# Spin dynamics across metallic layers on the few-femtosecond timescale

Romain Géneaux, Hung-Tzu Chang, Alexander Guggenmos, Renaud Delaunay, François Légaré, Katherine Légaré, Jan Lüning, Tymur Parpiiev, Ilana J. P. Molesky, Bethany R de Roulet, et al.

► To cite this version:

Romain Géneaux, Hung-Tzu Chang, Alexander Guggenmos, Renaud Delaunay, François Légaré, et al. Spin dynamics across metallic layers on the few-femtosecond timescale. Physical Review Letters, 2024, 133 (10), pp.106902. 10.1103/PhysRevLett.133.106902. cea-04693950

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Spin dynamics across metallic layers at the few-femtosecond timescale

Romain Géneaux,¹,²,³,* Hung-Tzu Chang,¹,† Alexander Guggenmos,¹ Renaud Delaunay,⁴ François

Légaré,⁵ Katherine Légaré,⁵ Jan Lüning,⁶ Tymur Parpiiev,¹ Ilana J.P. Molesky,¹ Bethany R. de

Roulet,¹ Michael W. Zuerch,¹,⁷ Sangeeta Sharma,⁸,⁹ Martin Schultze,¹⁰ and Stephen R. Leone¹, ¹¹, ¹²

¹Department of Chemistry, University of California, Berkeley, 94720, USA

²Université Paris-Saclay, CEA, LIDYL, 91191 Gif-sur-Yvette, France

³CY Cergy Paris Université, CEA, LIDYL, 91191 Gif-sur-Yvette, France

⁴Sorbonne Université, CNRS, Laboratoire de Chimie Physique-Matière et Rayonnement, LCPMR, 75005 Paris, France

⁵Institut National de la Recherche Scientifique, Centre Énergie Matériaux et Télécommunications, Varennes, Québec, Canada

⁶Helmholtz-Zentrum Berlin für Materialien und Energie,
Albert-Einstein-Strasse 15, 12489 Berlin, Germany

⁷Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

⁸Max-Born-Institute for Non-linear Optics and Short Pulse Spectroscopy, Max-Born Strasse 2A, 12489 Berlin, Germany

⁹Institute for Theoretical Solid-State Physics, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany

¹⁰Institute of Experimental Physics, Graz University of Technology, Petersgasse 16, 8010 Graz, Austria

¹¹Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

¹²Department of Physics, University of California, Berkeley, 94720, USA

We measure the light-driven response of a magnetic multilayer structure made of thin alternating layers of cobalt and platinum at the few-femtosecond timescale. Using attosecond magnetic circular dichroism, we observe how light rearranges the magnetic moment during and after excitation. The results reveal a sub-5 fs spike of magnetization in the platinum layer, which follows the shape of the driving pulse. With the help of time-dependent density functional theory, we interpret the observations as light-driven spin injection across the metallic layers of the structure. The light-triggered spin current is strikingly short, largely outpacing decoherence and dephasing. The findings suggest that the ability of shaping light fields in refined ways could be translated into shaping new forms of spin currents in materials.

In ferromagnetic materials, electrons of opposite spins exhibit different properties. This spin-dependent behavior can create spin-polarized electronic currents – most commonly called spin currents – which are prominent vectors of information [1, 2]. Most remarkably, electron dynamics following femtosecond laser excitation are also spin-dependent, which means that ultrashort laser pulses are able to create spin currents [3], resulting in time-compressed signals that can be transported across complex heterostructures [4]. These techniques allow to store and transport information [5], or to trigger subsequent processes such as terahertz emission [6, 7].

However, our abilities to create spin currents with laser pulses are still limited. To date, the spin-polarization of electrons arises from incoherent mechanisms. For instance, majority carriers may experience longer mean free paths [3, 8] or longer lifetime following optical excitation [9], which allows to selectively inject them into other materials. While this provides efficient spin injection, the incoherent nature of scattering means that the temporal shape of the created spin currents are set by inherent material properties, and not by the temporal structure of the driving laser pulse. As a result, it is hitherto unclear how to coherently control magnetic properties at femtosecond timescales, or to drive spin dynamics at optical frequencies.

