# Electric control of optically-induced magnetization dynamics in a van der
Waals ferromagnetic semiconductor

Freddie Hendriks  Zernike Institute for Advanced Materials, University of
Groningen, The Netherlands  Rafael R. Rojas-Lopez  Zernike Institute for
Advanced Materials, University of Groningen, The Netherlands  Departamento de
Física, Universidade Federal de Minas Gerais, Brazil  Bert Koopmans
Department of Applied Physics, Eindhoven University of Technology, The
Netherlands  Marcos H. D. Guimarães  Zernike Institute for Advanced Materials,
University of Groningen, The Netherlands<EMAIL_ADDRESS>
(22 September 2023)

###### Abstract

Electric control of magnetization dynamics in two-dimensional (2D) magnetic
materials is an essential step for the development of novel spintronic
nanodevices. Electrostatic gating has been shown to greatly affect the static
magnetic properties of some van der Waals magnets, but the control over their
magnetization dynamics is still largely unexplored. Here we show that the
optically-induced magnetization dynamics in the van der Waals ferromagnet
Cr2Ge2Te6 can be effectively controlled by electrostatic gates, with a one
order of magnitude change in the precession amplitude and over 10% change in
the internal effective field. In contrast to the purely thermally-induced
mechanisms previously reported for 2D magnets, we find that coherent opto-
magnetic phenomena play a major role in the excitation of magnetization
dynamics in Cr2Ge2Te6. Our work sets the first steps towards electric control
over the magnetization dynamics in 2D ferromagnetic semiconductors,
demonstrating their potential for applications in ultrafast opto-magnonic
devices.

magnetization dynamics, two-dimensional magnets, electric control, magneto-
optics, van der Waals materials

##  I Introduction

Ever since the experimental confirmation of magnetism in two-dimensional (2D)
van der Waals (vdW) materials [1, 2], researchers have tried to understand
their fundamentals and to utilise their unique properties for new
technologies, such as novel spintronic devices for information storage and
processing [3, 4, 5, 6]. The use of magnetization dynamics is particularly
interesting since it provides an energy efficient route to transfer and
process information [7, 8, 9, 10, 11]. A key challenge in this field, named
magnonics, is the effective control over the magnetization and its dynamics
using electrostatic means, allowing for energy efficient, on-chip,
reconfigurable magnonic circuit elements [12, 13, 14]. For conventional (tree-
dimensional) systems this control has been shown to be very promising to
reduce the energy barriers for writing magnetic bits using spin-orbit torques
[15, 16]. Nonetheless, the effect is still relatively modest [17, 18, 19, 20].
In contrast, 2D magnetic semiconductors provide an ideal platform for electric
manipulation of magnetization. Their low density of states and high surface-
to-volume ratio allow for an effective control over the magnetic parameters in
these systems, such as the magnetic anisotropy and saturation magnetization
[21, 22, 23, 24, 25]. Additionally, 2D magnetic semiconductors offer a bridge
to another exciting field: the combination of optics and magnetism. These
materials have shown to possess strong light-matter interaction and high
magneto-optic coefficients which strength can be further tuned by the use of
vdW heterostructures [26, 27, 28, 29, 30, 6, 31]. These properties make 2D
magnetic semiconductors ideal for the merger of two emerging fields: magnonics
and photonics.

Most works on the electric control of magnetization in vdW magnets have
focused on their magnetostatic properties, such as the magnetic anisotropy,
saturation magnetization and Curie temperature, in both metallic [32, 33, 34,
24, 25, 35] and semiconducting [22, 23, 21, 24, 25] materials. In contrast,
their magnetization dynamics have only recently started to receive more
attention, and studied using microwave driven magnetic resonance [36, 37, 38,
39, 40, 41, 42], or time-dependent magneto-optic techniques [43, 44, 45, 46,
47, 48, 49, 50, 51]. The latter were used on antiferromagnetic bilayer
CrI${}_{\text{3}}$ to show that its magnetic resonance frequency can be
electrically tuned by tens of GHz [52]. Nonetheless, the electric control over
the optical excitation of magnetization and its subsequent dynamics in 2D
ferromagnets remains to be explored.

Here we show that the magnetization dynamics of the vdW semiconductor
Cr2Ge2Te6 (CGT) can be efficiently controlled by electrostatic gating. Using
ultrafast (fs) laser pulses we bring the magnetization out of equilibrium and
study its dynamics with high temporal resolution through the magneto-optic
Faraday effect. Using both top and bottom electrostatic gates, we
independently control the gate-induced change in the charge carrier density
($\Delta n$) and the electric displacement field ($\Delta D$) in the CGT, and
show that both have drastic effects on the optically-induced oscillation
amplitudes and a more modest effect on its frequency. Finally, we observe a
strong asymmetric behavior on the magnetization oscillation amplitudes with
respect to a reversal of the external magnetic field, which is also strongly
affected by both $\Delta n$ and $\Delta D$. This asymmetry can be explained by
a strong influence of coherent opto-magnetic phenomena, such as the inverse
Cotton-Mouton effect and photo-induced magnetic anisotropy, on the excitation
of the magnetization dynamics.

Figure 1: Magnetization dynamics in a CGT based heterostructure. a,
Illustration of time-resolved Faraday ellipticity measurements, combined with
an optical micrograph of the sample (the scale bar is 10 $\mu$m). The CGT
flake is outlined in blue. b, Schematic of the layers comprising the sample,
including electrical connections for gating. c, Process of laser-induced
magnetization precession (see main text). d, Time-resolved Faraday ellipticity
traces at $\mu_{0}H_{\text{ext}}$ = 100 mT for three different values of
$\Delta n$ with $\Delta D$ = 0. A vertical offset was added for clarity. e,
RMS power of the frequency spectrum of the oscillations in the data shown in
d. Different transparencies indicate different values of $H_{\text{ext}}$.

##  II Device structure and measurement techniques

Our sample consists of a CGT flake, encapsulated in hexagonal boron nitride
(hBN), with thin graphite layers as top gate, back gate, and contact
electrodes, as depicted in Fig. 1a and b (see Methods for more details). The
measurements were performed at low temperatures (10 K), with the sample
mounted at 50 degrees with respect to the magnetic field axis for transmission
measurements. The laser light is parallel to the magnetic field axis.

We use the time-resolved magneto-optic Faraday effect to monitor the
magnetization dynamics in our system using a single-color pump-probe setup
similar to the one described in [53, 54] (more information in Methods). The
process of optical excitation of magnetization dynamics in van der Waals
magnets has been previously reported as purely thermal [43, 44, 45, 46, 47,
52], similar to many studies on conventional metallic thin-films [55, 56, 57].
Here we find strong evidence that coherent opto-magnetic phenomena also play
an important role in the excitation of the magnetization dynamics. The
detailed microscopic description of how the magnetization dynamics is induced
is described later in the article, but in short, the excitation of the
magnetization dynamics can be described as follows (Fig. 1c): In equilibrium
(1), the magnetization $\mathbf{M}$ points along the total effective magnetic
field $\mathbf{H}_{\text{eff}}$, which is the sum of the external field
($\mathbf{H}_{\text{ext}}$), and the internal effective field
($\mathbf{H}_{\text{int}}$) caused by the magnetocrystalline anisotropy
($K_{\text{u}}$) and shape anisotropy. For CGT, $\mathbf{H}_{\text{int}}$
points out-of-plane [58, 2, 45], meaning that $K_{\text{u}}$ dominates over
the shape anisotropy. The linearly polarized pump pulse interacts with the
sample (2), reducing the magnetization and changing the magnetocrystalline
anisotropy through the mechanisms mentioned above, which causes $\mathbf{M}$
to cant away from equilibrium. Since $\mathbf{M}$ and
$\mathbf{H}_{\text{eff}}$ are not parallel anymore, this results in a
precession of $\mathbf{M}$ around $\mathbf{H}_{\text{eff}}$, while they both
recover to their equilibrium value as the sample cools.

