Introduction

The finding of long-range magnetic ordering in 2D magnetic materials has been attracting considerable research interest on different forefronts ranging from fundamentals up to energy-efficient applications1,2,3,4,5,6,7,8,9,10,11. In this context, the ability of spin-light coupling to control the magnetic properties of atomically thin layers for integration in all-optical switching (AOS) devices12,13,14 might provide a feasible pathway for faster and low-power magneto-optical implementations. Previously demonstrated on different compounds under ultrafast laser pulses15,16,17,18, AOS has potential to give a major impact on data memory and storage technologies due to the fast, and scalable character of optical probes. Apart from the switching between various magnetic states under specific circumstances of field, laser energy and temperature, optical pulses can also lead to formation of different spin textures with specific topology or chirality19,20,21. In particular, topologically non-trivial spin quasiparticles that can be erased, nucleated and spatially manipulated as in writing and register-shifting of logical bits6,22,23,24,25,26 have been attracting substantial attention. The inherent localized nature of the spin textures and their coupling with the environment which is governed by exchange and spin-orbit interactions define the underlying femtosecond time scale of magnetic dynamics.

Different spin textures have been previously observed in vdW magnets (e.g., Fe3GeTe2, CrCl3, Cr2Te3, Fe5GeTe2, CrGeTe3). They range from magnetic bubbles4,27,28 and stripe domains29, up to topological quasiparticles, such as skyrmions30,31,32,33,34,35,36 and merons37,38, as recently summarised in the 2D Magnetic Genome9. These evidences provide a broad territory for exploration either in more fundamental levels or in functional applications where the control of spin textures in device platforms is the ultimate step. On that, the formation of skyrmions in vdW layers has been mainly due to the intrinsic magnetic features of the layers (e.g., sizeable Dzyaloshinskii-Moriya interactions, dipolar fields, etc.) or the application of external magnetic fields in order to break any inversion symmetry in the system. Nevertheless, the use of light probes such ultrafast laser pulses to generate and manipulate topological spin textures on 2D vdW compounds is currently unknown. There have been recent reports on pump probe measurements on 2D magnets39,40,41, but the demonstration of the formation of spin textures via ultrafast laser excitations is yet to be reported.

Here we show that ultrashot laser excitations can be used to imprint spin textures with different chiralities on the centrosymmetric CrGeTe3 magnet. We observe that skyrmions, anti-skyrmions, stripe domains can be generated throughout the surface after the application of laser pulses with high stability after thermal equilibration. Additional laser pulses can manipulate their topological character inducing the transformation of skyrmions into stripe domains, and vice versa, with an external magnetic field providing control on the polarity of the final state. This toggle switching mechanism is observed to be complete and reversible in CrGeTe3 providing a practical way to write and erase information with topological features in a short time scale.

Results

To probe the magnetic properties of CrGeTe3 crystal we use a complementary suite of theoretical and experimental techniques comprising multiscale theoretical approximation4,6,8,37,42–43 and wide-field Kerr microscopy (WFKM) in a polar geometry44 (see Methods for details). We start showing theoretically that ultrafast laser pulses (Fig. 1a) can be used to drive the formation of different spin textures on CrGeTe3 at different conditions. We describe the interactions via a spin Hamiltonian including most of the contributions previously found to play a role in the magnetic properties of 2D materials42:

$${{{{{{{\mathscr{H}}}}}}}}= -\frac{1}{2}\,\mathop{\sum}\limits_{i,j}{{{{{{{{\bf{S}}}}}}}}}_{i}{{{{{{{{\mathscr{J}}}}}}}}}_{ij}{{{{{{{{\bf{S}}}}}}}}}_{j}-\frac{1}{2}\,\mathop{\sum}\limits_{i,j}{K}_{ij}\,{({{{{{{{{\bf{S}}}}}}}}}_{i}\cdot {{{{{{{{\bf{S}}}}}}}}}_{j})}^{2}\\ -\mathop{\sum}\limits_{i}{D}_{i}{({{{{{{{{\bf{S}}}}}}}}}_{i}\cdot {{{{{{{\bf{e}}}}}}}})}^{2}-\mathop{\sum}\limits_{i,j}{{{{{{{{\boldsymbol{A}}}}}}}}}_{ij}\cdot \left({{{{{{{{\bf{S}}}}}}}}}_{i}\times {{{{{{{{\bf{S}}}}}}}}}_{j}\right)-\mathop{\sum}\limits_{i}{\mu }_{i}{{{{{{{{\bf{S}}}}}}}}}_{i}\,\cdot {{{{{{{{\bf{B}}}}}}}}}_{{{{{{{{\bf{dp}}}}}}}}}$$
(1)