Here we show that spin currents can actually be created at extremely short times – before incoherent processes start to play a role. One hint that it is indeed

possible was obtained in earlier works [10, 11] and particularly in a recent breakthrough [12], which showed that the magnetization of ferromagnetic layer reacted instantaneously to a laser-field, when put in contact with a Pt layer. Interpretation of these observations hypothesized the rapid onset of an interface spin current created by a mechanism called optical inter-site spin transfer (OISTR [13]), which we set out to explore here. Our strategy relies on driving ferromagnetic/paramagnetic heterostructures with few-cycle pulses, and to probe spin injection across the structure using attosecond metrology. We investigate spin dynamics in a multilayer sample of Co/Pt, containing 20 periods of cobalt and platinum interfaces, each layer being 6 and 8 Å thick, respectively (see Fig. 1a). This type of structure is ubiquitous in spintronic research, in particular to obtain giant magnetoresistance effects [14, 15]. This particular layer arrangement has two advantages for our purposes: (i) it creates an out-of-plane magnetic easy axis [16], maximizing magneto-optical effects with normally incident light; (ii) it multiplies the number of Co/Pt interfaces, so that potential injection taking place there becomes more measurable compared to bulk regions. The sample is placed in an external out-of-plane magnetic field, saturating the magnetization of the ferromagnetic Co layers as well as weakly magnetizing the Pt layers by proximity effects, even though the latter are paramagnetic [17, 18]. The sample is capped on both sides to prevent oxidation.

To resolve eventual spin transfer phenomena, we lever-
<figure><img src="image_2.png" /><figcaption>FIG. 1. **Schematic of the experiment and static characterization.** a. Co/Pt multilayer sample used in the experiment. It consists of 20 periods, and is capped on both sides to prevent oxidation. The inset shows that in an external magnetic field, both Co and Pt layers are magnetized b. Static XMCD measured with positive or negative XUV helicity (blue and red lines, respectively). c. Static optical density (without excitation) across the attosecond pulse bandwidth. Green and blue vertical lines indicate the Pt and Co absorption edges, respectively.</figcaption></figure>

age the element-sensitivity of core-level spectroscopy, together with the outstanding time resolution of attosecond spectroscopy. We measure the sample absorption using broadband XUV attosecond pulses covering 40-70 eV. Figure 1c displays the static optical density of the sample in this spectral region, in which absorptions from both the Co 4p and Pt 6p core-levels are visible, corresponding to the Co M$_{2,3}$ and O$_{3}$ edges. O$_{3}$-edge attosecond spectroscopy has recently been demonstrated in several elements [19–21]. To add spin resolution, the polarization of the attosecond pulses is set to elliptical by specialized XUV optics (Ultrafast Innovations). This allows measuring the XUV Magnetic Circular Dichroism (XMCD), defined as $\text{XMCD} = \log I_+/I_-$, where $I_\pm$ corresponds to the recorded transmission with the sample magnetized along or oppositely from the laser propagation axis, respectively. Figure 1b shows the static XMCD for the two helicities of incoming XUV radiation, displaying a nice mirroring. Compared to literature values, the amplitude of the peaks is reduced by the ellipticity of the XUV pulse (60% on average in the probed energy range), but their shape matches well: the larger peak around 60 eV is the M$_{2,3}$ XMCD of pure cobalt [22] and the broader peak at 51-56 eV corresponds to the Pt O$_{3}$ edge [23]. These two features will be used to analyze the respective spin dynamics of each element.

The sample is then excited by a sub-4 fs visible/near-infrared laser pulse, with linear polarization. The change