##  III Gate control of magnetization dynamics

The dual-gate geometry of our device allows for the independent control of
both the charge carrier density and the perpendicular electric field. The
dependence of $\Delta n$ and $\Delta D$ on the top and back gate voltages –
$V_{t}$ and $V_{b}$, respectively – is derived in the Methods. The change in
the Fermi level induced by $\Delta n$ is expected to affect the magnetic
anisotropy of CGT due to the different Cr $d$-orbitals composition of the
electronic bands [59]. The effect of $\Delta D$ is, however, more subtle. The
inversion symmetry breaking caused by $\Delta D$ can allow for an energy shift
of the (initially degenerate) electronic bands, potentially also modulating
the magnetization parameters. Additionally, the perpendicular electric field
can induce a non-uniform distribution of charge carriers along the thickness
of the CGT flake, leading to $\Delta n$-induced local changes in the
magnetization parameters.

Typical results from the time-resolved Faraday ellipticity (TRFE) measurements
for different values of $\Delta n$, with $\Delta D$ = 0, are shown in Fig. 1d.
For $\Delta t<0$ the signal is constant, since the magnetization is at its
steady state value. All traces show a sharp increase at $\Delta t=0$,
indicating a fast laser-induced dynamics. For $\Delta t>0$, the TRFE traces
show oscillations, indicating a precession of the magnetization induced by the
pump pulse.

We observe that the magnetization dynamics strongly depends on $\Delta n$,
with the amplitude, frequency and starting phase of the oscillations in the
TRFE signal all being affected. The most striking observation is that the
amplitude of the TRFE signal increases by more than a factor of seven when
$\Delta n$ is changed from $1.2\times 10^{13}$ cm-2 to $-1.8\times 10^{13}$
cm-2. The observations of modulation of both the amplitude and starting phase
of the oscillations hint at a change in the pump excitation process. The
change in oscillation frequency due to $\Delta n$ is better visible in the
Fourier transform of the signals, shown in Fig. 1e (see Methods for details on
the Fourier transform). This analysis clearly shows that both the frequency
and amplitude of the magnetization precession are tuned by $\Delta n$. All
these observations point to an effective control of the (dynamic) magnetic
properties of CGT by electrostatic gating.

Figure 2: Gate-dependence of precession frequency and internal effective
field. a, Frequency of oscillations as a function of external magnetic field,
for different values of $\Delta n$. The circles are the frequencies extracted
from the TRFE data for $\Delta t>26$ ps. Solid lines are best fits of Eq (1).
Inset: Close-up of the data for low fields, showing the frequency shift due to
gating. The error bars are smaller than the markers. b, Frequency of the
oscillations in the TRFE signal at $\mu_{0}H_{\text{ext}}=100$ mT for various
values of top ($V_{t}$) and back gate voltages ($V_{b}$). The black and gray
arrows indicate, respectively, the directions of constant $\Delta D$ and
varying $\Delta n$, and of constant $\Delta n$ and varying $\Delta D$. For
other values of $H_{\text{ext}}$ see Supplementary Fig. S10. c, Internal
effective field as a function of $V_{t}$ and $V_{b}$. d, e, The dependence of
the internal effective field on $\Delta n$ for fixed $\Delta D$ (d) and on
$\Delta D$ for fixed $\Delta n$ (e), with solid lines to guide the eye. The
traces are taken along the dotted lines indicated in c.

The origin of the electric control of the magnetization dynamics can be
further understood by analyzing the precession frequency at various magnetic
fields and values of $\Delta n$ (Fig. 2a). For magnetic fields below 250 mT we
observe a significant shift of the frequency (4 – 10%) by changing the charge
carrier density. This is clearly visible in the inset of Fig. 2a, which shows
a close-up of the data up to 150 mT. The change in precession frequency for
different values of $\Delta n$ strongly points towards a modulation of the
magnetization parameters of CGT as a function of the Fermi level, controlled
by $\Delta n$.

A quantitative analysis of the oscillation frequency ($f$) as a function of
$H_{\text{ext}}$ can be used to extract the magnetization dynamics parameters
of the device. Our data is well described by the ferromagnetic resonance mode
obtained from the Landau-Lifshitz-Gilbert (LLG) equation with negligible
damping [60]:

$\displaystyle
f=\frac{g\mu_{B}\mu_{0}}{2\pi\hbar}\sqrt{\left|\mathbf{H}_{\text{eff}}\right|\left(\left|\mathbf{H}_{\text{eff}}\right|-H_{\text{int}}\sin^{2}\left(\theta_{M}\right)\right)},$
(1)

where $g$ is the Landé g-factor, $\mu_{B}$ the Bohr magneton,
$\mathbf{H}_{\text{eff}}=\mathbf{H}_{\text{ext}}+H_{\text{int}}\cos(\theta_{M})\hat{\mathbf{z}}$,
with $H_{\text{int}}=2K_{\text{u}}/(\mu_{0}M_{\text{s}})-M_{\text{s}}$,
$M_{\text{s}}$ the saturation magnetization, and $\theta_{M}$ the angle
between $\mathbf{M}$ and the sample normal (z-direction). The angle
$\theta_{M}$ is calculated by minimizing the magnetic energy in the presence
of an external field, perpendicular magnetic anisotropy, and shape anisotropy
[45]. We obtain the $g$-factor and $H_{\text{ext}}$ of the CGT by fitting the
$f$ versus $H_{\text{ext}}$ data (e.g. the data presented in Fig. 2a) using
Eq. (1), as explained in the Methods. This yields $g\approx 1.89$ with no
clear dependence on $\Delta n$ or $\Delta D$, which is in agreement with
(albeit slightly lower than) the values reported for CGT [40, 45, 42] (see
Supplementary Sections 4 and 5 for more details). We also find no clear
dependence of the precession damping time ($\tau_{\text{osc}}$) on $\Delta n$
or $\Delta D$. The intrinsic Gilbert damping we obtain form our measurements
is about $6\times 10^{-3}$ (see Supplementary Section 6), in line with values
found in literature [45, 41].

The internal effective field shows a clear dependence on both $V_{t}$ and
$V_{b}$, as shown in Fig. 2c, with values similar to the ones found in other
studies [45]. Upon comparing Fig. 2c to 2b, one notices that the gate
dependence of $H_{\text{int}}$ is very similar to that of the precession
frequency at $\mu_{0}H_{\text{ext}}=100$ mT. This suggests that the gate
dependence of the precession frequency is caused by the gate-induced change in
$H_{\text{int}}$. From the dependence of $H_{\text{int}}$ on $V_{t}$ and
$V_{b}$, we extract its behavior as a function of $\Delta n$ and $\Delta D$,
shown in Fig. 2d and e. We observe that $H_{\text{int}}$ decreases with both
increasing $\Delta n$ and $\Delta D$. The dependence of $H_{\text{int}}$ on
$\Delta n$ is consistent with theoretical calculations [59], showing that
$K_{\text{u}}$, and therefore $H_{\text{int}}$, is reduced upon increasing the
electron density in the same order of what we achieve in our sample. The
$\Delta n$ dependence of $H_{\text{int}}$ is also consistent with the
dependence of the coercive field obtained from static measurements (see
Supplementary Section 3), providing further evidence that the change in $f$ is
driven by a change in $K_{\text{u}}$.

