# Optical creation and annihilation of skyrmion patches in a bulk chiral
magnet

J. Kalin∗<EMAIL_ADDRESS>Physikalisch-Technische Bundesanstalt, 38116
Braunschweig, Germany  D. Kalin  ESE Engineering und Software-Entwicklung
GmbH, 38122 Braunschweig, Germany  S. Sievers  Physikalisch-Technische
Bundesanstalt, 38116 Braunschweig, Germany  A. Bauer  Physik-Department,
Technische Universität München, 85748 Garching, Germany  Zentrum für
QuantumEngineering (ZQE), Technische Universität München, 85748 Garching,
Germany  H. W. Schumacher  Physikalisch-Technische Bundesanstalt, 38116
Braunschweig, Germany  R. Abram  Physikalisch-Technische Bundesanstalt, 38116
Braunschweig, Germany  H. Füser  Physikalisch-Technische Bundesanstalt, 38116
Braunschweig, Germany  C. Pfleiderer  Physik-Department, Technische
Universität München, 85748 Garching, Germany  Zentrum für QuantumEngineering
(ZQE), Technische Universität München, 85748 Garching, Germany  Munich Center
for Quantum Science and Technology (MCQST), Technische Universität München,
85748 Garching, Germany  M. Bieler  Physikalisch-Technische Bundesanstalt,
38116 Braunschweig, Germany

###### Abstract

A key challenge for the realization of future skyrmion devices comprises the
controlled creation, annihilation and detection of these topologically non-
trivial magnetic spin textures. In this study, we report an all-optical
approach for writing, deleting, and reading skyrmions in the cubic chiral
magnet Fe0.25Co0.75Si based on thermal quenching. Using focused femtosecond
laser pulses, patches of a skyrmion state are created and annihilated locally,
demonstrating unprecedented control of thermally metastable skyrmions in a
bulk compound. The skyrmion state is read-out by analyzing the microwave spin
excitations in time-resolved magneto-optical Kerr effect measurements.
Extracting the magnetic field and laser fluence dependence, we find well-
separated magnetic field regimes and different laser fluence thresholds for
the laser-induced creation and annihilation of metastable skyrmions. The all-
optical skyrmion control, as established in this study for a model system,
represents a promising and energy-efficient approach for the realization of
skyrmions as magnetic bits in future storage devices, reminiscent of magneto-
optical storage devices in the past.

The formation of skyrmions, nanometer-sized magnetic whirls, from a
topologically trivial state requires topological winding to build up the
skyrmion’s inherent spin structure. Consequently, once formed skyrmions tend
to be remarkably robust, characterized by high topological energy barrier and
long characteristic time scale for skyrmion unwinding. In cubic chiral
magnets, skyrmions are typically observed as an equilibrium state within a
narrow parameter range of the magnetic phase diagram at temperatures just
below the onset of long-ranged magnetic order. However, the large
characteristic time scales for skyrmion unwinding allows to create a
metastable skyrmion state across larger parts of the phase diagram by thermal
quenching [2, 3, 4, 5, 6, 7, 8, 9, 10]. Also in ferromagnetic multilayer
systems, where skyrmions may often not emerge as equilibrium states, a
metastable skyrmion state can be induced [11, 12, 13, 14, 15, 16, 17]. Most
notably, skyrmions may be locally created in such multilayer systems by the
irradiation with multiple [18] or even single femtosecond (fs) laser pulses
[19, 20, 21]. Thus, the focused laser light triggers topological winding in
this material class, which is commonly explained by lowering the topological
energy barrier by laser excitation [19, 13]. So far, the laser-induced
creation of skyrmions has only been demonstrated in multilayer and thin-film
systems [18, 20, 19, 21, 22, 23]. In bulk compounds of cubic chiral magnets no
laser writing of skyrmions has been achieved to date. Furthermore, the inverse
process, laser-induced skyrmion annihilation, is largely unexplored and laser
writing experiments have not yet been combined with optical readout
techniques. However, this presents the possibility of fast and energy-
efficient all-optical skyrmion devices, where the operations of writing,
deleting, and reading can be accomplished using optical means.

In this Letter, we explore the all-optical control of the metastable skyrmion
lattice state (MSkL) in a bulk sample of the cubic chiral magnet
Fe0.25Co0.75Si. By reading out the magnetic state in time-resolved magneto-
optical Kerr effect (TR-MOKE) measurements, we systematically track the
creation and annihilation of MSkL patches after the irradiation with multiple
fs laser pulses and subsequent cryogenic cooling. We find laser-induced MSkL
creation and annihilation in distinct and well-separated magnetic field
regimes for different laser fluence thresholds, reflecting the distinct
temperature regimes for the stabilization and destabilization of the MSkL.
Overall, this study demonstrates the feasibility of all-optical skyrmion read-
write-delete operations within a single experimental framework.

