In an AFM skyrmion lattice, long-range dipolar stray fields are suppressed, and short-range exchange and DMI, together with local anisotropy, dominate, setting the equilibrium lattice spacing. This is in stark contrast to ferromagnetic skyrmion lattices, where long-range dipolar interactions dominate over other contributions25,42. When subjected to weak excitations, the AFM lattice is driven out of equilibrium: pinned skyrmions serve as scattering centres for mobile ones, leading to either local lattice compression or trajectory deflection. Such scattering events encode the skyrmion–skyrmion interaction potential, which can be quantitatively extracted from measured real-space trajectories. Fully compensated SyAFMs offer an ideal platform for this, as the cancellation of gyrotropic terms suppresses the skyrmion Hall effect19,21, isolating longitudinal motion and potentially enabling a direct mapping between scattering geometry and interaction forces. To resolve the spatiotemporal dynamics of an AFM skyrmion lattice, we employ pump–probe X-ray microscopy, which enables real-time nanosecond tracking of individual skyrmion trajectories. This provides direct access to transient effects, such as skyrmion–skyrmion repulsion and inertial responses, that are not resolved in quasi-static measurements. To observe the dynamics of each magnetic sublattice, we perform sequential measurements at the Fe and Co L3 absorption edges, as only one X-ray energy can be used at a time.
We first discuss the low-current regime (Jx = 2.8 × 1011 A m−2), where the strength of the current-induced SOT is comparable to the local pinning potential. In this case, motion is governed by a spatially inhomogeneous energy landscape, where variations in pinning strength give rise to an incoherent dynamical regime in which different parts of the lattice respond differently to the same uniform drive. Despite the application of a uniform current, the lattice response is spatially heterogeneous: some skyrmions remain pinned (for example, I1 in Fig. 2a), others translate smoothly (for example, M1 in Fig. 2a), and some undergo pronounced deformation (for example, R1 in Fig. 2a). The pinning sites correspond to energy minima associated with material inhomogeneities, defects or grain boundaries that locally suppress skyrmion mobility. To address these strongly differing motion patterns within the imaged skyrmion ensemble, we conduct a classification of skyrmions into four clusters, as colour coded in Fig. 2a, according to their net displacement during current excitation: immobile skyrmions (class I, blue), mobile skyrmions (class M, red) and those located immediately adjacent to the mobile cluster on the left (class L, green) and right (class R, black). Class M skyrmions exhibit a large displacement during the pulse, whereas class I skyrmions show only minimal motion. We define this behaviour as an incoherent flow regime, where skyrmions in both sublattices move in synchrony, yet the overall lattice response remains spatially fragmented. The dynamics are highly reproducible across all cycles, confirming their non-stochastic origin. The effects of thermal fluctuations, which generate statistically random variations that average out in pump–probe measurements, are therefore not detectable in the present study; consequently, a thermally activated creep regime, while in principle potentially present in skyrmion lattice dynamics, is not resolved. The local behaviour varies substantially, from pinned to deforming skyrmions and to those undergoing smooth displacements. The spatial distribution of displacements (Fig. 2a) shows that this response extends throughout the interior rather than being localized at device edges, indicating that the energy landscape is governed by distributed microstructural disorder rather than geometric confinement. Such spatial heterogeneity under uniform excitation reflects a breakdown of global lattice coherence and distinguishes this particular regime from both thermally activated creep and viscous-flow regimes.
Fig. 2: Spatio-temporal evolution of an AFM skyrmion lattice during the cycle of bipolar current pulses.