Figure 3: Gate dependence of magnetization precession amplitude and phase. a,
b, Gate dependence of the amplitude (a) and starting phase (b) of the
oscillations in the TRFE measurements at $\mu_{0}H_{\text{ext}}=100$ mT. For
other values of $H_{\text{ext}}$ see Supplementary Figs. S8 and S9. c, d,
External magnetic field dependence of the amplitude (c) and starting phase (d)
of the oscillations for different values of $\Delta n$ at $\Delta D=0$. The
values are extracted from the TRFE data for $\Delta t>26$ ps. e, Schematics of
the inverse Cotton-Mouton effect for opposite directions of $H_{\text{ext}}$.
The magnetization direction is depicted by a red arrow, the external magnetic
field in blue, the effective magnetic field induced by the ICME and the
effective field are shown in cyan. The $xz$-plane is highlighted by the shaded
region.

Now we draw our attention to the large modulation of the oscillations in the
TRFE measurements with varying gate voltage, as shown in Fig. 1d and 1e. Here
we attribute this change in magneto-optical signal amplitude to an actual
increase in amplitude of the magnetization precession (increase in the
precession angle) and not to an increase in the strength of the Faraday
effect. This is supported by our observation that the time-resolved
measurements for different combinations of gate voltages are not simply scaled
– i.e. the amplitude of the oscillations and their (ultrafast demagnetization)
background scale differently. A detailed discussion can be found in
Supplementary Section 7.

Figure 3a clearly shows that the magnetization precession amplitude is mostly
affected by $\Delta n$, and to a much lesser extend by $\Delta D$. The
precession amplitude versus $H_{\text{ext}}$ for various values of $\Delta n$
is presented in Fig. 3c. We note that for $|\mu_{0}H_{\text{ext}}|<$ 50 mT the
magnetization is not completely saturated (see Supplementary Section 3), which
can lead to multi-domain formation [61] and a deviation from the general
trend. We find that not only the precession amplitude for a given
$H_{\text{ext}}$ is strongly modulated by $\Delta n$, but its decaying trend
with $H_{\text{ext}}$ is also strongly affected. Additionally, we observe
another interesting effect: the amplitude shows an asymmetry in the sign of
the applied magnetic field, which is also dependent on $\Delta n$. This latter
is unexpected, especially since the observed precession frequency is symmetric
in H${}_{\text{ext}}$ (see Supplementary Section 9). A similar precession
frequency for opposite magnetic fields indicates that the magnetocrystalline
anisotropy and the saturation magnetization are independent of the sign of
$H_{\text{ext}}$. Therefore, we conclude that the origin of the modulation of
the precession amplitude is related to the excitation mechanism of the
magnetization precession (see Supplementary Section 10 for the complete
discussion).

To get further insight into the microscopic mechanisms involved in the optical
excitation of magnetization dynamics, we analyze the magnetic field dependence
of the starting phase ($\phi_{0}$) of the precessions for different values of
$V_{t}$ and $V_{b}$ (Fig. 3b). Unlike the amplitude, we find that $\phi_{0}$
depends on both $\Delta n$ and $\Delta D$. As can be seen in Fig. 3d, the
behavior of $\phi_{0}$ with $H_{\text{ext}}$ is also modulated by $\Delta n$.
For a purely thermal excitation of the magnetization dynamics one would expect
$\phi_{0}(-H_{\text{ext}})=\pi+\phi_{0}(H_{\text{ext}})$ in our geometry.
Nonetheless, we observe that $\phi_{0}$ for positive and negative magnetic
fields differ by less than $\pi$. Moreover, $\Delta n$ seems to also affect
the trend on how $\phi_{0}$ approaches the values at high magnetic fields.
Combined with the observed asymmetry of the precession amplitude, our data
strongly suggests that the optical excitation of the magnetization dynamics is
not dominated by a thermal excitation ($\Delta$K mechanism) as previously
reported for other van der Waals magnets [43, 44, 45, 46, 47, 52].

##  IV Opto-magnetic effects

Coherent opto-magnetic mechanisms provide possible alternatives for the
optical excitation of magnetization dynamics in CGT. Here we find that our
data can be explained by two of these mechanisms that are compatible with a
linearly-polarized pump pulse, the inverse Cotton-Mouton effect (ICME) [62,
63, 64] and photo-induced magnetic anisotropy (PIMA) [65], in addition to the
conventional (thermal) $\Delta$K mechanism [66]. The ICME, which could be
described by impulsive stimulated Raman scattering, relies on the generation
of an effective magnetic field upon interaction with linearly polarized light
in a magnetized medium [62, 67, 63, 64, 68]. This effective magnetic field is
proportional to both the light intensity and magnetization. For pulsed laser
excitation, the ICME generates a strong impulsive change in $H_{\text{ext}}$
that results in a fast rotation of the magnetization. Therefore, this effect
can cause the amplitude of the precession to be asymmetric in $H_{\text{ext}}$
[64, 68].

Figure 3e illustrates how the ICME could result in an asymmetric magnetic
field dependence of the amplitude. For simplicity we only consider the
$y$-component of the generated effective magnetic field, since this component
is responsible for the asymmetry. (1) A sample with perpendicular magnetic
anisotropy is subject to an external magnetic field $\mathbf{H}_{\text{ext}}$
($-\mathbf{H}_{\text{ext}}$) in the $xz$-plane, pointing in the positive
(negative) direction of both axes. In equilibrium, the magnetization points
along the total effective field, as indicated by the light gray arrow. During
laser pulse excitation, the ICME results in an effective magnetic field along
the $y$-axis, rotating the magnetization either towards the $z$-axis or the
$x$-axis, depending on the sign of $\mathbf{H}_{\text{ext}}$. Additionally,
the ultrafast demagnetization process leads to a reduction of the
magnetization. (2) After the laser pulse, the magnetization precesses around
the total effective field that is comprised of $\mathbf{H}_{\text{ext}}$ and
$\mathbf{H}_{\text{int}}$. Depending on the sign of $\mathbf{H}_{\text{ext}}$,
the ICME has either rotated $\mathbf{M}$ towards or away from
$\mathbf{H}_{\text{eff}}$, resulting in different precession amplitudes.

The second coherent mechanism for laser-induced magnetization dynamics is
PIMA, which leads to a step-like change in $\mathbf{H}_{\text{eff}}$ due to
pulsed laser excitation [64]. This mechanism has been reported to arise from
an optical excitation of nonequivalent lattice sites (e.g. dopants and
impurities), which effectively redistributes the ions and hence changes the
magnetic anisotropy [69, 70, 71]. Unlike the ICME, the PIMA mechanism is not
expected to lead to an asymmetry of the magnetization precession amplitude of
upon a reversal of $H_{\text{ext}}$, because it is present for times much
longer than the period of precession and therefore acts as a constant change
of the effective magnetic field [65, 70, 72, 71].

All three discussed mechanisms for inducing magnetization precession – ICME,
PIMA and the $\Delta$K mechanism – are affected by electrostatic gating. The
opto-magnetic effects can be affected through a change in e.g. the
polarization-dependent refractive index and the occupation of charge states of
ions and impurities. Additionally, the $\Delta$K mechanism can be affected by
the changes in charge relaxation pathways through, for example, electron-
electron and electron-phonon interactions. We find that the combination of the
above mechanisms can describe quantitatively the starting phase and
qualitatively the amplitude of the observed magnetic field dependence shown in
Fig. 3 (see Supplementary Section 11). The balance between these three
mechanism affects the magnetic field dependence of the amplitude and the
starting phase, increases or decreases the asymmetry in the induced precession
amplitude, and changes the steepness of the starting phase versus magnetic
field graph. Therefore, since our data shows a change in these properties, we
conclude that the relative strength of the mechanisms for excitation of
magnetization precession are effectively controlled by electrostatic gating.

