# Imprinting of skyrmions and bimerons in an antiferromagnet

Coline Thevenard, Miina Leiviskä, Richard F. L. Evans, D Gusakova, Vincent Baltz

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Coline Thevenard, Miina Leiviskä, Richard F. L. Evans, D Gusakova, Vincent Baltz. Imprinting of skyrmions and bimerons in an antiferromagnet. Physical Review B, 2025, 111, pp.224429. 10.1103/753s-8nx4. hal-04930920v2

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Imprinting of skyrmions and bimerons in an antiferromagnet

Coline Thevenard<sup>1,*</sup> Miina Leiviskä<sup>1</sup> Richard F. L. Evans<sup>2,†</sup> Daria Gusakova<sup>1</sup> and Vincent Baltz<sup>1,‡</sup>

<sup>1</sup>*Univ. Grenoble Alpes, CNRS, CEA, Grenoble INP, IRIG-SPINTEC, F-38000 Grenoble, France*

<sup>2</sup>*School of Physics, Engineering and Technology, University of York, York YO10 5DD, United Kingdom*

<figure><img src="image_2.png" /></figure>

(Received 5 February 2025; accepted 2 June 2025; published 26 June 2025)

Topologically protected magnetic states in condensed matter physics, particularly antiferromagnetic (AFM) skyrmions (Sks) and bimerons (Bms), offer promising prospects for terahertz dynamics and sustained current-induced motion, thanks to their compensating multiple sublattice structure. However, nucleating AFM Sks and Bms is challenging due to the lack of net magnetization. Previous attempts to imprint predefined Sks and Bms in a ferromagnet and transfer them to an antiferromagnet using interfacial exchange bias in ferromagnetic (FM)/AFM heterostructures have been hindered by complex multilayers with discontinuities, polycrystallinity, or multipartite chiral antiferromagnets. Employing atomistic spin simulations, we demonstrate the viability of texture imprinting for nucleating Sks and Bms in antiferromagnets, using a prototypical bipartite AFM layer in a multilayer structure free from discontinuities. Such imprinting is a crucial step towards understanding the static and dynamic properties of natural AFM textures and their unique properties.

DOI: 10.1103/753s-8nx4

## I. INTRODUCTION

The interest in topologically protected states in condensed matter physics stems from their robustness against small perturbations and their significant impact on the physical properties of the system. This impact is closely tied to the system's symmetry which, for example, enables a nonzero geometric phase for electrons interacting with the spin structure. While topological objects in uncompensated magnets, like ferromagnets, have been extensively studied due to their fundamental significance and potential applications [1,2], the presence of multiple spin sublattices in compensated magnets with zero net magnetization, like antiferromagnets and altermagnets, opens interesting avenues for topological phenomena and spintronic applications [3-8]. Specifically, real-space topological states, such as antiferromagnetic (AFM) skyrmions (Sks) and bimerons (Bms) – in-plane topological homeomorphic counterparts of Sks – exhibit intriguing properties. Due to antiparallel interatomic exchange interactions, AFM Sks and Bms possess zero net magnetization and topological charge, ensuring robustness against external fields and vanishing net topological charge and Hall effects [9-11]. Moreover, they are predicted to induce unique transport properties, including a nonvanishing topological spin Hall effect [12,13] and a longitudinal Sk velocity unconstrained by the Sk Hall effect, exceeding that of ferromagnetic (FM) Sks due to the inherent THz dynamics in antiferromagnets [14,15]. These properties make AFM Sks and Bms not only fascinating subjects for studies on topology but also promising candidates for ultradense, ultrafast,

low-power spintronic devices. However, the main challenge in accessing these advantageous properties is the difficulty in experimentally nucleating AFM Sks and Bms due to the lack of net magnetization. Various nucleation techniques have been proposed, including field-assisted methods, magneto-electric effects and ultrafast laser pulses [7]. An alternative approach involves predefining Sks and Bms in a ferromagnet and subsequently imprinting them in an antiferromagnet using interfacial exchange bias in FM/AFM heterostructures, facilitated by appropriate thermal and magnetic field cycles. This method has successfully transferred spin textures in antiferromagnets, such as vortices, domain walls, and nontopologically protected bubbles [7,16-20]. For Sks and Bms, both simulations and experiments have attempted to validate this imprinting method, but complex multilayers with discontinuities, polycrystallinity, or multipartite chiral antiferromagnets have hindered accurate calculations of topological parameters [7,19,20]. In this study, we employ atomistic simulations to demonstrate the viability of texture imprinting for nucleating Sks and Bms in antiferromagnets. Using a prototypical bipartite AFM layer in a multilayer structure free from discontinuities, we quantitatively confirm the imprinting of actual Sks and Bms in an antiferromagnet, starting from predefined FM Sks and Bms (Fig. 1).

