# Homochiral antiferromagnetic merons, antimerons and bimerons realized in
synthetic antiferromagnets

Mona Bhukta  Institute of Physics, Johannes Gutenberg-University Mainz, 55099
Mainz, Germany  Takaaki Dohi  Institute of Physics, Johannes Gutenberg-
University Mainz, 55099 Mainz, Germany  Laboratory for Nanoelectronics and
Spintronics, Research Institute of Electrical Communication, Tohoku
University, 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan  Venkata Krishna
Bharadwaj  Institute of Physics, Johannes Gutenberg-University Mainz, 55099
Mainz, Germany  Ricardo Zarzuela  Institute of Physics, Johannes Gutenberg-
University Mainz, 55099 Mainz, Germany  Maria-Andromachi Syskaki  Institute of
Physics, Johannes Gutenberg-University Mainz, 55099 Mainz, Germany  Singulus
Technologies AG, Hanauer Landstrasse 107, 63796 Kahl am Main, Germany  Michael
Foerster  ALBA Synchrotron Light Facility, 08290 Cerdanyola del Vallès,
Barcelona, Spain  Miguel Angel Niño  ALBA Synchrotron Light Facility, 08290
Cerdanyola del Vallès, Barcelona, Spain  Jairo Sinova  Institute of Physics,
Johannes Gutenberg-University Mainz, 55099 Mainz, Germany  Robert Frömter
Institute of Physics, Johannes Gutenberg-University Mainz, 55099 Mainz,
Germany  Mathias Kläui  Institute of Physics, Johannes Gutenberg-University
Mainz, 55099 Mainz, Germany

###### Abstract

The ever-growing demand for device miniaturization and energy efficiency in
data storage and computing technology has prompted a shift towards
antiferromagnetic (AFM) topological spin textures as information carriers,
owing to their negligible stray fields, leading to possible high device
density and potentially ultrafast dynamics. We realize, in this work, such
chiral in-plane (IP) topological antiferromagnetic spin textures, namely
merons, antimerons, and bimerons in synthetic antiferromagnets by concurrently
engineering the effective perpendicular magnetic anisotropy, the interlayer
exchange coupling, and the magnetic compensation ratio. We demonstrate by
three-dimensional vector imaging of the Néel order parameter, the topology of
those spin textures and reveal globally a well-defined chirality, which is a
crucial requirement for controlled current-induced dynamics. Our analysis
reveals that the interplay between interlayer exchange and interlayer magnetic
dipolar interactions plays a key role in significantly reducing the critical
strength of the Dzyaloshinskii-Moriya interaction required to stabilize
topological spin textures, such as AFM merons, making synthetic
antiferromagnets a promising platform for next-generation spintronics
applications.

## Introduction

The recent years have witnessed an increasing interest in chiral magnetic
topological spin textures stabilized by the Dzyaloshinskii–Moriya interaction
(DMI), such as skyrmions[1, 2], biskyrmions[3, 4, 5], hopfions[6, 7], chiral
bobbers[8, 9], and skyrmionic cocoons [10] due to their potential use as
information carriers for high-density data storage and (un)conventional
computing [11, 12, 13, 14, 15]. For instance, skyrmions exhibit significant
topological robustness [16] and are amenable to electrical control [17, 18,
19, 20], but also entail disadvantages such as skyrmion Hall effect [18, 19,
20]. The growing demand for high-speed, low-power technologies has therefore
boosted the search for more complex topological spin textures beyond the
skyrmion paradigm. Topological spin textures in in-plane magnets, such as
merons and bimerons [21, 22, 23] are recently being explored, by virtue of
their richer current-induced dynamics compared to skyrmions [24] and the
stackability property that allows for denser quasi-one-dimensional racetracks
in three dimensions, resulting in higher storage density. Bimerons are robust
topological textures that are homeomorphic to skyrmions and offer more
topological states than conventional skyrmions, which makes them an important
focus in fundamental quasi-particle research as well as topology-based
computing approaches. Despite the advantage of stabilizing pure homochiral
spin textures, ferromagnetic (FM) topological spin textures suffer from
limitations in scalability with respect to sufficient thermal stability [25],
stackability due to long-range magnetic dipolar interactions [26] and,
gyrotropic forces resulting from their net intrinsic spin angular momentum.

Antiferromagnetic (AFM) systems can naturally overcome these inherent
limitations of FM textures, due to their compensated spin angular momentum and
negligible stray fields [27, 28, 29, 30, 31, 32, 33]. While one could envisage
using single-crystalline AFMs, the inherent technological advantages are
challenged by the difficulty of stabilizing pure homochiral spin textures.
These challenges stem from the absence of significant Lifshitz invariants,
resulting in the observed spin structures having random chirality [34, 35, 36,
37]. So far, the observation of in-plane (IP) topological spin textures such
as bimerons has been limited in antiferromagnets to observing their helicity,
in spite of recent advances in their creation via sophisticated protocols [34,
35, 36, 37]. For the dynamics, the anticipated motion of topological spin
textures in the presence of spin-orbit torques is heavily influenced by their
helicity, leading to Bloch-type and Néel-type structures moving perpendicular
and along the direction of spin-orbit torque (SOT), respectively [20].
However, the lack of homochirality of spin textures in native single-
crystalline antiferromagnets limits their use for controlled dynamics of spin
textures and thus prevents their utilization in future spintronics devices.

