First experiments with ultrashort, circularly polarized soft x-ray pulses at FLASH2 Open Access

Soft x-ray based resonant methods have provided one of the biggest contributions to the fundamental understanding of ultrafast magnetization dynamics in multi-element materials since the emergence of the field.¹ The importance hinges on the inherent element specificity of soft x-ray resonances, their sensitivity to the atomic magnetic state, the ability to analyze dissipation of individual spin and orbital moments that determine the materials' magnetization,^2–10 and even the possibility to obtain spatially resolved information.^11,12 These experimental results have significantly advanced the field of magnetization dynamics research.

Soft x-ray methods are element-specific since they probe resonant electronic transitions from localized atomic core levels to valence states. The resonances appear at characteristic, well-separated energies for each element. The sensitivity to the atomic magnetic properties, i.e., spin and orbital momenta, is essentially based on the effect of x-ray Magnetic Circular Dichroism (XMCD):¹³ the difference in absorption of circularly polarized x-rays of opposite helicity (i.e., photon angular momenta of +1  $ℏ$ or −1  $ℏ$⁠). Selection rules govern the spin-conserving resonant optical transition from a spin–orbit coupled core state into the spin-specific density of valence states induced by the magnetic order. This leads to a helicity-dependent absorption strength. The so-called sum rules can be derived for XMCD spectra, allowing for the determination of the absolute atomic orbital and spin magnetic moments for individual elements as well as their dynamic changes.^13–15 

The crucial requirement for ultrafast dynamics studies with the above-mentioned methods is the availability of circularly polarized ultrashort soft x-ray pulses. First, groundbreaking contributions allowed for fundamentally new insights into the ultrafast magnetization dynamics and have already been made by a storage ring based source starting in 2007.^2–10 Electron bunch slicing was used in combination with an Apple-II type undulator for the generation of circularly polarized soft x-ray radiation at the BESSY II Femtoslicing source.¹⁶ Nowadays, free-electron lasers (FELs) are capable of providing intense x-ray pulses of a few to a few tens of femtoseconds duration or even below. Oftentimes though, the experimental temporal resolution is rather limited by the pulse duration of external pump lasers and the employed synchronization and jitter correction schemes.

While free-electron laser facilities produce short wavelength radiation since 2005¹⁷ and soft x-rays since 2009,¹⁸ soft x-rays were initially provided only with linear polarization; ultrashort circularly polarized soft x-ray pulses were produced significantly later at these facilities.¹⁹ 

The first FEL based experiments using ultrashort circularly polarized soft x-ray pulses have been reported at the LCLS in 2016.^20,21 In 2023, first lasing results with circular polarization at the soft x-ray FEL beamline Athos of SwissFEL were published.^22,23 At the FERMI facility ultrashort pulses with circular polarization in the VUV, employing an APPLE-II type undulator was already available since the inception,²⁴ complementary to laser-based high-harmonic generation (HHG) lab sources;^25,26 the generation of elliptically polarized femtosecond pulses in a seeded operation mode at the $L3,2$-edges of magnetic transition metals (700–800 eV) though has only been demonstrated at FERMI recently.²⁷ At EuXFEL (SA3), an APPLE X (UE90) undulator for ultrashort x-ray pulse generation with variable polarization has recently entered user operation.²⁸ 

The increasing number of FEL facilities providing circularly polarized soft x-ray pulses offers new possibilities for ultrafast dynamics studies on magnetic materials. FEL sources have the potential for femtosecond temporal and sub-eV energetic resolutions combined with high x-ray intensities for high fidelity studies. In this contribution, we report on the first experiments with ultrashort circularly polarized soft x-ray pulses at FLASH2 in the photon energy range from 700 to 860 eV. We measured XMCD spectra of the $L3,2$-edges of the magnetic transition metals Fe, Co, and the $L3$-edge of Ni using circularly polarized x-ray pulses from the recently implemented afterburner undulator.²⁹ 

