Fractional Skyrmions: Mechanisms & Applications

• Fractional skyrmions are topological textures characterized by fractionalized magnetic or electric charge, arising when full sphere coverage is disrupted.
• They emerge via multiple mechanisms—including merons, layer averaging, and constituent splitting—in systems like frustrated magnets, quantum Hall fluids, and superconductors.
• Their study reveals the interplay of topology, symmetry, and interactions, offering practical insights for advanced magnetic devices and quantum materials.

Fractional skyrmions are topological textures related to ordinary skyrmions but carrying a fractionalized form of skyrmionic character. In the literature, that fractionality is realized in several inequivalent ways: as merons or half-skyrmions with $Q=\pm \tfrac12$, as fractionally charged spin textures in fractional quantum Hall fluids, as bound constituents carrying $1/N$ of an integer topological charge in $\mathbb{C}P^{N-1}$ or Skyrme-type models, as layer-averaged fractional skyrmion numbers in nonsymmorphic magnets, or as noninteger wrapping produced by singularities, confinement, or incomplete sphere coverage (Kharkov et al., 2017, Balram et al., 2014, Akagi et al., 2021, Hayami, 2022). The term is therefore not uniform across subfields. Some works speak instead of merons, half-skyrmions, fractional topological charges, or minimal fractionally charged skyrmions, and the precise meaning depends on what is being fractionalized: topological charge, electric charge, layer average, or constituent content (Ser et al., 2023, Williams et al., 9 Jun 2026).

1. Definitions and taxonomy

For magnetic textures with a smooth unit-vector field $\mathbf{S}(x,y)$, the standard skyrmion number is

$$Q=\frac{1}{4\pi}\int d^2x\,\mathbf{S}\cdot(\partial_x\mathbf{S}\times\partial_y\mathbf{S}),$$

with the corresponding density

$$\rho_Q(x,y)=\frac{1}{4\pi}\,\mathbf S\cdot\left(\partial_x\mathbf S\times \partial_y\mathbf S\right).$$

This is the convention used explicitly in frustrated magnets near the Lifshitz point and in several other magnetic contexts (Kharkov et al., 2017). When the map from compactified real space to the order-parameter sphere is smooth and complete, $Q$ is integer. Fractionality enters when that mapping is partial, singular, composite, or distributed among constituents or layers.

Realization of fractionality	Typical meaning	Representative papers
Merons / half-skyrmions	$Q=\pm \tfrac12$, often via half-sphere coverage	(Kharkov et al., 2017, Lin et al., 2014, Takeuchi, 2021)
Fractionally charged skyrmions	Electric charge is fractional, while spin texture remains skyrmionic	(Balram et al., 2014, Williams et al., 9 Jun 2026)
Constituent molecules	Integer $Q$ splits into confined $1/N$ parts	(Akagi et al., 2021, Gudnason et al., 2015)
Layer-averaged fractional numbers	Different layers carry integer $1/N$0, average becomes fractional	(Hayami, 2022)
Incomplete or singular wrapping	Noninteger $1/N$1 from partial sphere coverage or singularities	(Carvalho-Santos et al., 2014, Huh et al., 2024, Cao et al., 17 Feb 2026)

This taxonomy shows that “fractional skyrmion” is not a single object class. A plausible implication is that the phrase is best treated as an umbrella term for several mechanisms of skyrmion fractionalization rather than a unique topological species.

2. Magnetic realizations in frustrated, chiral, and layered systems

In easy-plane frustrated ferromagnets near a Lifshitz point, a $1/N$2 skyrmion transforms into a bound vortex–antivortex pair of merons, each carrying $1/N$3. The confinement mechanism is controlled by the spin stiffness $1/N$4, with logarithmic interaction

$1/N$5

As $1/N$6, the Coulomb confinement vanishes, and merons become asymptotically deconfined near the Lifshitz point, although residual interactions still leave a finite-separation bi-meron at $1/N$7 (Kharkov et al., 2017). The same work also showed that easy-axis frustrated magnets support attractive skyrmion–skyrmion interactions and ring-shaped multi-skyrmion bound states, while the easy-plane sector favors square arrangements of merons and antimerons for large $1/N$8 (Kharkov et al., 2017).

