Plasmonic Skyrmion Lattices: Fundamentals & Advances

• Plasmonic skyrmion lattices are 2D periodic topological textures realized in plasmonic near fields, mapping unit cells to the sphere with nontrivial charge.
• Experiments using interference of TM-polarized evanescent waves demonstrate robust hexagonal and meron lattice formations with skyrmion numbers close to unity.
• Symmetry and phase engineering, including moiré superlattices and inverse-Faraday effect designs, enable dynamic control for optical information processing and magnetic applications.

Searching arXiv for papers on plasmonic skyrmion lattices and closely related work. Plasmonic skyrmion lattices are two-dimensional periodic topological textures realized in plasmonic near fields or in plasmonically induced effective magnetic textures. The relevant unit vector field depends on the platform: in different formulations it is the normalized local electric field, the normalized local optical spin angular momentum density, or the normalized stationary magnetic field generated through the inverse Faraday effect. In all cases, the defining feature is a repeated real-space mapping from a unit cell to the sphere with nontrivial topological charge, rather than an isolated skyrmion confined to a single resonator or nanoantenna (Tsesses et al., 2018, Lei et al., 2021, Yang et al., 31 Mar 2025).

1. Definition, topology, and taxonomy

The standard topological descriptor is the skyrmion number

$$N=\frac{1}{4\pi}\iint \mathbf{n}\cdot\left(\partial_x \mathbf{n}\times \partial_y \mathbf{n}\right)\,dx\,dy,$$

with $\mathbf{n}$ the appropriate normalized three-component field. In plasmonic field-skyrmion work, $\mathbf{n}$ is typically the local unit electric-field vector $\mathbf{e}=\mathbf{E}/|\mathbf{E}|$; in spin-lattice work it is the normalized spin vector $\mathbf{n}=\mathbf{S}/|\mathbf{S}|$; in inverse-Faraday-effect platforms it is the normalized stationary magnetic field or effective magnetization direction (Tsesses et al., 2018, Lei et al., 2021, Yang et al., 31 Mar 2025).

Three distinctions organize the subject. First, a plasmonic skyrmion lattice is not necessarily a lattice of material magnetization textures; several foundational realizations are topological textures of electromagnetic fields themselves. Second, different order parameters produce different nomenclature: “optical skyrmion lattices” and “plasmonic field skyrmions” refer to electric-field textures, whereas “spin-skyrmion lattices” refer to textures of local optical spin angular momentum. Third, not every plasmonic skyrmion is a lattice. A repeated unit cell or a periodic/quasi-periodic arrangement is essential; nested multi-ring textures inside a single localized mode are topological objects, but they are not skyrmion crystals in the strict sense (Tsesses et al., 2018, Lei et al., 2021, Deng et al., 2021).

A further conceptual division concerns morphology. In evanescent-wave constructions, the textures can interpolate between bubble-type and Néel-type regimes as the degree of evanescence changes. In symmetry-engineered lattices, sixfold symmetry is associated with skyrmion lattices, whereas fourfold symmetry is associated with meron lattices. In moiré superlattices, the basic skyrmion lattice becomes a building block for higher-order composite objects such as skyrmion bags (Tsesses et al., 2018, Lei et al., 2021, Schwab et al., 2024).

2. Canonical surface-plasmon-polariton skyrmion lattices

The foundational plasmonic realization uses the interference of six TM-polarized evanescent waves, arranged as three standing waves at $0^\circ$, $60^\circ$, and $120^\circ$. The axial field is a sum of cosine terms, the in-plane components are sums of sine terms weighted by propagation direction, and the evanescent condition $k_{\parallel}>k_0$ ensures that the local electric field can serve as a real three-component order parameter over a two-dimensional plane. The resulting texture is hexagonal, periodic, and subwavelength because the lattice constant is set by $k_{\parallel}$, not by the free-space wavelength. In the ideal construction, each unit cell carries skyrmion number $\mathbf{n}$0 (Tsesses et al., 2018).

The experimental implementation was performed with surface plasmon polaritons at an air/gold interface using a 200 nm gold film on glass and a hexagonal six-grating coupler illuminated by circularly polarized 660 nm light from below. The measured plasmonic wavelength was 636 nm, and the effective SPP wave vector was reported as

$\mathbf{n}$1

placing the experiment in the bubble-like regime rather than the strongly Néel-like regime. Phase-resolved scattering near-field scanning optical microscopy with pseudo-heterodyne interferometric detection measured the complex $\mathbf{n}$2 field with 20 nm spatial resolution. Fourier filtering then enabled reconstruction of the in-plane components and of the skyrmion density. The measured topological charge per lattice site was $\mathbf{n}$3, and the sample contained 37 actual lattice sites (Tsesses et al., 2018).