a, x-displacement map following a negative pulse, used to classify the skyrmions into four categories: immobile (I, blue), mobile (M, red), laterally adjacent to the left (L, green) and to the right (R, black) of the mobile region. The colour scale encodes the net displacement along the x direction. Circles indicate representative skyrmions from each class exhibiting distinct responses to current excitation. b, Time-resolved evolution of AFM skyrmions under a current pulse (Jx = −2.8 × 1011 A m−2). Left: skyrmion contours extracted from STXM images, colour-coded by time over the displayed 15-ns interval (purple to yellow). Right: corresponding particle representation, where skyrmion cores are modelled as point particles and Delaunay triangulations are constructed at each time step using the same time colour scale. c,d, Average displacement traces for class I and M (c) and L and R (d). Shaded regions indicate the duration of the negative and positive current pulses during the bipolar pulse. Upon pulse termination, all skyrmion classes exhibit recoil opposite to their preceding motion, regardless of previous current polarity. I and M skyrmion classes, with the I skyrmions showing the strongest recoil and M types the weakest, are shown. The L and R skyrmion classes display asymmetric recoil dynamics, governed by their lateral position relative to the immobile class I. All timescales for the recoil dynamics, as extracted via exponential fitting, fall within 3–20 ns.
Figure 2b shows the evolution of skyrmion contours in sublattice A under a current pulse applied along the x axis, revealing their time-resolved response to SOTs during a pump cycle. The contours in Fig. 2b, left, are colour-coded over a 15-ns window, from purple at early times to yellow at late times, visualizing the progression of skyrmion boundary displacement. These contours are obtained by tracking individual skyrmion boundaries across consecutive frames. To analyse local lattice deformation, the skyrmion cores are modelled as point particles and Delaunay triangulations are constructed at each time step, as shown in Fig. 2b, right. This representation depicts the evolving geometry and local strain within the lattice during current excitation. Both sublattices A and B exhibit synchronized skyrmion motion (Supplementary Fig. 3 for sublattice B), following identical trajectories. The synchronized motion of both sublattices, despite the spatially heterogeneous response, shows that even the relatively weak interlayer AFM exchange in thin-film SyAFMs, compared with the strong intrinsic exchange in bulk antiferromagnets, is sufficient to overcome local pinning, enabling robust sublattice locking and offering a key advantage for AFM spintronic applications.
Pinned skyrmions act as rigid obstacles within the lattice, inducing constraints that can be described in a mechanical approach and lead to anisotropic strain in neighbouring skyrmions. As adjacent skyrmions are pushed by the applied current, these constraints result in boundary elongation or compression. For instance, skyrmions located just outside the boundary of pinned regions (for example, R1) cannot translate freely; instead, one domain wall is effectively anchored by the adjacent pinned skyrmion, while the opposite boundary remains free to move. Within the Thiele framework, this reflects a breakdown of the rigid-particle approximation, as asymmetric constraints induce spin structure deformation and redistribute internal stresses through the lattice. These deformations are visible in Fig. 2b, right, as irregularities in the triangulated lattice, where the otherwise regular hexagonal arrangement of skyrmions is locally distorted. Such distortions appear as variations in effective bond lengths and angles between neighbouring skyrmions in the Delaunay triangulation, indicating areas of localized strain in the lattice. Figure 2c,d displays the average time-resolved displacement of each of the previously defined four classes of skyrmions, obtained by tracking the trajectories of colour-coded skyrmions throughout the duration of the bipolar pulse. Class M skyrmions exhibit substantial motion during the current pulse, whereas class I skyrmions show only minimal displacement. Strikingly, upon removal of the current drive, the absence of external forcing allows internal skyrmion–skyrmion interactions to restore equilibrium, yielding a recoil opposite to the prior current-driven motion, irrespective of the applied polarity. The low-current-driven dynamics occur within a deformable AFM skyrmion lattice and involve a transient local compression during the pulse, followed by interaction-mediated recoil after the current is switched off. In this regime, ‘scattering’ does not denote an isolated dilute two-body collision but rather a local recoil event of mobile skyrmions from pinned neighbours, embedded within the collective lattice response. This recoil reflects a relaxation process in which mobile