where i, j represent the atoms index, \({{{{{{{{\mathscr{J}}}}}}}}}_{ij}\) represents the exchange tensor that for CrGeTe3 contains only the diagonal exchange terms, Aij is the Dzyaloshinskii-Moriya interaction (DMI), Kij is the biquadratic exchange interaction42, Di the uniaxial anisotropy, which is orientated out of plane (e = (0, 0, 1)), and Bdp is the dipolar field calculated using the macrocell method4. The exchange interactions for CrGeTe3 have been previously parameterized from first-principles calculations2 and contains up to three nearest neighbors. The inclusion of biquadratic exchange42, four-site four spin interactions and next-nearest exchange interactions have been shown to lead to the stabilisation of non-trivial spin structures in vdW magnets37,45 and thin films46. For the latter, large effects on the energy barriers preventing skyrmion and antiskyrmion collapse into the ferromagnetic state have been observed. In this context, we have also investigated the role of the different interactions in Eq. (1) in stabilising topological spin textures in CrGeTe3. Supplementary Table 1 provides a summary of the main driving forces used, where the presence of DMI is crucial (see Supplementary Movie S1) for the formation of skyrmions and more complex spin textures as discussed below. Even though the system is centrosymmetric which rules out DMI at first-nearest neighbours, the same is not applicable for second-nearest neighbours where a sizeable DMI is present. This magnitude has been both measured and calculated using inelastic neutron scattering47 and ab initio48 simulations, respectively, resulting in ∣Aij∣ ≈ 0.31 meV. The Landau-Lifshitz-Gilbert (LLG) equation is used to describe the dynamics4,42 at different times and temperatures. We include the effect of the laser pulse and further relaxations of the spins and ionic lattice via the two-temperature model (2TM)43,49 (see Methods). In the 2TM simulations the spin interactions (e.g., bilinear exchange, anisotropic exchange, biquadratic exchange, DMI, single-ion anisotropy) are not modified by the excitations, but rather the ultrashort pulses change the spin dynamics under different fluences, as commented below. This is an effect of the time-evolution of the system to minimize the energy towards thermal equilibration after being optically excited

Fig. 1: Laser-induced demagnetisation processes and spin textures.
figure 1

a Schematic of the ultrafast laser pulses with linear polarisation π on CrGeTe3. b Evolution of the electronic (Telec) and phonon (Tphon) temperatures using the 2TM approach after the application of a single pulse at different energy fluences (mJ cm−2). c Variation of the out-of-plane magnetisation Mz/Ms versus time (ps) at the fluences showed in b. Line breakings are used to separate the three regimes observed in the simulations. d–f Snapshots of the spin dynamics (Mz) following the pulse at 115 ps, 400 ps, and 8000 ps, respectively. A fluence of 0.14 mJ cm−2 was used. g–i Local view of the spin textures with their respective topological number Nsk = + 1 (anti-skyrmion), −1 (skyrmion), and 0 (skyrmionium), respectively. The scale bar of 5 nm applies to both g and h. Skyrmions are generally more energetically stable than anti-skyrmions or skyrmionium even though both can stay for several nanoseconds and disappear as observed in our spin dynamics simulations.

