Ultrafast Demagnetization Excited by Extreme Ultraviolet Light From a Free-Electron Laser

, , , , Ultrashort and intense extreme ultraviolet (XUV) and X-ray pulses readily available at free-electron lasers (FELs) enable studying non-linear light−matter interactions on femtosecond timescales. Here, we report on the non-linear fluence dependence of magnetic scattering of Co/Pt multilayers, using FERMI FEL’s 70-fs-long single and double XUV pulses, the latter with a temporal separation of 200 fs, with a photon energy slightly detuned to the Co M 2,3 absorption edge. We observe a quenching in magnetic scattering that sets-in already in the non-destructive fluence regime of a few mJ/cm² typically used for FEL-probe experiments on magnetic materials. Calculations of the transient electronic structure in tandem with a phenomenological modeling of the experimental data by means of ultrafast demagnetization unambiguously show that XUV-radiation-induced demagnetization is the dominant mechanism for the quenching in the investigated fluence regime of < 50 mJ/cm², while light-induced changes of the electronic core levels are predicted to additionally occur at higher fluences. The modeling of the data further indicates that the demagnetization proceeds on the sub-20-fs timescale. This ultrashort timescale is consistent with non-coherent models for ultrafast demagnetization, considering the sub-femtosecond lifetime of hot electrons with energies of a few 10 eV generated by the XUV radiation.

The starting point of the investigation of the nonlinear interaction of ultra-short FEL radiation and magnetic materials was the observation of a drastic quenching of the magnetic scattering signal of Co/Pt multilayers within the sub-100-fs long pulse duration, when using XUV-pulses with a fluence of = 5 J/cm², resonantly tuned to the Co M2,3 edge at '( = 59.6 eV [20]. This quenching was explained by a shift of the 3p core levels to lower energies due to the charged environment. At higher photon energies, corresponding to the Co L3 edge ( '( = 778 eV), a quenching of the magnetic-scattering signal was also observed for fluences ≳ 10 mJ/cm² [21] and was assigned to stimulated emission [22,23]. In the hard X-ray regime, magnetic-scattering experiments with high fluences are not reported [24]. However, Yoneda et al. performed X-ray-emission spectroscopy experiments for Fe [19] and Cu [18] using radiation resonantly tuned to the K edges. They found a saturable absorption accompanied by a band shift [19] and stimulated emission [18] for fluences ≳ 10 8 J/cm². Recently, ultrafast demagnetization was additionally put forward to explain the quenching of magnetic scattering [25] and XMCD effect in absorption [26] for FEL radiation resonantly tuned to the Co M2,3 and L edge, respectively [27]. In light of the contrasting explanations for the non-linear photonmagnetic material interaction, it becomes clear that a variety of mechanisms may play a role in the quenching of XMCD effect-based signals.
Here, we report on the XUV-fluence dependence of the resonant magnetic small-angle X-ray scattering (mSAXS) of Co/Pt multilayers. For the experiments, single and double-FEL-pulse modes with photon energies tuned closely above the M2,3 edge of Co are used ( Fig. 1(a)), enabling an unambiguous determination whether band shift, stimulated emission or demagnetization is the dominant mechanism. For both FEL modes, a quenching of magnetic scattering with increasing fluence is observed. Both sets of data are well-described by a phenomenological model that was developed to describe XUV-radiation-induced 3 (20) demagnetization, while calculations on light-induced transient changes in the population and energy level of the 3p shell cannot explain the experimental data. Our study provides evidence for the existence of ultrafast demagnetization in the XUV regime and additionally indicates that the demagnetization proceeds on a sub-20-fs timescale. This result is supported by the extremely short lifetime of XUV-generated hot electrons even when only considering conventional, i.e., non-coherent, demagnetization mechanisms, as detailed for Elliott-Yafet spin-flip scattering [4].

Results
Magnetic small-angle X-ray scattering and scattering efficiency. The mSAXS experiments on a (0.8nm Co/1.4nm Pt)16 multilayer, which exhibits perpendicular magnetic anisotropy [29] (see Methods) and nanoscale magnetic domains [9], were performed utilizing 70-fs-long circularly-polarized XUV-pulses at FERMI's DiProI beamline [30]. Two different FEL operation modes were used, namely the conventional single-pulse (1P) as well as the double-pulse mode (2P) [31,32] with a pulse separation of 200 fs ( Fig. 1(a), Methods). The wavelength of the FELradiation for the single-pulse mode was '(,;< = 20.3 nm ( '(,;< = 61.1 eV), whereas in the double-pulse mode the wavelengths of the sub-pulses were shifted by ∆ ≈ ±0.035 nm with respect to '(,;< ( Fig. 1(b)) allowing for a spectroscopic detection of the sub-pulse intensities ( Fig. 1(b), inset). All wavelengths were blue shifted with respect to the maximum in magnetic-scattering cross section located at '(,BCDE F,G HIJH = 20.8 nm ( BCDE F,G HIJH = 59.6 eV; Fig. 1(b)) [33]. The blue shift ensures a comparable scattering cross section for all used wavelengths, allowing for a direct comparison of the single and double-pulse data.