skyrmions recoil from their pinned neighbours, with the restoring forces arising from skyrmion–skyrmion repulsion and the surrounding pinning landscape. Rather than behaving as independent particles, the skyrmions respond collectively, revealing the elastically coupled and scattering-mediated nature of the lattice. This post-pulse relaxation is well described by an exponential decay, from which a characteristic relaxation time constant (τrelax) is extracted for each skyrmion class. The recoil amplitudes and relaxation time constants vary substantially across the I, M, L and R classes, both in magnitude and decay rate, suggesting differences in the local energy landscape experienced by each group and thereby providing a quantitative measure of skyrmion interaction potential. A table with the extracted values of magnitude and decay rate for each of the four classes and both current polarities is given in Supplementary Section A1, Table 1. In the single-skyrmion limit, current-driven skyrmion dynamics are typically classified into pinned, creep and viscous-flow regimes43,44, governed by the competition between driving forces, thermal excitations and the local energy landscape that governs pinning effects. With increasing skyrmion density, however, interactions become non-negligible45 and qualitatively modify the dynamical response46. To explicitly distinguish these limits, we performed time-resolved measurements in the weakly interacting regime of spatially separated individual skyrmions (Supplementary Section A3), where the measurements show independent dynamics of each skyrmion governed by the local pinning landscape. By contrast, the dense lattice exhibits the additional incoherent-flow regime, in which the coexistence of pinned and mobile skyrmions gives rise to interaction-mediated correlated distortions and collective recoil. The viscous-flow regime is thus the dense-lattice analogue of the familiar high-drive flow regime of single skyrmions, whereas the incoherent-flow regime is a unique collective dynamic phase of the interacting lattice.
This complex behaviour now allows us to extract the skyrmion interaction potential directly from the nanosecond relaxation dynamics of L and R skyrmions, which lie at the lateral boundary between mobile and pinned regions. In this geometry, the pinned I skyrmions act as reference scattering centres, providing boundary conditions for quantifying the skyrmion–skyrmion interaction potential. We track the experimentally measured recoil trajectories of the L and R skyrmions following the termination of the nanosecond current pulse and employ an inverse estimation based on the Thiele equation (Methods; Supplementary Section B). In the fully compensated SyAFM configuration, the gyrotropic term contribution disappears, and long-range dipolar interactions are markedly suppressed, so that the dynamics reduce to a purely longitudinal balance between dissipative drag and the skyrmion–skyrmion force. By restricting the analysis to the immediate post-pulse relaxation window, we ensure that the motion is governed solely by skyrmion–skyrmion interactions and dissipation, free from external SOTs because the current is off and free from stochastic thermal activation. F(r) is the interaction force one skyrmion exerts on another along the line connecting their centres, arising from the energy cost of adapting the spin texture between them as the separation between their centres changes. In our SyAFM system, this force is mediated predominantly by short-range exchange and interfacial DMI, with only local interlayer magnetostatic contributions. This stands in sharp contrast to the behaviour of conventional FM skyrmions, whose interactions have been extensively characterized25,28. We model the repulsive interaction as a radially symmetric exponentially decaying force
$${\bf{F}}_{(a,b)}({\bf{r}})=\frac{{\bf{r}}}{|{\bf{r}}|}{F}_{(a,b)}(|{\bf{r}}|),\,\frac{{F}_{(a,b)}(r)}{D}=1\,{\rm{m}}\,{{\rm{s}}}^{-1}\,\exp \left(-\frac{r-b}{a}\right),$$
(1)
where r is the skyrmion–skyrmion distance, a characterizes the steepness and effective range of the force and b determines the strength of the force, whereas D denotes the dissipation constant. In this geometry, the surrounding lattice enters through the instantaneous positions of all neighbouring skyrmions, such that the recoil dynamics are well described by an effective pairwise interaction kernel embedded in the many-body configuration. From the analysis of the scattering trajectories, we can determine only the ratio F(a,b)(r)/D. As the prefactor 1 m s−1 is of the same order of magnitude as the velocities in the system, b is also of the same order of magnitude as the approximate effective interaction distance. This physically grounded parametrization provides direct experimental access to the microscopic interaction law in the regime where exchange and DMI become important, a regime that has so far remained experimentally elusive at the nanoscale.
