Introduction

The discovery of graphene has pioneered the study and development of technological applications based on layered materials with appealing properties such as high flexibility and optical transparency1. Recently, magnetism has been discovered at the monolayer regime which opened a rapid exploration of a wide class of compounds containing ferromagnets2,3, antiferromagnets4,5,6 towards disparate design platforms7. Multiple layers of 2D materials can show intriguing properties such as crystal and layer dependent magnetic properties3,8 or unusual magnetic ground-states via twist engineering7,9. Since magnetic materials2,3,6,7,8,10,11,12,13 are highly used in technological applications, a natural question arises: what is the most efficient way to control the magnetism in such systems. Recent studies of current-driven domain wall dynamics6,12 or gate-controlled anisotropy14 can lead to low-power consumption, and high-speed devices.

Other alternatives through laser approaches15,16,17,18,19 also provide energy-efficient means to manipulate the magnetic properties via demagnetization, spin-reorientation, or even modification of magnetic structures at a short timescale17,20. Initially applied on elemental magnets21, ultrafast laser pulses have led to crucial discoveries including spin switching22,23, all-optical reversal24 and manipulation of topological properties on magnetic nanostructures15,25. Despite these achievements, 2D vdW magnets are largely unexplored through ultrafast laser excitations, in particular the behaviour of fundamental quantities such as magnetisation, magnetic domains and how to induce the appearance of strongly correlated phenomena remain yet to be elucidated. Here we use CrCl3 vdW magnet as a sample system and demonstrate the formation and control of topologically non-trivial vortex quasiparticles through laser radiation in the time-scale used in lab measurements. CrCl3 is a popular 2D magnetic material26,27,28 with XY ferromagnetic order (Fig. 1a) at the monolayer limit which can host merons and antimerons intrinsically in its magnetic structure29. The delicate interplay between strong in-plane dipole-dipole interactions and the weak out-of-plane magnetic anisotropy allows such quasiparticles to appear during zero-field cooling. Despite of this phenomenon, we show that the effective external torque given by the ultrafast laser excitation provided enough heat to overcome the exchange energy and reverse the spin orientations into specific topologies leading to a robust driving-force for generating vortices and anti-vortices in CrCl3.

Fig. 1: Excitation of 2D CrCl3 by a linearly polarised light.
figure 1

a Schematic of a monolayer CrCl3 with the magnetic Cr atoms represented by the pink honeycomb lattice, while the Cl atoms are given in yellow. The monolayer CrCl3 is deposited on a substrate to allow fast dissipation of the energy after the application of the laser pulse. b Evolution of the in-plane \({M}_{t}=\sqrt{{M}_{{{{\rm{x}}}}}^{2}+{M}_{{{{\rm{y}}}}}^{2}}\) and out-of-plane Mz components of the magnetisation as a function of time (ps) after the application of the laser pulse of fluence 0.01 mJ cm−2. The inset shows Mt at different fluences (mJ cm−2). c Evolution of the electronic Te and phononic Tp temperatures after the laser pulse excitation (0.01 mJ cm−2). Inset shows Te at different fluences following labels in the inset on (b).

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Results

A biquadratic spin Hamiltonian and the two-temperature model

We model the system through atomistic spin dynamic simulations11,30 with interactions being described by an all-round spin Hamiltonian:

$${{{\mathcal{H}}}}=-\frac{1}{2}\,\mathop{\sum}\limits_{i,j}{{{{\bf{S}}}}}_{i}{{{{\mathcal{J}}}}}_{ij}{{{{\bf{S}}}}}_{j}-\frac{1}{2}\,\mathop{\sum}\limits_{i,j}{K}_{ij}\,{({{{{\bf{S}}}}}_{i}\cdot {{{{\bf{S}}}}}_{j})}^{2}-\mathop{\sum}\limits_{i}{D}_{i}{({{{{\bf{S}}}}}_{i}\cdot {{{\bf{e}}}})}^{2}-\mathop{\sum}\limits_{i}{\mu }_{i}{{{{\bf{S}}}}}_{i}\,\cdot {{{{\bf{B}}}}}_{{{{\rm{dp}}}}}$$
(1)