Furthermore, it enables identifying the impact of the electronic level shift on the quenching as outlined below.
The radial intensity vs scattering vector is obtained by azimuthal averaging of the scattered intensity ( Fig. 1(c)). The peak position 'HMN ≈ 0.036 nm -1 corresponds to an average domain width of ≈ 90nm, consistent with previous studies on a nominally identical sample [8]. The peak value ( 'HMN ) serves as a quantitative measure for the strength of the magneticscattering cross section (Methods), given by [34] V is the saturation magnetization, |< 3 , m | ±; (;) |3 , p > | T the dipole-transition matrixelement describing core-to-valence transitions between 3p and 3d states under the action of the dipole-operator ±; (;) , and ∆ the resonance width of the 3d states [34].
As a measure for the quenching, we define the scattering efficiency Hss as the ratio of peak intensity ( 'HMN ) and pulse energy 'tuvH (proportional to the number of incident photons) 4 (20) normalized to one at small fluences < 1 wx yw F . The scattering efficiency Hss vs peak fluence behavior, extracted from single-pulse and double-pulse experiments, is given in Fig. 2. For the latter, is the sum of the peak-fluences of both sub-pulses, hence for the same , the single pulse has twice the peak-intensity as compared to the sub-pulses in the double-pulse mode.
Both Hss ( ) datasets can be described by single exponentials ( Hss ( ) = exp |−•€) suggesting the presence of one dominant mechanism for quenching. Characteristic fluences of ;<,H‚' = (26.3 ± 1.1) mJ/cm² and T<,H‚' = (25.1 ± 0.8) mJ/cm² are obtained, reflecting the similarity of both curves within the experimental resolution. As shown below, this similarity is a fingerprint for ultrafast demagnetization occurring on a sub-20-fs timescale. Note that the quenching sets in already in the few-mJ/cm² regime, which is much lower than the observed damage threshold of IMwMJH ≈ 20 mJ/cm², i.e., the minimum fluence irreversibly altering the sample's scattering pattern.
Modeling. In order to determine the underlying mechanism for quenching, the experimental results are compared with different models (for details see Supplement A-C). Calculations on the light-matter interaction using kinetic Boltzmann equations [35] (Supplement B) show the expected low-fluence behavior (linear-response regime), namely the 3p-3d absorption process ( Fig. 3(a)) is dominant and the preponderant decay-channel is the Auger process ( Fig. 3(b)). Around 88% of the Auger processes with a sub-femtosecond decay time of "tJH… = 0.4 fs are 3d-3p transitions refilling the 3p shell combined with excitations of 3d electrons up to an energy of 60 eV above the 3d level. Since "tJH… is two orders of magnitude shorter than the pulse length, significant intra-pulse repopulation of the 3p shell occurs. to the unperturbed 3p-3d transition and the fact that with increasing fluence the resonance energy of the 3p-3d transition gradually shifts to higher energies.
A plausible scenario to explain the quenching is an XUV-induced reduction of saturation (1)) as it provides an explanation for the observed shift of the double-pulse Hss ( ) curve with respect to the single-pulse Hss ( ) curve towards smaller fluences (solid lines) as outlined in the following. proportional to the instantaneous intensity ( ′) leading to a relative reduction of the saturation Fig. 4 like Pt, a significantly shorter demagnetization time is generally found [40,41], indicating an important impact of spin-orbit coupling on ultrafast demagnetization according to a IHwMJ ∝ 1/( • B ) scaling [40]. Note that particularly for multilayers, both the Curie temperature B and the effective depends on the detailed morphology of the interfaces. The shorter IHwMJ the smaller is the shift between the single and double-pulse curves, e.g., for IHwMJ,™š›,BC/<Ÿ = 40 fs observed as the shortest IHwMJ for Co/Pt [40], the shift obtained from the model reduces to ;< / T< ≈ 1.5. In the extreme case, for IHwMJ significantly shorter than the pulse length, the single-pulse and double-pulse curves converge. Hence, the experimental ratio of ;<,H‚' / T<,H‚' ≈ 1.05 indicates a relatively short demagnetization time.