## II. ATOMISTIC SIMULATION SYSTEM

The numerical study focuses on a single-crystal AFM (n)/NM (1)/FM (3)/HM (1 ML) system [Fig. 1(a)], where the number of monolayers (MLs) is indicated in parentheses, with n ranging 11–28 MLs. The crystal structure is consistently set to that of two interpenetrating single cubic lattices and is equivalent to rocksalt. The lattice parameter is 4.17 Å, that of the NiO antiferromagnet [21,22]. The area of the simulation system is 100 × 100 nm². The crystal is oriented along the

<footnote>*Contact author: coline.thevenard@cea.fr</footnote>

<footnote>†Contact author: richard evans@york.ac.uk</footnote>

<footnote>‡Contact author: vincent.baltz@cea.fr</footnote>
<figure><img src="image_3.png" /><figcaption>FIG. 1. (a) The atomic structure of the simple cubic monocristalline simulation system consisting of a HM/FM bilayer for Sk nucleation, a NM interface substituted with 25% of FM atoms for coupling, and a prototypical bipartite AFM layer made of two sublattices: AFMa and AFMb. In their ground state, the spins of AFMa and AFMb are collinear and opposite. The full size of the simulation system is 100 × 100 × 3.34 nm³ corresponding to 1 ML of HM, 3 MLs of ferromagnet, 1 ML of NM atoms, and 11 MLs of antiferromagnet. 3D views of the Sk (b) and Bm (c) tubes obtained in the ferromagnet and imprinted in the 11-MLs-thick antiferromagnet, following thermal and magnetic field cycling procedures. The simulated spins oriented in the xy- (b) and yz- (c) plane define the contour of the tube.</figcaption></figure>

[001] direction, taken as the z-axis and features a continuous structure. Periodic boundary conditions are applied in the x ([100]) direction and y ([010]) direction, to approach an infinite system. The roles of the nonmagnetic (NM) layer in inducing magnetic frustration for exchange bias coupling and the heavy metal (HM) layer in promoting perpendicular anisotropy and spin canting to stimulate spin texture formation [18,19] will be detailed later in the text.

Simulations are performed using the VAMPIRE atomistic simulation software [23] on the ARCHER2 supercomputer, each utilizing 1024 processors across 8 physical nodes. The large-scale simulation involves 10⁶ time steps and employs the adaptive Monte Carlo algorithm to minimize the energy of up to 7.6 × 10⁶ spins [24].

The interactions within the system are governed by the spin Hamiltonian [25]

$$ \mathcal{H} = -\sum_{i<j} J_{ij}(\mathbf{S}_i \cdot \mathbf{S}_j) - \sum_{i<j} \mathbf{D}_{ij} \cdot (\mathbf{S}_i \times \mathbf{S}_j) \\ - \sum_{i<j} k_{\text{N,ij}} (\mathbf{S}_i \cdot \mathbf{e}_{ij})^2 - \sum_{i} k_{\text{u,i}} (\mathbf{S}_i \cdot \mathbf{e}_i)^2 \\ - \sum_{i} \mu_{\text{s,i}} \mathbf{S}_i \cdot \mathbf{B}_{\text{ext}}, $$

where the indices i and j refer to the position of the atomic sites occupied by spins of vector S and magnetic moment μs. The Heisenberg exchange interaction, parametrized by the constant Jij, is represented by the first term. The second term accounts for the Dzyaloshinskii-Moriya interaction (DMI), described by the vector Dij = Dij(\hat{r}_{ik} × \hat{r}_{jk}), where Dij is the DMI strength and \hat{r}_{ik,jk} is the unit vector joining the magnetic atoms at sites i and j and the NM atom at site k. The third term introduces a radial spin rotation with respect to a specific nearest neighbor, relating to the Néel surface anisotropy characterized by the constant kN,ij. The fourth term introduces a uniaxial anisotropy of constant ku,i

along the axis of unit vector e_i and the last term is the Zeeman interaction, which couples the spins to an external induction Bext.