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Figure 1b shows that as a short laser pulse is applied into the system at 100 ps, the electron (Telec) and phonon (Tphon) reservoir temperatures are substantially modified as time evolves. An initial sharp increase of Telec is observed within the sub-picosecond regime (~0.5 ps) taking the system above the Curie temperature TC = 68 K2. Tphon follows the variation of Telec as thermal relaxation takes place shortly after the excitation. The behaviour of both temperatures is dependent on the fluence energy applied to the layers displaying variation on the stabilisation of Telec and Tphon towards equilibration. That is, the higher the fluence the larger the stabilised temperatures. This affects directly how the magnetisation (Mz/Ms) responds to the laser pulse, which is strongly fluence-dependent (Fig. 1c). At low fluence magnitudes (e.g., 0.03 mJ cm−2), the demagnetisation process completes before the electron-phonon temperature equilibration is reached (0.34 K). Supplementary Table S2 shows all the equilibration temperature at the different fluences used. There is a short decay of the magnetisation from the saturation state to Mz/Ms = 0.75 which rapidly recovers on the timescale of ~4 ps. This demagnetisation process can be classified as type-I dynamics as a single-step demagnetization within the electron-phonon equilibration is achieved50. At higher fluences (i.e., 0.2 mJ cm−2) there is an initial rapid demagnetisation (Mz/Ms = 0.04) of the CrGeTe3 (Fig. 1c) driven by the electron temperature. After the electron-phonon temperature equilibration is achieved (2.25 K) the magnetisation does not significantly recover, and instead a second, far slower stage of demagnetisation proceeds which is determined by the phonon temperature. This is a two-stage demagnetisation process defined as a type-II dynamics50. Indeed, this result is in good agreement with recent time-resolved magneto-optical Kerr effect measurements39 at similar energy fluence.

Interestingly, between the low and large fluence limits, there is a transitional regime where a rapid and almost complete recovery of the magnetisation occurs within 200 ps initially following a type-I dynamics. Nevertheless, over a much longer timescale ( >200 ps) the system enters in a second demagnetisation stage steered by the phonon temperature as in a type-II dynamics. In this transitional domain, the laser pulse drives the formation of a variety of magnetic objects such as bubbles (circular and elongated), spirals or stripe domains, and donut-shaped textures (e.g., 0.14 mJ cm−2 in Fig. 1d–f). By analysing the local spin distributions of the different textures (Fig. 1g–i), and through the computation of the total topological charge Nsk via37,51,52:

$${N}_{{{{{{{{\rm{sk}}}}}}}}}=\frac{1}{4\pi }\int{{{{{{{\bf{n}}}}}}}}\cdot \left(\frac{\partial {{{{{{{\bf{n}}}}}}}}}{\partial x}\times \frac{\partial {{{{{{{\bf{n}}}}}}}}}{\partial y}\right){d}^{2}{{{{{{{\bf{r}}}}}}}}$$
(2)

where n is the direction vector of magnetisation M (e.g., \({{{{{{{\bf{n}}}}}}}}=\frac{{{{{{{{\bf{M}}}}}}}}}{|{{{{{{{\bf{M}}}}}}}}|}\)), we identify the formation of skyrmions (Nsk = − 1) and anti-skyrmions (Nsk = + 1) of Bloch-type, and skyrmioniums (Nsk = 0)48,53. We estimated their diameters in the range of 20 − 35 nm using the magnetic parameters (e.g., exchange interactions, anisotropies, DMI)47,48 available for CrGeTe3. It is worth mentioning that these diameters can be changed with further optimisation of the parameters as previously demonstrated54. This associated with the limitations in length scale of the atomistic spin dynamics methods55,56 resulted in smaller diameters relative to the experiments as showed below. We however assumed a more qualitative approximation to demonstrate the existence of non-trivial spin textures into the layer, and how to control them through optical excitations. Domain wall widths were extracted and resulted in ~ 5.2 nm which follows those found in strong 2D ferromagnets such as CrI34, CrBr36, and Fe3GeTe245,57. It is worth mentioning that the formation of skyrmioniums into the system is more efficient via ultrafast laser pulses than via cooling. We have tested our simulation setup and found that statistically one out of four repeats of a field-cooling LLG-simulations (11.7 mT) yielded the formation of skyrmioniums. This suggests that excited ground states are be more feasible for the stabilisation of spin textures since any energy barrier for the formation might be overcome54.