where i, j represent the atoms index, \({{{{\mathcal{J}}}}}_{ij}\) represents the exchange tensor that for CrCl3 contains only the diagonal exchange terms, Kij is the biquadratic exchange interaction30, Di the uniaxial anisotropy, which is orientated out of plane (e = (0, 0, 1)) and Bdp is the dipolar field calculated via the macrocell method11 using a cell size of 2 nm. The exchange interactions for CrCl3 have been previously parameterized from first-principles calculations29,30 and contains up to three nearest neighbours. The inclusion of biquadratic exchange30 and next-nearest exchange interactions leads to the stabilisation of non-trivial spin structures29,31 as previously demonstrated.

The magnetisation dynamics is obtained by solving the Landau-Lifshitz-Gilbert (LLG) equation applied at the atomistic level:

$$\frac{\partial {{{{\bf{S}}}}}_{i}}{\partial t}=-\frac{\gamma }{(1+{\lambda }^{2})}{{{{\bf{S}}}}}_{i}\times ({{{{\bf{H}}}}}_{i}+\lambda {{{{\bf{S}}}}}_{i}\times {{{{\bf{H}}}}}_{i})$$
(2)

where λ represents the coupling to the heat bath, γ the gyromagnetic ratio and Hi the effective field that acts on the spin Si. The effective field can be calculated from the Hamiltonian of the model to which we add a thermal noise ξi:

$${{{{\bf{H}}}}}_{i}=-\frac{1}{{\mu }_{i}{\mu }_{0}}\frac{\partial {{{\mathcal{H}}}}}{\partial {{{{\bf{S}}}}}_{i}}+{\xi }_{i}$$
(3)

The thermal field is assumed to be a white noise, with the following mean, variance and strength, as calculated from the Fokker-Planck equation:

$$\langle {\xi }_{i\alpha }(t)\rangle =0,\,\,\langle {\xi }_{i\alpha }(t){\xi }_{j\beta }(s)\rangle =2D{\delta }_{\alpha ,\beta }{\delta }_{ij}\delta (t-s)$$
(4)
$$D=\frac{\lambda {k}_{{{{\rm{B}}}}}T}{\gamma {\mu }_{{{{\rm{i}}}}}{\mu }_{{{{\rm{0}}}}}}$$
(5)

where T represents the thermostat temperature, μi the magnetic moment and μ0 the magnetic permeability.

We include the effect of the laser pulse via the two-temperature model (2TM)32 which couples the electronic and phonon bath via:

$${C}_{{{{\rm{e0}}}}}{T}_{{{{\rm{e}}}}}\frac{d{T}_{{{{\rm{e}}}}}}{dt}=-{G}_{{{{\rm{ep}}}}}({T}_{{{{\rm{e}}}}}-{T}_{{{{\rm{p}}}}})+P(t)$$
(6)
$${C}_{{{{\rm{p}}}}}\frac{d{T}_{{{{\rm{p}}}}}}{dt}=-{G}_{{{{\rm{ep}}}}}({T}_{{{{\rm{p}}}}}-{T}_{{{{\rm{e}}}}})-{\kappa }_{{{{\rm{e}}}}}\nabla {T}_{{{{\rm{p}}}}}$$
(7)

where Ce0 and Cp are the electron and phonon heat capacity, respectively; Gep represents the electron-phonon coupling factor; Tp, Te are the phonon and electron temperatures, respectively; κe is the diffusion coefficient and P(t) is the time dependent laser pulse power.