An ideal system to explore and manipulate both structural and dynamical
properties of (IP) topological spin textures are synthetic antiferromagnetic
(SyAFM) platforms [28, 29, 30, 38], consisting of a multi-layered
heterostructure made of FM thin films separated by nonmagnetic metallic
spacers and antiferromagnetically coupled via the interlayer exchange
interaction[39, 40]. By tailoring the amount of compensation they can exhibit
an arbitrarily small magnetic moment and, therefore, combine the most
interesting features of both FM and AFM scenarios: minimal stray fields, the
ability to stabilize homochiral spin textures, and the potential for ultrafast
spin dynamics; all in a device-compatible easy to fabricate polycrystalline
multilayer setting. A precondition to assess the topological nature of such
spin textures is to be able to measure their chirality. In this regard, SyAFMs
offer the advantage to employ the advanced surface- or element-sensitive
imaging methods available for FM. Nonetheless, these AFM IP topological spin
textures can be formed locally during the magnetization reversal process[41],
spontaneously stable homochiral spin textures on a global scale are hitherto
not observed.

In this article, we employ three-dimensional (3D) vector imaging of the
staggered magnetization to demonstrate the successful stabilization of all
memebers of the class of IP AFM topological spin textures emerging in a newly
designed layered SyAFM, namely merons, antimerons, and bimerons at zero
magnetic fields. Our experiments combine magnetic force microscopy (MFM),
scanning electron microscopy with polarization analysis (SEMPA), and element-
specific photoemission electron microscopy using the X-ray magnetic circular
dichroism (XMCD-PEEM) that enable us to identify spin textures possessing
enhanced stability, classified by an integer topological invariants and those
that are topologically trivial. We find that in the vicinity of the spin-
reorientation transition (SRT), where the effective anisotropy vanishes, a
SyAFM platform can host homochiral AFM merons, as determined from their
helicity and core polarity. Furthermore, their helicity can be easily tailored
by the degree of magnetic compensation of the SyAFM, indicating thus that
interlayer dipolar interactions play a significant role in the stabilization
of these spin textures. Our micromagnetic and analytical calculations can
fully explain the experimental observations, elucidate the mechanism for the
stabilization of AFM topological textures in synthetic antiferromagnets, and
describe the corresponding phase diagram. Our findings provide crucial
insights into the formation and stability of homochiral IP AFM topological
textures, which pave the way towards better scalable soliton-based
technologies beyond the skyrmion paradigm.

## Antiferromagnetic merons/antimerons in SyAFM platforms

The magnetic order of the SyAFM platform can be described phenomenologically
by two parameters that reflect both its AFM and FM character, depending on the
chosen ratio of magnetic compensation: The Néel order parameter
$\bm{L}=\bm{M}_{\textrm{t}}-\bm{M}_{\textrm{b}}$ and the macroscopic spin
density $\bm{M}=\bm{M}_{\textrm{t}}+\bm{M}_{\textrm{b}}$, where
$\bm{M}_{\textrm{t}}$ and $\bm{M}_{\textrm{b}}$ denote the magnetization
fields of the top and bottom FM layers in each double layer, respectively. As
illustrated in Figure 1, the topological spin textures in the SyAFM can be
classified by their winding number $w$, topological charge $Q$, and helicity
$\gamma$, which are defined as follows: 1) $w$ provides a measure of the
wrapping of the Néel order around the unit sphere and it reads $w=\pm 1$ for
skyrmions/bimerons, whereas it becomes $w=\tfrac{1}{2}$ for a meron and
$w=-\tfrac{1}{2}$ for an antimeron. 2) $Q$ can be cast as the product of the
winding number and the core polarity, namely $Q=w\cdot
L_{z}|_{\textrm{core}}$, the core polarity being defined as the $z$ component
of the Néel order at the texture core. 3) $\gamma$ is given, akin to
skyrmions[11], by the angle between the IP projection of the Néel order and
the radial direction. The helicity of these (anti)meron composites can be
obtained from the IP rotation of the top-layer magnetization since the latter
determines the direction of the Néel order.

Figure 1: Spin configuration of AFM merons and antimerons in a SyAFM platform
(a)–(d) AFM merons with helicities $\gamma=0,\tfrac{\pi}{2},\pi$, and
$\tfrac{3\pi}{2}$, respectively. (e) AFM antimeron. Black and white arrows
represent upward and downward core polarities, respectively, while the IP
component of the moments is given by the color map in the top left corner.

Néel-type merons are characterized by $\gamma=0$ or $\pi$, depending on the
sign of the stabilizing DMI. Their spin structure is sketched in panels a) and
c) of Figure 1. Bloch-type merons are characterized by $\gamma=\tfrac{\pi}{2}$
or $\tfrac{3\pi}{2}$, as sketched in panels b) and d) of Figure 1. Note that
spin textures in adjacent FM layers exhibit identical winding numbers but
opposite core polarities, so their helicities differ by a factor of $\pi$.

## Tuning the magnetic properties to stabilize AFM (anti)merons

Choosing FM materials with low pinning, negligible perpendicular magnetic
anisotropy (PMA) and finite DMI, as well as a strong AFM coupling between
adjacent FM layers is a key requirement for the stabilization of (anti)merons
and bimerons in SyAFM platforms as devised later in the discussion section.

Figure 2: Material stack and magnetic properties of the SyAFM. (a) Multilayer
structure for the SyAFM, where FM${}_{\textrm{t}}$ and FM${}_{\textrm{b}}$
denote the AFM-coupled top and bottom FM layers, respectively. The unit in
parenthesis is in nm (b)–(d) OOP (blue curve) and IP (red curve) hysteresis
loops measured by means of SQUID magnetometry for the stack (b) #1 (fully
compensated OOP), (c) #2a (fully compensated IP) and (d) #3 (uncompensated
IP). The fully compensated stack #2a shows a complete overlap between the IP
and OOP $M(H)$ curves, which indicates that the multilayer is in the vicinity
of the SRT.