The formation of spin textures in CrGeTe3 after the laser pulses can be explained in terms of the spin correlations present in the system that do not vanish during the initial rapid quenching of the magnetisation (<250 fs) during the demagnetisation process58,59. Following the application of the laser pulse, ferromagnetic recovery occurs in localised regions of the surface which is driven by short-range exchange interactions. This localised recovery or magnon localisation, results in the nucleation of small, non-equilibrium magnetic structures known as magnon droplets60. The nucleation of these droplets at an early stage of the dynamics can be seen in Supplementary Fig. 1 at different fluences. 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 textures with a defined spin configuration ( >200 ps). Once this magnon coalescence step60 is finished, the magnon droplets evolved into skyrmions with a specific N and energetic stability against thermal fluctuations.

We observed that this phenomenon can be tuned by adjusting the energy fluence applied to the system. That is, different types of magnetic textures can be created in CrGeTe3 with the laser pulse. At low fluences, 0.001−0.055 mJ cm−2 (Fig. 2a, and Supplementary Movie S2) the final topological charge is nearly zero with the magnetisation in the type-I dynamics. This is expected at this weak spin-light interaction regime as the magnetisation recovers to a polarised ferromagnetic (FM) state after a few picoseconds. As the fluence increases within the range of 0.055−0.087 mJ cm−2, the pulse significantly demagnetises the system, creating densely packed magnon droplets transiting the system to the formation of non-trivial objects such as spin stripes (Supplementary Movie S3). The temperature equilibration in this case is not high enough to break the stripes in more localized spin quasiparticles. The formation of skyrmions however can be achieved as the energy is slightly increased to 0.09−0.180 mJ cm−2. At this limit, the temperature of the system is suitable for the magnon droplets to gain topological features, and hence they evolve into skyrmions rather than merging (Fig. 2b, Supplementary Movie S4). It is noteworthy that is within the region of 0.14−0.18 mJ cm−2 there is the simultaneous formation of skyrmioniums with skyrmions which are randomly distributed over the surface. At fluences above 0.18 mJ cm−2 (Fig. 2c, Supplementary Movies S5–S6), a hybrid spin state consisting of skyrmions, stripes and skyrmioniums are formed. The large amount of energy deposited in the CrGeTe3 layers at this limit results in thermal fluctuations which are sufficient to inhibit the creation of magnon droplets. Instead, the non-equilibrium spin textures tend to merge and evolve in mixed labyrinthine domains with the appearance of skyrmions and skyrmioniums. In all these different processes, the magnitude of Nsk can work as a descriptor indicating the different spin objects formed by the excitations. However, visualisation of the spin distributions is critical to further characterise their spatial correlation and interactions.

Fig. 2: Fluence-dependent spin textures.
figure 2

a Final topological charge (Nsk) versus energy fluence (mJ cm−2) of the applied laser. The different energies determine the spin states created in CrGeTe3 within the range considered: spin polarised ferromagnetic (FM), magnetic stripes, skyrmions and hybrid (stripes and skyrmions coexisting). In each case, CrGeTe3 was in a spin-polarised saturated state (Mz = 1) prior to the laser pulse. b–c Snapshots of the simulation results for 0.10 mJ cm−2 and 0.30 mJ cm−2, respectively. The out-of-plane magnetisation Mz after 3 ns relaxation following a single laser pulse is used. The white scale bar is 50 nm. d, e Experimental results obtained via WFKM after 100 and 10 laser pulses, respectively. The black scale bar is 5 μm and the laser fluence is 16 mJ/cm2. The measurements were performed at 18.5 K. A 25 mT magnetic field is used.