The electronic temperature is coupled to the magnetic system through the thermal field entering into the Landau-Lifshitz-Gilbert (LLG) equation. The laser power density takes a Gaussian form:

$$P(t)=\frac{2{F}_{{{{\rm{0}}}}}}{\delta {t}_{{{{\rm{p}}}}}\sqrt{\pi /\ln 2}}\exp [(-4\ln 2){(\frac{t}{{t}_{{{{\rm{p}}}}}})}^{2}]$$
(8)

where F0 is the laser fluence (in units of energy density), tp is the pulse temporal width and δ is the optical penetration depth, assumed to be δ = 10 nm. The 2TM can be extended to include a term to reflect the heat diffusion to the substrate, via a heat-sink coupling term of 1/(100 ps). The heat diffusion to the substrate has a time-scale in the order of pico- to nano-seconds and in the model is included as − κe ∇ Tp in Eq. (7). The parametrization of the 2TM (Supplementary Table 1) follows that used in the description of the experimental magnetisation dynamics recently measured for a parent halide compound33 and modelled via a three-temperature approach (Tp, Te, Ts). Since the spin dynamics is included directly into our model, we need to consider only two temperatures (Tp, Te) instead. The evolution of the spin temperature (Ts) will be given directly by the magnetisation dynamics. Parameters such as Ce0, Cp and Gep are considered temperature independent in the 2TM and can be extracted from the thermal conductivity, electronic specific heat, and phonon specific heat34,35. The electron-phonon coupling is approximated as CeTe/te-ph, where te-ph is the electron-phonon thermalisation time. Since CrCl3 has a low Curie Temperature (TC = 19 K29), we will approximate the electron-phonon coupling as that at T = 10 K. The values of thermal bath coupling (α = 0.1) and heat sink coupling (τ = 100 ps) shown in Supplementary Table 1 have been chosen to allow fast numerical simulations. The pulse duration of tp = 100 fs is a typical laser pulse width23, however this value is highly dependent on experimental capacities.

Ultrafast spin dynamics on CrCl3

We observe that as the system is excited with a short laser pulser (85 fs) with an energy fluence of 0.01 mJ cm−2 the initial in-plane magnetisation \({M}_{{{{\rm{t}}}}}=\sqrt{{M}_{{{{\rm{x}}}}}^{2}+{M}_{{{{\rm{y}}}}}^{2}}\) reduces rapidly from its saturated state (Mt/Ms = 1) to a minimum near zero within 25 ps (Fig. 1b). The demagnetisation process is noticed to be barely dependent on the applied fluence (inset in Fig. 1b) showing a similar demagnetised state behaviour. A close look at the variation of the temperatures with time indicates that the system peaks at Te = 60 K during the laser pulse (Fig. 1c) which is larger than the Curie temperature TC = 19 K29 of the monolayer CrCl3. Since the vdW layer is coupled to a heat sink, the energy deposited is quickly dissipated through the substrate, reaching Te = Tp ~ 0.10 K after 200 ps. During this thermal relaxation process, an increase in both transversal Mt and out-of-plane Mz magnetisation components is observed due to the decreased temperature. However, the saturated in-plane magnetisation is not recovered after the laser pulse, but rather it breaks into magnetic domains (Fig. 2a–e) leading to a transversal magnetisation of Mt/Ms = 0.2 at longer times. We noticed that after the application of the laser pulse, a small out-of-plane magnetisation Mz/Ms = 0.04 is developed. By looking at the spin maps (Fig. 2f–j) we identify small circular areas distributed randomly around the surface where the non-zero magnitudes of Mz/Ms are centred after 200 ps. The polarisation of those areas is an indication of the creation of merons and antimerons quasiparticles on the surface.

Fig. 2: Magnetic evolution after laser pulse.
figure 2

a-e Snapshots of the spin dynamics on the in-plane component Mx at different time steps (ps) and electronic temperature Te (K) of monolayer CrCl3. f–j Similar as (a–f), for Mz. The small circular dark/bright spots correspond to the emergence of vortices and antivortices with the laser excitation.