This platform also established robustness against realistic nonidealities. The central skyrmion lattice remained well defined in the presence of ohmic loss, finite propagation length, unequal wave amplitudes, and finite sample size. The same work quantified robustness by the number $\mathbf{n}$4 of sites for which $\mathbf{n}$5: $\mathbf{n}$6 was achievable if the waves persisted for roughly 400 periods before decaying, and even waves decaying after about 100 oscillations could still create skyrmion lattices (Tsesses et al., 2018).

3. Symmetry constraints and optical reconfigurability

A symmetry-based formulation generalized the subject from electric-field topology to spin topology. For guided evanescent modes with spin-orbit coupling, the local spin angular momentum density satisfies

$\mathbf{n}$7

with $\mathbf{n}$8 the Poynting vector, so the topology of the spin field is inherited from the structured energy flow. Within this framework, the field symmetry determines the allowed lattice topology: sixfold symmetry yields hexagonal spin-skyrmion lattices with $\mathbf{n}$9 per sublattice unit cell, whereas fourfold symmetry yields square spin-meron lattices with $\mathbf{n}$0. The experimental realization used SPPs at an air/silver interface, excited by a radially polarized beam with helical wavefront and topological charge $\mathbf{n}$1 at $\mathbf{n}$2 nm, with spin-resolved near-field scanning optical microscopy and a dielectric nanosphere probe recovering $\mathbf{n}$3 and the local spin orientation (Lei et al., 2021).

A later fully optical implementation shifted the control from nanofabricated gratings to pupil-plane symmetry engineering. In a three-layer air/Ag/glass structure with a 45 nm silver film and a high-NA objective ($\mathbf{n}$4), a left-handed circularly polarized vortex beam excited SPPs at the metal–air interface. A square aperture clipped the virtual SPP excitation ring into four corner arcs and generated a meron lattice, whereas a hexagonal aperture clipped it into six symmetry-related arcs and generated a skyrmion lattice. The topology was again defined directly from the electric field,

$\mathbf{n}$5

Representative skyrmion-cell values in the sixfold case were $\mathbf{n}$6 and $\mathbf{n}$7, and the transformation study reported skyrmion-lattice cells around $\mathbf{n}$8–$\mathbf{n}$9, whereas the fourfold meron lattice produced values around $\mathbf{e}=\mathbf{E}/|\mathbf{E}|$0 in the optimized design (Shen et al., 2024).

That same platform demonstrated continuous transformations among isolated skyrmion, meron lattice, and skyrmion lattice using mixed-symmetry apertures. Circular-fourfold, circular-sixfold, and fourfold-sixfold apertures, combined with variation of the initial phase $\mathbf{e}=\mathbf{E}/|\mathbf{E}|$1, provided continuous morphing pathways between these states. The key structural conclusion was that sixfold field symmetry produces a skyrmion lattice, fourfold field symmetry produces a meron lattice, and phase control changes the effective weighting of competing symmetry sectors without changing the underlying plasmonic excitation principle (Shen et al., 2024).

4. Magnetoelectric and inverse-Faraday-effect routes

A distinct line of work treats the plasmonic skyrmion lattice as a magnetoelectrically induced lattice of skyrmionic spin textures rather than as a purely electromagnetic field pattern. In that formulation, coherent or incoherent laser excitation generates SPP interference, the electric near field modulates the effective Dzyaloshinskii–Moriya interaction through

$\mathbf{e}=\mathbf{E}/|\mathbf{E}|$2

and skyrmions are confined to nodal points of the plasmonic lattice because the noncollinear spin texture couples selectively to the electric field. The magnetic subsystem is modeled by a finite spin-$\mathbf{e}=\mathbf{E}/|\mathbf{E}|$3 lattice with anisotropic exchange and DMI,

$\mathbf{e}=\mathbf{E}/|\mathbf{E}|$4

Topology is characterized by a winding parameter $\mathbf{e}=\mathbf{E}/|\mathbf{E}|$5 and a topological index $\mathbf{e}=\mathbf{E}/|\mathbf{E}|$6, with the ferromagnetic phase at $\mathbf{e}=\mathbf{E}/|\mathbf{E}|$7 and the antiskyrmion phase at $\mathbf{e}=\mathbf{E}/|\mathbf{E}|$8. For all studied $\mathbf{e}=\mathbf{E}/|\mathbf{E}|$9, $\mathbf{n}=\mathbf{S}/|\mathbf{S}|$0 increases significantly around $\mathbf{n}=\mathbf{S}/|\mathbf{S}|$1, and the paper states that skyrmion separations in the plasmonic lattice can be tuned to roughly $\mathbf{n}=\mathbf{S}/|\mathbf{S}|$2–$\mathbf{n}=\mathbf{S}/|\mathbf{S}|$3 (Vijayan et al., 2023).