##  V Conclusions

We envision that the electric control over the optically-induced magnetization
precession amplitude demonstrated here can be applied to devices which make
use of spin wave interference for signal processing [12, 13, 14]. This should
lead to an efficient electric control over the mixing of spin waves, leading
to an easier on-chip implementation of combined magnonic and photonic
circuits. Even though the control over the precession frequency shown here is
still modest ($\approx$10%), we believe it can be further enhanced by the use
of more effective electrostatic doping, such as using high-$\kappa$
dielectrics or ionic-liquid gating which is capable of achieving over one
order of magnitude higher changes in carrier densities than the ones reported
here [32, 73, 21, 24, 25]. We note that due to the non-monotonic behavior of
the magnetic anisotropy energy with changes in charge carrier density, one
might expect more drastic changes on $H_{\text{int}}$ for larger changes in
$\Delta n$. This control over the magnetic anisotropy can then be used for the
electrostatic guiding and confinement of spin waves, leading to an expansion
of the field of quantum magnonics. Finally, the presence of coherent optical
excitation of magnetization dynamics we observed in CGT should also lead to a
more energy-efficient optical control of magnetization [74]. Therefore, the
electric control over magnetization dynamics in CGT shown here provides the
first steps towards the implementation of vdW ferromagnets in magneto-photonic
devices that make use of spin waves to transport and process information.

##  VI Methods

###  VI.1 Sample fabrication

The thin hBN and graphite flakes are exfoliated from bulk crystals (HQ
graphene) on an oxidized silicon wafer (285 nm oxide thickness). The CGT
flakes are exfoliated in the same way in an inert (nitrogen gas) environment
glove box with less than 0.5 ppm oxygen and water to prevent degradation. The
flakes are selected using optical contrast and stacked using a
polycarbonate/polydimethylsiloxane stamp by a dry transfer van der Waals
assembly technique [75]. First an hBN flake (21 nm thick) is picked up,
followed by the CGT flake. Next, a thin graphite flake is picked up to make
electrical contact with a corner of the CGT, and extends beyond the picked-up
hBN flake. After this, a second hBN flake (20 nm thick) is picked up and a
thin graphite flake to function as the back gate electrode. This stack is then
transferred to an optically transparent fused quartz substrate finally a thin
graphite flake is transferred on top the stack to function as the top gate
electrode. The device is then contacted by Ti/Au (5/50 nm) electrodes
fabricated using conventional electron-beam lithography and thin metallic film
deposition techniques.

###  VI.2 Measurement setup

All measurements are done at 10 K under low-pressure (20 mbar) Helium gas. The
sample is mounted at an angle, such that the sample normal makes an angle of
50 degrees with the external magnetic field and the laser propagation
direction.

The $\sim$200 fs long laser pulses are generated by a mode-locked Ti:Sapphire
oscillator (Spectra-Physics MaiTai), at a repetition rate of 80 MHz. After a
power dump, the pulses are split in an intense pump and a weaker probe pulse
by a non-polarizing beam splitter. The pump beam goes through a mechanical
delay stage, allowing us to modify the time-delay between pump and probe by a
change in the optical path length. To allow for a double-modulation detection
[53, 54], the pump beam goes through an optical chopper working at 2173 Hz.
The polarization of the pump is set to be horizontal (p-polarized with respect
to the sample), to allow us to block the pump beam through a polarization
filter at the detection stage. The initially linearly polarized probe pulse
goes through a photoelastic modulator (PEM) which modulates the polarization
of the light at 50 kHz. A non-polarizing beam splitter is used to merge the
pump and probe beams on parallel paths, with a small separation between them.
From here, they are focused onto the sample by an aspheric cold lens with a
numerical aperture of 0.55. The probe spot size (Full Width at Half Maximum)
is $\sim$1.8 $\mu$m and the pump spot size is $\sim$3.4 $\mu$m, both elongated
by a factor of $1/\sin(50^{\circ})$ because the laser hits the sample at
$50^{\circ}$ with respect to the sample normal. The fluence of the pump and
probe pulses are $F_{\text{pump}}$ = 25 $\mu$J/cm2 and $F_{\text{probe}}$ =
5.7 $\mu$J/cm2, respectively. The transmitted light is collimated by an
identical lens on the opposite side of the sample and leaves the cryostat. The
pump beam is blocked and the probe beam is sent to a detection stage
consisting of a quarter wave plate, a polarization filter, and an amplified
photodetector. The quarter wave plate and the polarization filter are adjusted
until they compensate for the change in polarization caused by the optical
components between the PEM and the detection stage, ensuring that our signals
are purely due to the rotation or ellipticity of the probe polarization
induced by our samples. The first and second harmonic of the signal (50 or 100
kHz) obtained at the photodetector are then proportional to the change in
ellipticity and rotation due to the Faraday effect of the sample. For static
magneto-optic Faraday effect measurements we have blocked the pump beam before
reaching the sample.

###  VI.3 Calculating $\Delta n$ and $\Delta D$ from the gate voltages

The gate-induced change in charge carrier density ($\Delta n$) and
displacement field ($\Delta D$) at the CGT are calculated from the applied
gate voltages using a parallel plate capacitor model. The displacement field
generated by the top ($D_{\text{t}}$) and back ($D_{\text{b}}$) gates is given
by $D_{i}=\varepsilon_{\text{hBN}}E_{i}=\frac{1}{2}\sigma_{\text{free},i}$,
where $i$ denotes $t$ or $b$, $\varepsilon_{\text{hBN}}$ =
$3.8\varepsilon_{0}$ is the hBN dielectric constant [76] with
$\varepsilon_{0}$ the vacuum permittivity, and $\sigma_{\text{free}}$ the free
charge per unit area. The applied top and back gate voltages are related to
$\sigma_{\text{free}}$ by $V_{\text{i}}=-\int
D_{\text{i}}/\varepsilon\,\mathrm{d}z$. This equation, combined with the
condition of charge neutrality, gives the following 3 relations:

$\displaystyle V_{t}/d_{t}$
$\displaystyle=\frac{\sigma_{t}-\sigma_{\text{CGT}}-\sigma_{b}}{2\varepsilon_{\text{hBN}}},$
$\displaystyle V_{b}/d_{b}$
$\displaystyle=\frac{\sigma_{b}-\sigma_{\text{CGT}}-\sigma_{t}}{2\varepsilon_{\text{hBN}}},$
$\displaystyle 0$ $\displaystyle=\sigma_{t}+\sigma_{b}+\sigma_{\text{CGT}},$

where $d_{\text{t,b}}$ denotes the thickness of the top (21 nm) and bottom (20
nm) hBN flakes, and $\sigma_{i}$ the free charge per unit area in the top gate
($t$), back gate ($b$), and the CGT flake. Solving this set of equations
yields:

$\displaystyle\sigma_{t}$ $\displaystyle=\varepsilon_{\text{hBN}}V_{t}/d_{t},$
$\displaystyle\sigma_{b}$ $\displaystyle=\varepsilon_{\text{hBN}}V_{b}/d_{b},$
$\displaystyle\Delta n=\sigma_{\text{CGT}}/e$
$\displaystyle=-\frac{\varepsilon_{\text{hBN}}}{e}\left(\frac{V_{t}}{d_{t}}+\frac{V_{b}}{d_{b}}\right),$

where $e$ is the positive elementary charge. Note that for positive gate
voltages, a negative charge carrier density is induced in the CGT. For the
gate-induced change in the displacement field at the CGT layer, we get:

$\displaystyle\Delta
D=(\sigma_{b}-\sigma_{t})/2=-\varepsilon_{\text{hBN}}(V_{t}/d_{t}-V_{b}/d_{b})/2$

Filling in the values for the thickness of the hBN flakes and dielectric
constant of hBN gives $\Delta D/\varepsilon_{0}$ and $\Delta n$ at the CGT:

$\displaystyle\Delta n$ $\displaystyle=-\left(1.00V_{t}+1.05V_{b}\right)\times
10^{12}V^{-1}\text{cm}^{-2}$ $\displaystyle D/\varepsilon_{0}$
$\displaystyle=-\left(0.090V_{t}-0.095V_{b}\right)\text{nm}^{-1}.$

Throughout the main text we use $\Delta D/\varepsilon_{0}$ instead of $\Delta
D$ for easier comparison of our values of the gate-induced change in the
displacement field with values mentioned in other works. Note that we use the
conversion factor $\varepsilon_{0}$ and not the permittivity of CGT.
Therefore, the values for the $\Delta D$ that we report are the equivalent
electric field values in _vacuum_ , not in CGT.