We have therefore optimized a Pt/CoFeB/Ir-based multilayer SyAFM (see Methods
for details). The FM films consist of the bilayer
Fe0.6Co0.2B0.2(FCB)/Co0.6Fe0.2B0.2(CFB) and is sandwiched by nonmagnetic
spacers made of a heavy metal bilayer (Pt and Ir). The latter breaks the
mirror symmetry of the heterostructure and thus provides a finite DMI $D$. The
top and bottom FM layers are denoted by FM${}_{\textrm{t}}$ and
FM${}_{\textrm{b}}$, respectively, and their saturation magnetization by
$M_{\textrm{s,t}}$ and $M_{\textrm{s,b}}$. The CFB layer induces PMA
($K_{\textrm{u}}$) at the interface with the heavy metal, whereas the
thickness ratio to the FCB layer is used to control the magnetic dipolar
anisotropy $K_{\textrm{d}}=-\tfrac{1}{2}\mu_{0}M_{\textrm{s}}^{2}$.

Panels 2(b)–(d) depict the $M(H)$ loops of the stacks $\\#1$, $\\#2$a and
$\\#3$, respectively, where the red (blue) curve represents the magnetic
hysteresis loop for an IP (OOP) configuration of the external magnetic field.
The stack $\\#1$ has a small positive effective anisotropy. In Fig. 2(c), red
and blue hysteresis loops coincide, indicating a very small effective
anisotropy $K_{\textrm{eff}}=-0.04$ MJ$\cdot$m-2. Furthermore, the zero
remanence makes the stack $\\#2$a a potential candidate for hosting
(bi)merons, as the formation of a multi-domain magnetic ground state is
expected for this stack at zero fields. The effect of the magnetic
compensation in synthetic antiferromagnets on the formation of meron
structures has been studied via the stacks $\\#2$b and $\\#3$: the FM layers
of the former have small (normalized) uncompensated magnetization
$m_{\textrm{uncom}}=\tfrac{|M_{s,t}-M_{s,b}|}{M_{s,t}+M_{s,b}}=0.05$, which
enables the detection of the OOP spin components of the meron textures via MFM
imaging (see supplementary material (SM) section 4 for the $M(H)$ curve of
stack $\\#2$b). Figure 2(d) shows the hysteresis loops of the stack $\\#3$,
which indicates a negative value for $K_{\textrm{eff}}$.

## 3D-vector imaging of merons/antimerons in the SyAFM

Figure 3: Imaging the Néel order parameter of (anti)merons and bimerons in
synthetic antiferromagnets. (a) SEMPA image showing the IP spin components of
the meron texture in the stack $\\#2$b. (b) MFM image depicting the OOP spin
component of the meron structure in the same area. Dark brown and white MFM
contrasts indicate the upward and the downward direction, respectively. The
color map for the SEMPA image is shown on the left side. Black dotted circles
represent merons of helicity $\gamma=\pi$, whereas double black dotted circles
indicate antimerons with $Q$ = $-\tfrac{1}{2}$. White circles represent merons
having arbitrary helicity with $Q=\tfrac{1}{2}$ and white double circles
denote merons of helicity $\gamma=0$ with $Q$ = $\tfrac{1}{2}$. Two adjacent
black circles (single and double) are identified as bimerons with net
topological charge $Q=-1$ and additionally highlighted by ellipses. (c)
Histogram of the next-neighbour separation between merons, antimerons and
meron-antimeron composites obtained from SEMPA images. (d) Histogram of the
next-neighbour separation between up-up, down-down, and up-down core
polarities from MFM contrast.

Next we reveal the topological spin textures present and for the full vector
reconstruction of the Néel order requires imaging of both IP and OOP spin
components of the meron spin structues is required. Since the stack $\\#2$a
has full magnetic compensation, its OOP spin components are almost impossible
to visualize via MFM. However, since the stacks $\\#2$b and $\\#3$ produce
small stray fields, by using the combination of SEMPA and MFM imaging
techniques at the same spot we can reconstruct the Néel order describing the
topological textures in these SyAFM platforms.

Panels 3(a) and 3(b) show the SEMPA image (IP spin components) and the MFM
image (OOP spin component) taken in the same area of the stack $\\#2$b at room
temperature and zero magnetic fields. The observed topological textures are
created by applying a damped oscillating OOP magnetic field applied to
imaging. White and dark brown contrasts in Figure 3(b) show the downward and
upward core polarity, respectively. Furthermore, black and white circles in
both images correspond to $Q=-\tfrac{1}{2}$ and $Q=\tfrac{1}{2}$,
respectively. We note that $M_{\textrm{s,t}}>M_{\textrm{s,b}}$, so the stray
field detected in the MFM measurement is dominated by that of the topmost
layer. The analysis of both images yields the presence of different
topological spin textures: black dotted circles represent Néel-type merons
with core polarity pointing downward ($L_{z}=-1$), namely the $\gamma=\pi$
merons from Fig. 1(c). White double circles correspond to merons of helicity
$\gamma=0$ and upward core polarity, as described in panel 1(a). We note that
the helicities $\gamma=0,\pi$ largely correspond to the core polarities
$L_{z}=1$ and $-1$, respectively, which indicates the presence of homochiral
merons in the system. Double black dotted circles mark antimerons with
topological charge $Q=-\tfrac{1}{2}$, see Fig. 1(e). Changes in $\gamma$ do
not affect the topological structure of the antimeron except for a geometrical
rotation of its IP spin components, so that we consider all of them to be
topologically equivalent. The combination of a single black circle adjacent to
a double one is identified as a bimeron with $Q=-1$ and marked by an ellipse.
AFM coupling between the meronic spin textures present in the adjacent FM
layers having has been confirmed by means of XMCD-PEEM layer-resolved imaging
(see SM section 2).