The availability of circular polarization at the FLASH facility opens up the possibility to extend the available experimental time for soft x-ray methods based ultrafast magnetization dynamics studies. The future potential of ultrafast experiments with circularly polarized x-ray pulses on the elemental magnets Fe, Co, and Ni even goes beyond the analytical tools that have been discussed so far. Recent studies on the Co- $L3$ edge demonstrate new insight into the ultrafast occupation changes within the spin-dependent density of states, governing the magnetic dynamics at different times and timescales.^9,30

The measurements reported here were carried out at the XUV/soft x-ray free-electron laser FLASH at DESY in Hamburg. FLASH, as a user facility, serves FEL radiation to two different experimental halls.^17,31 The common FLASH linear accelerator consists of a normal-conducting radio frequency-gun, superconducting electron acceleration modules, including a third harmonic cavity, two bunch compressors, and a laser heater system. It is capable of generating bunch trains with several thousand electron bunches per second in 10 Hz bursts of up to 800 μs length. The electron bunches can reach beam energies up to 1.35 GeV and peak currents of up to a few kA. A beam distribution yard, based on a kicker and a septum magnet, enables the parallel operation of the two undulator beamlines called FLASH1 and FLASH2. The bunch trains can be divided into two variable parts with slightly different properties.

The FLASH2 undulator beamline contains 12 planar, variable gap undulators, each 2.5 m long. Downstream from these planar undulators, an APPLE-III type afterburner undulator was installed at the end of September 2023.²⁹ The afterburner undulator allows for the generation of FEL radiation with variable polarization at the third harmonic of the FLASH2 SASE FEL radiation, i.e., down to 1.33 nm, corresponding to 930 eV photon energy. The parameter settings of FLASH2 for the present measurements are given in Table I.

The afterburner can be tuned to produce differently polarized x-ray pulses (including circular left and right). The main challenge in operating this device is the strong linearly polarized background from the main FLASH2 undulator that would contaminate the desired photon polarization state. A method for suppression of such a background was proposed in Ref. 32: an application of the reverse undulator taper. The main effect of this technique is that the radiation is strongly suppressed, while the microbunching at the exit of the main undulator is practically the same as in the reference case of the non-tapered undulator. Then, the micro-bunched beam emits powerful radiation with required polarization properties in the afterburner. This method was successfully used to operate the helical afterburner at LCLS.¹⁹ 

Since the APPLE-III afterburner at FLASH2 is operated at the third harmonic of the main undulator, the reverse taper method is employed to suppress mostly the weaker linearly polarized radiation at the third harmonic, which worked very well during the experiment and provided high purity circularly polarized photons. The fundamental from the main undulator was also suppressed, although less efficiently than the third harmonic. The remaining fundamental radiation was then filtered out in the beamline monochromator, which was used to select the third harmonic. This allowed for optimization of the afterburner settings and the experiment itself. In addition to applying a reverse taper, a modification of the electron optics at the end of the undulator line was introduced in order to improve the electron beam focusing into the afterburner, thus increasing the radiation intensity and polarization purity.

The capability of this method has been successfully demonstrated previously for different undulator types and polarization setup schemes at FERMI and LCLS.^{19,20,36–38}

For the afterburner-undulator characterization at FLASH, we used rare gases as ionization targets. Values of ionization cross section $σ$ and angular distribution anisotropy parameters $β$ for the addressed electronic states of these gases, which are needed for reference, can be found in the literature over a wide range of photon energies. Photoelectron angular distribution measurements have been performed for different linear and circular polarization settings of the afterburner undulator at various photon energies of the third harmonic in the range from 74 to 414 eV. Details about the commissioning campaign will be published elsewhere.

As an example, in Fig. 1, we present the angular distribution patterns measured at 313.8 eV of the FEL's third harmonic for three different afterburner undulator settings corresponding to the horizontal linear, vertical linear, and circular polarization. The derived values $Plin$ for both linear polarization settings derived from this acquisition dataset are $Plinh=0.96±0.02$ and $Plinv=0.98±0.02$⁠, whereas for circular polarization $Plinc=0.07±0.02$⁠. The uncertainty of 2% is the error of the weighted mean of the results using different methods for the photoelectron yield determination, which we applied as a test for a robust analysis procedure suited for a fast diagnostics tool. With a more conservative error estimation, the deduced value of the degree of circular polarization of the third harmonic at 313.8 eV is $Pcirc=99.7 −0.4+0.3$%.