The magnetic properties of the HM/FM bilayer are based on those of Pt/Co which have been optimized to nucleate Sk in the ferromagnet [18,26]. Specifically, the interfacial perpendicular magnetic anisotropy is kN,HM-FM = 2 × 10⁻²⁴ J/atom and the DMI is DHM-FM = 10⁻²¹ J/link. The ferromagnet has an atomic magnetic moment μs,FM = 1.37μB, an exchange constant JFM = 13.3 × 10⁻²¹ J/link (which corresponds to the Curie temperature Tc = 1385 K, from JFM = 3kBTc ez [23] with ε = 0.719 [22] and z = 6 here) and (i) a uniaxial anisotropy ku,FM = 10⁻²⁴ J/atom for the Sk case [Fig. 1(b)] or (ii) a hard-axis anisotropy ku,FM = -10⁻²³ J/atom for the Bm case [Fig. 1(c)]. In its ground state, the antiferromagnet is composed of two collinear spin sublattices AFMa and AFMb hosting an atomic magnetic moment μs,AFM = 2μB, that of NiO [21], coupled antiparallel via a negative exchange constant JAFM = -5.04 × 10⁻²¹ J/link (which corresponds to the Néel temperature TN = 525 K of NiO [27]), and is subject to (i) a uniaxial anisotropy along the z-axis ku,AFM = 10⁻²⁵ J/atom for the Sk case [Fig. 1(b)], or (ii) a hard-axis anisotropy ku,AFM = -10⁻²⁴ J/atom for the Bm case [Fig. 1(c)]. The ferromagnet and the antiferromagnet are coupled via an interfacial exchange interaction JFM-AFM = 10⁻²¹ J/link, unless specified otherwise. We note that conversion to SI units is provided in Table S1 in the Supplemental Material (SM) [28]. A NM monolayer mixed with the ferromagnet and populated with 25% of substituted FM atoms, unless specified otherwise, generates a spatial distribution of magnetic exchange along the interface. This distribution results in a net interfacial magnetic moment within the antiferromagnet, providing a reasonable exchange bias to imprint spin textures in the antiferromagnet [25], while preserving a flat interface, which is essential for further calculating their topology. The influence of FM substitution on texture imprinting is detailed later in the text, with the example of Sk imprinting.
<figure><img src="image_4.png" /><figcaption>FIG. 2. Top view cross-section snapshots of the evolution of the spin textures in the ferromagnet (first row, 2nd ML from the FM/AFM interface), and the antiferromagnet in the core (second row: AFM sublattice, third row: AFM b sublattice, 6th ML from the FM/AFM interface). First column: field-induced nucleation in the ferromagnet, below the Curie temperature (T<sub>C</sub>) of the ferromagnet and above the Néel temperature (T<sub>N</sub>) of the antiferromagnet (Fig. S1 [28]). Second and third columns: imprinting and stabilization of Sk in the antiferromagnet, via cooling across T<sub>N</sub>. Fourth column: remanence state.</figcaption></figure>

### III. IMPRINTING OF AFM SPIN TEXTURES

The nucleation and stabilization processes of AFM Sks are depicted in Fig. 2. They require three successive simulation steps [7,16–20,26]. First, Sks are formed in the FM layer only, at 600 K under an applied field of 0.5 T along the z-axis. In this step, the ferromagnet is magnetically ordered (Fig. 2(a) and Fig. S1 in the Supplemental Material [28]) while the antiferromagnet remains disordered, as 600 K is below the ferromagnet’s Curie, T<sub>C</sub> = 1385 K, and above the antiferromagnet’s Néel temperature, T<sub>N</sub> = 525 K (Figs. 2(b)–2(c) and Fig. S1 [28]). The effect of the field strength and DMI in favoring the formation of Sks in the ferromagnet over maze domains or full saturation is shown in Fig. S2 [28]. Next, AFM spin textures are imprinted via exchange coupling at the FM/AFM interface. The system is cooled from 600 to 0 K, in the same applied field of 0.5 T. This thermal process leads to the collapse of one Sk and the stabilization of the other in the ferromagnet [Figs. 2(d) and 2(g)]. Upon crossing T<sub>N</sub>, the antiferromagnet orders and interfacial coupling is triggered, setting the Sk in the antiferromagnet [Figs. 2(e)–2(f)]. The resulting AFM texture consists of two interlocked FM Sks with opposite polarity [Figs. 2(h)–2(i)]. We note that using 0 K avoids thermal noise, facilitating the visual identification and quantification of the spin textures’ topological nature, as will be detailed later in the text. Finally, the applied field is removed to reach remanence. This step widens the FM and AFM Sk’s radius and wall width [Figs. 2(j)–2(l)], as

