# Laser-induced topological spin switching in a 2D van der Waals magnet

Maya Khela1 Maciej Da̧browski2† Safe Khan3 Paul S. Keatley2 Ivan
Verzhbitskiy4,5 Goki Eda4,5 Robert J. Hicken2 Hidekazu Kurebayashi3,6,7 Elton
J. G. Santos1,8†

###### Abstract

Two-dimensional (2D) van der Waals (vdW) magnets represent one of the most
promising horizons for energy-efficient spintronic applications because their
broad range of electronic, magnetic and topological properties[1, 2, 3, 4, 5,
6, 7, 8]. Of particular interest is the control of the magnetic properties of
2D materials by femtosecond laser pulses which can provide a real path for
low-power consumption device platforms in data storage industries[9]. However,
little is known about the interplay between light and spin properties in vdW
layers. Here, combining large-scale spin dynamics simulations including
biquadratic exchange interactions[10, 11] and wide-field Kerr microscopy
(WFKM), we show that ultrafast laser excitation can not only generate
different type of spin textures in CrGeTe3 vdW magnets but also induce a
reversible transformation between them in a toggle-switch mechanism. Our
calculations show that skyrmions, anti-skyrmions, skyrmioniums and stripe
domains can be generated via high-intense laser pulses within the picosecond
regime. The effect is tunable with the laser energy where different spin
behaviours can be selected, such as fast demagnetisation process ($\sim$250
fs) important for information technologies. The phase transformation between
the different topological spin textures is obtained as additional laser pulses
are applied to the system where the polarisation and final state of the spins
can be controlled by external magnetic fields. We experimentally confirmed the
creation, manipulation and toggle switching phenomena in CrGeTe3 due to the
unique aspect of laser-induced heating of electrons. Our results indicate
laser-driven spin textures on 2D magnets as a pathway towards ultrafast
reconfigurable architecture at the atomistic level.

Institute for Condensed Matter Physics and Complex Systems, School of Physics
and Astronomy, The University of Edinburgh, EH9 3FD, United Kingdom

Department of Physics and Astronomy, University of Exeter, EX4 4QL, United
Kingdom

London Centre for Nanotechnology, University College London, 17-19 Gordon
Street, London, WCH1 0AH, UK

Department of Physics, National University of Singapore, Singapore, Singapore

Centre for Advanced 2D Materials and Graphene Research Centre, Singapore,
Singapore

Department of Electronic & Electrical Engineering, UCL, London WC1E 7JE,
United Kingdom

WPI Advanced Institute for Materials Research, Tohoku University, 2-1-1,
Katahira, Sendai, 980-8577, Japan

Higgs Centre for Theoretical Physics, The University of Edinburgh, EH9 3FD,
United Kingdom
†Corresponding author<EMAIL_ADDRESS><EMAIL_ADDRESS>
## 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 applications[12, 13, 14, 11, 15, 6, 16, 4,
1, 7, 8]. 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) devices[9, 17, 18] might provide a feasible pathway for faster
and low-power magneto-optical implementations. Previously demonstrated on
different compounds under ultrafast laser pulses[19, 20, 21, 22], 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 chirality[23, 24, 25]. In
particular, topologically non-trivial spin quasiparticles that can be erased,
nucleated and spatially manipulated as in writing and register-shifting of
logical bits[26, 6, 27, 28, 29, 30] 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
bubbles[11, 31, 32] and stripe domains[33], up to topological quasiparticles,
such as skyrmions[34, 35, 36, 37, 38, 39, 40] and merons[2, 41], as recently
summarised in the 2D Magnetic Genome[1]. 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 magnets[42, 43, 44], 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 approximation[11, 10, 5, 6, 2, 45] and wide-field Kerr microscopy
(WFKM) in a polar geometry[46] (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
materials[10]:

$\mathcal{H}=-\frac{1}{2}\,\sum_{i,j}\mathbf{S}_{i}\mathcal{J}_{ij}\mathbf{S}_{j}-\frac{1}{2}\,\sum_{i,j}K_{ij}\,(\mathbf{S}_{i}\,\cdot\mathbf{S}_{j}\>)^{2}-\sum_{i}D_{i}(\mathbf{S}_{i}\,\cdot\mathbf{e})^{2}-\sum_{i,j}\bm{A}_{ij}\cdot\left({\bf
S}_{i}\times{\bf
S}_{j}\right)-\sum_{i}\mu_{i}\mathbf{S}_{i}\,\cdot\mathbf{B_{dp}}$ (1)

where $i$, $j$ represent the atoms index, $\mathcal{J}_{ij}$ represents the
exchange tensor that for CrGeTe3 contains only the diagonal exchange terms,
$\bm{A}_{ij}$ is the Dzyaloshinskii-Moriya interaction (DMI), $K_{ij}$ is the
biquadratic exchange interaction[10], $D_{i}$ the uniaxial anisotropy, which
is orientated out of plane ($\mathbf{e}=(0,0,1)$), and $\mathbf{B_{dp}}$ is
the dipolar field calculated using the macrocell method[11]. The exchange
interactions for CrGeTe3 have been previously parameterized from first-
principles calculations[13] and contains up to three nearest neighbors. The
inclusion of biquadratic exchange[10], 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 magnets[2, 3] and thin
films[47]. 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 scattering[48] and ab initio[49] simulations,
respectively, resulting in $|\bm{A}_{ij}|\approx 0.31$ meV. The Landau-
Lifshitz-Gilbert (LLG) equation is used to describe the dynamics[10, 11] 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)[50, 45] (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

Figure 1b shows that as a short laser pulse is applied into the system at 100
ps, the electron ($T_{\rm elec}$) and phonon ($T_{\rm phon}$) reservoir
temperatures are substantially modified as time evolves. An initial sharp
increase of $T_{\rm elec}$ is observed within the sub-picosecond regime
($\sim$0.5 ps) taking the system above the Curie temperature $T_{\rm C}=68$
K[13]. $T_{\rm phon}$ follows the variation of $T_{\rm elec}$ 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 $T_{\rm elec}$ and $T_{\rm phon}$
towards equilibration. That is, the higher the fluence the larger the
stabilised temperatures. This affects directly how the magnetisation ($M_{\rm
z}/{M_{\rm s}}$) 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 $M_{\rm z}/{M_{\rm
s}}=0.75$ which rapidly recovers on the timescale of $\sim$4 ps. This
demagnetisation process can be classified as type-I dynamics as a single-step
demagnetization within the electron–phonon equilibration is achieved[51]. At
higher fluences (i.e., 0.2 mJ cm-2) there is an initial rapid demagnetisation
($M_{\rm z}/{M_{\rm s}}=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 dynamics[51]. Indeed, this result is in good agreement with recent
time-resolved magneto-optical Kerr effect measurements[42] 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 $N_{\rm sk}$ via[2, 52, 53]:

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

where ${\mathbf{n}}$ is the direction vector of magnetisation ${\bf M}$ (e.g.,
${\mathbf{n}}=\frac{\bf M}{|\bf M|}$), we identify the formation of skyrmions
($N_{\rm sk}=-1$) and anti-skyrmions ($N_{\rm sk}=+1$) of Bloch-type, and
skyrmioniums ($N_{\rm sk}=0$)[54, 49]. We estimated their diameters in the
range of $20-35$ nm using the magnetic parameters (e.g., exchange
interactions, anisotropies, DMI)[49, 48] available for CrGeTe3. It is worth
mentioning that these diameters can be changed with further optimisation of
the parameters as previously demonstrated[55]. This associated with the
limitations in length scale of the atomistic spin dynamics methods[56, 57]
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
$\sim$5.2 nm which follows those found in strong 2D ferromagnets such as
CrI3[11], CrBr3[6] and Fe3GeTe2[58, 3]. 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 overcome[55].

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 process[59, 60]. 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 droplets[61]. The nucleation of these
droplets at an early stage of the dynamics can be seen in Supplementary Figure
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 step[61] 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 $N_{\rm sk}$ 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.

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 $\sim$18.4 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/$\mathrm{cm^{2}}$) agrees on the
hybrid spin structures found for magnitudes above 0.30 mJ/$\mathrm{cm^{2}}$ 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 $N\leq 10$
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 phenomenon[61].
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 ($\sim$1$-2.90$ $\mu$m)
exceeded those calculated in the atomistic computations ($\sim$17$-29$ nm).
However, we have observed smaller spin textures (Supplementary Figure 4)
within the range of the simulations ($\sim 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 switch[17]. This AOS
process normally requires two magnetic states with equal energies where the
switching between them can be realised at a negligible heat
generation[Ultrafast_Optical_Manipulation, 62]. The switching however needs to
be reproducible and reversible in order to allow full writing of the magnetic
information[62, 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 (Figure 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 Figure 2 which provided a theoretical
background for our observations.