In order to determine the demagnetization time, the phenomenological model for demagnetization is simultaneously fitted to the single and double-pulse data (Fig. 2). An upper bound for the demagnetization time of IHwMJ,¢£¤,BC/<Ÿ ≤ 20 fs is obtained which is at least a factor of two shorter compared to IHwMJ,™š›,BC/<Ÿ [40]. Recently, a slight reduction of the demagnetization time for using XUV compared to NIR radiation was also reported for Co/Pd [25].

Discussion
How can we understand a sub-20-fs demagnetization time? Very recently, comparably fast demagnetization times down to the sub-20 fs regime were reported even for NIR laser-induced demagnetization in Co/Cu [42] and Ni/Pt [43] and attributed to spin transfer across chemical interfaces. Both studies indicate that three different processes promote demagnetization occurring on subsequent time scales, namely coherent spin transfer and back transfer from ferromagnetic to paramagnetic lattice sites for < 20 fs, referred to as optically induced coherent spin transfer (OISTR) in Ref. [43], followed by coherent OISTR+SOC-mediated spin flips for 20 fs < < 100 fs. Finally, for timescales > 100 fs conventional, non-coherent demagnetization processes as local Elliott-Yafet-based scattering processes [44] and/or nonlocal superdiffusive spin currents occur [45].
Hereafter, the XUV radiation-induced demagnetization process is discussed with emphasis on explaining the sub-20-fs demagnetization time using conventional, i.e., non-coherent, demagnetization mechanisms. About 2/3 of the XUV-induced excitations are inter-band 3p-3d dipole transitions [33] followed by an Auger decay leading to hot electrons with energies of up to 60 eV above the Fermi level. The resulting fraction of photo-ionized Co is only ≈ 20% for the maximum fluence used experimentally, = 43 mJ/cm² (Supplement B), so that even for a possibly high polarization of the Auger electrons of a few 10% [46][47], the disparity of 3 ↑ and 3 ↓ electrons, i.e., V , is not significantly affected by the Auger processes. Consequently, subsequent electron-scattering processes trigger demagnetization analogous to conventional NIR-light-induced demagnetization, however, with a significantly shorter demagnetization time.
In the following it is shown that the key for a faster demagnetization are the fast electron scattering processes upon XUV-radiation. As the electron-electron scattering with a characteristic lifetime H ] H ] is the predominant scattering process for 60-eV-hot electrons [48], it is assumed that the demagnetization is mediated by the Elliott-Yafet mechanism based on electron-electron Coulomb-scattering in the presence of spin-orbit interaction [49].  [52,53]. Recently, the XUV-excited electron lifetime in Ni was found to be in the 10 as range, i.e., ≈ 100 as shorter as compared to Cu, which was explained in terms of spin-dependent scattering in Ni [54]. Hence, assuming a similarly shorter H ] H ] (60 eV) for Co, the above-mentioned The description of the faster demagnetization in the XUV regime in terms of electron-electron scattering should not rule-out other probable processes, proposed to explain ultrafast demagnetization. For instance, electron-phonon-mediated spin-flip-scattering processes might be much faster for an excitation with 60-eV than for 1.5-eV photons. In fact, the electronphonon interaction is reported to increase with the energy of the electronic system [45,[55][56][57], such that, in line with above reasoning, faster demagnetization is plausible. Future quantitative descriptions have to include the role of the Pt layers, as they significantly increase the spinorbit interaction of Co at the Co/Pt interfaces [40], play a decisive role for the coherent OISTR effect [43], and provide a spin sink for superdiffusive spin-polarized currents along the film normal [45]. Since the velocity of 60-eV-hot electrons is in the order of a few nm/fs [51] a fast spin transport from the 0.8 nm thick Co to the Pt layers is reasonable providing an alternative conventional (non-coherent) explanation for a sub-20-fs demagnetization time.
The fitting of the experimental data using the model for demagnetization also provides the fluence IHwMJ,¢£¤ leading to complete demagnetization (Fig. 2) when additionally considering

8(20)
the impact of the two-dimensional Gaussian-beam profile, as outlined in Supplement C and D.