expected from the field-dependent energy landscape of FM Sks [29].

We note that, due to the high computational cost of the simulations, the dipole-dipole interactions were not included for the main calculations. Here, the dipole fields, implemented using the tensor approach described in [30], are shown to have a quantitative effect acting as an effective in-plane anisotropy leading to the formation of Bms. Increasing the perpendicular anisotropy compensates for this effect, leading to the reappearance of Sks (Fig. S3 [28]).

The strength of the interfacial coupling plays an important role in the formation of the Sks, as shown in Fig. 3. For weak coupling between the ferromagnet and antiferromagnet, no Sk is imprinted, but increasing the exchange coupling increases the overall effective exchange in the system, leading to a decrease in the FM Sk size (Figs. 3(a)–3(f) and Fig. S4 [28]). For a critical strength of $5 \times 10^{-22}$ J/link, Sks do not stabilize in any layer, as the interfacial exchange is excessive to sustain them (Figs. 3(g)–3(i) and Fig. S5 [28]). For stronger exchange coupling the FM and AFM layers become tightly bond, enabling the direct imprinting of Sks from the ferromagnet to the antiferromagnet. Further increases in the interfacial exchange lead to a modest additional reduction in the Sk size, attributed to the overall increase in exchange in the system, but this is a relatively weak effect [Figs. 3(j)–3(r)].

We next discuss the influence of FM substitution in the NM interfacial layer, on texture imprinting. For the case of 0% FM atoms, no exchange coupling occurs as there is no
<figure><img src="image_5.png" /><figcaption>FIG. 3. Top view cross-section snapshots of the evolution of the final state of the Sks in the ferromagnet (first row, 2nd ML from the interface), and the antiferromagnet in the core (second row: AFMa, third row: AFMb, 6th ML from the interface) under the effect of the FM-AFM exchange interaction $J_{FM-AFM}$.</figcaption></figure>

exchange bond between the ferromagnet and the antiferromagnet. Sks form in the ferromagnet but they are naturally not replicated in the antiferromagnet, which then maintains two sublattices with opposite out-of-plane spins. We note that the Sk size of 13.9 nm matches the case when $J_{FM-AFM} = 0$ J/link [Fig. 3(a)], showing a radius of 13.2 nm, in line with the analytical calculation that can be made in this specific case: 15.3 nm from $R = \pi D_{HM-FM} \sqrt{\frac{J_{FM}}{16J_{FM}k_{eff}^2 - \pi^2 D_{HM-FM}^2 k_{eff}^2}}$ [29] where $k_{eff} = k_{u,FM} - \frac{2 \times k_{N,HM-FM}}{J_{FM}}$ with $t_{FM}$ the thickness of the ferromagnet. We further note that the difference in FM Sk density between Fig. 3(a) ($J_{FM-AFM} = 0$ J/link with 25% FM bonds leading to no coupling) and Fig. 4(a) (0% FM atoms leading to virtually no coupling), is likely due to random thermal fluctuations during the thermal process [Figs. 4(a)–4(c)].

Substituting some NM atoms, 25%, 50%, and 75%, creates a sufficient net interfacial magnetic moment, enabling texture imprinting in the antiferromagnet. However, the FM Sk size (and consequently the AFM Sk size) decreases as the percentage of FM atoms increases due to stronger exchange bias, resulting in the FM Sk experiencing a larger effective external field [29] [Figs. 4(d)–4(l)]. We anticipate similar effects for Bms. With a full FM layer at the interface (100%), exchange bias becomes too large, preventing Sk formation in the ferromagnet. Due to frustration (the two AFM sublattices cannot simultaneously achieve parallel coupling with the ferromagnet and maintain antiparallel coupling between themselves), the antiferromagnet undergoes a spin flop, with antiparallel spins lying in-plane [Figs. 4(m)–4(o)].