Fe0.25Co0.75Si exhibits the generic magnetic phase diagram of cubic chiral
magnets [3], displayed in Fig. 1(a). While being a paramagnet for temperatures
above the ordering temperature ${T_{\text{c}}=39\,\text{K}}$, magnetic order
sets in for $T<T_{\text{c}}$ comprising long-range helimagnetism (H), conical
order, and a field-aligned (FA) state under increasing magnetic field [24].
Most importantly, in a limited temperature and magnetic field range just below
$T_{\text{c}}$, a hexagonal lattice of skyrmions [25] is observed, which we
refer to as an equilibrium skyrmion lattice state (SkL). Previous studies
established that thermal quenching under magnetic fields crossing the SkL may
avoid the equilibrium phase transition between the skyrmion lattice and
conical state kinetically, resulting in a MSkL extending over large parts of
the magnetic phase diagram, see Fig. 1(b). The lifetime of the MSkL,
representing the characteristic time scale for MSkL unwinding, is
exponentially dependent on temperature and significantly influenced by the
applied magnetic field [31]. When the magnetic field is outside the SkL range,
an increase in temperature gradually induces the decay of the MSkL through
skyrmion unwinding on experimentally relevant time scales. This thermal
destabilization of the MSkL results in the full transition to the conical
state at $T_{\text{con}}$, see Fig. 1(b). So far, for cubic chiral magnets
MSkL was realized by thermal quenching of the entire sample [6, 3, 8, 5, 26],
leading to a homogenous MSkL that extends over the whole crystal. This was
achieved through techniques such as rapid field cooling [6, 3, 8], where the
sample is cooled at high cooling rates from temperatures above $T_{\text{c}}$
to lower temperatures using cryogenic temperature control. When magnetic
fields outside the SkL field regime are applied during this cooldown, the
equilibrium conical state forms. However, for magnetic fields within the SkL,
the rapid cooling results in the formation of the MSkL.

In a recent study [9], it was established that the TR-MOKE measurements of
out-of-plane magnetization dynamics serve a sensitive probe for MSkL
detection. While the equilibrium conical state, see upper panel in Fig. 1(c),
exhibit a non-oscillatory de- and remagnetization characteristic, in the MSkL,
under the same magnetic field and temperature, the skyrmion breathing mode
[27, 28, 29] is observed as a precessional signal, see lower panel in Fig.
1(c). In this work, we adopt this approach to study laser-induced MSkL
creation and annihilation by performing TR-MOKE measurements in a pump-probe
experiment. To that end, we apply laser pulses of about
${\tau_{\text{pulse}}=150\,\text{fs}}$ duration with photon wavelength of
${\lambda=800\,\text{nm}}$ and a repetition rate of ${G=76\,\text{MHz}}$. The
concentrical pump pulses with focal $1/e^{2}$ radius of
${w_{L}=60\,\mu\text{m}}$ and probe pulses with focal $1/e^{2}$ radius of
${30\,\mu\text{m}}$ are focused under near normal incidence onto the surface
of the sample. The latter is located in an optical cryostat with the magnetic
field pointing out-of the sample plane. The linearly polarized pump beam
thermally triggers the magnetization dynamics of the sample. The dynamics is
detected by the polarization change of the reflected probe beam as induced by
the magneto-optical Kerr effect (MOKE), i.e., by measuring the Kerr rotation
$\Delta\phi_{k}$ in a stroboscopic manner as a function of the time delay
between probe and pump beam $\tau_{\text{delay}}$. The measurement technique
is discussed in more detail in Ref. [9]. In this study, the laser fluence is
quantified by the peak fluence of the Gaussian laser beam profile absorbed by
the sample. For a non-invasive detection of the magnetic states we choose the
lowest possible pump laser fluence for the TR-MOKE measurements
${F=2.2\,\mu\text{Jcm}^{-2}}$ to limit the temperature increase by steady
state heating to about ${5\,\text{K}}$.

Figure 1:  Schematic magnetic phase diagram of Fe0.25Co0.75Si (a) in thermal
equilibrium and (a) following thermal quenching through the SkL. (c)
Characteristic out-of-plane magnetization dynamics of the equilibrium conical
state (top panel) and the MSkL (bottom panel) measured in TR-MOKE experiments
as Kerr angle change ($\Delta\phi_{k}$) as a function of the time delay
between pump and probe beam $\tau_{\text{delay}}$.