Remarkably, IHwMJ,¢£¤ = (12 ± 3) mJ/cm² is similar to the value estimated for the same multilayer using NIR radiation ( '( = 1.5 eV: IHwMJ,™š› ≈ 18 mJ/cm²) [8]. In fact, considering the slightly different attenuation lengths for Co, ℓ MŸŸ,BC , for both photon energies (ℓ MŸŸ,BC (60 eV) ≈ 9 nm [33], ℓ MŸŸ,BC (1.5 eV) ≈ 13 nm [58]), a similar fluence is absorbed by the Co layers for both IHwMJ values. Since the demagnetization was found to scale with the absorbed fluence, independent of the optical wavelength [59,60], the estimated IHwMJ,¢£¤ value appears reasonable under the prerequisite that the same mechanisms dictate ultrafast demagnetization for both regions of the electromagnetic spectrum. In contrast, a more than one order of magnitude higher IHwMJ,¢£¤ was reported recently for XUV-FEL radiation with similar pulse characteristics (spectrum, pulse length, coherence) [25] for which stimulated emission and a 3p-band shift are expected to significantly affect the magnetic scattering signal ( Fig. 3(f)).
In conclusion, the quenching of magnetic scattering as a function of fluence was investigated,

Methods
Magnetic Sample. As sample system, a Co/Pt multilayer with perpendicular magnetic anisotropy grown by sputtering techniques on 50 nm thick Si3N4 membranes with lateral dimensions of 200 x 200 μm 2 was used [29]. The thicknesses of the individual Co and Pt layers were 0.8 nm and 1.4 nm, respectively, and a total of 16 repetitions of the Co and Pt was deposited on a Pt seed layer of 5 nm thickness, i.e., Pt/(5.0 nm)/[Co(0.8 nm)/Pt(1.4 nm)]16/Pt(0.6 nm). The Pt cap layer is 2 nm thick to prevent oxidation. After growth, the sample was demagnetized in an out-of-plane magnetic field to generate a labyrinthlike close-to-equilibrium domain state with an average domain size of ≈ 90 nm. A chip with a total of 400 membranes (array of 20 x 20 with a pitch in both directions of 1 mm) was used for the experiment in order to enable repeated and comparable destructive single-shot measurements on membranes from the same production batch.
Scattering mechanism. The peak value of the distribution function ( 'HMN ) serves as a quantitative measure for the strength of the scattering cross section = ², where is the scattering factor ³ , '( , ¶ = -( ) + · ³ '( , , ¶ − ·· ³ '( , , ¶ [34]. Here, is the atomic form factor corresponding to the atomic number for forward scattering, while · and · ′ are the anomalous scattering factors. is the light's polarization unit vector and M the magnetization. As no charge inhomogeneity exists on the length scale of the magnetic multi-domain pattern, i.e., 100 nm, the azimuthally averaged ( ) (including the peak value ³ 'HMN ¶) are only sensitive to the magnetic part of the scattering factor [61], which for light propagation parallel/antiparallel to M is given by [34] [62]. We employed the standard single-pulse and the recently developed double-pulse mode [31] setting the time delay between both FEL sub-pulses to 200 fs. For both modes, we used circularly polarized radiation allowing for the most stable operation of the FEL. For the single-pulse mode, the wavelength was set to '(,;< = 20.3 nm. In the double-pulse mode, the wavelengths were shifted away from the single-pulse wavelength by ≈ ±0.035 nm. The wavelength separation in the double-pulse mode of ∆ / ≈ 0.2% is about twice the bandwidth (inset of Fig. 1(a)), allowing the determination of the energy of the sub-pulses on a (double-)shot-to-(double-)shot basis [63]. The mSAXS measurements were performed in transmission geometry and the scattered intensity was recorded using a CCD detector placed 50 mm behind the sample. Multi-shot measurements with exposure times of the CCD between 2 s and 50 s (20 to 500 FEL shots, respectively) were performed at low FEL fluences in the range from 0.3 ≤ ≤ 15 mJ/cm 2 (non-destructive regime). Additionally, single-shot measurements were carried out for fluences 15 < ≤ 43 mJ/cm 2 (destructive regime for ⪆ 20 mJ/cm 2 ).
The spatial FEL-spot profile is composed of an intense center and broad tails that have been cut horizontally and vertically before the focusing optics of the beamline (bendable planar mirrors in Kirkpatrick-Baez (KB) configuration) by a set of beam-defining blades in front of the KB system, so that the beam profile at the sample position is almost 2D-Gaussian with an elliptical cross-section. The horizontal ( Ê,ªËÌÍ ) and vertical spot sizes ( Î,ªËÌÍ ) at full width half maximum intensity (FWHM) determine the peak fluence for a given pulse energy according to = /( Ê,ªËÌÍ • Î,ªËÌÍ ) with = 4ln2/ ≈ 0.88. A critical comment on the fluence definition in the case of a 2D-Gaussian beam profile is given in Supplement D. The spot sizes Ê,ªËÌÍ and Î,ªËÌÍ at the sample position were determined from CCD images of the scintillation excited by the beam on a phosphorous screen. The spot sizes are determined to (70 ± 10(20) 5) x (145 ± 5) µm² for the multi-shot data and (65 ± 10) x (130 ± 10) µm² for the single-shot data.