Figure 3a shows, as an example for skyrmion R1, the experimental trajectory and the predicted trajectory obtained using the estimated interaction-potential parameters (a* = (44 ± 4) nm, b* = (247 ± 4) nm) (Methods and Supplementary Section B). Furthermore, micromagnetic simulations were carried out in a system closely matching the experimental dynamic simulation with skyrmion scattering, and the resulting interaction-potential parameters in this case are a* = (31 ± 3) nm and b* = (288 ± 13) nm (Supplementary Section B2). As the dissipation constant D in the experiment deviates from its value in a homogeneous, defect-free system due to nanoscale roughness45,47,48, the force parameter b differs between the experiment and the value expected for a homogeneous, defect-free system. By comparing F(a,b)(r) over the relevant range of r in the experiment and in the homogeneous case, we infer that the effective dissipation constant D in the experiment is approximately four times larger than in a homogeneous system. By contrast, the parameter a does not depend on the value of D in the extraction of the potential. The interaction potential is then obtained via equation (1) with the respective D obtained via V(a,b)(r) = −∫dr F(a,b)(r), resulting in an exponentially decaying repulsive functional dependence. Figure 3b shows the experimentally estimated potential (orange) alongside the micromagnetic result (blue). Figure 3b, bottom, shows a histogram of skyrmion–skyrmion separations among skyrmions whose trajectories were predicted, as well as separations between those skyrmions and the boundary skyrmions, confirming that the potential is well constrained within the measurement window. The overlapping uncertainty bands between experiment and simulation validate the robustness of the inverse parameter estimation method and support the physical picture of a short-range, rapidly decaying repulsion governed by the finite spatial extent of the skyrmion spin texture. The overlap between experiment and simulation also shows that the dominant contributions in both cases were identified, and that the potential from the Thiele equation can be fully explained in this study from the underlying micromagnetism. Such a determination of potential is enabled by the unique L and R skyrmions that reside at the lateral boundary between mobile and immobile regions, experiencing a well-defined repulsive interaction with pinned I skyrmions that act as reference neighbours. This configuration produces reproducible skyrmion–skyrmion scattering trajectories that are absent in the conventional flow regime of skyrmion dynamics (discussed in the following section), where collective motion dominates and relative separations remain constant. This approach provides a direct and quantitative determination of the skyrmion–skyrmion interaction potential from the real-time relaxation of nanosecond scattering trajectories, without relying on equilibrium structure factors25, thermal statistics28 or other indirect inference methods. By extracting the potential from well-defined scattering events, we probe the interaction on its intrinsic length and timescales, accessing a regime previously unreachable in experiments. The potential has been tested against the dependence on skyrmion areal density and micromagnetic parameters (Supplementary Section B2). Although interaction potentials have been inferred in ferromagnetic systems, these measurements are largely qualitative26,29, and quantitative estimates have relied on indirect approaches such as iterative Boltzmann inversion28, which require thermal equilibrium and stochastic motion. Such conditions are inapplicable for dynamics that are reproducible over billions of cycles, which we, however, can analyse using our approach.
Fig. 3: Quantitative extraction of the skyrmion–skyrmion interaction potential from the dynamics of skyrmions.
a, Comparison between experimentally measured skyrmion trajectories and those predicted by the inverse method based on the Thiele equation for skyrmion R1, capturing their relaxation dynamics after the application of each polarity of the bipolar current pulse. Experimental trajectories are shown for both positive (blue to green) and negative (purple to yellow) current polarities, overlaid with model-predicted trajectories (dashed and solid black lines) obtained by numerical integration of the Thiele equation using the estimated interaction parameters a* and b*. b, The extracted skyrmion–skyrmion interaction potential per bilayer, \({V}_{({a}^{* },{b}^{* })}(r)/N\), as a function of distance r, where N is the number of bilayer repetitions. Derived from the estimated force parameters, with experimental results (orange) compared with micromagnetic simulations (blue). Shaded regions indicate 68% uncertainty bands. Bottom: the skyrmion–skyrmion distances among skyrmions whose trajectories were predicted, as well as separations between those skyrmions and the boundary skyrmions, illustrating the range over which the potential is estimated by the data. The grey vertical line indicates the periodicity of the lattice.