Complementing the observation of a MSkL after homogeneous rapid field cooling
of cubic chiral magnets in previous studies, a local heating process was
implemented in terms of a series of high-fluence fs laser pulses in this
study. The cumulative heat load of the laser pulses leads to a local increase
of the sample temperature in a spatially confined volume in the vicinity of
the laser focal spot, which is much smaller than the sample dimension of
${(2\times 2\times 2)\,\text{mm}^{3}}$, see thermal simulations in Ref. [30].
Experimentally, this condition is realized by increasing the laser fluence of
the TR-MOKE pump beam for less than a second. After reducing the laser fluence
again, the local temperature increase is rapidly compensated by the thermal
reservoir provided by the cryostat resulting in a fast and local cryogenic
sample cooling. As a first implementation test of this local heating process,
we start in the conical state at ${13\,\text{K}}$ and ${55\,\text{mT}}$, see
circle in Fig. 1(a), and apply high-fluence laser pulses of
${F=13\,\mu\text{Jcm}^{-2}}$ to the sample. After the high-fluence laser
irradiation and subsequent cryogenic cooling, the magnetic state is probed
spatially-resolved in TR-MOKE experiments. Figure 2(a) exemplarily shows
magnetization dynamics at four sample positions with different distances $d$
to the center of the laser irradiation spot. While for large distances,
${d=240\mu\text{m}}$, we observe the characteristic dynamics of the initial
conical state, in proximity to the irradiation spot the precessional dynamics
of the skyrmion breathing mode emerge. With increasing distance, the
magnetization dynamics gradually evolve from the characteristic behavior of
the MSkL to that of the conical state. This result shows that local laser
irradiation of the sample can drive a conical-to-MSkL transition in a confined
area and thus permits the laser-induced creation of a skyrmion patch in a bulk
chiral magnet. By that, we are able to locally create a thermodynamically
metastable state with non-trivial topology, which persists over long time
scales (${>12\,\text{h}}$, not shown) and is embedded in a topologically
trivial equilibrium phase. This laser-written state shows a comparable
magnetic field and temperature stability as the homogeneous MSkL created by
rapid field cooling [30], demonstrating the high robustness of the spatially
confined MSkL. As we observe the laser-induced magnetic phase transition only
for magnetic fields in the regime of the SkL [30], we attribute the formation
of the laser-written MSkL to local thermal quenching of the equilibrium SkL by
laser heating.

Using a similar approach, the inverse process can be achieved: laser-induced
MSkL annihilation. Following the formation of a spatially homogeneous MSkL by
means of rapid field cooling to ${13\,\text{K}}$, the magnetization dynamics
are studied after irradiation with high-fluence laser pulses and subsequent
cryogenic cooling at ${70\,\text{mT}}$, i.e., at a magnetic field above the
SkL pocket, see circle in Fig. 1(b). In a situation reverse to laser-induced
MSkL creation, we observe a local formation of the conical state in proximity
to the irradiation spot, as shown in Fig. 2(b). Dynamics characteristic of the
initial MSkL is detected far from the laser irradiation spot, continuously
evolving into the dynamics of the conical state with decreasing distance. As
anticipated from the phase diagram in Fig. 1(b), a switching from MSkL to the
conical state after laser irradiation occurs exclusively for magnetic field
values outside the equilibrium SkL [30]. Consequently, we attribute the laser-
induced annihilation of the MSkL to its thermal destabilization by laser
heating. In line with our understanding of MSkL creation in the field regime
of the equilibrium SkL, the MSkL persists after intense laser irradiation
within this regime Thus, laser-induced MSkL creation and annihilation takes
place in well-defined and separated magnetic field regimes, allowing selective
optical writing and deleting of MSkL controlled by the applied magnetic field.
From an application point of view, this might enable all-optical MSkL creation
and annihilation sequences with readout operation without the need of rapid
temperature control and extensive magnetic field sweeps.

Figure 2:  Spatially resolved magnetization dynamics of Fe0.75Co0.25Si after
laser-induced MSkL creation (${55\,\text{mT}}$) and annihilation
(${70\,\text{mT}}$) at ${13\,\text{K}}$: (a) and (b) Magnetization dynamics
measured by TR-MOKE at different distances $d$ from the irradiation spot. The
solid lines represent fits to the experimental data using Eq. (1). (c) and (d)
MSkL ratio ${x_{\text{MSkL}}}$ in the probed area as a function of distance to
the irradiation spot for laser-induced MSkL creation and annihilation after
irradiation with different laser fluences. The solid lines represent fits to
the experimental data using the model introduced in the main text.