<figure><img src="image_6.png" /><figcaption>FIG. 4. Top view cross-section snapshots of the evolution of the final state of the Sks in the ferromagnet (first row, 2nd ML from the interface), and the antiferromagnet in the core (second row: AFMa, third row: AFMb, 6th ML from the interface) under the effect of the FM population of NM sites at the interface.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>FIG. 5. (a) Temperature dependence of the topological charge $Q = \sum_{x^*} q(x^*)$ for the ferromagnet and both sublattices of the antiferromagnet. The dotted arrow indicates the timeline. Inset: schematic showing the discretization method for calculating $q$, for a two-dimensional square cell. (b)–(m) Spatial distribution of the topological charge density $q$ after postprocessing the raw data images (Fig. S10 [28]) with a Gaussian filter for better visibility. Note that $Q$ was calculated from the unprocessed $q$.</figcaption></figure>

## IV. TUBULAR SKYRMION

The assignment of the given topological class to the Sk s is obtained by calculating their topological charge $Q$ [Fig. 5(a)] [1,2,7]. For a two-dimensional discrete lattice of spins (i.e., for each ML in the system) $Q$ is the sum of local densities $q$ calculated for a square cell [inset of Fig. 5(a)] [31,32]:

$$q(x^*) = \frac{1}{4\pi} \sum_{(i,j,k) \in \{(1,2,3), (1,3,4)\}} 2\tan^{-1} \left( \frac{\mathbf{s}_i \cdot (\mathbf{s}_j \times \mathbf{s}_k)}{1 + \mathbf{s}_i \cdot \mathbf{s}_j + \mathbf{s}_i \cdot \mathbf{s}_k + \mathbf{s}_j \cdot \mathbf{s}_k} \right).$$

Figure 5 demonstrates the topological nature of the nucleated Sk s in the ferromagnet below 529 K, with a topological charge $Q = 2$, which reduces to 1 upon annihilation of one FM Sk at 359 K. It also demonstrates the topological nature of the imprinted Sk in the antiferromagnet below 207 K with $Q = +(-) 1$ for the AFMb (AFMa) sublattices. The values were confirmed throughout the depth of the antiferromagnet. At higher temperatures, thermal fluctuations can cause

neighboring spins to deviate significantly from each other resulting in the deviation of $Q$ from an integer value [31] [Figs. 5(b)–5(m)]. Note that the Sk imprinted in the antiferromagnet consists of two intercalated FM Sk s with mutually reversed spins [Fig. 6(a)] resulting in an AFM Sk with a net topological charge of zero [33].

To investigate the intricate topology of the Sk s formed with more accuracy, the usual three key parameters are introduced and calculated: polarity, vorticity, and helicity [1,2,7]. Polarity $p$ quantifies the out-of-plane magnetization density of the Sk core, vorticity $m$ represents the magnetization density winding number, and helicity $\gamma$ describes the angular phase shift between the spatial magnetization rotation and the positional winding. We note that $Q = pm$. In the final state [Figs. 2(j)–2(l)], $(p, m, \gamma) = (1, 1, \pi)$ for the FM layer and $(-1, 1, 0)$ and $(1, 1, \pi)$ for the AFMb and AFM sublattices, respectively. These values indicate that the initial Sk in the ferromagnet is of the Néel type, consistent with the DMI strength of $10^{-21}$ J/link which exceeds the critical strength for a Bloch to Néel domain wall transition $D_c = 4\mu_0 M_s^2 t_{FM} \ln 2 / (2\pi^2) = 10^{-23}$ J/link [34]. The Sk imprinted in the AFM sublattices naturally replicates the morphology and topology (in terms of $p, m$, and $\gamma$) of the Sk s from which it originates in the FM layer.