###  VI.4 Windowed Fourier transform

The RMS power spectra of the TRFE oscillations shown in Fig. 1e are calculated
from the TRFE measurements using a windowed Fourier transform. The type of
window used for this calculation if the Hamming window, which extends from
$\Delta t=0$ up to the last data point. The RMS power spectrum
($P_{\text{RMS}}(f)$) of the TRFE oscillations is calculated as

$\displaystyle P_{\text{RMS}}(f)=\Bigg{(}\sum_{\Delta t>0}$
$\displaystyle\left[W_{\text{Ham}}(\Delta t)y(\Delta t)\sin(2\pi f\Delta
t)\right]^{2}+$ $\displaystyle\left[W_{\text{Ham}}(\Delta t)y(\Delta
t)\cos(2\pi f\Delta t)\right]^{2}\Bigg{)}^{1/2},$

where $W_{\text{Ham}}$ is the Hamming window, y the data points of the TRFE
measurements, and $f$ the frequency.

###  VI.5 Determining the $g$-factor and $H_{\text{int}}$

The Landé $g$-factor and $H_{\text{int}}$ can be extracted by fitting the
magnetic field dependence of the precession frequencies with Eq. (1). The
values of $g$ and $H_{\text{int}}$ we obtained from the fit were, in most
cases, strongly correlated. Therefore, we first determined $g$ by fitting the
data for $\mu_{0}H_{\text{ext}}\geq 125$ mT, since $g$ is most sensitive to
the slope at high fields. This yields $g$ = 1.89 $\pm$ 0.01. I we further
allow for an additional uncertainty in the mounting angle of the sample, the
g-factor can change by $\sim 0.1$. Then we determine $H_{\text{int}}$ by
fitting Eq. (1) for all remaining measurements fixing $g$ = 1.89. We note that
the values for $H_{\text{int}}$ do depend on the exact value of $g$, but the
modulation due to electrostatic gating is not affected, as is shown in
Supplementary Section 4.

###  VI.6 Extracting the magnetization precession parameters from the TRFE
measurements

We extract the amplitude, frequency, and starting phase of the oscillations in
the TRFE measurements by fitting the data for $\Delta t>26$ ps with the
phenomenological formula [60, 45]

$\displaystyle y=$ $\displaystyle y_{0}+ae^{-\Delta
t/\tau_{\text{osc}}}\cos\left(2\pi f\Delta t-\phi_{0}\right)$
$\displaystyle+A_{\text{l}}e^{-\Delta
t/\tau_{\text{l}}}+A_{\text{s}}e^{-\Delta t/\tau_{\text{s}}}.$ (2)

This formula describes a phase shifted sinusoid on top a double exponential
background. The background captures the demagnetization and remagnetization of
the CGT, while the sinusoid describes the magnetization precession.

##  VII Data availability

The raw data and the data underlying the figures in the main text are publicly
available through the data repository Zenodo at
https://doi.org/10.5281/zenodo.8321758.

##  VIII Acknowledgments

We thank Bart J. van Wees for critically reading the manuscript and providing
valuable feedback, and we thank J. G. Holstein, H. Adema, H. de Vries, A.
Joshua and F. H. van der Velde for their technical support. This work was
supported by the Dutch Research Council (NWO) through grants STU.019.014 and
OCENW.XL21.XL21.058, the Zernike Institute for Advanced Materials, the
research program “Materials for the Quantum Age” (QuMat, registration number
024.005.006), which is part of the Gravitation program financed by the Dutch
Ministry of Education, Culture and Science (OCW), and the European Union (ERC,
2D-OPTOSPIN, 101076932). Views and opinions expressed are however those of the
author(s) only and do not necessarily reflect those of the European Union or
the European Research Council. Neither the European Union nor the granting
authority can be held responsible for them. The device fabrication and
nanocharacterization were performed using Zernike NanoLabNL facilities.

##  IX Author information

M.H.D.G. conceived and supervised the research. F.H. designed and fabricated
the samples, performed the measurements, analyzed the data, and calculated the
effect of coherent excitations on the magnetization precession under M.H.D.G.
supervision. F.H. and R.R.R.L built and tested the measurement setup. F.H.,
M.H.D.G, and B.K discussed the data and provided the interpretation of the
results. F.H. and M.H.D.G co-wrote the manuscript with input from all authors.

##  X Ethics declaration

###  X.1 Competing interests

The authors declare no competing interests.