A distinct route appears in ultrathin chiral magnets with easy-plane anisotropy. There, increasing $1/N$9 causes neighboring skyrmions in the triangular lattice to overlap, so the spins no longer wrap the full sphere and the skyrmion number decreases continuously from $\mathbb{C}P^{N-1}$0. Interstitial antivortices emerge at the centers of triangles, carrying a small topological charge $\mathbb{C}P^{N-1}$1 that grows with $\mathbb{C}P^{N-1}$2. At larger $\mathbb{C}P^{N-1}$3, the system undergoes a first-order transition to a square vortex–antivortex lattice, and near the subsequent transition to the canted ferromagnet the model supports metastable meron solutions with $\mathbb{C}P^{N-1}$4 (Lin et al., 2014). Here the fractionalization is not initially a clean split into isolated half-skyrmions; it is a continuous deformation and overlap process in a dense lattice.

Fractional topological charges beyond merons arise in 2D magnets with cubic anisotropy. In that setting, the meeting of multiple domains can produce point defects with $\mathbb{C}P^{N-1}$5 or $\mathbb{C}P^{N-1}$6, and a skyrmion with $\mathbb{C}P^{N-1}$7 can explode into four defects with $\mathbb{C}P^{N-1}$8 after a field quench. The same work also identified non-quantized fractional defects moving along domain walls and argued that only defects with $\mathbb{C}P^{N-1}$9 produce an Aharonov–Bohm effect for magnons (Ser et al., 2023). This extends fractional skyrmion physics beyond the familiar half-skyrmion paradigm.

In layered magnets with a threefold screw axis, the fractionality can be purely layer resolved. The nonsymmorphic model of layered triangular planes supports skyrmion-crystal layers with $\mathbf{S}(x,y)$0 and spiral-like 3$\mathbf{S}(x,y)$1-I layers with $\mathbf{S}(x,y)$2. In the fractional phases, the layer pattern $\mathbf{S}(x,y)$3 gives an average skyrmion number $\mathbf{S}(x,y)$4, while $\mathbf{S}(x,y)$5 gives $\mathbf{S}(x,y)$6 (Hayami, 2022). The charge is therefore fractional only after averaging across the three-layer magnetic unit cell.

Related, but conceptually different, is the fractional antiferromagnetic skyrmion lattice proposed for MnSc$\mathbf{S}(x,y)$7S$\mathbf{S}(x,y)$8. There the field-induced triple-$\mathbf{S}(x,y)$9 phase is interpreted as a three-sublattice antiferromagnetic skyrmion lattice with incipient meron character, because the skyrmion-like whorls are so closely packed that they do not wrap the full sphere. The paper quantified topology through the scalar chirality

$$Q=\frac{1}{4\pi}\int d^2x\,\mathbf{S}\cdot(\partial_x\mathbf{S}\times\partial_y\mathbf{S}),$$0

rather than a direct half-integer skyrmion number for each object (Gao et al., 2020). In Cu$$Q=\frac{1}{4\pi}\int d^2x\,\mathbf{S}\cdot(\partial_x\mathbf{S}\times\partial_y\mathbf{S}),$$1OSeO$$Q=\frac{1}{4\pi}\int d^2x\,\mathbf{S}\cdot(\partial_x\mathbf{S}\times\partial_y\mathbf{S}),$$2, a multiscale theory similarly predicted a precursor-region phase in which ordinary skyrmions fractionalize into $$Q=\frac{1}{4\pi}\int d^2x\,\mathbf{S}\cdot(\partial_x\mathbf{S}\times\partial_y\mathbf{S}),$$3 half-skyrmions to increase the packing density of double-twist cores (Janson et al., 2014).