Due to the regularity of the atomic lattice and continuity at the interfaces, the FM (AFM) Sk in its final state [Figs. 2(j)–2(l)] forms a disk with in-plane spins describing a circle of radius $R = 7.8$ (7.1) nm and wall width $w = 8.5$ (9.7) nm, estimated by fitting $s_z(r) = \cos\{2\tan^{-1}[\sinh(R/w)/\sinh(r/w)]\}$ [35]. The close values for both materials clearly indicate that the arrangement of the AFM spins follows that of the FM spins.

Next, we investigate how the topological texture propagates from the interface through the depth of the antiferromagnet and how temperature affects this propagation. To quantify the depth-dependent arrangement of each AFM sublattice spins relative to the FM spins, we employ the partial spin-spin correlation function [Fig. 6(b)]

$$C(\Delta z) = \frac{1}{N} \sum_{(i,j)} s_{z,i} s_{z,j}(\Delta z),$$

where $\Delta z$ is the distance to the FM/AFM interface and $N$ is the number of spin pairs formed by the FM spin $i$ and AFM spin $j$ of the same in-plane coordinates $(x, y)$ [19]. This quantitative method enhances the bare observation of cross-sections [Fig. 6(c)]. The sign of $C$ is naturally opposite when considering the two AFM sublattices of opposite spins.

Starting from fully anticorrelated spins ($C \approx 0$) at 600 K, when the antiferromagnet is disordered, the system gradually reaches full correlation ($|C| \approx 1$) at 0 K, across the entire AFM layer. This indicates that the replication is effective throughout the 5.8-nm-thick AFM layer, which corresponds to the maximum penetration depth allowed for this set of parameters (Fig. S6 [28]). We note however that, when the correlation remains constant in the core of the AFM layer, it deteriorates in the few MLs at the FM/AFM interface due to the loss of surface exchange bonds and a local decrease in AFM surface order. Similarly, the correlation also
<figure><img src="image_8.png" /><figcaption>FIG. 6. (a) Zoom on the top view cross-section of the intertwined AFMa and AFMb sublattice Sk, imprinted in the 28-MLs-thick antiferromagnet (6th ML from the FM/AFM interface), at remanence, following thermal and magnetic field cycling procedures. To facilitate the reading of the image, only 1 out of every 7 spins is shown. (b) Temperature dependence of the modulus of the sublattice-resolved partial spin-spin correlation function applied in the center of the spin texture imprinted in the antiferromagnet. (c) Side view cross-section at selected temperatures, showing the formation of the Sk tube in the antiferromagnet.</figcaption></figure>

deteriorates in the last few MLs away from the free AFM
edge, due to missing magnetic bonds. In other words, close to
the edge, the decorrelation from the ferromagnet prevents the
rearrangement of the AFM spins. We also consider the
different energy terms during formation of the Sks and
see no significant difference of energy for the system with
and without Sks (Fig. S7 [28]). Unlike micromagnetic
simulations, the total energy is dominated by exchange and so
an analysis of the energy does not provide significant insight
into the imprinting process.

V. TUBULAR BIMERON

To test the universality of the replication, we next simulate
the same heterostructure under identical energetic conditions,
with the sole modification being the change of anisotropy
from out-of-plane to in-plane. Specifically, the FM constant
$k_{u,FM} = -10^{-23}$ J/atom and the AFM constant $k_{u,AFM} =
-10^{-24}$ J/atom now confine the magnetization to the $xy$-
plane. This allows us to nucleate an in-plane Sk, or Bm,
in the FM layer and to imprint it throughout the thickness
of the AFM layer [Figs. 1(c) and 7], using the thermal and
field procedure (Figs. S8 and S9 [28]) described earlier in
the text. In the final state, the axis of the Bm, which joins
the centers of the two merons, is angled by $-3.3^\circ$ in the
$xy$-plane with respect to the $x$-axis. This in-plane orientation
is a consequence of using $z$ as the hard-axis, allowing the Bm
axis to lie anywhere within the isotropic $xy$-plane. Addition-
ally, the axis is slightly titled out-of-plane by $1.5^\circ$ ascribed
to magnetic frustration at the FM/AFM interface, combined

with the residual interfacial anisotropy $k_N$. Moreover, by anal-
ogy with a Sk, the topological parameters of the Bm are
$(p, m, \gamma) = (1, 1, \pi)$ for the FM layer, and $(-1, 1, 0)$ and
$(1, 1, \pi)$ for the AFMa and AFMb sublattices, respec-
tively. These parameters were calculated after applying a spin
rotation operation in spin space to align the Bm axis with the
$z$-axis. The invariance of the topological parameters, along
with an identical topological charge $Q = 1$ for the FM layer
and AFMb sublattice and $-1$ for the AFMa sublattice, con-
firms that the texture we imprinted in the AFM layer is a Bm,
a quasiparticle homeomorphic to the Sk imprinted in the first
part of this work [9,36].