By observing the arrangement shown in 3(a), it is evident that merons and
antimerons are positioned in close proximity to each other. To gain a more
comprehensive understanding of the range of their interaction, we conducted a
statistical analysis of the distance between meronic textures over a larger
sample area. Panel 3(c) shows the histogram of separations between the
constituents of various meron composites as seen in the SEMPA images. Meron-
antimeron pairs average at a separation of (490 $\pm$ 32) nm, closer than that
between two antimerons or two merons, suggesting a different interaction
potential with an energy minimum at smaller distance between merons and
antimerons due to the presence of DMI. Based on the core polarities, meron-
antimeron composites can have non-zero topological charge or be trivial spin
textures with $Q$ = 0. In panel 3(d), histograms of the next-neighbour
distances between core polarities as seen in MFM images are presented. The
average separation between up-down core polarities, (425 $\pm$ 40) nm,
coincides within the experimental uncertainty with the average separation
between merons and antimerons in the SEMPA images and is smaller than the
separation between up-up or down-down polarities. This supports the existence
of non-zero topological charges in the meron-antimeron pairs and the dominance
of bimerons in the sample as shown in Panels 3(a) and 3(b).

## Tailoring the helicity of (anti)merons in synthetic antiferromagnets

The measured helicity values are essential in identifying the mechanism of
stabilization and in engineering the SOT-induced dynamics of meron structures.

Figure 4: Manipulating the helicity of (anti)merons in SyAFM. (a) SEMPA image
showing the IP spin components of the meronic spin texture in the stack
$\\#2$a indicating the IP orientation of the staggered magnetization. Black
and white circles denote antimerons and merons, respectively. b) Distribution
of helicities of the meron present in the SyAFM. The abudance of helicity at 0
and $\pi$ indicates homochiral Néel meron in the stack. c) SEMPA image showing
the IP spin components of the meronic spin texture the (uncompensated) case of
stack $\\#3$. (d) shows the dominance of Bloch merons having helicity $\pi/2$
and 3$\pi/2$ in the stack.

In this section, we demonstrate the control of helicity in synthetic
antiferromagnets through variation of the magnetic compensation ratio.

Figures 4(a) shows a SEMPA images of the topmost-layer magnetization, hence
the direction of the Néel order, for the stack $\\#2$a in the absence of
magnetic field. We have marked all merons with white circles and all
antimerons with black circles, and find an almost equal proportion of both
types of topological spin textures. We elucidate the relevance of the helicity
by analyzing its values for the emergent merons through a histogram, as shown
in panel 4(b). This histogram has been generated by considering additional
SEMPA images of the stack $\\#2$a obtained under comparable conditions. Values
of $\gamma=0,\pi$ are significantly favoured in this SyAFM platform, which
corresponds to the Néel-type rotation, and therefore confirms that the
stabilization mechanism for merons in the compensated case originates from the
DMI [24, 42, 43]. Similarly, Néel bimerons are energetically favourable in the
same range of DMI [24].

The more uncompensated case has been studied in stack $\\#3$, which presents
an uncompensated magnetization of $m_{\textrm{uncomp}}=0.20$ and thus a small
but significant interlayer dipolar field. SEMPA images of its topmost layer
magnetization is shown in figure 4(c) with the direction of the net IP
magnetization. We observe again a nearly equal number of merons and antimerons
(same white/black color convention as before). The analysis of the
distribution of meron helicities, see panel 4(d), yields a prevalence of
values around $\gamma=\tfrac{\pi}{2},\tfrac{3\pi}{2}$, which indicates a
Bloch-type rotation. We conclude that the presence of a small uncompensated
magnetization in the SyAFM promotes the stabilization of Bloch-meron textures.
Thus by tuning the compensation ratio, we can effectively manipulate the
helicity and consequently, the resulting SOT-induced dynamics.

## Theoretical model and Discussion

In the preceding sections, we experimentally demonstrate the occurrence of AFM
merons, antimerons, and bimerons in the SyAFM platform. The stabilization of
meronic spin textures in SyAFMs results from the subtle interplay between
interlayer exchange, interlayer magnetic dipolar interactions (IMD), and
interfacial DMI, as well as the effective anisotropies of the FM layers. This
mechanism of bimeron stabilization in a SyAFM platform is analyzed and
explained in this section, supported by theoretical models and micromagnetic
simulations.

We start with a SyAFM that can be effectively described, irrespective of its
magnetic compensation ratio, as a ferrimagnetic platform with magnetic
sublattices given by the top and bottom FM layers, respectively. In the
compensated case, the minimal model for the SyAFM contains exchange, DMI, and
anisotropy contributions, and thus its total free energy reads

$\displaystyle\mathcal{E}[\bm{L}]$
$\displaystyle=\int_{\mathcal{S}}d^{2}\bm{r}\,\bigg{[}\tfrac{A}{2}(\nabla\bm{L})^{2}+D\bm{L}\cdot(\tilde{\nabla}\times\bm{L})-KL_{z}^{2}\bigg{]},$
(1)

where $A$ is the AFM spin stiffness constant and $\mathcal{S}$ denotes the
SyAFM surface, see SM. The effective (easy-axis) anisotropy constant for the
Néel order,
$K=K_{\textrm{eff}}-\tfrac{H_{\textrm{d}}^{2}}{2\lambda\bm{L}^{2}}$, has an
additional contribution originating in the competition between the interlayer
exchange and IMD interactions. Here, $H_{\textrm{d}}$ and $\lambda$ denote the
interlayer stray field and half of the interlayer exchange constant,
respectively. In the vicinity of the SRT point,
$K_{\textrm{eff}}\sim\tfrac{H_{\textrm{d}}^{2}}{2\lambda\bm{L}^{2}}\ll
K_{\textrm{u}}$, and therefore the IMD field can induce the reorientation
(from OOP to IP) of the staggered magnetization describing the SyAFM, which in
turn favours the stability of in-plane meron textures. We note that FM systems
can be tuned close to zero effective anisotropy but lack the IMD field,
whereas AFM platforms have a spin-flop contribution to the effective
anisotropy but their SRT is usually driven by temperature [34]. AFM lacks
inversion symmetry due to antiferromagnetic ordering, which significantly
reduces the magnitude of the Lifshitz invariants, and therefore it lacks the
necessary criteria to stabilize homochiral spin structures. The interplay
between the tunable (near-zero) effective FM-layer anisotropy and the IMD
field lowers significantly the DMI needed to stabilize IP AFM textures, which
makes synthetic antiferromagnets optimal platforms to explore the physics of
these AFM spin textures. Furthermore, in the uncompensated scenario, a Zeeman-
like interaction $-\tfrac{\Theta}{\bm{L}^{2}}H_{\textrm{d}}L_{z}$ contributes
to the energetics of the SyAFM, which favours the OOP orientation of the Néel
order and, therefore, the stability of Bloch-type IP merons at low DMI. Here,
$\Theta=M_{s,t}^{2}-M_{s,b}^{2}$ parametrizes the absence of magnetic
compensation in the SyAFM.

