Magnetic Skyrmion Encoding by Structured Light

Structured light fields, featuring unique topological properties and high tunability, have opened new frontiers in light-matter interactions with magnetic systems. However, the ultrafast and reconfigurable optical encoding of various types of topological magnetic textures remains a significant challenge. Here, we systematically investigate the encoding mechanism of structured light in magnets via the higher-order Poincaré sphere. By uncovering the precise relationship between the winding number of structured light and the topological charge of magnetic textures, we establish a fundamental topological connection between light and magnetism. This framework enables ultrafast, all-optical encoding of diverse topological spin textures in magnetic media, including skyrmions, antiskyrmions and skyrmion bags. Our work advances the fundamental understanding and all-optical control of topological magnetism, offering a promising route for designing skyrmion-based devices.

💡 Research Summary

The paper presents a comprehensive study on the all‑optical generation and control of topological magnetic textures—skyrmions, antiskyrmions, and skyrmion bags—using structured light described on the higher‑order Poincaré sphere (HOPS). The authors first introduce HOPS as a unified representation of vector vortex beams, where each point on the sphere is defined by latitude θ and longitude φ, and the sphere’s order m corresponds to the orbital angular momentum (OAM) of the beam. By expressing the magnetic field of a Laguerre‑Gaussian beam as a Gaussian‑enveloped pulse (Eq. 1) and decomposing its polarization into a superposition of two circular eigenstates (Eq. 2), they derive the field distribution |Bₘ⟩ (Eq. 3). The crucial insight is that the azimuthal phase factor e^{±i m Θ} leads to a total phase winding Φ = 2π m when the azimuthal angle Θ traverses a full circle, giving a winding number l = m (Eq. 4). Thus the topological charge of the light field is directly equal to its OAM.

To couple this structured light to a magnetic medium, the authors adopt a Zeeman interaction term –B(r,t)·mᵣ in the Hamiltonian (Eq. 5). The magnetic film is modeled as a 2‑D ferromagnetic lattice (201 × 201 sites) with exchange J, Dzyaloshinskii‑Moriya interaction (DMI) D, and an external field H_z. Two DMI forms are considered: one stabilizing Bloch‑type skyrmions and the other stabilizing antiskyrmions. Spin dynamics follows the Landau‑Lifshitz‑Gilbert equation (Eq. 6), integrated with a fourth‑order Runge‑Kutta scheme (Δt = 0.001 ℏ/J ≈ 0.5 ps). All quantities are nondimensionalized (ℏ = J = 1).

Simulation results focus on π‑vector beams (θ = π/2) with two azimuthal phases φ = 0 (radial) and φ = π (azimuthal), for both m = +1 and m = –1. For m = –1, the radial beam creates two Bloch skyrmions in a Bloch‑DMI film, while the same field in an antiskyrmion‑DMI film yields a single antiskyrmionium (a skyrmion bag). The azimuthal beam (φ = π) produces a single skyrmionium in the Bloch‑DMI case and two antiskyrmions in the antiskyrmion‑DMI case. Increasing the field amplitude leads to four‑fold textures, demonstrating a nonlinear amplification of the light‑magnet topological interaction. Circular and elliptically polarized beams (θ ≠ π/2) share the same winding number and therefore generate identical topological textures, confirming that all points on a given HOPS share the same topological class.

A key quantitative relationship is established between the total skyrmion number Q_t and the light’s winding number: Q_t = Q · |Q_v · m – 1| (Eq. 7), where Q is the skyrmion charge (±1) and Q_v the vorticity (±1). This extends previous work linking circularly polarized vortex light’s total angular momentum to skyrmion charge, now applicable to arbitrary HOPS states.

Building on this encoding principle, the authors propose a sequential excitation protocol: applying two HOPS pulses in succession can create skyrmion bags of two distinct families. The S₁ bag consists of an outer skyrmion enclosing inner skyrmions (Q_bag = +1), while the S₂ bag features an outer closed domain surrounding multiple inner skyrmions (|Q_bag| = 2, 8, etc.). Energy‑versus‑time curves illustrate the relaxation into stable bag configurations. The ability to deterministically encode both single‑particle and multi‑particle topological objects with picosecond optical pulses represents a major advance for ultrafast, low‑energy spintronic devices.

In summary, the work (i) provides a rigorous topological mapping between structured light’s OAM and magnetic texture charge via the higher‑order Poincaré sphere, (ii) formulates a general light‑magnet coupling model that accommodates various polarizations, (iii) demonstrates ultrafast, all‑optical generation of a wide spectrum of topological spin textures, and (iv) introduces a practical route to encode skyrmion bags, opening pathways for high‑density, reconfigurable magnetic memory and logic based on light‑controlled topology.