3. Fractionally charged skyrmions in quantum Hall systems

In the fractional quantum Hall effect near $$Q=\frac{1}{4\pi}\int d^2x\,\mathbf{S}\cdot(\partial_x\mathbf{S}\times\partial_y\mathbf{S}),$$4, fractionality refers primarily to electric charge. The minimal positively and negatively charged fractional skyrmions, FS$$Q=\frac{1}{4\pi}\int d^2x\,\mathbf{S}\cdot(\partial_x\mathbf{S}\times\partial_y\mathbf{S}),$$5 and FS$$Q=\frac{1}{4\pi}\int d^2x\,\mathbf{S}\cdot(\partial_x\mathbf{S}\times\partial_y\mathbf{S}),$$6, are bound states of a single spin-flip exciton with a pre-existing composite-fermion quasihole or spin-reversed quasiparticle, respectively. They carry charge $$Q=\frac{1}{4\pi}\int d^2x\,\mathbf{S}\cdot(\partial_x\mathbf{S}\times\partial_y\mathbf{S}),$$7, one additional spin flip, and a smooth spin texture distinct from the bare quasiparticle or quasihole (Balram et al., 2014). Their energy is written as

$$Q=\frac{1}{4\pi}\int d^2x\,\mathbf{S}\cdot(\partial_x\mathbf{S}\times\partial_y\mathbf{S}),$$8

with thermodynamic-limit zero-width binding energies

$$Q=\frac{1}{4\pi}\int d^2x\,\mathbf{S}\cdot(\partial_x\mathbf{S}\times\partial_y\mathbf{S}),$$9

before finite-width corrections (Balram et al., 2014). Resonant inelastic light scattering on a 33 nm GaAs well detected the corresponding modes slightly below the long-wavelength spin wave, and the FS$$\rho_Q(x,y)=\frac{1}{4\pi}\,\mathbf S\cdot\left(\partial_x\mathbf S\times \partial_y\mathbf S\right).$$0 mode disappeared above the polarization transition near $$\rho_Q(x,y)=\frac{1}{4\pi}\,\mathbf S\cdot\left(\partial_x\mathbf S\times \partial_y\mathbf S\right).$$1, consistent with the composite-fermion interpretation (Balram et al., 2014).

A later spectroscopic study generalized this line of thought across $$\rho_Q(x,y)=\frac{1}{4\pi}\,\mathbf S\cdot\left(\partial_x\mathbf S\times \partial_y\mathbf S\right).$$2 using cavity-polariton spectroscopy in high-mobility GaAs quantum wells. Fully polarized fractional quantum Hall states exhibited symmetric depolarization away from quantized fillings, and the depolarization followed the empirical law

$$\rho_Q(x,y)=\frac{1}{4\pi}\,\mathbf S\cdot\left(\partial_x\mathbf S\times \partial_y\mathbf S\right).$$3

where $$\rho_Q(x,y)=\frac{1}{4\pi}\,\mathbf S\cdot\left(\partial_x\mathbf S\times \partial_y\mathbf S\right).$$4 is the number of spin flips per added flux quantum and $$\rho_Q(x,y)=\frac{1}{4\pi}\,\mathbf S\cdot\left(\partial_x\mathbf S\times \partial_y\mathbf S\right).$$5 is the effective composite-fermion filling factor (Williams et al., 9 Jun 2026). That work interpreted the data as evidence for Minimal Fractionally Charged Skyrmions formed from bound spin-flip and quasiparticle excitations (Williams et al., 9 Jun 2026). The fractionality again resides in the quasiparticle charge sector rather than in a bare $$\rho_Q(x,y)=\frac{1}{4\pi}\,\mathbf S\cdot\left(\partial_x\mathbf S\times \partial_y\mathbf S\right).$$6 texture.