Figure 5: Critical point and micromagnetics of bimerons in synthetic
antiferromagnets. (a) Dependence of the critical DMI $D_{\textrm{c}}$ on the
interlayer exchange constant $2\lambda$. The inset shows the phase diagram
corresponding to the point A along the curve $D_{\textrm{c}}(\lambda)$. The
ground-state phases coalesce at the triple point $(\lambda,D_{\textrm{c}})$ in
the $D-K_{\textrm{eff}}$ phase diagram, marked with a red star. Dark green,
yellow and bronze colors illustrate the uniform IP, uniform OOP and helical in
the $rz$ plane ground-state phases, respectively, with $r$ being any radial
direction. Light green color depicts the region where AFM merons are
stabilized in micromagnetic simulations. The magenta zigzag line illustrates
the lower bound of optimal AFM interlayer exchange (energies) accessible in
our stacks. The phase diagrams corresponding to the points B and C along the
critical curve, which illustrate a displacement of the triple point to the
right, are discussed in the SM section 5. (b) Illustration of an AFM bimeron
corresponding to a system with parameters at point A. Black and grey arrows
depict the antiparallel alignment of the spins of the top and bottom FM
layers, respectively. Green and red colors show the OOP projections of the
localized spins.

Panel 5(a) depicts the dependence of the critical DMI ($D_{\textrm{c}}$)
marking the onset of the meron instability (towards the helical phase) on the
interlayer exchange constant $2\lambda$. For a strongly AFM-coupled SyAFM
(i.e., large $\lambda$) in the vicinity of the SRT point (namely,
$K_{\textrm{eff}}\simeq 0$), only a very small DMI is needed to induce the
phase transition from the uniform IP configuration to a helical phase (denoted
by green and bronze domains in the inset). We note that the expression for the
DMI at the triple point can be always obtained from the condition
$K_{\textrm{eff}}=0$, which yields
$D_{\textrm{c}}=\frac{4}{\pi}\sqrt{A\left[\frac{H_{\textrm{d}}^{2}}{2\lambda\bm{L}^{2}}\right]}$
(see Methods). The low $D_{\textrm{c}}$ stems from the fact that the only
contribution to the effective anisotropy at the SRT point comes from the IMD
field. As the SyAFM is tuned away from the SRT point towards an IP
configuration (i.e, $K<0$), the critical value $D_{\textrm{c}}$ increases
since one needs to overcome a larger anisotropy barrier to induce the OOP
tilting of the staggered magnetization. The phase boundary between the uniform
IP and helical phases has been calculated analytically (see Methods) and
described parametrically by the curve
$D_{\textrm{c}}^{\textrm{IP}}=\frac{4}{\pi}\sqrt{A\left[\frac{H_{\textrm{d}}^{2}}{2\lambda\bm{L}^{2}}-K_{\textrm{eff}}\right]}$.
Furthermore, the ground state is the uniform OOP configuration when $K>0$
(depicted as a yellow domain in the inset) and, as the DMI increases above
$D_{c}$, a phase transition towards the helical state is induced, which is
well known in magnetic films with PMA. We conclude the discussion by noting
that, as seen in the inset C of SM figure s9, attaining the critical value
$D_{\textrm{c}}\propto\tfrac{1}{\sqrt{\lambda}}$ for weak AFM interlayer
couplings can be very difficult experimentally, consequently, systems with
strong AFM interlayer coupling offer a more viable route for stabilizing
bimerons.

## Outlook

In conclusion, we demonstrate the presence of chiral merons, antimerons, and
topologically stabilized bimerons in synthetic antiferromagnets at zero
magnetic fields. The direction of the net magnetization and the emergent field
created by topology in bimerons are mutually orthogonal, a key difference to
their out-of-plane counterparts, skyrmions. Thus meronic spin textures offer
an approach to directly explore and tune the topological Hall physics. Their
Hall signal will be directly sensitive to the topology, enabling the
electrical readout of the topological winding number and leading to new
possibilities for the designing of magnetic topology-based technology where
the topology can encode the informations. Our findings show that these AFM
textures can be detected with accurate helicity and topological charge through
a combination of surface-sensitive SEMPA imaging and MFM imaging. The fully
compensated synthetic antiferromagnets host homochiral Néel bimerons that are
stable at room temperature. In SyAFM, bimerons exhibit an important advantage
over previously demonstrated AFM bimerons due to the presence of homochiral
spin textures, which makes them amenable to controlled manipulation using
spin-orbit torques and in turn opens up new possibilities for designing
spintronic devices in SyAFMs. This combine the advantages of FM, such as easy
detection, with those of AFMs, such as the absence of the long-range stray
fields.