In the present measurements, FLASH2 was tuned for the third harmonic radiation to reach the Co and Fe $L3,2$ and the Ni $L3$-edges. Employing the FLASH2 afterburner undulator (see Sec. II), circularly polarized photons were generated delivering 400 FEL-laser pulses per train. The train repetition rate was 10 Hz, and the intra-train pulse repetition rate was 1 MHz (i.e., 1  $μ$s single pulse time spacing, total pulse train duration 400  $μ$s; compare also Table I).

The XMCD experiment was carried out at the monochromator beamline FL23⁴⁰ of the FLASH2 FEL facility^17,31 employing the MUSIX (multidimensional spectroscopy and inelastic x-ray scattering) endstation,^41,42 see Fig. 2. Two 3 mm iris apertures were used upstream of FL23 to constrain the beam path. The beamline was operated in first-order single-diffraction grating mode to select the third harmonic radiation, using the high-energy grating with a groove density of 600 lines/mm and an energy dispersion of 0.017 nm/mm in the energy range 700–860 eV. An exit slit of 100  $μ$m width led to an energy resolution of approximately 800 meV. In order to maximize the beamline transmission, the coatings of all beamline optics were either set to Ni (Fe and Co $L3,2$-edge) or Pt (Ni $L3$-edge). The first diffraction order of a transmission grating placed after the middle slit of the first FL23 monochromator was detected by a photo diode to act as monitor of the incidence x-ray intensity $I0$⁠, while the zeroth order was guided further towards the sample.^43,44 The transmission grating consists of a 100 nm Si₃N₄ membrane on which grating lines made from a HSQ (hydrogen silsesquioxane) resist with a height of >200 nm, a duty cycle of 0.5, and a grating period of 320 nm are fabricated. For the zeroth order, a focusing Kirkpatrick-Baez active optics system (KAOS2) was used to focus the beam onto the FeNi or CoPt sample to a transversal spot size of 12 × 36 μm². The intensity $I1$ of the transmitted beam was measured with a second biased photo diode. The signals of both x-ray photo diodes were measured for every individual x-ray pulse enabling normalization on a shot-to-shot basis. To avoid saturation of the photo diode during the measurements at the Fe $L3,2$-edge, a 197 nm Nb filter was inserted into the beamline while at the Ni $L3$-edge, the gas attenuator (Krypton) was used at $1.5×10−2$ mbar to further attenuate the fundamental.

To excite the sample in the time-resolved measurements, a fixed time-structure pulse train of 80 optical laser pulses (1030 nm) at a frequency of 100 kHz (i.e., 10  $μ$s pulse spacing; pulse train duration 800  $μ$s) and a train repetition rate of 10 Hz was provided. Since the optical laser pulse train showed an almost linear pulse energy build-up for the first 20 pulses before reaching a constant pulse energy level, the delay to the x-ray pulse trains was set such that the first FEL pulse in a train overlapped with laser pulse 21. Due to the different repetition rates of FEL (1 MHz) and optical laser pulses (100 kHz), every tenth FEL pulse was temporally overlapped with an optical pump-laser pulse, such that a total of 40 FEL pulses of a pulse train could be used for the time-resolved measurements. The pulse energy of the optical laser pulses was varied by combining two sets of neutral density filters in the beam path. The spot size of the optical laser on the sample was separately determined by knife-edge scans (see Table I) and substantially larger than that of the FEL beam. Spatial overlap of laser and FEL spots was verified by a Ce-doped YAG based fluorescence crystal (imaged with a long-working distance microscope and a CCD camera) at the sample position. The BAM (beam arrival monitor, measuring the electron beam timing relative to a master clock) and the LAM (laser arrival monitor, referencing the laser pulses to the same master clock) were used to correct the data for jitter and drifts between FEL and pump laser.^45–47 