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We can experimentally validate the formation of spin textures and further tuning with the laser pulses via WFKM techniques (see Methods for details). We initially zero-field cooled the system to ≈ 18.5 K, and then applied a sequence of N = 1, 10, and 100 pulses under an out-of-plane field of 25 mT. Figure 2d, e show the spin states obtained in CrGeTe3 after N = 100 and N = 10 pulses, respectively. Strikingly, these results follow closely those obtained in the simulations (Fig. 2b, c) with the formation of magnetic bubbles and their coexistence with magnetic stripes throughout the surface. The nominal fluence used in the measurements (16 mJ/cm2) agrees on the hybrid spin structures found for magnitudes above 0.30 mJ/cm2 in the phase diagram in Fig. 2a. This indicates a complex scenario for the stabilisation of the spin textures with the laser excitations. We also noticed that a high number of pulses is normally necessary in the measurements to induce the creation of the spin textures (Fig. 2d, e). That is, for N ≤ 10 we barely observed any modifications of the spin textures at the same laser fluence. As discussed previously, this is related with the number of magnon droplets populating the surface during the magnon localisation phenomenon60. A closer look at the magnetisation dynamics reveals that depending on the amount of energy transferred to the layers via the different number of pulses N, the magnon droplets can either be isolated and give place to the formation of skyrmions or magnetic bubbles; or, they can coalesce and form long stripe domains with smaller contributions from localised droplets. We noticed that both situations are possible in CrGeTe3 depending on the number of pulses applied under an external magnetic field. Moreover, the size of the magnetic spin textures stabilised in the areas studied (~1−2.90 μm) exceeded those calculated in the atomistic computations (~17−29 nm). However, we have observed smaller spin textures (Supplementary Fig. 4) within the range of the simulations (~20−60 nm) which could not be resolved due to optical limitations of the technique. Higher resolution techniques, e.g., Lorentz transmission electron microscopy, would be required to resolve such small-diameter textures.

An outstanding question raised by these results is whether the ultrafast laser pulses can induce the transformation of magnetic stripes into bubbles/skyrmions, and vice-versa, like in a spin-toggle switch13. This AOS process normally requires two magnetic states with equal energies where the switching between them can be realised at a negligible heat generation61,62. The switching however needs to be reproducible and reversible in order to allow full writing of the magnetic information62,63. To investigate this we probed the variation of the spin textures with laser excitations but also taken into account an external field to unveil any polarisation effect that might be present in the system. As laser pulses are applied to CrGeTe3, there are clear transformations of the magnetic textures from one state to another which can be further manipulated via a magnetic field (Fig. 3). We considered three steps in this switching phenomenon under a field of +25 mT (Fig. 3a–c), 0 mT (Fig. 3d–f) and −25 mT (Fig. 3g–i). We initially obtained a spin state with mixed labyrinthine domains (Fig. 3b) prior laser application, which will be used as a reference for the switching process. We then applied N = 100 laser pulses at +25 mT on this state to generate a switching between a stripe dominant-state (Fig. 3b) to a random network of magnetic bubbles (Fig. 3c). We continued this process through magnetic fields of 0 mT (Fig. 3d–f) and −25 mT (Fig. 3g–i) to show that this toggle switching is reversible, complete and reproducible. It is noticed that the polarity reversal of the spin textures with magnetic fields (Fig. 3c, i) provides an additional ingredient for controlling on-demand the polarisation of the spin textures or to determine which spin textures are created. For instance, the switch from magnetic bubbles to stripe domains occurs without the application of magnetic fields. However, the transition from stripes to bubbles has been noticed to require a bias field. This indicates a switch mechanism where a defined spin state can be obtained through the interplay between laser pulses and field-induced symmetry breaking into the lattice. Simulation results of the toggle switch found in the experiments are given in Supplementary Fig. 2 which provided a theoretical background for our observations.

Fig. 3: Light-induced spin toggle switch.
figure 3

a Schematic of CrGeTe3 crystal under laser excitations (N = 100 pulses) and an out-of-plane magnetic field (+25 mT). b–c, Spin toggle switching observed between two magnetic configurations dominated by stripe domains (b) and bubbles/skyrmions (c) via WFKM measurements. A magnetic field of + 25 mT and N = 100 laser pulses are applied to induce the transition. d Similar as in a but without any applied field. e–f The magnetic configuration in c is used as a reference state to a new switching process in e with zero field and under N = 100 laser pulses. The final equilibrated state is shown in f with a predominant amount of stripe domains throughout the surface. g Similar as in a but with a magnetic field of opposite polarity (−25 mT). h,i The magnetic state in f is used as the reference state in h to induce a new switching step under −25 mT and N = 100 laser pulses. The reversal of the field from + 25 mT (a–c) to −25 mT (g–i) with an intermediate step at 0 mT can generate a full switching loop with a different polarisation of the magnetic skyrmions and stripe domains. The scale bar is 5 μm and the laser fluence is 16 mJ/cm2. The measurements were performed at 18.5 K.