in optical density is measured successively when magnetizing the sample along or opposed to the laser propagation direction, yielding $\Delta OD_{B+}$ and $\Delta OD_{B-}$ (shown separately in the Supplemental Material [24]). Figure 2a shows the purely electronic response, isolated by taking $\Delta OD = (\Delta OD_{B+} + \Delta OD_{B-})/2$. As soon as the sample is excited (delay $t > 0$), changes are measured across the entire probed spectral range. The strongest features are red shifts of both Pt and Co edges (lineouts are shown in SM [24]), similar to the behavior of laser-heated nickel described in great detail in earlier work [25]. The magnetic response is quantified through the change in XMCD: $\Delta \text{XMCD} = \Delta OD_{B+} - \Delta OD_{B-}$, shown in Figure 2b. Reversing the helicity of the XUV light results in a sign change of the entire measurement (see SM [24]), confirming that all observed features originate from a real dichroic response. In this 200 fs-long trace, we can readily see that the overall trend is mostly a decrease of the magnitude of the dichroism at all energies, consistent with femtosecond demagnetization of the sample at a slow timescale. To our knowledge, this is the first time that time-resolved XMCD is measured over such a broad and continuous energy range, covering core transitions of both elements of the heterostructure. Since the probe light spectrum is continuous, we measure not only changes of amplitudes at specific discrete energies, but also any change in the spectral shape of magnetic dichroism. This ability was also demonstrated in a recent study
<figure><img src="image_3.png" /><figcaption>FIG. 2. Time-dependent XUV magnetic circular dichroism. a. Change in optical density obtained by averaging the measurements for each magnetization direction. The overlaid black line is the static optical density. The experimental excitation fluence is 25±2 mJ/cm² and the pump pulse duration is 3.5±0.4 fs. b. Change in XUV magnetic circular dichroism, obtained by subtracting the two optical density maps. The black line is the static XMCD of the sample.</figcaption></figure>

on Heusler alloys [26]. Distinguishing between lineshape or amplitude changes is a known hindrance when using narrowband light, such as discrete HHG sources, most free-electron lasers and synchrotron radiation [27]. Moreover, because the entire XMCD is captured at once, the approach is particularly time-efficient. Thus, the method should be advantageous to probe magnetic dynamics at any timescale.

We focus on the few femtoseconds timescale, which is experimentally attainable here, contrary to the majority of previous experiments. To this end, we perform finer transient XMCD scans with time steps of 333 as. We first consider the electronic dynamics obtained by averaging the two sample magnetizations. Following previously established methodology for XUV transient absorption in pure transition metals [25], we integrate the prominent positive signal right below the absorption edges (around 52 eV for Pt and 59 for Co) to quantify the edge shifts, and show the resulting signal rise in Fig. 3(a). We find that the electronic charges respond simultaneously in Co and Pt within an uncertainty of 1.5 fs, which is in line with previous attosecond measurements in metals [12, 25, 28]. However, in all measurements including the one shown here, the Pt signal rises 1.5 times faster than in Co. One possibility for this disparity is that each element has different electron-electron thermalization times [25, 29]. However, we found that the same measurement performed in elemental Co and Pt clearly showed the opposite trend, with electrons in Co thermalizing faster than in Pt [30]. Thus we conclude that the disparity must be specific to the heterostructure and thus rooted in charge flow across the interfaces.

To now gain insight into the response of the spin system, the transient XMCD trace needs to be converted into physically meaningful parameters for each layer. At

each time delay, we have [23]:

$$XMCD(t, \omega) = -\frac{4d_{Pt}\omega}{cP}\beta_{Pt}(t, \omega) - \frac{4d_{Co}\omega}{cP}\beta_{Co}(t, \omega), \quad (1)$$

where $d_{Pt/Co}$ are the total thicknesses and $\beta_{Pt/Co}$ the imaginary part of the magneto-optical function of each element, c the speed of light, P the degree of circular polarization and w the photon frequency. The broadband measurement shows that none of the observed peaks are spectrally shifting, nor are they changing shape (see SM [24]). Therefore we consider that the magneto-optical functions of Pt and Co are not changing shape as a function of time, a possibility that was raised in Ref. [27]. Thus we write the time dependence of $\beta_{Pt}$ and $\beta_{Co}$ as a time-varying scaling coefficient, $a_{Pt/Co}(t)$, meaning the XMCD is a linear combination of two spectral components corresponding to the two elements:

$$XMCD(t) \propto d_{Pt}a_{Pt}(t) \cdot \beta_{Pt}(\omega) + d_{Co}a_{Co}(t) \cdot \beta_{Co}(\omega), \quad (2)$$