The results presented so far demonstrate that laser-induced MSkL creation and
annihilation leads to a gradual phase transition in space. The spatially
resolved measurements can be modeled by a linear superposition of the conical,
$\Delta\phi_{k,\text{conical}}$, and MSkL contributions,
$\Delta\phi_{k,\text{MSkL}}$, to the measured signal

$\Delta\phi_{k}(\tau_{\text{delay}})=x_{\text{MSkL}}\cdot\Delta\phi_{k,\text{MSkL}}(\tau_{\text{delay}})+\left(1-x_{\text{MSkL}}\right)\cdot\Delta\phi_{k,\text{conical}}(\tau_{\text{delay}}).$
((1))

The MSkL ratio ${x_{\text{MSkL}}}$ describes the areal percentage of MSkL in
the probed region, as the TR-MOKE technique averages over magnetization
dynamics in the probed area. The line plots in Figs. 2(a) and 2(b) are fits to
the experimental data using Eq. (1) with ${x_{\text{MSkL}}}$ as fitting
parameter, in excellent agreement with the data. By plotting
${x_{\text{MSkL}}}$ as a function of distance $d$ from the laser irradiation
spot, as shown in Fig. 2 (c) and 2(d) after laser irradiation with different
fluences $F$, the spatial dimensions of the patches of laser-induced MSkL
creation and annihilation may be determined quantitatively. Extracting the
spatial MSkL distribution ${\rho_{\text{MSkL}}(r)}$ requires to deconvolve
${x_{\text{MSkL}}(r)}$ with the intensity profile of the probe beam
${\frac{I(r+d)}{I_{0}}}$ [30] to take into account the spatial averaging of
TR-MOKE. The spatial MSkL distribution after laser-induced MSkL creation is
best described by a high-order Gaussian function given by

$\rho_{\text{MSkL}}(r)=\rho_{0}\cdot\exp\left(\frac{-2|r|^{n}}{|w_{\text{MSkL}}|^{n}}\right),$
((2))

with radius ${w_{\text{MSkL}}}$ corresponding to the distance from the center
where ${\rho_{\text{MSkL}}}$ drops to $1/e^{2}$. For laser-induced MSkL
annihilation, the MSkL distribution is described by
${1-\rho_{\text{MSkL}}(r)}$. The line plots in Figs. 2(c) and 2(d) show that
the experimental data can be well approximated with the chosen model using
${w_{\text{MSkL}}}$, $n$, and $\rho_{0}$ as fit parameters. The resulting
values are listed in Ref. [30]. The radius ${w_{\text{MSkL}}}$ increases with
the laser fluence and gets larger than the laser focal width for high
fluences, consistent with sizable thermal diffusion, see thermal simulations
in Ref. [30]. Moreover, the shape of the MSkL distribution changes with laser
fluence. Irradiation with smaller laser fluence results in the formation of a
Gaussian MSkL distribution ($n\leq 2$), shown for ${8\,\mu\text{Jcm}^{-2}}$
and ${7\,\mu\text{Jcm}^{-2}}$ for laser-induced MSkL creation and annihilation
in Figs. 2(c) and 2(d). For higher laser fluence, the MSkL distribution forms
a flat top ($n>2$) that broadens under further increasing laser fluences. The
spatial MSkL distribution ${\rho_{\text{MSkL}}}$ differs for laser-induced
creation and annihilation as reflected by different ${w_{\text{MSkL}}}$ and
$n$. Most notably, for the same irradiation fluence of
${13\,\mu\text{Jcm}^{-2}}$, the MSkL is annihilated in a larger region than it
is created, leading to different patch sizes of laser-induced MSkL creation
and annihilation.

Figure 3:  Fluence dependence of laser-induced MSkL creation and annihilation
in Fe0.75Co0.25Si: (a) and (b) magnetization dynamics after the irradiation
with fs laser pulses of different laser fluences starting in the equilibrium
conical state (a) and MSkL (b). (c) and (d) MSkL ratio ${x_{\text{MSkL}}}$ as
a function of irradiation fluence for laser-induced MSkL creation (c) and
annihilation (d) at ${13\,\text{K}}$ and ${27\,\text{K}}$. The dashed blue
lines show exemplary the 5% and 95% fluence thresholds at ${13\,\text{K}}$.
(e) and (f) Comparison of the laser fluence required to increase the sample
temperature to $T_{\text{c}}$, $T_{\text{SkL}}$ and $T_{\text{con}}$ for
different temperatures and the fluence thresholds of laser-induced MSkL
creation ($F_{\text{t1}}$, $F_{\text{t2}}$) and annihilation
($F_{\text{t2}}^{\dagger}$).

