Domain Wall Skyrmions

• Domain Wall Skyrmions are topologically protected excitations confined within magnetic domain walls, exhibiting a full 360° rotation of the internal magnetization.
• Their formation is driven by interplay between exchange interactions, perpendicular anisotropy, and Dzyaloshinskii–Moriya interactions, enabling control through voltage, laser, and current pulses.
• They are key to next-generation applications in spintronics and magnonics, offering robust, internally-guided channels for data storage and logic devices.

Domain Wall Skyrmions (DWSKs) are topologically protected, particle-like excitations confined within magnetic domain walls, distinguished by a full 360° rotation of the internal magnetization vector along the wall. DWSKs have arisen as a central concept in both condensed matter and quantum field theory, crossing from magnetic nanostructures to non-abelian gauge theories under extreme conditions. Their intricate formation mechanisms, energetic stability within wall geometries, and controllable dynamics underlie their promise for next-generation spintronic, magnonic, and information storage devices, as well as for elucidating topological phase transitions in high-energy physics.

1. Theoretical Foundations and Structures

DWSKs are most fundamentally characterized by a localized, complete rotation of the magnetization within a magnetic domain wall, yielding a topological charge $Q = \pm1$ in typical O(3) sigma-model formats. In contrast to 2D or 3D bulk skyrmions, which are localized in all directions and exhibit the skyrmion Hall effect, DWSKs are effectively one-dimensional: their movement and stability are governed by the domain wall profile, channeling their dynamics along the wall itself (Cheng et al., 2018).

In a chiral magnet, the Hamiltonian incorporates exchange interactions, perpendicular magnetic anisotropy, and critical Dzyaloshinskii–Moriya interaction (DMI):

$$E = \int d^2x \left[ \tfrac12 (\nabla \mathbf{m})^2 + D \mathbf{m} \cdot (\hat{z} \times \nabla) \times \mathbf{m} - K m_z^2 \right] + \textrm{demag. terms}.$$

Here the DMI both supports the Néel-type nature of the domain wall and lowers the energetic cost of twisting the wall’s internal magnetization, enabling DWSK formation at sufficiently strong DMI (Cheng et al., 2018). The DWSK can be described analytically through a modulation of the wall profile $\theta(y)$ (domain wall) and an in-wall phase $\phi(x)$ (skyrmion winding) leading to reduced sine-Gordon-like models along the wall (Ross et al., 2022, Jennings et al., 2013).

2. Formation Mechanisms

DWSKs arise under several contexts:

• Energetic Trapping on a Domain Wall: Even in the absence of a bulk Skyrme term, a domain wall provides the spatial “substrate” on which a nontrivial winding (skyrmion) can be stabilized, typically through field configurations such as $$n = (\sin\phi \,\sin\theta,~\cos\phi\,\sin\theta,~\cos\theta)$$ (Jennings et al., 2013).
• Voltage-Controlled DMI/Nucleation: Application of a local voltage can reversibly invert the DMI in a selected segment, locally switching the magnetization and nucleating DWSK pairs. Only one topological charge typically remains due to wall curvature and energetics, enabling controlled chain formation (Wang et al., 24 Sep 2025).
• Domain Wall Distortion and Vertical Bloch Line (VBL) Anchoring: In the regime where the domain wall is driven above the Walker threshold, precessional dynamics and wall corrugation yield VBL pairs. The anchoring of the wall at a VBL results in lateral expansion that nucleates a skyrmion, marked by burst spin-wave dissipation; the DMI drives the transition from trivial bubble to stable DWSK (Jeong et al., 7 Nov 2024).
• Laser-Induced Transient Formation: Ultrafast demagnetization pulses (fs time scale) can drive transient DWSK formation during rapid recovery, which then annihilate on short timescales but mediate the population of stable skyrmions, enforcing a Poissonian distribution (Lepadatu, 2020).
• Quantum Hall and QCD Systems: In quantum Hall ferromagnets, DWSKs serve as ground state crystallites (“Wigner solids”) stabilized by long-range Coulomb repulsion (Yang et al., 2021). In QCD, domain wall skyrmions are induced by strong magnetic fields and baryon chemical potential as solitonic excitations on chiral soliton lattices, linked to gauged ℂP¹ (or O(3)) worldvolume effective field theories (Amari et al., 13 Sep 2024, Dengiz et al., 18 Sep 2025).

3. Dynamics, Stability, and Interactions

DWSKs are stabilized by the underlying structure of the wall; their size and energy scale with DMI and anisotropy. Their stability is robust against perturbations, as confirmed by numerical and analytical studies (Jennings et al., 2013, Cheng et al., 2018). The wall acts both as a trap and a guide, dictating the DWSK’s mobility, which is further controlled by current-induced torques:

• Current-Driven Motion: Under spin-transfer torque (STT), DWSKs move along the wall with velocity $v_x = (\beta/\alpha) u_x$ for parallel currents. Perpendicular currents induce lateral (Hall effect) deflection, but the wall’s confining potential converts this into guided motion along the wall for STT, while SOT (spin–orbit torque) results in more nuanced behavior depending on spin polarization orientation—sometimes stalling the DWSK after initial motion (Nie et al., 29 Nov 2024).
• Inter-DWSK Interactions: DWSKs on the same wall exhibit repulsive, effectively one-dimensional scattering analogous to sine-Gordon kinks (Jennings et al., 2013, Ross et al., 2022). In more complex geometries, e.g., annular or lattice structures, multi-DWSK configurations can stabilize ring-like or lattice states depending on system parameters (Gudnason et al., 2014, Amari et al., 2023).
• Domain Wall–Mediated Enhancement of Skyrmion Transport: Introduction of a strip domain wall parallel to a nanowire edge not only prevents skyrmion annihilation at the boundaries but also generates a longitudinal repulsive force that enhances skyrmion drift velocities and suppresses the skyrmion Hall effect (Xing et al., 2019).