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Discussion

The discovery of laser-induced spin switching in 2D vdW magnetic materials creates exciting avenues for imprinting and tailoring topological properties at the atomic level in layered systems. Several compounds such CrGeTe3 have been explored, isolated and integrated in devices geometries9 which could be applied to the exploration of ultrafast spintronics. Our results suggest that even center-symmetric lattices but with sizeable non-collinear asymmetric exchange (e.g., DMI) in the second nearest-neighbors47 may be able to hold similar features. The ultrafast laser-induced heating of electrons in CrGeTe3 is able to trigger magnetization control which liaised with external magnetic fields create a spin switch mechanism. Different field polarisation also controls the polarity of the created spin textures (e.g., stripes, bubbles, skyrmions, anti-skyrmions) as we compare the final spin state with fields of different signs (Fig. 3). Indeed, the skyrmions are stable after removal of the magnetic field and can be switched back to the initial stripe pattern by exposing the material to the same number of pulses without applying any external field. This gives further flexibility to tune the spin configurations on-demand without constraint on the setup to be coupled to large magnets. The number of pulses N however still needs to be large relative to single-pulse toggle switch in 3D ferrimagnets62,64 in order to observe phase transformation of the magnetic textures (e.g., skyrmions into stripe domains, and/or vice-versa) or induce the initial formation of topologically non-trivial spin objects. Even though such difference could be seen as a limitation in terms of single-pulses applications, it suggests that if a 2D ferrimagnet could be isolated and chemically stabilised such system could potentially be probed using the guidelines demonstrated in our work. This opens a broad range of material possibilities to be explored where fast high-throughput screening can be used to select potential candidates. Moreover, to be able to write information and switch magnetization between different spin states as those demonstrated on CrGeTe3, the laser energy plays an important role. The challenge therefore is to find a balance where minimum energy fluence can be used whereas allowing efficient interaction between spins, light and crystal symmetry towards topological modifications. It is worth mentioning that the reversible topological switch mechanism reported here is different to that shown in Pt/CoFeB/MgO and Pt/Co systems65. On that, just one-way switching (either from a uniform magnetisation state, or stripe domains, into skyrmions, but not vice-versa) was found. In this aspect, the finding of a fully reversible topological spin switch based on a 2D vdW magnet without any interface issues or elaborate sample preparation presents as a leap onward writing/reading topological information. The natural next-step however is how to encode these magnetic objects with specific information (e.g., bytes) and read them afterwards. Much work is needed to fully explore the whole sets of switch phenomena at strictly 2D compounds.

Methods

Atomistic simulations

We model the system through atomistic spin dynamic simulations methods4,42,56. Spin interactions are described via Eq. (1) with parameters from ab initio calculations2. The Landau-Lifshitz-Gilbert (LLG) equation is used to describe the dynamics at different times and temperatures. The LLG equation is a differential equation that describes the precessional motion of magnetisation in a crystal. It is given by:

$$\frac{\partial {{{{{{{{\bf{S}}}}}}}}}_{i}}{\partial t}=-\frac{\gamma }{(1+{\lambda }^{2})}\left[{{{{{{{{\bf{S}}}}}}}}}_{i}\times {{{{{{{{\bf{B}}}}}}}}}_{{{{{{{{\rm{eff}}}}}}}}}^{i}+\lambda {{{{{{{{\bf{S}}}}}}}}}_{i}\times ({{{{{{{{\bf{S}}}}}}}}}_{i}\times {{{{{{{{\bf{B}}}}}}}}}_{{{{{{{{\rm{eff}}}}}}}}}^{i})\right]$$
(3)

where Si is a unit vector describing the spin moment orientation of site i. γ is the ratio of a spin’s magnetic moment to its angular momentum, known as the gyromagnetic ratio, and \({{{{{{{{\bf{B}}}}}}}}}_{{{{{{{{\rm{eff}}}}}}}}}^{i}\) is the effective net magnetic field. This effective field can be derived from the first derivative of the spin Hamiltonian:

$${{{{{{{{\bf{B}}}}}}}}}_{{{{{{{{\rm{eff}}}}}}}}}^{i}=-\frac{1}{{\mu }_{S}}\frac{\partial {{{{{{{\mathscr{H}}}}}}}}}{\partial {{{{{{{{\bf{S}}}}}}}}}_{i}}$$
(4)

where μS is the local spin moment. The Heun method is used to numerically integrate the LLG equation42.