## References

  * Huang  _et al._ [2017] B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, “Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit,” Nature 546, 270–273 (2017).
  * Gong  _et al._ [2017] C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, “Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals,” Nature 546, 265–269 (2017).
  * Gong and Zhang [2019] C. Gong and X. Zhang, “Two-dimensional magnetic crystals and emergent heterostructure devices,” Science 363 (2019).
  * Ningrum  _et al._ [2020] V. P. Ningrum, B. Liu, W. Wang, Y. Yin, Y. Cao, C. Zha, H. Xie, X. Jiang, Y. Sun, S. Qin, X. Chen, T. Qin, C. Zhu, L. Wang, and W. Huang, “Recent Advances in Two-Dimensional Magnets: Physics and Devices towards Spintronic Applications,” Research 2020 (2020).
  * Huang  _et al._ [2020] B. Huang, M. A. McGuire, A. F. May, D. Xiao, P. Jarillo-Herrero, and X. Xu, “Emergent phenomena and proximity effects in two-dimensional magnets and heterostructures,” Nature Materials 19, 1276–1289 (2020).
  * Wang  _et al._ [2022] Q. H. Wang, A. Bedoya-Pinto, M. Blei, A. H. Dismukes, A. Hamo, S. Jenkins, M. Koperski, Y. Liu, Q.-C. Sun, E. J. Telford, H. H. Kim, M. Augustin, U. Vool, J.-X. Yin, L. H. Li, A. Falin, C. R. Dean, F. Casanova, R. F. L. Evans, M. Chshiev, A. Mishchenko, C. Petrovic, R. He, L. Zhao, A. W. Tsen, B. D. Gerardot, M. Brotons-Gisbert, Z. Guguchia, X. Roy, S. Tongay, Z. Wang, M. Z. Hasan, J. Wrachtrup, A. Yacoby, A. Fert, S. Parkin, K. S. Novoselov, P. Dai, L. Balicas, and E. J. G. Santos, “The Magnetic Genome of Two-Dimensional van der Waals Materials,” ACS Nano 16, 6960–7079 (2022).
  * Cornelissen  _et al._ [2015] L. J. Cornelissen, J. Liu, R. A. Duine, J. B. Youssef, and B. J. van Wees, “Long-distance transport of magnon spin information in a magnetic insulator at room temperature,” Nature Physics 11, 1022–1026 (2015).
  * Chumak  _et al._ [2015] A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, “Magnon spintronics,” Nature Physics 11, 453–461 (2015).
  * Lebrun  _et al._ [2018] R. Lebrun, A. Ross, S. A. Bender, A. Qaiumzadeh, L. Baldrati, J. Cramer, A. Brataas, R. A. Duine, and M. Kläui, “Tunable long-distance spin transport in a crystalline antiferromagnetic iron oxide,” Nature 561, 222–225 (2018).
  * Manipatruni  _et al._ [2019] S. Manipatruni, D. E. Nikonov, C. C. Lin, T. A. Gosavi, H. Liu, B. Prasad, Y. L. Huang, E. Bonturim, R. Ramesh, and I. A. Young, “Scalable energy-efficient magnetoelectric spin–orbit logic,” Nature 565, 35–42 (2019).
  * Puebla  _et al._ [2020] J. Puebla, J. Kim, K. Kondou, and Y. Otani, “Spintronic devices for energy-efficient data storage and energy harvesting,” Communications Materials 1, 24 (2020).
  * Wang  _et al._ [2017] Q. Wang, A. V. Chumak, L. Jin, H. Zhang, B. Hillebrands, and Z. Zhong, “Voltage-controlled nanoscale reconfigurable magnonic crystal,” Physical Review B 95, 134433 (2017).
  * Chumak, Serga, and Hillebrands [2017] A. V. Chumak, A. A. Serga, and B. Hillebrands, “Magnonic crystals for data processing,” Journal of Physics D: Applied Physics 50, 244001 (2017).
  * Merbouche  _et al._ [2021] H. Merbouche, I. Boventer, V. Haspot, S. Fusil, V. Garcia, D. Gouéré, C. Carrétéro, A. Vecchiola, R. Lebrun, P. Bortolotti, L. Vila, M. Bibes, A. Barthélémy, and A. Anane, “Voltage-Controlled Reconfigurable Magnonic Crystal at the Sub-micrometer Scale,” ACS Nano 15, 9775–9781 (2021).
  * Fan  _et al._ [2016] Y. Fan, X. Kou, P. Upadhyaya, Q. Shao, L. Pan, M. Lang, X. Che, J. Tang, M. Montazeri, K. Murata, L.-T. Chang, M. Akyol, G. Yu, T. Nie, K. L. Wong, J. Liu, Y. Wang, Y. Tserkovnyak, and K. L. Wang, “Electric-field control of spin–orbit torque in a magnetically doped topological insulator,” Nature Nanotechnology 11, 352–359 (2016).
  * Jiang  _et al._ [2023] M. Jiang, H. Asahara, S. Ohya, and M. Tanaka, “Electric Field Control of Spin–Orbit Torque Magnetization Switching in a Spin–Orbit Ferromagnet Single Layer,” Advanced Science 10, 2301540 (2023).
  * Weisheit  _et al._ [2007] M. Weisheit, S. Fähler, A. Marty, Y. Souche, C. Poinsignon, and D. Givord, “Electric field-induced modification of magnetism in thin-film ferromagnets,” Science 315, 349–351 (2007).
  * Endo  _et al._ [2010] M. Endo, S. Kanai, S. Ikeda, F. Matsukura, and H. Ohno, “Electric-field effects on thickness dependent magnetic anisotropy of sputtered MgO/Co40Fe40B20/Ta structures,” Applied Physics Letters 96, 212503 (2010).
  * Chiba  _et al._ [2011] D. Chiba, S. Fukami, K. Shimamura, N. Ishiwata, K. Kobayashi, and T. Ono, “Electrical control of the ferromagnetic phase transition in cobalt at room temperature,” Nature Materials 10, 853–856 (2011).
  * Dietl and Ohno [2014] T. Dietl and H. Ohno, “Dilute ferromagnetic semiconductors: Physics and spintronic structures,” Reviews of Modern Physics 86, 187–251 (2014).
  * Wang  _et al._ [2018] Z. Wang, T. Zhang, M. Ding, B. Dong, Y. Li, M. Chen, X. Li, J. Huang, H. Wang, X. Zhao, Y. Li, D. Li, C. Jia, L. Sun, H. Guo, Y. Ye, D. Sun, Y. Chen, T. Yang, J. Zhang, S. Ono, Z. Han, and Z. Zhang, “Electric-field control of magnetism in a few-layered van der Waals ferromagnetic semiconductor,” Nature Nanotechnology 13, 554–559 (2018).
  * Huang  _et al._ [2018] B. Huang, G. Clark, D. R. Klein, D. MacNeill, E. Navarro-Moratalla, K. L. Seyler, N. Wilson, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao, P. Jarillo-Herrero, and X. Xu, “Electrical control of 2D magnetism in bilayer CrI3,” Nature Nanotechnology 13, 544–548 (2018).
  * Jiang  _et al._ [2018] S. Jiang, L. Li, Z. Wang, K. F. Mak, and J. Shan, “Controlling magnetism in 2D CrI3 by electrostatic doping,” Nature Nanotechnology 13, 549–553 (2018).
  * Verzhbitskiy  _et al._ [2020] I. A. Verzhbitskiy, H. Kurebayashi, H. Cheng, J. Zhou, S. Khan, Y. P. Feng, and G. Eda, “Controlling the magnetic anisotropy in Cr2Ge2Te6 by electrostatic gating,” Nature Electronics 3, 460–465 (2020).
  * Zhuo  _et al._ [2021] W. Zhuo, B. Lei, S. Wu, F. Yu, C. Zhu, J. Cui, Z. Sun, D. Ma, M. Shi, H. Wang, W. Wang, T. Wu, J. Ying, S. Wu, Z. Wang, and X. Chen, “Manipulating Ferromagnetism in Few‐Layered Cr2Ge2Te6,” Advanced Materials 33, 2008586 (2021).
  * Fang  _et al._ [2018] Y. Fang, S. Wu, Z.-Z. Zhu, and G.-Y. Guo, “Large magneto-optical effects and magnetic anisotropy energy in two-dimensional Cr2Ge2Te6,” Physical Review B 98, 125416 (2018).