This finding implies the need to investigate the fluence dependence of these
process, which we accomplish by means of analyzing the magnetic state at the
center of the laser spot (${d=0\,\mu\text{m}}$). Figures 3(a) and 3(b) show
TR-MOKE measurements after laser irradiation with four different laser
fluences and subsequent cryogenic cooling starting in the equilibrium conical
state (${55\,\text{mT}}$, ${13\,\text{K}}$) and the laser-written MSkL
(${70\,\text{mT}}$, ${13\,\text{K}}$), respectively. With increasing fluence,
the magnetization dynamics gradually evolves from the characteristic behavior
of the conical state to that of the MSkL and vice versa. Again, the fluence-
dependent measurements are described well by Eq. (1), see solid lines in Figs.
3(a) and 3(b). In Figs. 3(c) and 3(d) for two different temperatures the
evolution of the MSkL ratio ${x_{\text{MSkL}}}$ is presented as a function of
laser fluence for MSkL creation and annihilation, respectively. We observe a
double-threshold behavior for laser-induced MSkL creation ($F_{\text{t1}}$,
$F_{\text{t2}}$) and annihilation ($F_{\text{t1}}^{\dagger}$,
$F_{\text{t2}}^{\dagger}$). The laser-induced magnetic phase transition sets
in for fluences larger than a lower threshold $F_{\text{t1}}^{(\dagger)}$ and
completes above an upper fluence threshold $F_{\text{t2}}^{(\dagger)}$. In the
fluence regime between $F_{\text{t1}}^{(\dagger)}$ and
$F_{\text{t2}}^{(\dagger)}$ the MSkL ratio ${x_{\text{MSkL}}}$ scales with the
irradiation fluence. Thus, for fluences smaller than
$F_{\text{t2}}^{(\dagger)}$, the laser irradiation leads to only a partial
switching between MSkL and equilibrium conical state and to a coexistence of
both states with a fluence-dependent MSkL ratio.

In Figs. 3(c) and 3(d) the fluence thresholds $F_{\text{t1}}^{(\dagger)}$ and
$F_{\text{t2}}^{(\dagger)}$, approximated by 5% and 95% switching ratios
toward the final state, are shown as dashed vertical lines. The comparison of
the thresholds for laser-induced MSkL creation and annihilation shows that the
annihilation of the MSkL sets in and completes at lower fluences than the
creation process at the same temperature. With that, the different patch sizes
of laser-induced MSkL creation and annihilation can be traced back to the
different fluence dependencies. Namely, by irradiation with the same laser
fluence the lower fluence threshold for MSkL annihilation is exceeded in a
larger area than the higher threshold for MSkL creation. Moreover, the
transition from a Gaussian to a flat-top MSkL distribution, characterized by
an increase of $n$ in Eq. (2), aligns closely with the concept of laser-
induced MSkL creation and annihilation as a two-threshold process. This is
evident by the saturation of the final state at the center of the irradiation
beam when locally reaching the threshold $F_{\text{t2}}^{(\dagger)}$.

Figs. 3(c) and 3(d) demonstrate that the fluence thresholds of laser-induced
MSkL creation and annihilation decreases at higher temperatures, consistent
with the laser-induced temperature rise in the material being key for MSkL
formation. To quantitatively assess this, we estimate the temperature increase
caused by laser heating by comparing fluence and temperature-dependent TR-MOKE
measurements [30]. In Fig. 3(e), the laser fluence values leading to a local
increase of the sample temperature to $T_{\text{SkL}}$ (turquoise circles) and
$T_{\text{c}}$ (gray square) are compared to the upper $F_{\text{t1}}$ (white
diamonds) and lower $F_{\text{t2}}$ (black triangle) fluence threshold of
laser-induced MSkL creation. Here, $T_{\text{SkL}}$ represents the lowest
temperature within the SkL regime for a given magnetic field, as illustrated
in Fig. 1(a). Notably, Fig. 3(e) reveals that $F_{\text{t1}}$ and
$F_{\text{t2}}$ correspond to a local temperature increase to $T_{\text{SkL}}$
and $T_{\text{c}}$, respectively. This aligns well with laser-induced MSkL
creation due to local thermal quenching, as the equilibrium SkL stabilizes in
this temperature regime and is then subsequently quenched. The increase of the
MSkL ratio in the fluence regime from $F_{\text{t1}}$ to $F_{\text{t2}}$,
i.e., for higher temperature rises in the SkL, might be attributed to the
speedup of the topological winding process for temperatures approaching
$T_{\text{c}}$. This influences the probability of SkL stabilization and
consequently affects the number of skyrmions preserved following laser
heating. In agreement with the phase diagram shown the Fig. 1b) local
temperature increases to $T_{\text{con}}$ corresponds to the upper threshold
of MSkL annihilation $F_{\text{t2}}^{\dagger}$, as shown in Fig. 3(f). This
confirms that laser-induced MSkL annihilation can be explained by local
transient laser heating of the sample to temperatures that destabilize the
MSkL and lead to the formation of the conical state. Additionally, this study
demonstrates that even temperature rises much smaller than $T_{\text{con}}$
are sufficient to partially switch from MSkL to the conical state, likely due
to the temperature-dependent lifetime of the MSkL. As temperature increases
the MSkL lifetime, representing the characteristic time scale for skyrmion
unwinding, decreases, resulting in an increased transition probability between
the MSkL and conical state during high fluence laser irradiation.