where $\beta_{Pt/Co}$ are taken as their ground-state values known from synchrotron measurements [22]. The time-dependent amplitudes obtained by fitting the change in XMCD are displayed in Figure 3(b) and represent the change in magnetic moment in each layer [23]. Here, attosecond spectroscopy brings a key advantage: we distinguish magnetic dynamics taking place during or after the pump pulse. This uncovers a striking behavior: during excitation (highlighted area in Fig. 3(b)), the cobalt magnetization is quenched at a very high rate, with the magnetic moment being already suppressed by 10% only 2 fs after the peak of the pump pulse. At the same time, the platinum magnetic moment shows a clear increase of a few percent. Once the pump pulse has passed, the sample follows a more conventional field-free behavior: both
<figure><img src="image_4.png" /><figcaption>FIG. 3. Electronic and magnetic dynamics at the few-femtosecond timescale a. Normalized change in op- tical density at the Co (blue) and Pt (green) edges. Dots are data points, with error bars the standard deviation of several measurement for each time delay. Full lines are exponential fits of the response. b. Change in magnetic moment ex- pressed in percent of the ground-state value for Co (blue) and Pt (green). Circles are data points, with error bars obtained by Monte Carlo propagation of uncertainties. Full lines show a moving average of data points. In both panels, the brown shaded area is the experimental pump intensity profile ob- tained by a dispersion-scan measurement.</figcaption></figure>

layers begin to demagnetize on timescales in correspon- dence with literature reports on laser induced demagne- tization. Measurements at longer times (shown in SM [24]) show that the maximum quenching is attained at t = 150 fs and amounts to 30% for Co and 20% for Pt, compared to their equilibrium value.

The observed behavior strongly suggests that the laser
pulse triggers a net transfer of charge and spin from
cobalt layers into platinum, consistently with the OISTR
mechanism [13]. To confirm this, we turn to state-of-the-
art time-dependent density functional theory (TDDFT),
which has been very successful at calculating magnetic

dynamics at short times [10, 12, 13, 23]. The compu-
tational cost of such calculations limits us to simulat-
ing only a few atomic layers. Therefore, we consider an
L1₀-ordered 50-50 alloy of CoPt, which reproduces well
the Co/Pt interface of our sample at the atomic level.
This model will not be able to reproduce any bulk ef-
fect in individual layers, nor an effect due to the periodic
multilayer structure of the real sample. However, the
physics of such thin layers are known to be dominated
by interface effects [31] and as such should be reasonably
reproduced by the theory. We use the highly accurate
full potential linearized augmented-plane-wave method,
as implemented in the ELK code [32]. For time prop-
agation we used a time step of 2 attoseconds and the
algorithm outlined in Ref. [33]. More details are avail-
able in the SM [24]. Figure 4(a) displays the obtained
relative change in magnetic moment for each element,
with a pump intensity of 2 × 10¹¹ W cm⁻². The calcu-
lation reproduces well the behavior observed experimen-
tally during the pump pulse. The magnetic moment of
Co and Pt are decreasing and increasing, respectively,
with a shape that closely follows β(t) ∝ ∫t I<sub>pump</sub>(τ)dτ,
which is consistent with the phenomenon being driven
by electronic injection. We also calculate the relative
change in XMCD for the Co M<sub>2,3</sub> and Pt O<sub>3</sub> edges at
a few time delays, shown as crosses in Fig. 4(a). We
find that the XMCD amplitudes follow the dynamics of
the local spin moments in each element, confirming the
validity of the experimental data analysis. However, the
calculation overestimates the change of Pt moment, com-
pared to the experiment. This is most likely because the
computation does not include any incoherent interaction,
such as scattering with phonons or spin diffusion, which
are additional channels for demagnetization. Addition-
ally, the many Co/Pt interfaces present in the experiment
are imperfect, and the measurement averages the signal
over all of them. These factors can result in an overall
reduction of the measured Pt moment. The calculations
also display fast oscillations of the magnetic moments at
twice the laser field period, which are inaccessible to the
experiment due to insufficient sensitivity. We note that
these oscillations could be spurious effects from the cal-
culation, which does not include dissipation channels.