## 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 geometries[1] 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-neighbors[48] 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 ferrimagnets[62, Unai21] 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 systems[64]. 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

###  0.1 Atomistic simulations.

We model the system through atomistic spin dynamic simulations methods[11, 10,
57]. Spin interactions are described via Eq.1 with parameters from ab initio
calculations[13]. 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:

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

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

$\textbf{B}_{\mathrm{eff}}^{i}=-\frac{1}{\mu_{S}}\frac{\partial\mathcal{H}}{\partial\textbf{S}_{i}}$
(4)

where $\mu_{S}$ is the local spin moment. The Heun method is used to
numerically integrate the LLG equation[10].

###  0.2 Two-Temperature Model.

The semiclassical two-temperature model (2TM)[50, 45] was utilised to simulate
the thermal transport during the ultrafast laser heating on CrGeTe3. We
previously modeled the laser-induced spin texture formation in CrCl3[45] 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:

$m\frac{\partial\overline{v}}{\partial
t}+m\overline{v}\cdot\nabla_{r}\overline{v}+\left[k_{b}\left(1+\frac{T_{\rm
elec}}{C_{e}}\frac{\partial C_{e}}{\partial T_{\rm
elec}}\right)-e\beta\right]\nabla T_{\rm elec}=-\frac{eT_{\rm
elec}\overline{v}}{\mu_{0}T_{\rm phon}}$ (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, $k_{b}$ is the Boltzmann constant, $C_{e}$ is the electron heat
capacity constant, $\beta$ is the electric field coefficient, $e$ is the
electron charge, $\mu_{0}$ 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 $C_{l}$ 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 $\tau_{e}$ is the electron relaxation time, $K_{e}$ is the electronic
thermal conductivity coefficient, $\tau_{l}$ is the lattice relaxation time,
and $K_{l}$ is the lattice thermal conductivity coefficient. The
parametrization of the 2TM is fitted accordingly to experimental magnetisation
dynamics on CrGeTe3 and parent compounds[65, 66, 67] 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
$\times$ 250 nm2) which are unpractical using other techniques, for instance,
time-dependent density functional theory[68] (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)[69]. 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
equation[68]. 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.

###  0.3 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 $N_{\rm sk}=-1$ while antiskyrmions have $N_{\rm sk}=+1$. Trivial
bubbles have a trivial topological charge $N_{\rm sk}=0$, similarly as
skyrmioniums. Note that the topological charge depends on both chirality and
polarity; reversal of either will correspondingly reverse the sign of $N_{\rm
sk}$. In this convention a core-down, right-handed skyrmion has a topological
charge of $N_{\rm sk}=-1$. In the continuum case the topological charge is
defined as in Eq.2. In the discrete approach, we calculate $N_{\rm sk}$ via
the triangulation method[2] 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.

###  0.4 Samples

Single-crystalline CrGeTe3 (CGT) flakes were synthesized using the chemical
vapor transport method. Elemental precursors of chromium ($\geq 99.995\%$),
germanium ($\geq 99.999\%$), 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 $\sim$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 oC. The ampule was kept at 950
oC for 1 week and then slowly cooled (0.4 oC/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 oC,
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 $\sim$1 mm
thick, and 1.5 $\times$ 1.5 mm for lateral dimensions. Supplementary Figures
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.

###  0.5 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 $\mu$m diameter
spot (intensity at $1/e^{2}$). Measurements were performed at temperatures
ranging from 15 - 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.

## Data Availability

The data that support the findings of this study are available within the
paper, Supplementary Information and upon reasonable request.