Two-temperature model

The semiclassical two-temperature model (2TM)43,49 was utilised to simulate the thermal transport during the ultrafast laser heating on CrGeTe3. We previously modeled the laser-induced spin texture formation in CrCl343 using this technique. We did not observe any spin-toggle switch as that found in CrGeTe3, but rather the formation of merons or anti-merons from a homegeneous magnetic state. This suggests that the intrinsic magnetic properties of the vdW layer (e.g., easy-plane or easy-axis) play a role in the switching phenomena. The 2TM separates the temperature of the system into electron and phonon (lattice) contributions represented by Telec and Tphon, respectively. The model assumes that internal relaxations are faster then the coupling heat baths which allow to describe the interactions between lattice and electrons via coupled differential equations given by:

$$m\frac{\partial \overline{v}}{\partial t}+m\overline{v}\cdot {\nabla }_{r}\overline{v}+\left[{k}_{b}\left(1+\frac{{T}_{{{{{{{{\rm{elec}}}}}}}}}}{{C}_{e}}\frac{\partial {C}_{e}}{\partial {T}_{{{{{{{{\rm{elec}}}}}}}}}}\right)-e\beta \right]\nabla {T}_{{{{{{{{\rm{elec}}}}}}}}}=-\frac{e{T}_{{{{{{{{\rm{elec}}}}}}}}}\overline{v}}{{\mu }_{0}{T}_{{{{{{{{\rm{phon}}}}}}}}}}$$
(5)
$${C}_{e}\left(\frac{\partial {T}_{{{{{{{{\rm{elec}}}}}}}}}}{\partial t}+\overline{v}\cdot {\nabla }_{r}{T}_{{{{{{{{\rm{elec}}}}}}}}}+\frac{2}{3}{T}_{{{{{{{{\rm{elec}}}}}}}}}{\nabla }_{r}\cdot \overline{v}\right)+{\nabla }_{r}\cdot {\overline{Q}}_{e}=-G({T}_{{{{{{{{\rm{elec}}}}}}}}}-{T}_{{{{{{{{\rm{phon}}}}}}}}})+S(\overline{r},t)$$
(6)

where m is the electron mass, \(\overline{v}\) is the mean (drift) velocity vector, kb is the Boltzmann constant, Ce is the electron heat capacity constant, β is the electric field coefficient, e is the electron charge, μ0 is the mobility of electrons at room temperature, \({\overline{Q}}_{e}\) is the electronic heat flux, G is the electron-phonon coupling, and \(S(\overline{r},t)\) is the volumetric laser heat source. Equations (5)–(6) describe the conservation of momentum and energy in the electron subsystem. The description of the lattice is given by:

$${C}_{l}\frac{\partial {T}_{l}}{\partial t}=-\nabla \cdot {\overline{Q}}_{l}+G({T}_{e}-{T}_{l})$$
(7)

where Cl is the lattice heat capacity, and \({\overline{Q}}_{l}\) is the lattice heat flux. The coupling between lattice and electronic subsystems is given via:

$${\tau }_{e}\frac{\partial {\overline{Q}}_{e}}{\partial t}+{\overline{Q}}_{e}=-{K}_{e}\nabla {T}_{e}$$
(8)
$${\tau }_{l}\frac{\partial {\overline{Q}}_{l}}{\partial t}+{\overline{Q}}_{l}=-{K}_{l}\nabla {T}_{l}$$
(9)

