Ultrafast laser-driven topological spin textures on a 2D magnet

The study of layered materials following the discovery of graphene has expanded to include intrinsic 2D magnets, enabling exploration of ferromagnets and antiferromagnets down to the monolayer limit for device concepts requiring low power and high speed. While electrical gating and current-driven domain-wall motion offer means to control magnetism, ultrafast laser approaches provide an energy-efficient route to manipulate magnetic order on femtosecond time scales, having already enabled spin switching and all-optical reversal in conventional magnets. For 2D van der Waals magnets, the response to ultrafast optical excitation remains largely unexplored, particularly regarding magnetization dynamics, domain evolution, and laser-induced emergence of correlated topological spin textures. This work addresses whether experimentally relevant ultrashort laser pulses can manipulate a prototypical 2D XY ferromagnet, CrCl₃, to generate and control nontrivial topological quasiparticles (merons and antimerons). The importance lies in establishing an ultrafast, low-energy optical route to create and steer topological spin textures in atomically thin magnets, with implications for magneto-optical and spintronic applications.

Prior ultrafast magnetism studies on elemental and thin-film magnets demonstrated demagnetization, spin switching, all-optical reversal, and laser-driven control of topological properties. However, analogous studies in 2D vdW magnets are scarce. CrCl₃ is a widely investigated 2D XY ferromagnet with known propensity for meron/antimeron formation due to strong in-plane dipolar interactions and weak out-of-plane anisotropy. Theoretical works have highlighted roles of biquadratic exchange and further-neighbor interactions in stabilizing nontrivial spin textures. Laser-induced skyrmion writing/erasing and tunable topological textures have been reported in other systems, motivating investigation of whether similar mechanisms—via ultrafast heating and nonequilibrium spin dynamics—can generate meron-like textures in 2D magnets. Techniques such as X-ray scattering and MOKE provide potential experimental routes to detect topological numbers and ultrafast magnetization dynamics.

The authors perform atomistic spin dynamics simulations of monolayer CrCl₃ governed by a Hamiltonian including: (i) diagonal isotropic exchange up to third neighbors parameterized from first-principles, (ii) biquadratic exchange, (iii) out-of-plane uniaxial anisotropy, and (iv) long-range dipole-dipole interactions computed via a macrocell method (cell size 2 nm). Spin dynamics follow the Landau–Lifshitz–Gilbert equation with coupling to a thermal bath and a stochastic thermal field (white noise) consistent with the Fokker–Planck formalism. Ultrafast excitation is modeled by a two-temperature model (2TM) coupling electron and phonon baths via electron–phonon coupling Gep, with electron (Ce0) and phonon (Cp) heat capacities treated as temperature independent. The electronic temperature Te is coupled to the spins via the thermal field in the LLG. The laser power density is a Gaussian P(t)=2F0/(δ t√(π/ln 2)) exp[−4 ln2 (t/tp)^2] with F0 the fluence, tp the pulse width, and δ the optical penetration depth (assumed δ=10 nm). Heat diffusion to the substrate is included via a heat-sink coupling term (≈1/100 ps) and a diffusion term Ke∇Tp in the phonon temperature equation. Parameterization follows literature for related halide systems (CrI₃) adapted to CrCl₃, with electron–phonon coupling approximated as Ce0 Te/τe-ph at T≈10 K (CrCl₃ has low Tc≈19 K). Simulation parameters chosen for computational efficiency include thermal bath coupling α=0.1 and heat sink time τ=100 ps. Typical laser pulse widths considered are 30–100 fs; key results use an 85 fs pulse with fluence 0.01 mJ cm⁻². The temporal evolution of magnetization components (Mx, My, Mz), in-plane M∥, transverse M⊥, and temperatures (Te, Tp) are tracked over ps–ns scales. Topological characterization uses the topological number N (N=wp/2, with winding number w and polarity p) computed by integrating the magnetization field to identify merons (N≈−1/2), antimerons (N≈+1/2), and higher-order textures. Cooling protocol studies (variable cooling times from 0.1–4 ns) assess the role of quench rate in texture formation. Long-time dynamics (to >2 ns, with mention of longer precession) are analyzed to capture motion, collisions, and annihilations accompanied by spin-wave emission.