Both experiment (Fig. 3(b)) and theory (Fig. 4(a))
are consistent with OISTR with a net spin transfer from
Co to Pt, accompanying majority carriers from Co to Pt
and minority carriers from Pt to Co. The mechanism
is also compatible with the faster electronic excitation
observed in Pt(Fig. 3(a)): as the laser injects Co ma-
jority spins into Pt, it leads to more excited carriers in
Pt layers at early times. Most importantly, at timescales
considered here, spin injection is not mediated by inco-
herent effects. Instead, it is made possible by the favor-
able band alignment at the Co/Pt interface, as already
noticed in Ref. [13]. Although dichroism measurements
do not directly probe currents, the concomitant change in
<figure><img src="image_5.png" /><figcaption>FIG. 4. Ab initio simulations of magnetic dynamics</figcaption></figure>

a. Computed change in magnetic moment expressed in per-
cent of the ground-state value for Co (blue) and Pt (green).
Dots are raw data points, full lines are a moving average and
crosses are computed integrated XMCD for specific time de-
lays. The brown shaded area is the pump intensity profile
used in the calculation. b. Maximum change in platinum
moment expressed in units of μ<sub>B</sub> computed for varying pump
intensities.

magnetic moments of both layers indicates a spin current
which stands out due to its extremely short, few fem-
tosecond duration. Finally, we computationally explored
the intensity dependence of the effect. Figure 4(b) shows
the maximum Pt moment as a function of pumping inten-
sity. The dependence is found to be sub-linear, and the
spin injection seems to take place even at lower inten-
sities. Experimentally, we only observed spin injection
with very short pulses, most likely because overcoming
the experimental noise floor required sufficient intensity,
while staying below the sample damage threshold. But
the calculations suggest that the effect is more universal
and could be observed for longer or less intense driving
pulses.

In summary, we investigated the electronic and mag-
netic dynamics of a Co/Pt multilayer structure at the
few-femtosecond timescale. While spin responses on such
timescale have been reported before [10–12], our work
provides new information mainly because of the ability
to directly capture charge and spin dynamics simultane-
ously for both elements. As a result, we uncover a di-
rect observation of laser-induced spin injection between
metallic layers. This effect takes place in synchrony with
the laser envelope, which is a key difference with other
types of light-triggered spin dynamics, such as the ones
responsible for terahertz emission [6]. This opens the
way to the possibility of shaping the envelope of laser
pulses to manipulate the magnetization in time, which
can eventually lead to the enhancement and control of
spin currents. The dynamics measured here can be seen
as the first example of such shaping: by using temporally
compressed driving pulses, we create a spin current last-

ing only a few femtoseconds, which is the shortest spin
current observed to date.

Generally, we show that attosecond methodology
answers two questions that are key for fundamental
understanding and potential applications of spintronic
devices at ultrafast timescales: it captures how ultra-
short spin-polarized currents can be created and how
they are injected across materials. We believe that
it is not only this specific multilayer structure that
can display ultrashort spin currents – any spintronic
structure with proper band alignment between its layers
might do the same. With ever-increasing sensitivity
in attosecond metrology, light-induced manipulation of
magnetization could even evolve from envelope-driven
effects, such as captured here, to coherent field-driven
effects, as initially formulated by Bigot et al. [34]. While
our experiment had insufficient sensitivity to capture
them, future attosecond technology will surely allow to
tackle these fascinating questions.

Investigations at UC Berkeley were supported by the U.S. Air Force Office of Scientific Research Nos. FA9550-19-1-0314 (primary), FA9550-20-1-0334, FA9550-22-1-0451, FA9550-15-0037 (concluded), and FA9550-14-1-0154 (concluded), the Defense Advanced Research Projects Agency PULSE Program Grant W31P4Q-13-1-0017 (concluded), and the W.M. Keck Foundation award No. 046300-002 (concluded). R.G. acknowledges funding by the European Union (ERC Spinfield, Project No. 101041074). H.T.C acknowledges funding from the Alexander von Humboldt Foundation. K.L. acknowledges support from the NSERC Alexander Graham Bell Canada Graduate Scholarships program. Sharma would like to thank the DFG for funding through project-ID 328545488 TRR227 (project A04) and Leibniz Professorin Program (SAW P118/2021).

<footnote>* romain.geneaux@cea.fr</footnote>

<footnote>† Current address: Max Planck Institute for Multidisciplinary Sciences, 37077 Goettingen, Germany</footnote>

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