In summary, our study explores the all-optical manipulation of a spatially-
confined metastable skyrmion lattice state (MSkL) in a bulk compound of the
cubic chiral magnet Fe0.25Co0.75Si. Probed by the magnetization dynamics in
TR-MOKE experiments, we demonstrate the feasibility of laser-induced MSkL
creation and annihilation in spatially confined areas for well-defined
magnetic field regimes. Spatially resolved and fluence-dependent measurements
indicate that creation and annihilation in Fe0.25Co0.75Si are linked to
distinct temperature regimes for the stabilization and destabilization of the
MSkL. Aside from promising steps towards the all-optical local control of
skyrmions for a fast and energy efficient manipulation in future storage or
microwave devices [32], our study provides insights into optically-induced
topological phase transitions in terms of thermal quenching.

###### Acknowledgements.

Funding: This work was supported by the European Metrology Research Programme
(EMRP) and EMRP participating countries under the European Metrology Programme
for Innovation and Research (EMPIR) Project No. 17FUN08-TOPS Metrology for
topological spin structures. In part, this study has been funded by the
Deutsche Forschungsgemeinschaft (DFG, German ResearchFoundation) under TRR80
(From Electronic Correlations to Functionality, Project No. 107745057, Project
E1), SPP2137 (Skyrmionics, Project No. 403191981, Grant PF393/19 and Grant
SCHU 2250/8-1), the excellence cluster MCQST under Germany’s Excellence
Strategy EXC-2111 (ProjectNo. 390814868) and EXC-2123 QuantumFrontiers
(ProjectNo. 390837967). Financial support by the European Research Council
(ERC) through Advanced Grants No. 291079 (TOPFIT) and No. 788031 (ExQuiSid) is
gratefully acknowledged. Author contributions: JK initiated the study. AB and
CP grew the crystal. JK performed the TR-MOKE study under the supervision of
MB and HF. The data analysis was carried out by JK. DK and RA supported the
study with simulations. MB, HF, SS, HWS, DK, RA, JK, AB and CP discussed the
results. JK wrote the paper. Competing interests: The authors declare that
they have no competing interests. Data availability: All data needed to
evaluate the conclusions of the paper are present in the paper and in the
supplemental material.