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Topological number as a descriptor

We can further characterise those spins structures created by the laser pulse through the topological number29,36,37:

$$N=\frac{1}{4\pi }\int {{{\bf{n}}}}\cdot \left(\frac{\partial {{{\bf{n}}}}}{\partial x}\times \frac{\partial {{{\bf{n}}}}}{\partial y}\right)dx\,dy$$
(9)

where n is the direction vector of magnetisation M, e.g., \({{{\bf{n}}}}=\frac{{{{\bf{M}}}}}{| {{{\bf{M}}}}| }\). Equation (9) can also be represented by38N = wp/2 indicating a product between the vorticity or winding number w = ± 1 (which determines the in-plane components of the magnetic moment) with the polarity p = ± 1 (which defines the out-of-plane core polarisation). For different combinations of w and p, standard spin configurations are those for merons (N = −1/2) and antimerons (N = 1/2). However, higher order quasiparticles with w = ± 2 are possible which resulted in second-order antimerons (N = 1) and second-order merons (N = −1)39. By looking at the local profile of the magnetisation after the laser excitation (Fig. 3a–d) we can identify several non-trivial topological spin textures characteristic of meron and antimerons. The slightly smaller values computed for the spin features observed within the range of N ~ 0.40 − 0.45 is due to the finite area considered on the integration of Eq. (9).29,36. However, the clear spin distributions with the magnetic moment at the core pointing out-of-plane and the surrounding perimeter with spins aligning in-plane hallmarked the formation of merons and antimerons. More complex quasiparticles composed by two antimerons (N = 0.95) are also possible to be generated during the thermal equilibration (Fig. 3d).

Fig. 3: Vortex and antivortex creation after light excitation.
figure 3

a, b Antivortex (vorticity w = −1) formation with meron (N ~ − 0.45) and antimeron (N ~ 0.40) quasiparticle features, respectively. c Vortex (w = +1) stabilisation with antimeron characteristics (N ~ 0.44). The big arrows in (a, b) indicate the average behaviour of the in-plane components in the perimeter of quasiparticle. d Creation of a higher order topological spin textures (N = 0.95) composed of two antimerons. The variation of the magnitudes of N is observed within ± 0.03 within the area considered for the integration of Eq. (9).

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It is worth mentioning that the formation of these spin textures in CrCl3 is not related with the presence of non-collinear Dzyaloshinskii-Moriya interactions not considered in the spin Hamiltonian in Eq. (1), but on the interplay between the laser pulse heat and the system thermal equilibration. As the laser pulse quickly quenches the total magnetisation, magnon localisation takes place at small areas of the surface due to short-range exchange interactions40,41. This makes the magnetisation increases with the nucleation of magnetic droplet solitons with unstable spin textures42,43 perpendicular and/or parallel to the easy-plane of CrCl3. Within a time scale of a few picoseconds, these droplets can split, merge and scatter until thermal equilibration is reached which induced the formation of more stable merons and antimerons with a defined spin configuration at longer times (>400 ps). We studied as well whether thermal effects present in cooling processes can help in the creation of meron and antimerons (Supplementary Fig. 1). We noticed the formation of these spin textures at all cooling times considered (0.1 ns, 0.5 ns, 3 ns and 4 ns) suggesting that indeed they can also be produced via thermal effects. The cooling time however will influence the amount of merons/antimerons present in the system, with faster cooling leading to the creation of more spin textures. Hence a fast heating or cooling as the one provided by the laser pulse can lead to a higher number of merons or antimerons, in comparison to a slow cooling process.

We next investigate the long time-scale dynamics of the topological spin structures that are created with the ultrafast laser pulse (Fig. 4 and Supplementary Movie S2). We can observe different collision interaction scenarios throughout the layer at different time frames and spatial locations. Such as, at the selected area 1 in Fig. 4a, e which shows a surprising annihilation dynamics followed by the emission of a spin-wave isotropically along the surface shortly after the collision (Supplementary Movie S2). We noticed events involving pairs of multiple vortex and antivortex (area 2, Fig. 4b, f) with the subsequent annihilation and spin-wave emission happening at each pair separately (areas 2-3, Fig. 4b, c, f, g) and at different time frames (1.5 ns, 1.75 ns). This suggests a 1:1 vortex-antivortex relation for the emission of spin-waves despite the number of quasiparticles involved. Simultaneous collisions can also occur as displayed in area 4 (Fig. 4c, h) with no apparent correlations on other events. The relative distance between the vortex and antivortex plays a role on the lifetime of the spin textures. We observe that the vortex/antivortex pair in area 5 (Fig. 4d, i) survived longer relative to other events (>2 ns) and has a more complex dynamics given by a precession motion. Since such spiraling orbit is present during the annihilation process for timescales beyond the simulation time (~20 ns), there is a probability that the vortex/antivortex pair might be annihilated.