  * Wu  _et al._ [2019] M. Wu, Z. Li, T. Cao, and S. G. Louie, “Physical origin of giant excitonic and magneto-optical responses in two-dimensional ferromagnetic insulators,” Nature Communications 10, 2371 (2019).
  * Kumar Gudelli and Guo [2019] V. Kumar Gudelli and G.-Y. Guo, “Magnetism and magneto-optical effects in bulk and few-layer CrI 3 : a theoretical GGA + U study,” New Journal of Physics 21, 053012 (2019).
  * Molina-Sánchez  _et al._ [2020] A. Molina-Sánchez, G. Catarina, D. Sangalli, and J. Fernández-Rossier, “Magneto-optical response of chromium trihalide monolayers: chemical trends,” Journal of Materials Chemistry C 8, 8856–8863 (2020).
  * Yang  _et al._ [2021] X. Yang, X. Zhou, W. Feng, and Y. Yao, “Strong magneto-optical effect and anomalous transport in the two-dimensional van der Waals magnets Fe${}_{\text{n}}$GeTe${}_{\text{2}}$ ($n=3$, 4, 5),” Physical Review B 104, 104427 (2021).
  * Hendriks and Guimarães [2021] F. Hendriks and M. H. D. Guimarães, “Enhancing magneto-optic effects in two-dimensional magnets by thin-film interference,” AIP Advances 11 (2021).
  * Deng  _et al._ [2018] Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen, and Y. Zhang, “Gate-tunable room-temperature ferromagnetism in two-dimensional Fe3GeTe2,” Nature 563, 94–99 (2018).
  * Zheng  _et al._ [2020] G. Zheng, W.-Q. Xie, S. Albarakati, M. Algarni, C. Tan, Y. Wang, J. Peng, J. Partridge, L. Farrar, J. Yi, Y. Xiong, M. Tian, Y.-J. Zhao, and L. Wang, “Gate-Tuned Interlayer Coupling in van der Waals Ferromagnet Fe3GeTe2 Nanoflakes,” Physical Review Letters 125, 047202 (2020).
  * Chen  _et al._ [2021] G. Chen, Y. Zhang, S. Qi, and J.-H. Chen, “Gate-controlled magnetic transitions in Fe 3 GeTe 2 with lithium ion conducting glass substrate,” Chinese Physics B 30, 097504 (2021).
  * Wu  _et al._ [2023] Q. Wu, Y. Zhang, Z. Cui, P. Liu, B. Xiang, Z. Li, Z. Fu, and Y. Lu, “Giant and Nonvolatile Control of Exchange Bias in Fe3GeTe2/Irradiated Fe3GeTe2/MgO Heterostructure Through Ultralow Voltage,” Advanced Functional Materials 33, 2214007 (2023).
  * Ni  _et al._ [2021] L. Ni, Z. Chen, W. Li, X. Lu, Y. Yan, L. Zhang, C. Yan, Y. Chen, Y. Gu, Y. Li, R. Zhang, Y. Zhai, R. Liu, Y. Yang, and Y. Xu, “Magnetic dynamics of two-dimensional itinerant ferromagnet Fe3GeTe2,” Chinese Physics B 30, 097501 (2021).
  * Zeisner  _et al._ [2020] J. Zeisner, K. Mehlawat, A. Alfonsov, M. Roslova, T. Doert, A. Isaeva, B. Büchner, and V. Kataev, “Electron spin resonance and ferromagnetic resonance spectroscopy in the high-field phase of the van der Waals magnet CrCl3,” Physical Review Materials 4, 064406 (2020).
  * MacNeill  _et al._ [2019] D. MacNeill, J. T. Hou, D. R. Klein, P. Zhang, P. Jarillo-Herrero, and L. Liu, “Gigahertz Frequency Antiferromagnetic Resonance and Strong Magnon-Magnon Coupling in the Layered Crystal CrCl3,” Physical Review Letters 123, 047204 (2019).
  * Zeisner  _et al._ [2019] J. Zeisner, A. Alfonsov, S. Selter, S. Aswartham, M. P. Ghimire, M. Richter, J. van den Brink, B. Büchner, and V. Kataev, “Magnetic anisotropy and spin-polarized two-dimensional electron gas in the van der Waals ferromagnet Cr2Ge2Te6,” Physical Review B 99, 165109 (2019).
  * Khan  _et al._ [2019] S. Khan, C. W. Zollitsch, D. M. Arroo, H. Cheng, I. Verzhbitskiy, A. Sud, Y. P. Feng, G. Eda, and H. Kurebayashi, “Spin dynamics study in layered van der Waals single-crystal Cr2Ge2Te6,” Physical Review B 100, 134437 (2019).
  * Zollitsch  _et al._ [2023] C. W. Zollitsch, S. Khan, V. T. T. Nam, I. A. Verzhbitskiy, D. Sagkovits, J. O’Sullivan, O. W. Kennedy, M. Strungaru, E. J. G. Santos, J. J. L. Morton, G. Eda, and H. Kurebayashi, “Probing spin dynamics of ultra-thin van der Waals magnets via photon-magnon coupling,” Nature Communications 14, 2619 (2023).
  * Xu  _et al._ [2023] H. Xu, K. Jia, Y. Huang, F. Meng, Q. Zhang, Y. Zhang, C. Cheng, G. Lan, J. Dong, J. Wei, J. Feng, C. He, Z. Yuan, M. Zhu, W. He, C. Wan, H. Wei, S. Wang, Q. Shao, L. Gu, M. Coey, Y. Shi, G. Zhang, X. Han, and G. Yu, “Electrical detection of spin pumping in van der Waals ferromagnetic Cr2Ge2Te6 with low magnetic damping,” Nature Communications 14, 3824 (2023).
  * Gong  _et al._ [2022] Y. Gong, M. Hu, N. Harris, Z. Yang, T. Xie, A. Teklu, N. Kuthirummal, J. Koenemann, X. Xu, S.-W. Cheong, W. McLoud, and C. Gong, “Strong laser polarization control of coherent phonon excitation in van der Waals material Fe3GeTe2,” npj 2D Materials and Applications 6, 9 (2022).
  * Lichtenberg  _et al._ [2023] T. Lichtenberg, C. F. Schippers, S. C. P. van Kooten, S. G. F. Evers, B. Barcones, M. H. D. Guimarães, and B. Koopmans, “Anisotropic laser-pulse-induced magnetization dynamics in van der Waals magnet Fe 3 GeTe 2,” 2D Materials 10, 015008 (2023).
  * Zhang  _et al._ [2020a] T. Zhang, Y. Chen, Y. Li, Z. Guo, Z. Wang, Z. Han, W. He, and J. Zhang, “Laser-induced magnetization dynamics in a van der Waals ferromagnetic Cr2Ge2Te6 nanoflake,” Applied Physics Letters 116, 223103 (2020a).
  * Sun  _et al._ [2021] T. Sun, C. Zhou, Z. Jiang, X. Li, K. Qiu, R. Xiao, C. Liu, Z. Ma, X. Luo, Y. Sun, and Z. Sheng, “Ultra-long spin relaxation in two-dimensional ferromagnet Cr2Ge2Te6 flake,” 2D Materials 8, 045040 (2021).
  * Sutcliffe  _et al._ [2023] E. Sutcliffe, X. Sun, I. Verzhbitskiy, T. Griepe, U. Atxitia, G. Eda, E. J. G. Santos, and J. O. Johansson, “Transient magneto-optical spectrum of photoexcited electrons in the van der Waals ferromagnet Cr2Ge2Te6,” Physical Review B 107, 174432 (2023).
  * Bae  _et al._ [2022] Y. J. Bae, J. Wang, A. Scheie, J. Xu, D. G. Chica, G. M. Diederich, J. Cenker, M. E. Ziebel, Y. Bai, H. Ren, C. R. Dean, M. Delor, X. Xu, X. Roy, A. D. Kent, and X. Zhu, “Exciton-coupled coherent magnons in a 2D semiconductor,” Nature 609, 282–286 (2022).
  * Cho  _et al._ [2023] C. W. Cho, A. Pawbake, N. Aubergier, A. L. Barra, K. Mosina, Z. Sofer, M. E. Zhitomirsky, C. Faugeras, and B. A. Piot, “Microscopic parameters of the van der Waals CrSBr antiferromagnet from microwave absorption experiments,” Physical Review B 107, 94403 (2023).
  * Afanasiev  _et al._ [2021] D. Afanasiev, J. R. Hortensius, M. Matthiesen, S. Mañas-Valero, M. Šiškins, M. Lee, E. Lesne, H. S. J. van der Zant, P. G. Steeneken, B. A. Ivanov, E. Coronado, and A. D. Caviglia, “Controlling the anisotropy of a van der Waals antiferromagnet with light,” Science Advances 7, eabf3096 (2021).