## References

  * Mühlbauer  _et al._ [2009] S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Böni, Skyrmion lattice in a chiral magnet, Science 323, 915 (2009).
  * Okamura  _et al._ [2016] Y. Okamura, F. Kagawa, S. Seki, and Y. Tokura, Transition to and from the skyrmion lattice phase by electric fields in a magnetoelectric compound, Nature Communications 7, 1 (2016).
  * Münzer  _et al._ [2010] W. Münzer, A. Neubauer, T. Adams, S. Mühlbauer, C. Franz, F. Jonietz, R. Georgii, P. Böni, B. Pedersen, M. Schmidt, _et al._ , Skyrmion lattice in the doped semiconductor Fe${}_{\text{1- x}}$Co${}_{\text{x}}$Si, Physical Review B 81, 041203 (2010).
  * Bauer  _et al._ [2018] A. Bauer, A. Chacon, M. Halder, and C. Pfleiderer, Skyrmion lattices far from equilibrium, in  _Topology in Magnetism_ (Springer, 2018) pp. 151–176.
  * Oike  _et al._ [2016] H. Oike, A. Kikkawa, N. Kanazawa, Y. Taguchi, M. Kawasaki, Y. Tokura, and F. Kagawa, Interplay between topological and thermodynamic stability in a metastable magnetic skyrmion lattice, Nature Physics 12, 62 (2016).
  * Bannenberg  _et al._ [2016] L. Bannenberg, K. Kakurai, F. Qian, E. Lelièvre-Berna, C. Dewhurst, Y. Onose, Y. Endoh, Y. Tokura, and C. Pappas, Extended skyrmion lattice scattering and long-time memory in the chiral magnet Fe${}_{\text{1- x}}$Co${}_{\text{x}}$Si, Physical Review B 94, 104406 (2016).
  * Takagi  _et al._ [2021] R. Takagi, M. Garst, J. Sahliger, C. H. Back, Y. Tokura, and S. Seki, Hybridized magnon modes in the quenched skyrmion crystal, Physical Review B 104, 144410 (2021).
  * Seki  _et al._ [2020] S. Seki, M. Garst, J. Waizner, R. Takagi, N. Khanh, Y. Okamura, K. Kondou, F. Kagawa, Y. Otani, and Y. Tokura, Propagation dynamics of spin excitations along skyrmion strings, Nature communications 11, 1 (2020).
  * Kalin  _et al._ [2022] J. Kalin, S. Sievers, H. Füser, H. W. Schumacher, M. Bieler, F. García-Sánchez, A. Bauer, and C. Pfleiderer, Optically excited spin dynamics of thermally metastable skyrmions in Fe0.75Co0.25Si, Physical Review B 106, 054430 (2022).
  * Milde  _et al._ [2013] P. Milde, D. Köhler, J. Seidel, L. Eng, A. Bauer, A. Chacon, J. Kindervater, S. Mühlbauer, C. Pfleiderer, S. Buhrandt, _et al._ , Unwinding of a skyrmion lattice by magnetic monopoles, Science 340, 1076 (2013).
  * Hrabec  _et al._ [2017] A. Hrabec, J. Sampaio, M. Belmeguenai, I. Gross, R. Weil, S. M. Chérif, A. Stashkevich, V. Jacques, A. Thiaville, and S. Rohart, Current-induced skyrmion generation and dynamics in symmetric bilayers, Nature Communications 8, 15765 (2017).
  * Legrand  _et al._ [2017] W. Legrand, D. Maccariello, N. Reyren, K. Garcia, C. Moutafis, C. Moreau-Luchaire, S. Collin, K. Bouzehouane, V. Cros, and A. Fert, Room-temperature current-induced generation and motion of sub-100 nm skyrmions, Nano Letters 17, 2703 (2017).
  * Büttner  _et al._ [2017] F. Büttner, I. Lemesh, M. Schneider, B. Pfau, C. M. Günther, P. Hessing, J. Geilhufe, L. Caretta, D. Engel, B. Krüger, _et al._ , Field-free deterministic ultrafast creation of magnetic skyrmions by spin–orbit torques, Nature Nanotechnology 12, 1040 (2017).
  * Lemesh  _et al._ [2018] I. Lemesh, K. Litzius, M. Böttcher, P. Bassirian, N. Kerber, D. Heinze, J. Zázvorka, F. Büttner, L. Caretta, M. Mann, _et al._ , Current-induced skyrmion generation through morphological thermal transitions in chiral ferromagnetic heterostructures, Advanced Materials 30, 1805461 (2018).
  * Zhang  _et al._ [2018] S. Zhang, J. Zhang, Q. Zhang, C. Barton, V. Neu, Y. Zhao, Z. Hou, Y. Wen, C. Gong, O. Kazakova, _et al._ , Direct writing of room temperature and zero field skyrmion lattices by a scanning local magnetic field, Applied Physics Letters 112, 132405 (2018).
  * Temiryazev  _et al._ [2018] A. G. Temiryazev, M. Temiryazeva, A. V. Zdoroveyshchev, O. V. Vikhrova, M. V. Dorokhin, P. B. Demina, and A. V. Kudrin, Formation of a domain structure in multilayer CoPt films by magnetic probe of an atomic force microscope, Physics of the Solid State 60, 2200 (2018).
  * Qin  _et al._ [2018] Z. Qin, C. Jin, H. Xie, X. Li, Y. Wang, J. Cao, and Q. Liu, Size-tunable skyrmion bubbles in Ta/CoFeB/MgO multilayers, Journal of Physics D: Applied Physics 51, 425001 (2018).
  * Finazzi  _et al._ [2013] M. Finazzi, M. Savoini, A. Khorsand, A. Tsukamoto, A. Itoh, L. Duo, A. Kirilyuk, T. Rasing, and M. Ezawa, Laser-induced magnetic nanostructures with tunable topological properties, Physical Review Letters 110, 177205 (2013).