The converse result is also informative. In a spinful extended Hofstadter–Fermi–Hubbard model, a spin-polarized $$\rho_Q(x,y)=\frac{1}{4\pi}\,\mathbf S\cdot\left(\partial_x\mathbf S\times \partial_y\mathbf S\right).$$7-Laughlin-like fractional Chern insulator was identified, but no skyrmions were found in the ground state around $$\rho_Q(x,y)=\frac{1}{4\pi}\,\mathbf S\cdot\left(\partial_x\mathbf S\times \partial_y\mathbf S\right).$$8 in the studied regime, even though particle- and hole-skyrmions were stabilized around the integer quantum Hall ferromagnet at $$\rho_Q(x,y)=\frac{1}{4\pi}\,\mathbf S\cdot\left(\partial_x\mathbf S\times \partial_y\mathbf S\right).$$9 (Pauw et al., 15 Sep 2025). This suggests that fractional quantum Hall ferromagnetism and fractional skyrmion formation need not coincide automatically in lattice realizations.

4. Spinor superfluids and Bose–Einstein condensates

Spin-1 condensates provide both smooth and singular routes to fractionalization. In rapidly quenched, fast-rotating spin-1 BECs, stochastic projected Gross–Pitaevskii simulations found a phase-selective dichotomy: ferromagnetic $Q$0 condensates form a hexagonal lattice of integer skyrmions, while antiferromagnetic or polar $Q$1 condensates form a square lattice of half-quantized vortices. Those HQVs are fractional in the sense of a combined $Q$2 gauge twist and $Q$3 spin rotation, although the paper does not label them merons or half-skyrmions (Su et al., 2011).

A more specific fractional-skyrmion mechanism appears at magnetic domain walls in easy-axis ferromagnetic spin-1 superfluids. Theoretical analysis showed that a spin current along an AF-core or BA-core domain wall becomes unstable above critical velocities due to competition between transverse magnons and ripplons. In the nonlinear regime, Kelvin–Helmholtz-type wall deformation emits closed wall loops carrying an off-centered spin singularity. These are eccentric fractional skyrmions with

$Q$4

so that $Q$5 implies $Q$6 (Takeuchi, 2021). The work emphasized that the resulting texture is not similar to a meron because the fractionalization is mediated by a singular point where $Q$7 and $Q$8 on the wall (Takeuchi, 2021).

That mechanism was later observed experimentally in a quasi-2D ferromagnetic $Q$9 superfluid. The reported eccentric fractional skyrmions are singular, non-axisymmetric textures with an off-centered spin singularity, a “C”-shaped $Q=\pm \tfrac12$0 density profile, and an approximate half-skyrmion charge obtained by integrating the skyrmion density over the domain excluding the singularity (Huh et al., 2024). Matter-wave Raman self-interference revealed a singly quantized vortex through a two-to-one Y-shaped fork dislocation, and the Mermin–Ho relation again yielded $Q=\pm \tfrac12$1 (Huh et al., 2024). Because the normalized spin field is undefined at the singular point, the paper explicitly treated these objects as going beyond standard smooth-field topological classification (Huh et al., 2024).

5. Constituent molecules and fractionalization in sigma models, Skyrme models, superconductors, and dense matter

In baby-Skyrme models on $Q=\pm \tfrac12$2, fractionalization can be exact at the constituent level while the total charge remains integer. With a generalized easy-plane potential, the $Q=\pm \tfrac12$3 model supports stable molecules made of three $Q=\pm \tfrac12$4-charged constituents for total $Q=\pm \tfrac12$5, six constituents for $Q=\pm \tfrac12$6, and so on; more generally the paper conjectured $Q=\pm \tfrac12$7 fractional skyrmions of charge $Q=\pm \tfrac12$8 in the $Q=\pm \tfrac12$9 model (Akagi et al., 2021). The topological charge remains

$Q$0

but the density splits into localized partons associated with zeros of the homogeneous coordinates (Akagi et al., 2021).