Fig. 4: Large timescale evolution of merons and antimerons.
figure 4

a–d Spin dynamics at long times (1.25 − 2 ns) showing the dynamics of the topological spin textures after the application of a laser pulse of fluence 0.01 mJ cm−2. The topological number N is computed at each snapshot. The small highlighted areas (1, 2, 3, 4, 5) display specific events of the interactions between vortex and antivortex. Zoom-in at the small areas showing an annihilation event (e, h) followed by the emission of spin-waves, collisions between two pairs of vortex and antivortex (f), collision between single vortex and antivortex (g) and precession of vortex and antivortex pair (i). See Supplementary Movie S2 for additional details.

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Additionally we can track down the variation of the different topological spin textures via the variation of N (Figs. 4-5) as a function of time. The large fluctuations of N observed at early stages of the equilibration (~5−120 ps) are due to the increased thermal fluctuations after the laser pulse (Fig. 5a). At later times (>300 ps) N varies in a much smaller scale (Fig. 5b) which allows to identify unit steps correlating directly with the presence of vortex-antivortex pairs (Fig. 5c–f). The annihilation phenomena appear at specific moments during the dynamics at a time-scale even beyond 1 ns. Hence the process of creation and annihilation of magnetic merons or antimerons can be tracked down via the temporal variation of N which in principle is general for any spin textures on 2D magnets. A recent protocol44 involving X-ray scattering techniques could be adapted to the measurement of N via the scattering signal from the spin textures.

Fig. 5: Topological number as a descriptor.
figure 5

a, b Variation of the topological number N within 0−400 ps and 400−1000 ps intervals, respectively. Laser pulse fluence at 0.01 mJ cm−2. c–f, Snapshots of the spin dynamics of monolayer CrCl3 at different times highlighted in (b). The different jumps (c–f) represent selected areas where the annihilation of a vortex/antivortex pair is present which is associated with an unit variation of N.

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Discussion

The discovery of laser-induced topologically non-trivial merons and antimerons quasiparticles on 2D CrCl3 magnets creates open routes for tailoring the magnetic properties of other vdW materials holding similar features. As more materials have been isolated and implemented on device platforms7, our findings indicate that other layered compounds may develop laser-driven topological spin textures following the recipes included here. The laser pulse heating is clearly the main driving force for the formation of the quasiparticles which occurs within the experimental regime of observation. On the particular case of CrCl3 with a low Curie temperature (19.4 K)30, it is necessary to couple the system to a heat-sink so the energy deposited by the laser pulse is dissipated via a substrate. Such approach induces an efficient stabilisation of vortices and antivortices on CrCl3 during the equilibration process. This suggests that in order to observe topological spin textures on atomically thin vdW magnets the appropriate substrate needs to be selected and implemented on the stacking. A few options in terms of insulating substrates, i.e. BN45, which hold high thermal conductivity may provide solution to avoid strong interactions with underneath atoms. As a matter of fact, a recent molecular beam epitaxy (MBE) of CrCl3 on graphene/6H-SiC(0001)46 has been fabricated which provides chemical, mechanical stability to measure the magnetic features via pumb-probe techniques. These include the utilisation of an ultrafast laser setup able to induce rapid heating of the CrCl3 with a consequent modification of the magnetisation which can be measured through magneto-optical Kerr effect20. In principle such approach involving good quality MBE CrCl3 samples and a high-energy femtosecond laser would be able to probe the topological features of the system and unveil the presence of merons and antimerons on a 2D XY vdW magnet.

Methods

We model the system through atomistic spin dynamic simulation methods11,30 with interactions described by a biquadratic spin Hamiltonian (Eq. (1)). All methods are included in the main text with additional details at Supplementary Information.