## Acknowledgments

The authors thank A. Bose, A. Rajan and E. Galindez Ruales for their
participation in additional experiments included in the Supplementary
Material. This work has received funding from the European Union’s Horizon
2020 research and innovation program under the Marie Skłodowska-Curie Grant
Agreement No. 860060 “Magnetism and the effect of Electric Field” (MagnEFi) as
well as from Synergy Grant No. 856538, project “3D-MAGiC”. It has also been
supported by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) - TRR 173 – 268565370 (project A03), the Grant Agency of the Czech
Republic grant no. 19-28375X, and the Dynamics and Topology Centre TopDyn
funded by the State of Rhineland Palatinate.

## Methods

### Material deposition

The thin-film material stacks were deposited on thermally oxidized Si/SiO2
substrates employing the Singulus Rotaris magnetron sputtering tool, which
provides reproducibility and sub-Angstrom thickness accuracy. DC-magnetron
sputtering at a base pressure of 4 $\times$ 10-8 mbar was employed for the
growth of the metallic layers Ta, Pt, Ir, Co0.6Fe0.2B0.2(CFB),
Fe0.6Co0.2B0.2(FCB), and Co0.8B0.2 at room temperature. The respective
deposition rates were determined with X-ray reflectivity to be 0.54, 0.91,
0.56, 0.51, 0.66, and 0.37 Ås-1 under pure Ar flow used as sputtering gas.

The top Pt layer serves as capping for the material stack to prevent oxidation
over time and during post processing (patterning). The thickness
$d_{\textrm{Ir}}=0.4$ nm of the Ir layer is chosen so as to maximize the AFM
interlayer exchange between the FM layers. The value of $x$ is 0.2 in stack
$\\#1$, whereas it is 0.7 in $\\#2$a. In $\\#3$, the FM layers correspond to
different values of the parameter $x$ ($x_{\textrm{FM}_{t}}=0.7$ and
$x_{\textrm{FM}_{b}}=0.2$). We have kept the FM layers as thin as possible to
maximize the interlayer exchange coupling ($d_{\textrm{FM}}=0.9$ nm) as well
as optimized the ratio between the FCB ($x$ nm) and CFB ($0.9-x$ nm)
thicknesses to be in the vicinity of the SRT (namely, to obtain a vanishing
effective anisotropy $K_{\textrm{eff}}=K_{\textrm{u}}+K_{\textrm{d}}$).

As depicted in Figure 2(a), a heterostructure consisting of multiple
repetitions ($14$ times) of the single bilayer SyAFM has been prepared to 1)
reduce the thermal diffusion of (anti)merons across the low-pinning SyAFM, and
2) obtain a high saturation field in the hysteresis loops. In Stack 3, bottom
and top FM layers are made of Co0.8B0.2 and FCB, respectively, and have
thicknesses of $d_{\textrm{FM}_{\textrm{b}}}=1.305$ nm and
$d_{\textrm{FM}_{\textrm{t}}}=0.9$ nm, which yields the value
$m_{\textrm{uncom}}=0.20$ for the uncompensated magnetization.

### SEMPA imaging

For imaging the in-plane component of the magnetic spin texture we used a
surface-sensitive technique, the Scanning Electron Microscope with
Polarization Analysis (SEMPA) [44]. SEMPA is a powerful in-house imaging
technique that uses the spin-polarized secondary electrons emitted from a
magnetic material and gives a two-dimensional (2D) vector map of the IP
magnetization. The sensitivity of SEMPA is limited to $1-2$ nm depth from the
surface, which enables us to image the topological spin textures present only
in the topmost magnetic layer. This unique feature of SEMPA is especially
effective on synthetic antiferromagnets enabling us to investigate the
formation of topological spin textures even in a fully compensated
composition.

SEMPA color-coded images enable us to determine the winding number of the
topological spin textures and classify them accordingly. Also, the sense of
the in-plane rotation gives information about the exact helicity of these
meronic spin structures. We note that SEMPA images do not differentiate the
OOP component of the magnetization, hence merons and antimerons of equal
helicity (e.g., 1 (a) and 1 (f)) give similar SEMPA color contrast, as shown
in figure 1(k). This prohibits to determine $Q_{T}$ solely from the IP
contrast. Similarly, Figures 1 (l)–(n) denote SEMPA images with $w$ =
$\frac{1}{2}$ having $\gamma$ values $\tfrac{\pi}{2}$, $\pi$, and
$\tfrac{3\pi}{2}$.

### Micromagnetic approach

#### Analytical expression for the phase boundaries

We explore the possible ground states of the model (1) along the lines of Ref.
[24]. We consider the most generic ansatz for a helix in the real space, which
can be parametrized by the normal $\vec{\bm{n}}$ to the plane of the helix and
the helical pitch vector $\vec{q}$. The Néel order can be cast in terms of
this parametrization as

$\displaystyle\bm{l}(\vec{r}\,)=\cos(\vec{q}\cdot\vec{r})\hat{\bm{e}}_{1}+\sin(\vec{q}\cdot\vec{r})\hat{\bm{e}}_{2}+m_{0}\hat{\bm{n}}$
(2)

where $\bm{l}(\vec{r}\,)=\bm{L}(\vec{r}\,)/|\bm{L}|$ and
$\\{\hat{\bm{e}}_{1},\hat{\bm{e}}_{2},\vec{\bm{n}}\\}$ defines a local frame
of reference in the spin space. Upon substituting this expression into Eq.
(1), we obtain the following identity for the energy density functional:

$\displaystyle\varepsilon\big{[}\bm{l}(\vec{r}\hskip 1.42271pt)\big{]}$
$\displaystyle=\tfrac{1}{1+m_{0}^{2}}\Big{\\{}\tfrac{J}{2}\vec{q}\hskip
1.9919pt^{2}+D\left(q_{x}\sin\theta\sin\phi-
q_{y}\sin\theta\cos\phi\right)+K\big{(}\left[\tfrac{1}{2}+m_{0}^{2}\right]+\left[\tfrac{1}{2}-m_{0}^{2}\right]\cos^{2}\theta\big{)}\Big{\\}}.$
(3)

This functional is minimized with respect to the variables
$\\{\theta,\phi,\vec{q},m_{0}\\}$ and the different possible extrema are
found. The lowest energy configuration for a given set of parameters
determines the ground state. The phase boundaries separating any two possible
ground states are determined by equating their corresponding energies, from
which the expression of the DMI $D$ as a function of $K_{\textrm{eff}}$ is
obtained. For instance, the phase boundary for the OOP-helical transition is
parametrized by the curve
$D_{\textrm{c}}^{\textrm{OOP}}(\lambda)=\frac{4}{\pi}\sqrt{A\left[K_{\textrm{eff}}-\frac{H_{\textrm{d}}^{2}}{2\lambda\bm{L}^{2}}\right]}$.