Between single-pulse and double-pulse mode, the source point and hence the irradiated area at the sample position was slightly different of the order of ±5% (corresponding to different spot sizes of about ±2 − ±3 µm, which was below the detection limit of our optical control of the beam profile) [31]. This difference was considered as a relative systematic error in the fluence determination between both single and double-pulse mode as mentioned in the text. For the determination of the pulse energy 'tuvH at the sample, the measured value <"Ñ›HV obtained by using PADReS' calibrated gas-detector intensity monitors [64] located at the beginning of the photontransport section, was propagated along the beamline. In order to take into account the effect of the above-mentioned spatial filtering in front of the KB system, the intensity of the incoming beam profile was measured on a scintillator screen with and without the beam-defining blades in the optical path. We estimate a loss of 30% (20%) in the pulse energy at the sample position for multi-shot mode (singleshot mode) due to the introduced spatial filtering.  [8,20]. Hence, the absolute fluence scale is reliable within the above-mentioned accuracy of ±20%.
For the scattering experiments the beam was centered on a membrane (dimensions of 200 x 200 µm²), so that scattering from the membrane edges was minimized. Since the spot sizes were by a factor of ≈ 3 (horizontal) and ≈ 1.5 (vertical) smaller than the membrane size, one membrane was addressed at a time. The sample was mounted in such a way that the FEL beam impinged on the Si3N4 membrane first before being scattered from the Co/Pt multilayer.
In the single-shot case (25-shot, i.e., multi-shot case), for a fluence of 43 mJ/cm² (7 mJ/cm², see Fig. 1(c)), the number of photons per pixel in the maximum of the scattering ring is ≈ 0.42 (≈ 3.6). Since the signal to noise ratio is < 0.05 photons/pixel this intensity is sufficient to get smooth ³ = ‡ Ê T + Î T ¶ curves (obtained from azimuthal averaging). All data for the multi-shot experiments (fluences ≤ 15 mJ/cm²) were acquired using 3 individual membranes in total. In order to prove that there was no degradation of the structural and magnetic properties during the multi-shot experiments, we have checked that there is no dependence of theposition of the maximum scattering intensity wM‚ on the FEL fluence. From all the multi-shot data, we determined an average value of wM‚ = (0.036 ± 0.001) nm -1 . For the whole fluence range ≤ 15 mJ/cm², we can therefore rule out any structural damages (like intermixing of Co and Pt) which had otherwise affected the intrinsic magnetic properties like magnetic anisotropy and/or saturation magnetization. Since both dictate the domain size = / wM‚ , a constant wM‚ indicates structural integrity during the multi-shot experiments. For the single-shot experiments, i.e., for fluences > 15 mJ/cm², we used a fresh membrane after each shot. In total, 23 membranes were used (5 membranes for single-pulse and 18 membranes for doublepulse mode).
In the single-pulse mode, the pulse-intensity variation from shot to shot was around 20% (which is relevant only for the multi-shot mode).
In the double-pulse mode, typical intensity differences between both sub-pulses were ( ; − T )/( ; + T ) = 0.0 ± 0.4. No correlation between asymmetry in intensity and scattering efficiency was observed for the single-shot data.
Data Analysis. The analysis of the scattering images, as shown in Fig. 1(b), was performed analog to Ref. [8]. The scattering images were azimuthally averaged after masking of the beamstop shadow and the charge-scattering streaks generated from the membrane edges. The resulting curves were fitted by 11(20) where Ù accounts for a constant background and -D• describes a residual charge-scattering signal originating, e.g., from waviness of the membranes on the micrometer length scale due to strain after film growth, close to the center of the scattering image where the magnetic signal is small. The first term is the split Pearson type-VII distribution function that successfully describes the magnetic scattering signal as skewness and kurtosis are accounted for, originating from the domain-size distribution [64]. ³ peak ¶ is the intensity of the distribution function at the peak position peak , and ;,T T and ;,T are parameters which have different values on the low and highside of the peak (indices 1 and 2, respectively) reflecting the asymmetry of ( ).

Data availability
The data that support the findings of this study are available from the corresponding authors upon request.