where τe is the electron relaxation time, Ke is the electronic thermal conductivity coefficient, τl is the lattice relaxation time, and Kl is the lattice thermal conductivity coefficient. The parametrization of the 2TM is fitted accordingly to experimental magnetisation dynamics on CrGeTe3 and parent compounds66,67,68 as shown in Supplementary Table 3. The use of 2TM liaised with the LLG equation allows the simulations of systems for several nanoseconds (>8 ns) at large areas (e.g., 250 × 250 nm2) which are unpractical using other techniques, for instance, time-dependent density functional theory69 (TDDFT). Normally TDDFT is well suited for simulating attosecond to picosecond phenomena which occurred immediately after the photo-excitation of the system (i.e., charge transfer pathways)70. The time-step in such simulations is generally within the sub-attosecond timescale (1 attosecond = 10−18 s) as high-frequency fluctuations arise from the electron dynamics included in the time-dependent Kohn-Sham equation69. In our case however the critical equilibration where the topological spin textures are observed takes place long after the laser pulses (>1 ns), and no electronic effects are present apart from the thermal electronic bath provided via the 2TM. The sound agreement between the experimental results and the simulations indicates the LLG-2TM as a suitable approach to study photon-excitation in 2D magnets.

Topological number

Calculations of the topological charge have been used to identify different spin textures in the CrGeTe3. By convention skyrmions have a topological charge Nsk = − 1 while antiskyrmions have Nsk = + 1. Trivial bubbles have a trivial topological charge Nsk = 0, similarly as skyrmioniums. Note that the topological charge depends on both chirality and polarity; reversal of either will correspondingly reverse the sign of Nsk. In this convention a core-down, right-handed skyrmion has a topological charge of Nsk = − 1. In the continuum case the topological charge is defined as in Eq. (2). In the discrete approach, we calculate Nsk via the triangulation method37 where the spin texture lattice is partitioned into triangles involving the spins and the sum is evaluated over the whole surface. The calculation is performed 3 ns of relaxation after the laser pulse.

Samples

Single-crystalline CrGeTe3 (CGT) flakes were synthesized using the chemical vapor transport method. Elemental precursors of chromium (≥99.995%), germanium (≥99.999%), and tellurium (99.999%) in the molar ratio of Cr:Ge:Te = 10:13.5:76.5 were sealed in a thick-walled quartz ampule evacuated by the turbomolecular pump down to ~10-5 mbar. Excess tellurium was added as a flux. To ensure the high purity of the product, no other transport agents were used. Once sealed, the ampule was thoroughly shaken to mix the precursors. Then, the ampule was loaded into a horizontal two-zone annealing furnace with both zones slowly ramping to 950 °C. The ampule was kept at 950 °C for 1 week and then slowly cooled (0.4 °C/h) with a temperature gradient between two zones of the furnace. The gradient ensured the crystallization predominantly at the cold end of the ampule. Once the furnace reached 500 °C, the heaters at both zones were switched off allowing the furnace to cool naturally to room temperature. The crystals were extracted from the ampule under inert conditions and stored for future use. Our samples are ~ 1 mm thick, and 1.5 × 1.5 mm for lateral dimensions. Supplementary Figs. S3–S5 show the results for the characterisation on x-ray diffraction patterns, domain structures obtained via WFKM and hysteresis loop, respectively. Supplementary Movies S7 and S8 provide additional details on the measurements.

Microscopy

The measurements were performed by wide-field Kerr microscopy (WFKM) in a polar geometry to sense the out-of-plane magnetization in response to either a magnetic field or optical pulses. The sample illumination was linearly polarized, while polarization changes of the reflected light due to the polar Kerr effect were detected as intensity changes using a nearly crossed analyzer, quarter-waveplate, and high sensitivity CMOS camera. For switching experiments, an optical pump beam (1035 nm) with linear polarization and 300 fs pulse duration, 1 MHz repetition rate and different number of pulses N was incident at 45∘ to the sample plane and focused to a 100 μm diameter spot (intensity at 1/e2). Measurements were performed at temperatures ranging from 15 to 50 K. All images presented in this work are acquired for the final magnetization state which remains the same until the sample is exposed either to more optical pulses, or to an external magnetic field.