  * Khusyainov  _et al._ [2023] D. Khusyainov, T. Gareev, V. Radovskaia, K. Sampathkumar, S. Acharya, M. Šiškins, S. Mañas-Valero, B. A. Ivanov, E. Coronado, T. Rasing, A. V. Kimel, and D. Afanasiev, “Ultrafast laser-induced spin–lattice dynamics in the van der Waals antiferromagnet CoPS3,” APL Materials 11 (2023).
  * Zhang  _et al._ [2020b] X.-X. Zhang, L. Li, D. Weber, J. Goldberger, K. F. Mak, and J. Shan, “Gate-tunable spin waves in antiferromagnetic atomic bilayers,” Nature Materials 19, 838–842 (2020b).
  * Guimarães and Koopmans [2018] M. H. D. Guimarães and B. Koopmans, “Spin Accumulation and Dynamics in Inversion-Symmetric van der Waals Crystals,” Physical Review Letters 120, 266801 (2018).
  * Rojas-Lopez  _et al._ [2023] R. R. Rojas-Lopez, F. Hendriks, C. H. van der Wal, P. S. S. Guimarães, and M. H. D. Guimarães, “Magnetic field control of light-induced spin accumulation in monolayer MoSe2,” 2D Materials 10, 035013 (2023).
  * Koopmans  _et al._ [2010] B. Koopmans, G. Malinowski, F. Dalla Longa, D. Steiauf, M. Fähnle, T. Roth, M. Cinchetti, and M. Aeschlimann, “Explaining the paradoxical diversity of ultrafast laser-induced demagnetization,” Nature Materials 9, 259–265 (2010).
  * Kim  _et al._ [2022] S. K. Kim, G. S. D. Beach, K.-J. Lee, T. Ono, T. Rasing, and H. Yang, “Ferrimagnetic spintronics,” Nature Materials 21, 24–34 (2022).
  * Scheid  _et al._ [2022] P. Scheid, Q. Remy, S. Lebègue, G. Malinowski, and S. Mangin, “Light induced ultrafast magnetization dynamics in metallic compounds,” Journal of Magnetism and Magnetic Materials 560, 169596 (2022).
  * Carteaux  _et al._ [1995] V. Carteaux, D. Brunet, G. Ouvrard, and G. Andre, “Crystallographic, magnetic and electronic structures of a new layered ferromagnetic compound Cr2Ge2Te6,” Journal of Physics: Condensed Matter 7, 69–87 (1995).
  * Ren  _et al._ [2021] W.-n. Ren, K.-j. Jin, J.-s. Wang, C. Ge, E.-J. Guo, C. Ma, C. Wang, and X. Xu, “Tunable electronic structure and magnetic anisotropy in bilayer ferromagnetic semiconductor Cr2Ge2Te6,” Scientific Reports 11, 2744 (2021).
  * Mizukami  _et al._ [2010] S. Mizukami, E. P. Sajitha, D. Watanabe, F. Wu, T. Miyazaki, H. Naganuma, M. Oogane, and Y. Ando, “Gilbert damping in perpendicularly magnetized Pt/Co/Pt films investigated by all-optical pump-probe technique,” Applied Physics Letters 96 (2010).
  * Lohmann  _et al._ [2019] M. Lohmann, T. Su, B. Niu, Y. Hou, M. Alghamdi, M. Aldosary, W. Xing, J. Zhong, S. Jia, W. Han, R. Wu, Y.-T. Cui, and J. Shi, “Probing Magnetism in Insulating Cr2Ge2Te6 by Induced Anomalous Hall Effect in Pt,” Nano Letters 19, 2397–2403 (2019).
  * Pershan, van der Ziel, and Malmstrom [1966] P. S. Pershan, J. P. van der Ziel, and L. D. Malmstrom, “Theoretical discussion of the inverse faraday effect, raman scattering, and related phenomena,” Physical Review 143, 574–583 (1966).
  * Gridnev [2008] V. N. Gridnev, “Phenomenological theory for coherent magnon generation through impulsive stimulated Raman scattering,” Physical Review B 77, 094426 (2008).
  * Kalashnikova  _et al._ [2008] A. M. Kalashnikova, A. V. Kimel, R. V. Pisarev, V. N. Gridnev, P. A. Usachev, A. Kirilyuk, and T. Rasing, “Impulsive excitation of coherent magnons and phonons by subpicosecond laser pulses in the weak ferromagnet FeBO3,” Physical Review B 78, 104301 (2008).
  * Hansteen  _et al._ [2005] F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond Photomagnetic Switching of Spins in Ferrimagnetic Garnet Films,” Physical Review Letters 95, 047402 (2005).
  * van Kampen  _et al._ [2002] M. van Kampen, C. Jozsa, J. T. Kohlhepp, P. LeClair, L. Lagae, W. J. de Jonge, and B. Koopmans, “All-optical probe of coherent spin waves,” Physical Review Letters 88, 227201 (2002).
  * Yan, Gamble, Jr., and Nelson [1985] Y.-X. Yan, E. B. Gamble, Jr., and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” The Journal of Chemical Physics 83, 5391–5399 (1985).
  * Kirilyuk, Kimel, and Rasing [2010] A. Kirilyuk, A. V. Kimel, and T. Rasing, “Ultrafast optical manipulation of magnetic order,” Reviews of Modern Physics 82, 2731–2784 (2010).
  * Alben  _et al._ [1972] R. Alben, E. M. Gyorgy, J. F. Dillon, and J. P. Remeika, “Polarization-dependent photoinduced effects in silicon-doped yttrium iron garnet,” Physical Review B 5, 2560–2577 (1972).
  * Hansteen  _et al._ [2006] F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Nonthermal ultrafast optical control of the magnetization in garnet films,” Physical Review B 73, 014421 (2006).
  * Shen  _et al._ [2018] L. Q. Shen, L. F. Zhou, J. Y. Shi, M. Tang, Z. Zheng, D. Wu, S. M. Zhou, L. Y. Chen, and H. B. Zhao, “Dominant role of inverse Cotton-Mouton effect in ultrafast stimulation of magnetization precession in undoped yttrium iron garnet films by 400-nm laser pulses,” Physical Review B 97, 224430 (2018).
  * Yoshimine  _et al._ [2014] I. Yoshimine, T. Satoh, R. Iida, A. Stupakiewicz, A. Maziewski, and T. Shimura, “Phase-controllable spin wave generation in iron garnet by linearly polarized light pulses,” Journal of Applied Physics 116, 043907 (2014).
  * Tang  _et al._ [2022] M. Tang, J. Huang, F. Qin, K. Zhai, T. Ideue, Z. Li, F. Meng, A. Nie, L. Wu, X. Bi, C. Zhang, L. Zhou, P. Chen, C. Qiu, P. Tang, H. Zhang, X. Wan, L. Wang, Z. Liu, Y. Tian, Y. Iwasa, and H. Yuan, “Continuous manipulation of magnetic anisotropy in a van der Waals ferromagnet via electrical gating,” Nature Electronics 6, 28–36 (2022).
  * Stupakiewicz  _et al._ [2017] A. Stupakiewicz, K. Szerenos, D. Afanasiev, A. Kirilyuk, and A. V. Kimel, “Ultrafast nonthermal photo-magnetic recording in a transparent medium,” Nature 542, 71–74 (2017).
  * Zomer  _et al._ [2014] P. J. Zomer, M. H. D. Guimarães, J. C. Brant, N. Tombros, and B. J. van Wees, “Fast pick up technique for high quality heterostructures of bilayer graphene and hexagonal boron nitride,” Applied Physics Letters 105, 013101 (2014).
  * Laturia, van de Put, and Vandenberghe [2018] A. Laturia, M. L. van de Put, and W. G. Vandenberghe, “Dielectric properties of hexagonal boron nitride and transition metal dichalcogenides: from monolayer to bulk,” npj 2D Materials and Applications 2, 6 (2018).