#### Micromagnetic simulations

Micromagnetic simulations were performed using the Mumax3 software [45]. The
following setup was implemented in the simulations leading to Fig. 5. A
bilayer square geometry of lateral size 256 nm and thickness 1 nm for each of
the FM layers was considered and dipolar interaction included. The system was
discretized with a mesh size of $1\times 1\times 1$ nm3 and periodic boundary
conditions along the $x$ and $y$ directions were imposed, with period equal to
16 repetitions. The material parameters are $A=1\times 10^{-11}$ Jm-1 for the
exchange constant, $M_{s}$ = 0.145 MAm-1 for the saturation magnetization and
$\alpha=0.01$ for the Gilbert damping. The strength of the interlayer exchange
coupling was chosen to be $\lambda=0.44\times 10^{-3}$ Jm-2, which corresponds
to the value obtained from SQUID measurements. We note that, in Mumax3,
interlayer exchange interactions are properly accounted for by rescaling the
material parameters by the thickness of the spacer (see ext$\\_$scaleExchange
function)[45]. To explore the $D-K_{\textrm{eff}}$ phase diagram, the
effective out-of-plane uniaxial anisotropy $K_{\textrm{eff}}$ and the DMI $D$
were varied in the range $\left[-3\times 10^{5},3\times 10^{5}\right]$ Jm-3
and $\left[0,2\times 10^{-3}\right]$ Jm-2, respectively. An initial meron
configuration is chosen in the simulations, which is minimized to find the
equilibrium configuration. The parameter space of $(D,K_{\textrm{eff}})$ was
swept to obtain the light green shaded region in Fig. 5.

The stability of the bimerons was confirmed via micromagnetic simulations
performed on MuMax3. Their size and shape were analyzed in the domain
$D<D_{\textrm{c}}^{\textrm{IP}}$ of the parameter space $\lambda-D$. Panel
5(b) depicts the magnetization profile of a bimeron stabilized for the
material parameters summarised in the Methods section. To gain deeper insight
into the impact of various magnetic parameters on the properties of AFM
bimerons, we conduct micromagnetic simulations (see SM section 6). Our
simulations demonstrate that both the DMI and the $K_{z}$ jointly assist in
the formation of larger bimerons in SyAFM, while stronger interlayer exchange
stabilizes smaller bimerons. These findings show that by tunning the
properties we can design and optimize of AFM bimeron-based devices.