A related but higher-dimensional mechanism appears in a $Q$1-dimensional Skyrme-type model with $Q$2 vacua. There, a unit skyrmion becomes a molecule of two half-Skyrmions, each a global monopole carrying baryon number $Q$3, and stable solutions for $Q$4 take the form of beads on rings (Gudnason et al., 2015). By deforming the potential to $Q$5, the same framework also supports asymmetric molecules with constituent charges $Q$6 (Gudnason et al., 2015). In this case the fractionalization is topological but the isolated constituents have divergent energy, so the physical objects are confined molecules rather than free particles (Gudnason et al., 2015).

In layered multicomponent superconductors, a half-flux quantum vortex can also be interpreted as a half-skyrmion, although the relevant order parameter is the Bogoliubov–de Gennes pseudospin rather than a magnetic spin. For a half-flux vortex with vorticity $Q$7, the vortex contributes

$Q$8

to the skyrmion number of the pseudospin field, while the associated kink or domain wall contributes the complementary

$Q$9

so that the total index remains $1/N$0 (Yanagisawa et al., 2019). The same work connected this boundary decomposition to the absence of low-lying Andreev bound states near zero energy in the half-flux vortex core (Yanagisawa et al., 2019).

In dense hadronic matter, fractionality takes yet another form. Skyrmion matter on an FCC crystal undergoes a topology change near $1/N$1 into a half-skyrmion phase in which the baryon-number distribution reorganizes into $1/N$2 substructures (Harada et al., 2016). The space-averaged quark condensate vanishes while $1/N$3, so the phase is not a vacuum gas of free half-baryons but an emergent medium-induced crystalline reorganization (Harada et al., 2016). This usage is closely related to half-skyrmion matter in dense QCD rather than to isolated fractional skyrmions on a plane.

6. Incomplete wrapping, geometry, and interpretive issues

Several recent works realize noninteger skyrmion numbers through confinement, curvature, or singular map structure rather than through constituent partons. On curved rotationally symmetric surfaces with a radial or azimuthal magnetic field $1/N$4, the effective potential shifts the minima away from $1/N$5 and $1/N$6, so the field-induced texture connects only

$1/N$7

for $1/N$8. The resulting weak-field excitation has noninteger charge

$1/N$9

and is not topologically protected by homotopy arguments (Carvalho-Santos et al., 2014). This is a clear example where fractionality arises from incomplete sphere coverage enforced by the field-modified vacuum structure.

A room-temperature three-dimensional version was reported in FEBID-grown cobalt double-helix nanowires with opposite geometric chirality joined at a central interface. There the relevant quantity is the plane-resolved skyrmion number

$1/N$00

evaluated slice by slice along the wire (Fullerton et al., 2024). The fractional Bloch skyrmion tube has $1/N$01, typically $1/N$02, because the confined geometry prevents full sphere wrapping; the state is metastable, zero-field, and induced by frustration between geometric chirality and magnetic continuity at the interface (Fullerton et al., 2024).

Optics provides a formally analogous but physically different setting. Fractional optical skyrmions are generated by superposing orthogonal polarizations with non-integer orbital angular momentum, and the local normalized Stokes vector $1/N$03 defines the skyrmion number

$1/N$04

Because fractional OAM introduces a branch cut, the polarization map covers only part of the Poincaré sphere, giving noninteger $1/N$05 and abrupt jumps near half-integer OAM values (Cao et al., 17 Feb 2026). The authors explicitly interpreted those jumps as reinforcing the underlying integer character of skyrmion topology even in the presence of fractional wrapping (Cao et al., 17 Feb 2026).

These cases clarify a common misconception. A noninteger skyrmion number does not always imply a deconfined half-skyrmion. In some papers it denotes a constituent of an integer molecule, in others an incomplete or singular mapping, a slice-wise or layer-averaged topological number, or a fractionally charged excitation whose electric charge rather than Pontryagin index is fractional (Gudnason et al., 2015, Hayami, 2022, Huh et al., 2024, Balram et al., 2014). This suggests that the research field is organized less by a single universal invariant than by a recurring physical theme: skyrmion structure can fractionalize whenever symmetry, boundary conditions, competing interactions, or emergent internal degrees of freedom obstruct the usual integer wrapping of the order-parameter sphere.