Transient Magnetic Skyrmion Dynamics

• Transient Dynamics of Magnetic Skyrmions is the study of rapid, non-equilibrium processes governing the nucleation, evolution, and collapse of nanoscale, topologically protected spin textures.
• Advanced methods such as micromagnetic simulations, Lorentz TEM imaging, and analytical models quantify energy barriers and transient timescales in defect-mediated transitions.
• Key insights reveal opportunities for designing fast, energy-efficient spintronic devices by tuning DMI, anisotropy, and current/field protocols to control skyrmion dynamics.

Magnetic skyrmions are nanoscale, topologically nontrivial spin textures stabilized by chiral interactions, notably Dzyaloshinskii–Moriya interaction (DMI), in noncentrosymmetric magnets. Their transient dynamics encompass the full spectrum of non-equilibrium processes by which skyrmion configurations emerge, transform, and relax on sub-ns to ms timescales under thermal, current, or field-driven perturbations. This article delineates the microscopic mechanisms, characteristic timescales, pathways, and application-relevant principles underlying the transient behavior of magnetic skyrmions.

1. Topological Charge Evolution and Defect-Mediated Skyrmion Nucleation

The transient creation of isolated skyrmions from disordered magnetic regions is fundamentally controlled by annihilation processes of localized topological defects, rather than by global smooth variations of the total topological charge $Q$. The topological charge is defined as

$$Q = \frac{1}{4\pi} \int \mathbf{m}\cdot(\partial_x \mathbf{m} \times \partial_y \mathbf{m})\, dx\,dy,$$

where $\mathbf{m}(\mathbf{r})$ is the normalized magnetization. High-resolution micromagnetic simulations reveal that—when a thermally demagnetized patch is quenched in a thin-film DMI ferromagnet under a small bias field—magnetization first fragments into a labyrinth of narrow domains bounded by Néel walls. Along these walls, discrete "domain wall skyrmions" (DW skyrmions, $Q = \pm1$) spontaneously nucleate, corresponding to $2\pi$ twists stabilized by the DMI.

The transient evolution of $Q(t)$ is governed by a series of unit jumps at discrete events: DW skyrmion annihilation with oppositely wound wall segments, merging or annihilation with vertical Bloch lines ($Q = \pm1/2$), and relaxation of the core into a compact Néel skyrmion. The sequence and pairing of these events determines the final number and configuration of skyrmions. Notably, the energy barriers for these transitions are set by the local DMI, anisotropy, and wall geometry, making the process inherently multistable and sensitive to layer structure and pinning (Je, 2020).

2. Spontaneous Annihilation, Splitting, and Antiskyrmion-Mediated Transients

In skyrmion crystals (SkX), especially at grain boundaries or lattice defects, spontaneous (thermally assisted) transitions between skyrmion configurations involve rapid splitting (creation) or merging (annihilation) events. High-speed Lorentz TEM imaging in FeGe shows that highly deformed skyrmions at 5-7 lattice defects can undergo transitions between dumbbell-like elongated "primary" states and topologically distinct "transition" states within ~10 ms. Such transitions always proceed via transient antiskyrmion states of opposite charge, ensuring rigorous topological charge conservation at every stage: $$(-1) \rightarrow (-1) + (-1) + (+1) \rightarrow (-2)$$ for splitting, and the reverse for merging. The characteristic timescales are determined by Arrhenius rates with attempt frequencies $v_0\sim 10^9\,$Hz and activation barriers $\Delta E\approx 0.55$ eV, set by strain, exchange, DMI, and Zeeman contributions (Rendell-Bhatti et al., 2019). Local compressive strain and skyrmion deformation exceeding ~10–15% or nearest-neighbor distance compressions beyond 20% are the key triggers.

3. Stochastic Blinking and Surface-State-Mediated Reversible Nucleation

Near the phase boundary between conical and skyrmion lattice states in helimagnets, persistent stochastic creation-annihilation cycles ("blinking") of skyrmion-like chiral bobber (CB) surface states occur. Spin-dynamics simulations and harmonic transition state theory (HTST) quantitatively capture this as thermally activated transitions over two barriers—nucleation and annihilation—each set by Bloch-point formation. The mean blinking interval,

$$\tau_{\rm blink}(B,T) = \tau_0^N e^{\Delta E^N / k_BT} + \tau_0^{AN} e^{\Delta E^{AN}/k_BT},$$

can be tuned from microseconds to sub-nanoseconds. The oscillation modes and prefactor structure differ markedly from bulk or thin-film skyrmionites, with chiral-bobber collapse featuring a temperature-independent prefactor. This regime supports fast, stochastic bit generation for probabilistic devices (Menezes et al., 12 Jun 2024).