4. Topological Phase Transitions and Novel Quantum States

DWSKs underpin topological phase transitions in both condensed matter and field theory:

• Crystalline Phases and Wigner Solids: In quantum Hall systems with Ising anisotropy, DWSKs organize into crystalline arrays (Wigner solids), leading to rich phase diagrams characterized by temperature/filling factor-dependent relaxation rates and clear signatures in nonlocal resistance and NMR relaxation times (Yang et al., 2021).
• Skyrmion Networks and Half-Integer Charges: In chiral magnets with square anisotropy, ground states self-assemble as domain wall networks whose junctions carry half-integer skyrmion charge, effectively constructing a skyrmion crystal via network topology. The lattice symmetry and domain size are tunable by external fields (Lee et al., 4 Jul 2024).
• QCD and Holography: In the Sakai–Sugimoto model of holographic QCD, DWSKs arise as baryonic D4-brane configurations localized on top of domain walls formed by chiral soliton lattices. The phase diagram features transitions from a uniform CSL, through a hybrid with bound skyrmions (at $\mu_B |B| \gtrsim \Lambda \cdot m_\pi f_\pi^2$), into a full skyrmion crystal phase. DWSKs in this context are electrically charged due to the chiral anomaly and serve as nonperturbative carriers of baryon number (Dengiz et al., 18 Sep 2025, Amari et al., 13 Sep 2024).

5. Manipulation, Device Integration, and Applications

DWSKs provide a versatile platform for information processing, storage, and manipulation:

• Reconfigurable Magnonic Crystals: Chains of DWSKs act as periodic potentials (“magnonic crystals”) for spin-wave propagation along domain walls. Bandgaps can be dynamically adjusted through field-modulated DWSK sizes or by varying chain periodicity via voltage-controlled DMI, enabling adaptable, low-dissipation magnonic nanocircuits (Wang et al., 24 Sep 2025).
• Racetrack Memory Architectures: DWSKs can serve as data carriers in racetrack memory, with bit encoding mapped to skyrmion charge sign instead of mere presence and location. This approach allows coexistence of skyrmions and anti-skyrmions within one track, reducing error rates due to spacing or edge annihilation and providing a natural guidance “rail” for robust current-driven information transfer (Nie et al., 29 Nov 2024).
• Logic Devices: Skyrmion–domain wall collisions and DW pinning can realize logic gates (NOT, NAND, NOR) in nanowire geometries, with device output determined by the blocking or transmission of skyrmions past domain wall gatekeepers (Xing et al., 2016).
• Skyrmion–DW Interconversion: Reversible transformation between DWs and skyrmions via variable-width nanowire sections enables hybrid information transport architectures, leveraging the energy efficiency and error-resilience of skyrmions with the ease of domain wall manipulation (Kang et al., 2016).
• Controlled Creation and Erasure: DWSKs can be controllably created or annihilated via phase manipulation of the wall (rotating the internal domain wall phase away from equilibrium using localized external fields) or through laser-driven ultrafast phase transitions, with precise phase tuning essential to avoid unwanted annihilation or instability (Gudnason et al., 27 Jun 2024, Lepadatu, 2020).

6. Analytical, Numerical, and Experimental Methods

DWSKs have been elucidated through a suite of analytical reductions (moduli approximation, sine-Gordon and double sine-Gordon theories), numerical techniques (gradient flow, micromagnetic simulation, nonlinear conjugate gradient minimization), and experimental probes (Lorentz TEM Fresnel imaging, NRDNMR in IQHF). Analytical results, e.g., the wall-skyrmion profile $u_\mathrm{DW} = e^{m(x-X) + i\phi}$ and effective 1D sine-Gordon energies, provide insight into existence and stability (Ross et al., 2022, Amari et al., 2023). Numerics confirm transitions, cusp formation, domain wall chain stability, and complex dynamics in curved or interconnected walls.

Experimental imaging relies on the unique magnetic signature: DWSKs in Néel walls produce dipole-like or braid-like contrast in Lorentz-TEM, distinguishable from the background, and NMR relaxation times probe collective skyrmion ordering in Hall systems, detecting phase transitions and solidification (Cheng et al., 2018, Yang et al., 2021).

7. Outlook, Future Directions, and Open Challenges

DWSKs provide a unifying framework for understanding topological solitons in systems with coexisting domain wall and skyrmion content across condensed matter, quantum Hall physics, and gauge theories. Critical open issues include:

• Controlled deterministic creation and erasure—optimizing laser, voltage, or field-driven mechanisms for single-skyrmion-level control.
• Robust transport in device geometries—understanding pinning, unidirectional mobility, and error correction in racetrack and magnonic devices.
• Phase transition characterization—mapping detailed topological and energetic phase diagrams, particularly near the boundaries between skyrmion, domain wall, and hybrid crystal states.
• Crossover physics between 1D, 2D, and 3D skyrmion manifolds—such as behavior in domain wall/anti-domain wall pairs (chiral soliton lattices), Wigner solid formation, and inhomogeneous QCD matter.
• Material engineering—tailoring DMI, anisotropy, exchange, and pinning for application-specific performance (e.g., Rashba vs Dresselhaus DMI for phase control (Gudnason et al., 27 Jun 2024)).

A plausible implication is that the confining, topologically robust nature of DWSKs and their tunable interactions will inspire the next generation of quantum, spintronic, and magnonic circuit elements where information is encoded, routed, and processed by networks of interlinked topological excitations.