## References

## References

  * [1] Wang, Q. H. _et al._ The magnetic genome of two-dimensional van der waals materials.  _ACS Nano_ 16, 6960–7079 (2022).
  * [2] Augustin, M., Jenkins, S., Evans, R. F. L., Novoselov, K. S. & Santos, E. J. G.  Properties and dynamics of meron topological spin textures in the two-dimensional magnet CrCl3.  _Nature Communications_ 12, 185 (2021).  URL https://doi.org/10.1038/s41467-020-20497-2.
  * [3] Macy, J. _et al._ Magnetic field-induced non-trivial electronic topology in Fe3-xGeTe2.  _Appl. Phys. Rev._ 8, 041401 (2021).
  * [4] Alliati, M., Evans, R. F. L., Novoselov, K. S. & Santos, E. J. G.  Relativistic domain-wall dynamics in van der waals antiferromagnet mnps3.  _npj Comput. Mater._ 8, 3 (2022).
  * [5] Alliati, I. M., Evans, R. F. L., Novoselov, K. S. & Santos, E. J. G.  Relativistic domain-wall dynamics in van der Waals antiferromagnet MnPS3.  _npj Computational Materials_ 8, 3 (2022).  URL https://doi.org/10.1038/s41524-021-00683-6.
  * [6] Abdul-Wahab, D. _et al._ Domain wall dynamics in two-dimensional van der Waals ferromagnets.  _Appl. Phys. Rev._ 8, 041411 (2021).
  * [7] Jenkins, S. _et al._ Breaking through the mermin-wagner limit in 2d van der waals magnets.  _Nature Communications_ 13, 6917 (2022).
  * [8] Kurebayashi, H., Garcia, J. H., Khan, S., Sinova, J. & Roche, S.  Magnetism, symmetry and spin transport in van der waals layered systems.  _Nature Reviews Physics_ 4, 150–166 (2022).
  * [9] Kimel, A., Kirilyuk, A. & Rasing, T.  Femtosecond opto-magnetism: ultrafast laser manipulation of magnetic materials.  _Laser & Photonics Reviews_ 1, 275–287 (2007).
  * [10] Kartsev, A., Augustin, M., Evans, R. F., Novoselov, K. S. & Santos, E. J.  Biquadratic exchange interactions in two-dimensional magnets.  _npj Computational Materials_ 6, 1–11 (2020).
  * [11] Wahab, D. A. _et al._ Quantum rescaling, domain metastability, and hybrid domain-walls in 2d cri3 magnets.  _Advanced Materials_ 33, 2004138 (2021).
  * [12] Huang, B. _et al._ Layer-dependent ferromagnetism in a van der waals crystal down to the monolayer limit.  _Nature_ 546, 270–273 (2017).
  * [13] Gong, C. _et al._ Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals.  _Nature_ 546, 265–269 (2017).  URL https://doi.org/10.1038/nature22060.
  * [14] Guguchia, Z. _et al._ Magnetism in semiconducting molybdenum dichalcogenides.  _Sci. Adv._ 4 (2018).  URL https://advances.sciencemag.org/content/4/12/eaat3672.  https://advances.sciencemag.org/content/4/12/eaat3672.full.pdf.
  * [15] Meseguer-Sánchez, J. _et al._ Coexistence of structural and magnetic phases in van der Waals magnet CrI3.  _Nat. Commun._ 12, 6265 (2021).
  * [16] Cantos-Prieto, F. _et al._ Layer-dependent mechanical properties and enhanced plasticity in the van der waals chromium trihalide magnets.  _Nano Lett._ 21, 3379–3385 (2021).  URL https://doi.org/10.1021/acs.nanolett.0c04794.  https://doi.org/10.1021/acs.nanolett.0c04794.
  * [17] Kimel, A., Kalashnikova, A., Pogrebna, A. & Zvezdin, A.  Fundamentals and perspectives of ultrafast photoferroic recording.  _Physics Reports_ 852, 1–46 (2020).
  * [18] Dabrowski, M. _et al._ All-optical control of spin in a 2d van der waals magnet.  _Nature Communications_ 13, 5976 (2022).
  * [19] Hansteen, F., Kimel, A., Kirilyuk, A. & Rasing, T.  Femtosecond photomagnetic switching of spins in ferrimagnetic garnet films.  _Phys. Rev. Lett._ 95, 047402 (2005).  URL https://link.aps.org/doi/10.1103/PhysRevLett.95.047402.
  * [20] Ostler, T. _et al._ Ultrafast heating as a sufficient stimulus for magnetization reversal in a ferrimagnet.  _Nature communications_ 3, 1–6 (2012).
  * [21] Mangin, S. _et al._ Engineered materials for all-optical helicity-dependent magnetic switching.  _Nature Materials_ 13, 286–292 (2014).
  * [22] Lambert, C.-H. _et al._ All-optical control of ferromagnetic thin films and nanostructures.  _Science_ 345, 1337–1340 (2014).
  * [23] Lalieu, M. L. M., Lavrijsen, R. & Koopmans, B.  Integrating all-optical switching with spintronics.  _Nature Communications_ 10, 110 (2019).