## References

  * [1] Mühlbauer, S. _et al._ Skyrmion lattice in a chiral magnet.  _Science_ 323, 915–919 (2009).
  * [2] Yu, X. _et al._ Real-space observation of a two-dimensional skyrmion crystal.  _Nature_ 465, 901–904 (2010).
  * [3] Yu, X. _et al._ Biskyrmion states and their current-driven motion in a layered manganite.  _Nature Communications_ 5, 1–7 (2014).
  * [4] Wang, W. _et al._ A centrosymmetric hexagonal magnet with superstable biskyrmion magnetic nanodomains in a wide temperature range of 100–340 k.  _Advanced Materials_ 28, 6887–6893 (2016).
  * [5] Peng, L. _et al._ Real-space observation of nonvolatile zero-field biskyrmion lattice generation in mnniga magnet.  _Nano Letters_ 17, 7075–7079 (2017).
  * [6] Kent, N. _et al._ Creation and observation of hopfions in magnetic multilayer systems.  _Nature Communications_ 12, 1–7 (2021).
  * [7] Wang, X., Qaiumzadeh, A. & Brataas, A.  Current-driven dynamics of magnetic hopfions.  _Physical Review Letters_ 123, 147203 (2019).
  * [8] Zheng, F. _et al._ Experimental observation of chiral magnetic bobbers in b20-type fege.  _Nature Nanotechnology_ 13, 451–455 (2018).
  * [9] Ran, K. _et al._ Creation of a chiral bobber lattice in helimagnet-multilayer heterostructures.  _Physical Review Letters_ 126, 017204 (2021).
  * [10] Grelier, M. _et al._ Three-dimensional skyrmionic cocoons in magnetic multilayers.  _arXiv:2205.01172_ (2022).
  * [11] Nagaosa, N. & Tokura, Y.  Topological properties and dynamics of magnetic skyrmions.  _Nature Nanotechnology_ 8, 899 (2013).
  * [12] Fert, A., Cros, V. & Sampaio, J.  Skyrmions on the track.  _Nature Nanotechnology_ 8, 152–156 (2013).
  * [13] Luo, S. _et al._ Reconfigurable skyrmion logic gates.  _Nano Letters_ 18, 1180–1184 (2018).
  * [14] Raab, K. _et al._ Brownian reservoir computing realized using geometrically confined skyrmion dynamics.  _Nature Communications_ 13, 1–6 (2022).
  * [15] Zázvorka, J. _et al._ Thermal skyrmion diffusion used in a reshuffler device.  _Nature Nanotechnology_ 14, 658–661 (2019).
  * [16] Je, S.-G. _et al._ Direct demonstration of topological stability of magnetic skyrmions via topology manipulation.  _ACS nano_ 14, 3251–3258 (2020).
  * [17] Jiang, W. _et al._ Blowing magnetic skyrmion bubbles.  _Science_ 349, 283–286 (2015).
  * [18] Woo, S. _et al._ Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets.  _Nature Materials_ 15, 501–506 (2016).
  * [19] Litzius, K. _et al._ Skyrmion hall effect revealed by direct time-resolved x-ray microscopy.  _Nature Physics_ 13, 170 (2017).
  * [20] Dohi, T., Reeve, R. M. & Kläui, M.  Thin film skyrmionics.  _Annual Review of Condensed Matter Physics_ 13, 73–95 (2022).
  * [21] Yu, X. _et al._ Transformation between meron and skyrmion topological spin textures in a chiral magnet.  _Nature_ 564, 95–98 (2018).
  * [22] Kharkov, Y., Sushkov, O. & Mostovoy, M.  Bound states of skyrmions and merons near the lifshitz point.  _Physical Review Letters_ 119, 207201 (2017).
  * [23] Janson, O. _et al._ The quantum nature of skyrmions and half-skyrmions in Cu2OSeO3.  _Nature Communications_ 5, 1–11 (2014).
  * [24] Zarzuela, R., Bharadwaj, V. K., Kim, K.-W., Sinova, J. & Everschor-Sitte, K.  Stability and dynamics of in-plane skyrmions in collinear ferromagnets.  _Physical Review B_ 101, 054405 (2020).
  * [25] Büttner, F., Lemesh, I. & Beach, G. S.  Theory of isolated magnetic skyrmions: From fundamentals to room temperature applications.  _Sci. Rep._ 8, 4464 (2018).
  * [26] Lemesh, I. & Beach, G. S.  Walker breakdown with a twist: Dynamics of multilayer domain walls and skyrmions driven by spin-orbit torque.  _Physical Review Applied_ 12, 044031 (2019).
  * [27] Baltz, V. _et al._ Antiferromagnetic spintronics.  _Rev. Mod. Phys._ 90, 015005, DOI: 10.1103/RevModPhys.90.015005 (2018).
  * [28] Dohi, T., DuttaGupta, S., Fukami, S. & Ohno, H.  Formation and current-induced motion of synthetic antiferromagnetic skyrmion bubbles.  _Nature Communications_ 10, 1–6 (2019).
  * [29] Legrand, W. _et al._ Room-temperature stabilization of antiferromagnetic skyrmions in synthetic antiferromagnets.  _Nature Materials_ 19, 34–42 (2020).
  * [30] Dohi, T. _et al._ Enhanced thermally-activated skyrmion diffusion in synthetic antiferromagnetic systems with tunable effective topological charge.  _arXiv preprint arXiv:2206.00791_ (2022).
  * [31] Caretta, L. _et al._ Fast current-driven domain walls and small skyrmions in a compensated ferrimagnet.  _Nature Nanotechnology_ 13, 1154–1160 (2018).
  * [32] Hirata, Y. _et al._ Vanishing skyrmion hall effect at the angular momentum compensation temperature of a ferrimagnet.  _Nature Nanotechnology_ 14, 232–236 (2019).
  * [33] Jungwirth, T., Marti, X., Wadley, P. & Wunderlich, J.  Antiferromagnetic spintronics.  _Nature Nanotechnology_ 11, 231–241 (2016).
  * [34] Jani, H. _et al._ Antiferromagnetic half-skyrmions and bimerons at room temperature.  _Nature_ 590, 74–79 (2021).
  * [35] Ross, A. _et al._ Structural sensitivity of the spin hall magnetoresistance in antiferromagnetic thin films.  _Phys. Rev. B_ 102, 094415 (2020).
  * [36] Amin, O. _et al._ Antiferromagnetic half-skyrmions electrically generated and controlled at room temperature.  _arXiv preprint arXiv:2207.00286_ (2022).
  * [37] Chmiel, F. P. _et al._ Observation of magnetic vortex pairs at room temperature in a planar $\alpha$-fe2o3/co heterostructure.  _Nature Materials_ 17, 581–585 (2018).
  * [38] Juge, R. _et al._ Skyrmions in synthetic antiferromagnets and their nucleation via electrical current and ultra-fast laser illumination.  _Nature Communications_ 13, 4807 (2022).
  * [39] Tomasello, R. _et al._ Performance of synthetic antiferromagnetic racetrack memory: domain wall versus skyrmion.  _Journal of Physics D: Applied Physics_ 50, 325302 (2017).
  * [40] Chen, R. _et al._ Realization of isolated and high-density skyrmions at room temperature in uncompensated synthetic antiferromagnets.  _Nano Letters_ 20, 3299–3305 (2020).
  * [41] Kolesnikov, A. _et al._ Composite topological structure of domain walls in synthetic antiferromagnets.  _Sci. Rep._ 8, 1–9 (2018).
  * [42] Moon, K.-W., Yoon, J., Kim, C. & Hwang, C.  Existence of in-plane magnetic skyrmion and its motion under current flow.  _Physical Review Applied_ 12, 064054 (2019).
  * [43] Shen, L. _et al._ Current-induced dynamics and chaos of antiferromagnetic bimerons.  _Physical Review Letters_ 124, 037202 (2020).
  * [44] Schönke, D., Oelsner, A., Krautscheid, P., Reeve, R. M. & Kläui, M.  Development of a scanning electron microscopy with polarization analysis system for magnetic imaging with ns time resolution and phase-sensitive detection.  _Review of Scientific Instrum._ 89, 083703 (2018).
  * [45] De Clercq, J., Leliaert, J. & Van Waeyenberge, B.  Modelling compensated antiferromagnetic interfaces with mumax3.  _Journal of Physics D: Applied Physics_ 50, 425002 (2017).