The same work made a stronger dynamical claim: during electric-field-driven adiabatic strokes, if the propagator remains diagonal in the instantaneous eigenbasis so that $\mathbf{n}=\mathbf{S}/|\mathbf{S}|$4, then the irreversible work vanishes,

$\mathbf{n}=\mathbf{S}/|\mathbf{S}|$5

This was presented as numerical evidence that the quantum skyrmion phase acts as a topologically protected working medium. At the same time, the paper reduced the plasmonic subsystem to the effective scalar control parameter $\mathbf{n}=\mathbf{S}/|\mathbf{S}|$6, so the detailed optical field profile of the lattice was not solved microscopically in the thermodynamic calculations (Vijayan et al., 2023).

A second noninterference route uses the inverse Faraday effect in a periodic plasmonic metasurface. In a hexagonal array of gold nanodisks on glass, illuminated by circularly polarized light from the glass side, localized plasmonic modes induce drift photocurrents inside each disk and counter-rotating “phantom” currents in the hexagonal interstices. The metasurface geometry was fixed at disk radius $\mathbf{n}=\mathbf{S}/|\mathbf{S}|$7, thickness $\mathbf{n}=\mathbf{S}/|\mathbf{S}|$8, observation plane 1 nm above the gold, and optimized at period $\mathbf{n}=\mathbf{S}/|\mathbf{S}|$9 and excitation wavelength $0^\circ$0. The electric-field spin density,

$0^\circ$1

drives the inverse-Faraday photocurrent, and the resulting stationary magnetic field yields a Néel-like skyrmionic texture with skyrmion number

$0^\circ$2

The reported magnetic-field amplitude ratio between positive core and negative edge amplitudes was $0^\circ$3. Reversing RHCP and LHCP reverses the current circulation and flips the skyrmion polarity throughout the lattice (Yang et al., 31 Mar 2025).

5. Moiré superlattices, twistronics, and skyrmion bags

Plasmonic twistronics extends the basic hexagonal skyrmion lattice into a moiré regime by superimposing two twisted lattices. In that construction, a single-crystalline gold flake supports SPPs launched from two interleaved twisted hexagons, and the total field is the coherent superposition of two six-wave plasmonic skyrmion lattices. Commensurate examples were reported at $0^\circ$4, $0^\circ$5, $0^\circ$6, and $0^\circ$7. The local order parameter is the normalized electric field $0^\circ$8, the skyrmion density is $0^\circ$9, and the local charge is $60^\circ$0. Under suitable twist and rotation center, the moiré supercell contains a plasmonic skyrmion bag: $60^\circ$1 interior skyrmions of charge $60^\circ$2 enclosed by a larger skyrmion of charge $60^\circ$3, so that

$60^\circ$4

Time-resolved 2PPE-PEEM with an 800 nm pump, $60^\circ$5, and four probe polarizations reconstructed the full vector field. For the experimentally emphasized $60^\circ$6 structure, the measured and simulated values were $60^\circ$7 and $60^\circ$8, consistent with a $60^\circ$9-skyrmion bag. The same paper reported bag formation over the angle range $120^\circ$0 to $120^\circ$1 for the $120^\circ$2-type structure, and showed that changing the rotation center to $120^\circ$3 or $120^\circ$4 enables bags with $120^\circ$5 (Schwab et al., 2024).