  * [24] Aiello, C. D. _et al._ A chirality-based quantum leap.  _ACS Nano_ 16, 4989–5035 (2022).
  * [25] Zayko, S. _et al._ Ultrafast high-harmonic nanoscopy of magnetization dynamics.  _Nature Communications_ 12, 6337 (2021).
  * [26] Fert, A., Cros, V. & Sampaio, J.  Skyrmions on the track.  _Nature Nanotechnology_ 8, 152–156 (2013).
  * [27] Büttner, F. _et al._ Field-free deterministic ultrafast creation of magnetic skyrmions by spin–orbit torques.  _Nature Nanotechnology_ 12, 1040–1044 (2017).
  * [28] Parkin, S. S. P., Hayashi, M. & Thomas, L.  Magnetic domain-wall racetrack memory.  _Science_ 320, 190–194 (2008).
  * [29] Kent, A. D. & Worledge, D. C.  A new spin on magnetic memories.  _Nature Nanotechnology_ 10, 187–191 (2015).
  * [30] Dai, Y. _et al._ Ultrafast microscopy of a twisted plasmonic spin skyrmion.  _Applied Physics Reviews_ 9, 011420 (2022).
  * [31] Gao, Y. _et al._ Manipulation of topological spin configuration via tailoring thickness in van der waals ferromagnetic ${\mathrm{fe}}_{5\text{$-$}x}\mathrm{Ge}{\mathrm{te}}_{2}$.  _Phys. Rev. B_ 105, 014426 (2022).  URL https://link.aps.org/doi/10.1103/PhysRevB.105.014426.
  * [32] Sun, Q.-C. _et al._ Magnetic domains and domain wall pinning in atomically thin crbr3 revealed by nanoscale imaging.  _Nature Communications_ 12, 1989 (2021).
  * [33] Fujita, R. _et al._ Layer-dependent magnetic domains in atomically thin fe5gete2.  _ACS Nano_ 16, 10545–10553 (2022).
  * [34] Han, M.-G. _et al._ Topological magnetic-spin textures in two-dimensional van der waals cr2ge2te6.  _Nano Letters_ 19, 7859–7865 (2019).
  * [35] Ding, B. _et al._ Observation of magnetic skyrmion bubbles in a van der waals ferromagnet fe3gete2.  _Nano Letters_ 20, 868–873 (2020).
  * [36] Park, T.-E. _et al._ Neel-type skyrmions and their current-induced motion in van der waals ferromagnet-based heterostructures.  _Phys. Rev. B_ 103, 104410 (2021).
  * [37] Chen, J. _et al._ Evidence for magnetic skyrmions at the interface of ferromagnet/topological-insulator heterostructures.  _Nano Letters_ 19, 6144–6151 (2019).
  * [38] Huang, K., Shao, D.-F. & Tsymbal, E. Y.  Ferroelectric control of magnetic skyrmions in two-dimensional van der waals heterostructures.  _Nano Letters_ 22, 3349–3355 (2022).
  * [39] Li, D., Haldar, S. & Heinze, S.  Strain-driven zero-field near-10 nm skyrmions in two-dimensional van der waals heterostructures.  _Nano Letters_ 22, 7706–7713 (2022).
  * [40] Li, C.-K., Yao, X.-P. & Chen, G.  Writing and deleting skyrmions with electric fields in a multiferroic heterostructure.  _Phys. Rev. Res._ 3, L012026 (2021).
  * [41] Gao, Y. _et al._ Spontaneous (anti)meron chains in the domain walls of van der waals ferromagnetic fe5xgete2.  _Advanced Materials_ 32, 2005228 (2020).
  * [42] Sun, T. _et al._ Ultra-long spin relaxation in two-dimensional ferromagnet cr2ge2te6 flake.  _2D Materials_ 8, 045040 (2021).
  * [43] Lichtenberg, T. _et al._ Anisotropic laser-pulse-induced magnetization dynamics in van der waals magnet fe3gete2.  _arXiv:2206.01452_ (2022).  URL https://arxiv.org/abs/2206.01452.
  * [44] Afanasiev, D. _et al._ Controlling the anisotropy of a van der waals antiferromagnet with light.  _Science Advances_ 7, eabf3096 (2021).
  * [45] Strungaru, M., Augustin, M. & Santos, E. J. G.  Ultrafast laser-driven topological spin textures on a 2d magnet.  _npj Computational Materials_ 8, 169 (2022).
  * [46] Dabrowski, M. _et al._ Transition metal synthetic ferrimagnets: Tunable media for all-optical switching driven by nanoscale spin current.  _Nano Letters_ 21, 9210–9216 (2021).
  * [47] Paul, S., Haldar, S., von Malottki, S. & Heinze, S.  Role of higher-order exchange interactions for skyrmion stability.  _Nature Communications_ 11, 4756 (2020).
  * [48] Zhu, F. _et al._ Topological magnon insulators in two-dimensional van der waals ferromagnets crsite3 and crgete3: Toward intrinsic gap-tunability.  _Science Advances_ 7, eabi7532 (2021).