- Ultrafast demagnetization and domain formation: An 85 fs laser pulse with fluence 0.01 mJ cm⁻² reduces the initial in-plane magnetization from saturation (M/Ms=1) to near zero within ~25 ps. Peak electronic/phonon temperatures reach ~60 K during the pulse, exceeding CrCl₃’s Tc≈19 K, then relax to ~0.10 K by ~200 ps due to substrate heat sinking. The in-plane saturated state is not recovered; instead, magnetic domains form, yielding a long-time transverse magnetization M⊥/Ms≈0.2 and a small out-of-plane component Mz/Mx≈0.04. - Laser-induced topological textures: After ~200 ps, small circular regions with finite Mz indicate the emergence of meron and antimeron quasiparticles. Computed topological numbers for localized textures are N≈±0.40–0.45 (slightly below ±0.5 due to finite integration area), consistent with merons/antimerons. Higher-order textures are also observed, including a composite of two antimerons with N≈0.95. - Formation mechanism: Texture formation does not rely on Dzyaloshinskii–Moriya interactions (not included); it arises from ultrafast heating and subsequent thermal equilibration. Rapid quenching localizes magnons and nucleates droplet solitons with unstable spin textures that evolve via splitting/merging into more stable merons/antimerons within >400 ps. - Cooling-rate dependence: Thermal cooling alone can generate merons/antimerons across tested cooling times (0.1, 0.5, 3, 4 ns). Faster cooling produces more textures, indicating ultrafast heating/cooling from a laser enhances texture density relative to slow cooling. - Long-time dynamics and spin-wave emission: Over 1–2 ns, multiple interaction scenarios occur: vortex–antivortex collisions and annihilations emit spin waves isotropically; events can involve multiple pairs with apparent 1:1 vortex–antivortex relations to spin-wave emission; some pairs exhibit long-lived precessional orbits (>2 ns) before probable annihilation. - Topological number as a descriptor: The temporal evolution of N shows large fluctuations during early equilibration (~5–120 ps) due to thermal noise, then smaller variations for t>300 ps with unit-step changes corresponding to creation/annihilation of vortex–antivortex pairs. This suggests N(t) as a general metric to track spin-texture dynamics, potentially measurable via adapted X-ray scattering protocols. - Experimental relevance: The entire process occurs within experimentally accessible time scales (ps–ns) and laser parameters (30–100 fs, ~0.01 mJ cm⁻²). Substrate coupling (heat sink) is key for stabilizing textures in low-Tc CrCl₃.

The study demonstrates that experimentally realistic ultrafast laser pulses can drive the creation and control of topological spin textures in a 2D XY ferromagnet. By surpassing Tc transiently and enabling rapid cooling via a substrate, the system transitions from a demagnetized state to a textured domain state hosting merons and antimerons. This addresses the central question of whether optical excitation can manipulate 2D vdW magnets to generate robust topological textures, showing that DMI is not a prerequisite in such XY systems; instead, the balance of exchange, biquadratic exchange, dipolar interactions, weak out-of-plane anisotropy, and ultrafast thermal dynamics governs texture nucleation and stability. The identification of characteristic spin-wave emission upon vortex–antivortex annihilation and the use of the topological number N as a temporal descriptor provide concrete observables. Practically, ensuring efficient heat dissipation via appropriate substrates (e.g., high-thermal-conductivity BN or graphene/SiC platforms) is crucial for stabilizing textures and enabling detection (e.g., via MOKE or X-ray scattering). The findings are broadly relevant for designing magneto-optical topological phenomena and device concepts in 2D magnets.

Ultrashort laser excitation of monolayer CrCl₃ induces rapid demagnetization, followed by the formation and evolution of topological meron and antimeron textures within ~100–400 ps, with rich ns-scale dynamics including motion, collision, annihilation, and spin-wave emission. The mechanism relies on ultrafast heating and substrate-assisted cooling without requiring DMI, leveraging the intrinsic XY anisotropy, exchange, biquadratic exchange, and dipolar interactions. The work provides a computational roadmap for laser-driven topological control in 2D vdW magnets and identifies the topological number N as a practical descriptor for tracking spin-texture dynamics. Future directions include experimental verification in high-quality epitaxial CrCl₃ on thermally conductive substrates, ultrafast magneto-optical measurements (e.g., MOKE), adaptation of X-ray scattering to measure N, optimization of laser parameters and cooling rates to tune texture density, and extension to other 2D magnets with similar magnetic anisotropy and interactions for topological spintronic applications.

- Modeling approximations: The two-temperature model assumes temperature-independent Ce0, Cp, and Gep, with Gep≈Ce0 Te/τe-ph at T≈10 K due to CrCl₃’s low Tc, which may limit quantitative accuracy at higher temperatures. - Parameter choices for efficiency: Thermal bath coupling (α=0.1) and heat-sink coupling (τ=100 ps) were chosen to enable fast simulations and may not exactly match experimental conditions. - No DMI: While not required for observed textures in CrCl₃, omission of Dzyaloshinskii–Moriya interactions precludes assessing their potential influence in materials where DMI is present. - Optical parameters: The optical penetration depth is fixed (δ=10 nm), and the pulse width/fluence space is sampled sparsely; broader parameter sweeps could reveal thresholds and phase diagrams. - Finite-size and integration effects: Finite integration areas yield N values slightly below ideal ±0.5 for merons/antimerons; finite simulation size and time may affect interaction statistics and lifetimes (e.g., long-lived precession beyond simulated time).