown in the color wheel in the top panel (d). The bottom
panels show the magnetization component along the $x$-axis. The color code of
the intensity of $M_{\textrm{x}}$ is given in the bottom panel (d).

###  S5.3 Case 3: Simulations for the magnetic parameters corresponding to an
intermediate DMI parameter at 26K

As we describe in the main text, the minimal value of the interfacial-type DMI
constant required to stabilize Néel-type skyrmions in the micromagnetic
simulations is found at $D_{\textrm{int}}=0.0015$ Jm-2, while lower values
result in Bloch- or hybrid-type skyrmion textures. An example of such a hybrid
skyrmion is shown in Figure S10. Here, the skyrmion winding changes from
Bloch-type in the top layer of the film ($z=1$) to Néel-type in the bottom
layer ($z=25$) via an intermediate state in the middle. This behavior
correspond well to predictions given by Lemesh and Beach in their analytical
theory for multilayers Lemesh and Beach (2018).

Figure S10: Magnetic structure of hybrid skyrmions in DyCo3 film with an
intermediate value of the DMI constant $D_{\textrm{int}}=0.00125$ Jm-2 at 470
mT as obtained from the micromagnetic simulations. The panels show the single
skyrmion structure in the top ($z=1$), middle ($z=12$) and bottom ($z=25$)
layers of the film, respectively.

##  S6 Possible origin of a "bulk" DMI in the ferrimagnetic alloys

One main outcome of the resolve of the domain walls as Néel-type is that they
require a "bulk" DMI of an interfacial-type symmetry Buhl (2019) to occur. In
the absence of a DMI, the domain walls are Bloch-type as revealed by the
micromagnetic simulations. It is well known that Ta or Pt buffer layers induce
an interfacial DMI which has positive or negative sign, respectively. However,
a DMI that is localized at the interface only is too weak to stabilize Néel
walls. For instance, in FM/Ta bilayers, the iDMI has an noticeable impact only
for a FM layer thickness that is below 1 nm Kopte  _et al._ (2017). In our
case, the ferrimagnetic layer is 50 nm thick, and therefore a DMI localized at
the interface only, is not likely to stabilize skyrmions as observed
experimentally. Instead a bulk DMI owes to be responsible for the skyrmions
formation in this system Chen  _et al._ (2020).

The DyCo3 single crystal has a complex rhombohedral structure where Dy
occupies two sites, whereas Co occupies three sites in the unit cell.
According to Ref. Yakinthos and Chappert (1975), for one site the Dy will
align itself with the easy axis, whereas the Dy on the second site will prefer
to align parallel to the c-axis of the crystal which is oriented perpendicular
to the easy axis. As such, a non-collinear spin arrangement is possible due to
the frustrated site magnetic anisotropy of the rare earth ions. For the
amorphous DyCo3 there is also strong experimental evidence for the occurrence
of a noncollinear spin state. In Ref. Coey  _et al._ (1976) an amourphous
DyCo3 thick film has been studied by Mössbauer spectroscopy. It has been
observed that the Dy ion exhibit a sperimagnetic arrangement, whereas the Co
sublattice is ferromagnetically ordered. The above experimental evidence for
noncollinear behavior manifest intrinsically for both single crystal and
amourphous DyCo3.

Certainly, non-collinear interactions are yet not sufficient to lead to
skyrmion formation. Two more aspects play an important role for the formation
of skyrmions in our DyCo3 thin film, namely: an amorphous thin film naturally
lacks a rotational and transnational symmetry, (i. e. a lack of inversion
symmetry that is similar to the B20 structures) which, according to Ref. Fert
(1990) may lead to a DMI that amounts up to about 10% of the isotropic
exchange; and the dipolar interaction strength for thin ferrimagnetic films
with perpendicular magnetic anisotropy varies as a function of temperature(see
section S1). All these three preconditions concur in our system on the
formation of small isolated Néel skyrmions and Néel walls in the maze domain
state.

The exchange energy for DyCo3 reported in Ref.Yakinthos and Mentzafos (1975)
is 621 $cm^{-1}$. Using the conversion factor 1 meV = 8 cm-1 and considering
an average lattice parameter equal to unit volume 0.52635 nm3 to the power of
1/3, we obtain an estimated exchange energy per surface area equal to 0.019
$\textrm{J/m}^{2}$. It is remarkable the minimal value of the DMI required for
Néel-type skyrmion stability determined through micromagnetic simulations (see
the main texts) of 0.0015 $\textrm{J/m}^{2}$ is within the 20% of the
estimated isotropic exchange, in agreement with the suggestion in Ref. Fert
and Levy (1980); Fert (1990).

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