4. Transient Dynamics in Skyrmion Lattices: Coarsening, Defect Motion, and Scaling

Following a deep quench from a disordered state, skyrmion crystals evolve through a two-stage ordering kinetics. The initial stage is rapid: domain structures with characteristic double-$\mathbf{Q}$ periodicity form within $\mathcal{O}(10^2)$ simulation units. In the late stage, ordering is governed by the annihilation of dislocations (topological defects corresponding to stripe terminations), with their density $\rho_d(t)$ decaying as

$\rho_d(t) \sim t^{-1} [\ln t]^{-1}.$

Dynamical scaling symmetry is observed: correlation length $\xi(t) \sim t^\alpha$, with $\alpha\approx0.48$. This universality places SkL coarsening in the same class as 2D XY models (vortex–antivortex annihilation) (Shimizu et al., 2023). In hexagonal SkLs, rotating domains separated by grain boundaries rich in 5–7 disclination pairs (defect densities following Frank’s law) reconstruct transiently in "surge" events—collective, rapid affiliation switches of clusters—without net skyrmion number change, further highlighting the particle character and topological stability of skyrmions (Pöllath et al., 2017).

5. Current and Field-Driven Fast Transient Skyrmion Dynamics

The collective coordinate (Thiele) equation provides the principal analytical framework for skyrmion center-of-mass motion under current or field drives: $$\mathbf{G} \times (\dot{\mathbf{R}} - \mathbf{v}_s) + \alpha \mathcal{D} (\dot{\mathbf{R}} - \mathbf{v}_s) = 0.$$ Here, $\mathbf{G}=4\pi Q \hat{z}$ is the gyrovector, $\mathcal{D}$ the dissipative tensor, $\alpha$ the Gilbert damping, and $\mathbf{v}_s$ the spin current velocity. For current pulses, acceleration times $\tau_{\rm acc}$ are set by $\tau_{\rm acc} = \mathcal{G}/(\alpha\mathcal{D})$, yielding response times of $10^{-9}$–$10^{-7}$ s for typical $\alpha\sim0.01$.

Notably, in the Galilean-invariant regime ($\alpha=\beta$), inertial terms vanish for current-driven motion, ensuring that skyrmion velocity tracks the current with negligible delay ("ultra-low inertia") (Schütte et al., 2015). Field-driven transients, in contrast, exhibit large effective mass, frequency-dependent response and significantly non-Newtonian decay—underlying the importance of gyrocoupling and damping in device design (Komineas et al., 2015).

In confined geometries (nano-tracks, racetracks), edge effects and mutual skyrmion repulsion induce complex, non-linear transients: interacting skyrmions exhibit damped helical paths, oscillation of radii, and collapse via either fast core burst or slow bubble-contraction, depending on position and current density. For two Néel skyrmions under $j=8\times 10^{11}\,\rm A/m^2$, a $\sim 30$ ps core-collapse of the leading skyrmion occurs at a reduced threshold ($j_{c1}\sim 8\times 10^{11}\,\rm A/m^2$), followed by slower collapse of the trailing skyrmion at $j_{c2}\sim 1.3\times 10^{12}$ A/m$^2$ (Saidi et al., 2023).

6. Field-Induced Collapsing Dynamics and Layer-Resolved Mechanisms

Field-induced collapse mechanisms in multilayer systems show strong dependence on the skyrmion type (pure Néel vs. hybrid). In [Pt/Co/Ir]$_{15}$, with strong DMI, skyrmions undergo discrete, abrupt morphological transitions: isolated Néel skyrmions elongate and percolate into labyrinth domains as $H_z$ is swept negative, followed by re-nucleation of skyrmions with inverted core polarity at well-defined critical fields (e.g., $H_{c1}$, $H_{c2}$). Each transition completes in a few nanoseconds beyond the critical field. By contrast, in [Ta/CoFeB/MgO]$_{15}$ with hybrid wall textures, the collapse proceeds via smooth, continuous changes in skyrmion size, reversible under field reversal, without topological jumps or wall-instabilities.

Layer-dependent spin profiles (uniform Néel vs. hybrid (Néel–Bloch–Néel)) thus serve as fingerprints for dynamic collapse pathways (Tomasello et al., 2023). These mechanisms can be directly engineered via material selection (DMI and anisotropy tuning) to deliver fast, reversible switching or analog expansion modes for memory, logic, or neuromorphic functionality.

7. Engineering Transient Skyrmion Dynamics for Device Applications

Control of skyrmion transient dynamics is central for high-speed, low-energy, and reliable spintronic applications. Deterministic writing/erasure of skyrmions can be achieved by:

• Engineering local defects/pinning sites to modulate DW-skyrmion nucleation/annihilation pathways and select desired $Q$ changes.
• Utilizing ultrafast current or thermal pulses for controlled proliferation/annihilation of topological defects, followed by quenching.
• Tuning DMI strength, anisotropy, and interlayer coupling to set critical fields/currents and operating timescales (Je, 2020, Tomasello et al., 2023).

Stochastic blinking and multi-level transitions open avenues for probabilistic and neuromorphic operations. The quantized, discrete nature of $Q(t)$ jumps and defect-mediated relaxation paths is essential for robust device functionality, as are sub-ns response times and suppressed thermal diffusion enabled by large gyrocoupling and optimal damping (Schütte et al., 2015, Menezes et al., 12 Jun 2024).

Transient dynamics studies form the basis for rational “topological engineering” of future memory and logic platforms, leveraging skyrmion solitons’ non-volatile, fast, and topologically-protected character.