A trilayer extension superimposes three twisted skyrmion lattices, with $120^\circ$6, using three twisted hexagons and thus 18 line segments. The field topology is again extracted from

$120^\circ$7

Mirror-symmetric trilayers with $120^\circ$8 reproduce the bilayer bag family, including $120^\circ$9, while generic trilayers enable new bag shapes and nested bags. The paper introduced a robustness metric based on whether the bag charge and cluster charge survive addition of a disturbance field composed of 50 random SPP plane waves. For the $k_{\parallel}>k_0$0 bag at disturbance strength $k_{\parallel}>k_0$1, robustness in the exact SPP/Huygens model increased from $k_{\parallel}>k_0$2 in the bilayer case to $k_{\parallel}>k_0$3 in the trilayer case, and the trilayer reached $k_{\parallel}>k_0$4 in the plane-wave approximation. The optimal twist for $k_{\parallel}>k_0$5 was reported as approximately $k_{\parallel}>k_0$6 for bilayers and $k_{\parallel}>k_0$7 for trilayers. The same analysis concluded that smaller bags are generally more robust, trilayers are better for small bags, and bilayers are better for large bags (Schwab et al., 2024).

These moiré results recast plasmonic skyrmion lattices as a hierarchical design space. The underlying skyrmion lattice remains the primitive periodic texture, but twisting reorganizes it into supercells with large integrated topological charge and composite quasiparticles whose existence depends jointly on twist angle, commensurability, and rotation center (Schwab et al., 2024, Schwab et al., 2024).

6. Relation to localized plasmonic skyrmions, applications, and persistent ambiguities

A persistent source of ambiguity is the inclusion of localized skyrmionic plasmonic textures under the heading of “plasmonic skyrmion lattices.” A microwave spoof-plasmon experiment demonstrated topologically robust localized magnetic plasmon skyrmions in a space-coiling metastructure, with resonances forming a near-equidistant ladder $k_{\parallel}>k_0$8. The fundamental mode is a $k_{\parallel}>k_0$9-twist elementary skyrmion with topological charge $k_{\parallel}$0, the second mode is a $k_{\parallel}$1-twist skyrmionium with charge $k_{\parallel}$2, and higher modes are multi-$k_{\parallel}$3-twist target skyrmions, with odd modes carrying total charge $k_{\parallel}$4 and even modes total charge $k_{\parallel}$5. The fundamental texture had lateral size $k_{\parallel}$6, half vertical size $k_{\parallel}$7, and reported mode volume $k_{\parallel}$8. Yet this system was explicitly not a lattice: it comprised isolated or nested concentric textures in one resonator at a time, even when deformed into elliptical, polygonal, or heart-shaped boundaries (Deng et al., 2021).

Other localized platforms likewise provide mechanisms rather than true lattices. A gold nanoring operating in its anti-bonding dark mode under circularly polarized illumination generated counter-propagating inverse-Faraday photocurrents between inner and outer ring segments and produced an isolated Néel-type skyrmionic magnetic texture with $k_{\parallel}$9; this was presented as a nanoscale unit-cell mechanism rather than an array realization (Yang et al., 2024). A separate coupled electromagnetic–thermal–micromagnetic study used a gold nanoparticle above a dielectric-capped magnetic film to generate a single skyrmion, a two-skyrmion state, and a skyrmionium. For the large-contact particle, a 50 ps pulse produced $\mathbf{n}$00, a 100 ps pulse produced $\mathbf{n}$01, and a 150 ps pulse produced $\mathbf{n}$02, while an array of nanoparticles was proposed only as a future route to creating many textures in parallel (Saidi et al., 2024).

These distinctions matter because the literature spans heterogeneous physical objects. Some realizations are electric-field skyrmion lattices in linear SPP interference systems; some are spin-skyrmion lattices of optical SAM; some are plasmonically controlled magnetic textures in spin models; some are inverse-Faraday-effect stationary magnetic-field crystals in metasurfaces; and some are isolated resonator or nanoantenna textures that are conceptually relevant but not periodic lattices. A plausible implication is that “plasmonic skyrmion lattice” functions less as a single device class than as a family of topological near-field architectures linked by a common skyrmion-number formalism but separated by order parameter, stabilization mechanism, and degree of periodicity (Deng et al., 2021, Vijayan et al., 2023, Yang et al., 31 Mar 2025).

The application space follows this heterogeneity. Reported directions include optical information processing, transfer, and storage; optical information storage and encoding; flexible sensors, wearable electronics, ultra-compact antennas, miniaturized spectroscopy, THz sources, and microwave photonics; and quantum heat engines whose working substance is a plasmonically controlled skyrmion phase (Tsesses et al., 2018, Shen et al., 2024, Deng et al., 2021, Vijayan et al., 2023). Across these applications, the recurring technical motives are subwavelength confinement, symmetry-selective topology, helicity control, and the possibility of scaling from single skyrmionic units to periodic arrays, moiré superlattices, or metasurface-wide crystals.