  * [49] Zhang, Y. _et al._ Emergence of skyrmionium in a two-dimensional ${\mathrm{crge}(\mathrm{se},\mathrm{te})}_{3}$ janus monolayer.  _Phys. Rev. B_ 102, 241107 (2020).  URL https://link.aps.org/doi/10.1103/PhysRevB.102.241107.
  * [50] Chen, J., Tzou, D. & Beraun, J.  A semiclassical two-temperature model for ultrafast laser heating.  _International Journal of Heat and Mass Transfer_ 49, 307–316 (2006).
  * [51] Koopmans, B. _et al._ Explaining the paradoxical diversity of ultrafast laser-induced demagnetization.  _Nature Materials_ 9, 259–265 (2010).  URL https://doi.org/10.1038/nmat2593.
  * [52] Eriksson, F.  On the measure of solid angles.  _Mathematics Magazine_ 63, 184–187 (1990).  URL https://doi.org/10.1080/0025570X.1990.11977515.  https://doi.org/10.1080/0025570X.1990.11977515.
  * [53] Rózsa, L., Simon, E., Palotás, K., Udvardi, L. & Szunyogh, L.  Complex magnetic phase diagram and skyrmion lifetime in an ultrathin film from atomistic simulations.  _Phys. Rev. B_ 93, 024417 (2016).  URL https://link.aps.org/doi/10.1103/PhysRevB.93.024417.
  * [54] Finazzi, M. _et al._ Laser-induced magnetic nanostructures with tunable topological properties.  _Phys. Rev. Lett._ 110, 1–5 (2013).  1304.1754.
  * [55] Wang, X. S., Yuan, H. Y. & Wang, X. R.  A theory on skyrmion size.  _Communications Physics_ 1, 31 (2018).  URL https://doi.org/10.1038/s42005-018-0029-0.
  * [56] Etz, C., Bergqvist, L., Bergman, A., Taroni, A. & Eriksson, O.  Atomistic spin dynamics and surface magnons.  _Journal of Physics: Condensed Matter_ 27, 243202 (2015).
  * [57] Evans, R. F. L. _et al._ Atomistic spin model simulations of magnetic nanomaterials.  _Journal of Physics: Condensed Matter_ 26, 103202 (2014).  URL https://doi.org/10.1088/0953-8984/26/10/103202.
  * [58] Yang, H.-H. _et al._ Magnetic domain walls of the van der waals material fe3gete2.  _2D Materials_ 9, 025022 (2022).
  * [59] Kazantseva, N., Nowak, U., Chantrell, R. W., Hohlfeld, J. & Rebei, A.  Slow recovery of the magnetisation after a sub-picosecond heat pulse.  _EPL (Europhysics Letters)_ 81, 27004 (2008).  URL https://iopscience.iop.org/article/10.1209/0295-5075/81/27004.
  * [60] Barker, J. _et al._ Two-magnon bound state causes ultrafast thermally induced magnetisation switching.  _Scientific Reports_ 3, 3262 (2013).
  * [61] Maiden, M. D., Bookman, L. D. & Hoefer, M. A.  Attraction, merger, reflection, and annihilation in magnetic droplet soliton scattering.  _Phys. Rev. B_ 89, 180409 (2014).  URL https://link.aps.org/doi/10.1103/PhysRevB.89.180409.
  * [62] Kimel, A. V. & Li, M.  Writing magnetic memory with ultrashort light pulses.  _Nature Reviews Materials_ 4, 189–200 (2019).
  * [63] Liu, T.-M. _et al._ Nanoscale confinement of all-optical magnetic switching in tbfeco - competition with nanoscale heterogeneity.  _Nano Letters_ 15, 6862–6868 (2015).
  * [64] Büttner, F. _et al._ Observation of fluctuation-mediated picosecond nucleation of a topological phase.  _Nature Materials_ 20, 30–37 (2021).
  * [65] Selter, S., Bastien, G., Wolter, A. U. B., Aswartham, S. & Büchner, B.  Magnetic anisotropy and low-field magnetic phase diagram of the quasi-two-dimensional ferromagnet ${\mathrm{cr}}_{2}{\mathrm{ge}}_{2}{\mathrm{te}}_{6}$.  _Phys. Rev. B_ 101, 014440 (2020).  URL https://link.aps.org/doi/10.1103/PhysRevB.101.014440.
  * [66] Suo, P. _et al._ Terahertz Emission on the Surface of a van der Waals Magnet CrSiTe3.  _Laser & Photonics Reviews_ 14, 2000025 (2020).  URL https://onlinelibrary.wiley.com/doi/abs/10.1002/lpor.202000025.  _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/lpor.202000025.
  * [67] Sadasivam, S., Chan, M. K. Y. & Darancet, P.  Theory of Thermal Relaxation of Electrons in Semiconductors.  _Physical Review Letters_ 119, 136602 (2017).  URL http://arxiv.org/abs/1709.00451.  ArXiv: 1709.00451.
  * [68] Runge, E. & Gross, E. K. U.  Density-functional theory for time-dependent systems.  _Phys. Rev. Lett._ 52, 997–1000 (1984).
  * [69] Provorse, M. R. & Isborn, C. M.  Electron dynamics with real-time time-dependent density functional theory.  _International Journal of Quantum Chemistry_ 116, 739–749 (2016).