VI. CONCLUSION

In conclusion, we have theoretically validated the feasibil-
ity of texture imprinting for the nucleation of actual skyrmions
and bimerons in a compensated magnet with zero net mag-
netization, employing predefined skyrmions and bimerons in
an adjacent exchange-coupled ferromagnet as a template. Our
study involves engineering a prototypical bipartite antifer-
romagnetic layer within a multilayer structure, ensuring the
presence of the necessary Dzyaloshinskii-Moriya interaction,
perpendicular anisotropy, and interfacial magnetic frustra-
tions, all while avoiding discontinuities. This approach has
enabled us to calculate the topological parameters of the
imprinted spin textures, providing quantitative data that was
previously inaccessible due to the complexities of multilayers
with discontinuities, polycrystallinity, or multipartite chiral
antiferromagnets. We have successfully tracked the formation
<figure><img src="image_9.png" /><figcaption>FIG. 7. Top view cross-section snapshots of the final state of the Bm in the ferromagnet (first row, 2nd ML from the FM/AFM interface), and the antiferromagnet in the core (second row: AFMa sublattice; third row: AFMb sublattice, 6th ML from the FM/AFM interface) showing (a)–(c) the in-plane and (d)–(f) out-of-plane component of the spins. (g) Zoom on the top view cross-section of the intertwined AFMa and AFMb sublattice Bm, imprinted in the 11-MLs-thick antiferromagnet (6th ML from the FM/AFM interface), at remanence, following thermal and magnetic field cycling procedures. To facilitate the reading of the image, only 1 out of every 7 spins is shown. (h) Side view cross-section, showing the Bm tube in the antiferromagnet, after the imprinting process.</figcaption></figure>

of the topological objects throughout the thermal procedure, first nucleating skyrmions and bimerons in the ferromagnet, and then replicating them in the antiferromagnet after crossing the Néel temperature. The replicated skyrmions and bimerons were found to extend beyond the interface, spanning the core of the antiferromagnet. This work addresses the challenge of nucleating quantitatively proven topological magnetic textures in compensated magnets with zero net magnetization. Its primary interest is fundamentally driven as it paves the way for extending the study of topological spin textures beyond ferromagnets, into materials with intriguing electrodynamic properties, such as antiferromagnets and altermagnets. Specifically, because the method is independent of the electronic nature of the materials used, one could envisage an insulating ferromagnet and a metallic antiferromagnet, potentially in contact with a heavy metal, for the fundamental study of the dynamics of skyrmion propagation in antiferromagnets under current by spin torques, and the reciprocal effects concerning the influence of an antiferromagnetic skyrmion on electron dynamics. Given that the dynamics of antiferromagnets are in the THz regime, from an applicative perspective, one could imagine nucleating a skyrmion in a ferromagnet and then leveraging the THz dynamics of the antiferromagnet, unconstrained by the skyrmion Hall effect [14,15] to prop-

agate information, detecting the antiferromagnetic skyrmion via nonvanishing topological spin Hall effects [12,13] or through the inverse nucleation of a ferromagnetic skyrmion. The use of this method for applications will be limited by the speed of imprinting. However, one could envisage the use of femtosecond lasers for the combined nucleation of ferromagnetic skyrmions [37] and imprinting of antiferromagnetic skyrmions.

## ACKNOWLEDGMENTS

This study was partially supported by the CNRS international research project (IRP) "CITRON," U.K. EPSRC International Network for Spintronics (Grant No. EP/V007211/1), and the French National Research Agency through France 2030 Government Grant No. PEPR-SPIN "ALTEROSPIN" ANR-24-EXPR-0002. This work used the ARCHER2 U.K. National Supercomputing Service [38].

## DATA AVAILABILITY

The data that support the findings of this article are openly available [39].

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