  * Gerlinger  _et al._ [2021] K. Gerlinger, B. Pfau, F. Büttner, M. Schneider, L.-M. Kern, J. Fuchs, D. Engel, C. M. Günther, M. Huang, I. Lemesh, _et al._ , Application concepts for ultrafast laser-induced skyrmion creation and annihilation, Applied Physics Letters 118, 192403 (2021).
  * Je  _et al._ [2018] S.-G. Je, P. Vallobra, T. Srivastava, J.-C. Rojas-Sánchez, T. H. Pham, M. Hehn, G. Malinowski, C. Baraduc, S. Auffret, G. Gaudin, _et al._ , Creation of magnetic skyrmion bubble lattices by ultrafast laser in ultrathin films, Nano Letters 18, 7362 (2018).
  * Kern  _et al._ [2022a] L.-M. Kern, B. Pfau, M. Schneider, K. Gerlinger, V. Deinhart, S. Wittrock, T. Sidiropoulos, D. Engel, I. Will, C. M. Günther, _et al._ , Tailoring optical excitation to control magnetic skyrmion nucleation, Physical Review B 106, 054435 (2022a).
  * Kern  _et al._ [2022b] L.-M. Kern, B. Pfau, V. Deinhart, M. Schneider, C. Klose, K. Gerlinger, S. Wittrock, D. Engel, I. Will, C. M. Günther, _et al._ , Deterministic generation and guided motion of magnetic skyrmions by focused He+-ion irradiation, Nano Letters 22, 4028 (2022b).
  * Büttner  _et al._ [2021] F. Büttner, B. Pfau, M. Böttcher, M. Schneider, G. Mercurio, C. M. Günther, P. Hessing, C. Klose, A. Wittmann, K. Gerlinger, _et al._ , Observation of fluctuation-mediated picosecond nucleation of a topological phase, Nature Materials 20, 30 (2021).
  * Bauer  _et al._ [2016] A. Bauer, M. Garst, and C. Pfleiderer, History dependence of the magnetic properties of single-crystal Fe${}_{\text{1- x}}$Co${}_{\text{x}}$Si, Physical Review B 93, 235144 (2016).
  * Yu  _et al._ [2010] X. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. Han, Y. Matsui, N. Nagaosa, and Y. Tokura, Real-space observation of a two-dimensional skyrmion crystal, Nature 465, 901 (2010).
  * Berruto  _et al._ [2018] G. Berruto, I. Madan, Y. Murooka, G. Vanacore, E. Pomarico, J. Rajeswari, R. Lamb, P. Huang, A. Kruchkov, Y. Togawa, _et al._ , Laser-induced skyrmion writing and erasing in an ultrafast cryo-Lorentz transmission electron microscope, Physical Review Letters 120, 117201 (2018).
  * Mochizuki [2012] M. Mochizuki, Spin-wave modes and their intense excitation effects in skyrmion crystals, Physical Review Letters 108, 017601 (2012).
  * Onose  _et al._ [2012] Y. Onose, Y. Okamura, S. Seki, S. Ishiwata, and Y. Tokura, Observation of magnetic excitations of skyrmion crystal in a helimagnetic insulator Cu2OSeO3, Physical Review Letters 109, 037603 (2012).
  * Schwarze  _et al._ [2015] T. Schwarze, J. Waizner, M. Garst, A. Bauer, I. Stasinopoulos, H. Berger, C. Pfleiderer, and D. Grundler, Universal helimagnon and skyrmion excitations in metallic, semiconducting and insulating chiral magnets, Nature Materials 14, 478 (2015).
  * [30] See Supplemental Material for more information on the temperature, magnetic field and fluence dependence of the laser-written MSkL state, discussion of laser heating effects, thermal modelling, and details of the spatially resolved measurements and modelling procedure.
  * Wild  _et al._ [2017] J. Wild, T. N. Meier, S. Pöllath, M. Kronseder, A. Bauer, A. Chacon, M. Halder, M. Schowalter, A. Rosenauer, J. Zweck, _et al._ , Entropy-limited topological protection of skyrmions, Science Advances 3, e1701704 (2017).
  * Wang and Liu [2020] C. Wang and Y. Liu, Ultrafast optical manipulation of magnetic order in ferromagnetic materials, Nano Convergence 7, 1 (2020).
  * [33] COMSOL Multiphysics ® v. 5.0. www.comsol.com. COMSOL AB, Stockholm, Sweden.
  * Koshibae and Nagaosa [2014] W. Koshibae and N. Nagaosa, Creation of skyrmions and antiskyrmions by local heating, Nature Communications 5, 1 (2014).
  * Olleros-Rodríguez  _et al._ [2022] P. Olleros-Rodríguez, M. Strungaru, S. Ruta, P.-I. Gavriloaea, A. Gudín, P. Perna, R. Chantrell, and O. Chubykalo-Fesenko, Non-equilibrium heating path for the laser-induced nucleation of metastable skyrmion lattices, Nanoscale 14, 15701 (2022).
  * Polyakov  _et al._ [2020] O. Polyakov, I. Gonoskov, V. Stepanyuk, and E. Gross, Generation of magnetic skyrmions by focused vortex laser pulses, Journal of Applied Physics 127, 073904 (2020).
  * Koralek  _et al._ [2012] J. Koralek, D. Meier, J. Hinton, A. Bauer, S. Parameswaran, A. Vishwanath, R. Ramesh, R. Schoenlein, C. Pfleiderer, and J. Orenstein, Observation of coherent helimagnons and Gilbert damping in an itinerant magnet, Physical Review Letters 109, 247204 (2012).