## Acknowledgement

M.D., P.S.K. and R.J.H. gratefully acknowledge the support of the Engineering
and Physical Sciences Research Council (EPSRC) through grants EP/V054112/1 and
EP/V048538/1. H.K. acknowledges support from EPSRC on EP/T006749/1. G.E.
acknowledges support from the Ministry of Education (MOE), Singapore, under
AcRF Tier 3 (MOE2018-T3-1-005) and the Singapore National Research Foundation
for funding the research under medium-sized centre program. EJGS acknowledges
computational resources through CIRRUS Tier-2 HPC Service (ec131 Cirrus
Project) at EPCC (http://www.cirrus.ac.uk) funded by the University of
Edinburgh and EPSRC (EP/P020267/1); ARCHER UK National Supercomputing Service
(http://www.archer.ac.uk) via Project d429, and the UKCP consortium (Project
e89) funded by EPSRC grant ref EP/P022561/1. EJGS acknowledge the Spanish
Ministry of Science’s grant program “Europa-Excelencia” under grant number
EUR2020-112238, and the EPSRC Open Fellowship (EP/T021578/1) for funding
support. For the purpose of open access, the author has applied a Creative
Commons Attribution (CC BY) licence to any Author Accepted Manuscript version
arising from this submission.

#### Author Contributions

E.J.G.S., H.K. and R.H. conceived the project. M.K. performed the simulations
under the supervision of E.J.G.S. M.D., S.K. and P.S.K. performed the
experiments. M.D., S.K., R.H., H.K., E.J.G.S. analysed the experimental data.
I.V. and G.E. provided the samples and characterisation. E.J.G.S. wrote the
paper with inputs from all authors. All authors contributed to this work, read
the manuscript, discussed the results, and agreed on the included contents.

## Competing interests

The authors declare no competing interests.

Figure 1:  Laser-induced demagnetisation processes and spin textures. a,
Schematic of the ultrafast laser pulses with linear polarisation $\pi$ on
CrGeTe3. b, Evolution of the electronic ($T_{\rm elec}$) and phonon ($T_{\rm
phon}$) 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 $M_{\rm z}$/$M_{\rm s}$ 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 ($M_{\rm z}$) 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 $N_{\rm sk}=+1$ (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.  Figure 2: Fluence-dependent spin
textures. a, Final topological charge ($N_{\rm sk}$) 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
($M_{\rm z}=1$) 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 $M_{\rm z}$ 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
$\mu$m and the laser fluence is 16 mJ/$\mathrm{cm^{2}}$. The measurements were
performed at 18.5 K. A 25 mT magnetic field is used.  Figure 3: Light-induced
spin toggle switch. 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 d 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 $\mu$m and the laser fluence
is 16 mJ/$\mathrm{cm^{2}}$. The measurements were performed at 18.5 K.