The x-ray absorption spectra of the Fe, Co $L3,2$⁠, and Ni $L3$-edges (⁠ $L2$ corresponding to the $2p1/2→3d$⁠, and $L3$ to the $2p3/2→3d$ transitions) were obtained by simultaneously moving the gap of the planar undulators and the helical afterburner together with the monochromator pitch angle. For the XMCD measurements, the x-ray beam transmitted through the samples at 35° - 45° with respect to the sample normal, and their magnetization was flipped horizontally in the sample plane by an external magnetic field (see Fig. 2). The latter was generated by an in-vacuum electromagnet, which is able to generate a maximum magnetic field of approximately 100 mT. Magnetic saturation of the samples was ensured by applying a magnetic field of $±$ 36 mT, exceeding the saturation field of the sample (see the exemplary hysteresis scan for the FeNi sample in Fig. 2). During the measurements, the magnetic field direction was inverted every 10 s. The helicity of the FEL beam was kept fixed for all measurements.

The samples were grown by magnetron sputtering at the Max Born Institute Berlin. The substrates were Si frames (Silson Ltd.) with 15 Si₃N₄ windows of 0.5 × 0.5 mm² lateral size. The layer structure of the CoPt sample was Al(100 nm)/SiN(200 nm)/Ta(2 nm)/Co₅₀Pt₅₀(25 nm)/MgO(2 nm), and that of the FeNi sample was Al(100 nm)/SiN(200 nm)/Ta(2 nm)/Fe₄₀Ni₆₀(25 nm)/MgO(2 nm). The Al layer served as a heat sink and the MgO layer as protection against oxidation.

For analyzing the degree of x-ray polarization at FLASH2, reference XMCD measurements were done after the FLASH2 studies on the identical samples at the PM3 beamline of the BESSY II storage ring.⁴⁸ 

The XMCD spectra are calculated by subtracting both spectra, $XASM+(E)$ and $XASM−(E)$⁠, recorded for opposite magnetic field directions. To correct for the different projections of the sample magnetization onto the x-ray direction of individual measurements, the XMCD spectra are divided by the factor $sin(ϑ)$ [see Eq. (6)].¹³ Hence, all XMCD spectra are scaled to the unified configuration with the magnetic field vector parallel to the x-ray direction. The resulting XMCD spectra for Fe, Co, and Ni are shown in Figs. 3(d)–3(f) (open blue circles), respectively. All elements show significant XMCD.

We compare these spectra with reference spectra taken from the identical samples at the PM3 beamline of the BESSY II storage ring [see Figs. 3(g)–3(i)].⁴⁸ The latter are derived from the raw data in the same way as those recorded at FLASH2; here, $I1$ is the photo-current of a photo diode detecting the sample transmitted intensity, and $I0$ is the corresponding signal measured without any sample (incident intensity). For proper comparison, we have to consider that the XMCD spectra for FeNi have been recorded at different temperatures (PM3: 295 K; FL23: 80 K). The lower temperature for the FL23 measurements results in a slightly larger saturation magnetization, hence an increased XMCD. Referring to temperature-dependent studies on similar samples from literature,⁴⁹ we find an $∼$8% larger magnetization for FeNi at 80 K, which we assume to directly translate into the XMCD amplitude. This factor is considered in the comparison of the FLASH2 spectra and their PM3 reference spectra in Figs. 3(g)–3(i).

We notice that the spectral shape differs between the FL23 and PM3 data, in particular in the background regions on the high-energy sides of the Fe and Ni $L2$ peaks. The FL23 data also show jumps, e.g., in the low-energy slope of the Co $L3$ or Fe $L2$ peaks. We assign these to the imperfect normalization mentioned earlier.

Since the imperfect normalization mostly affects the energy regions further away from the absorption maxima, where the XMCD mostly vanishes, we expect that with some limitations, the XMCD signal allows us to estimate the degree of circular polarization. For this, we use the known degree of circular polarization for the PM3 measurements^48,50 and the unified representation of all XMCD spectra. To correct for the different energy resolution of the two monochromators (FL23: 800 meV; PM3: 300 meV), we integrate the XMCD spectra over the individual $L3,2$-resonances. The absolute values of this integration are shown in Table II for each resonance (row XMCD_PM3 and XMCD_FL23).

For the PM3 reference measurements, the degree of the x-ray circular polarization (⁠ $S3$⁠, Stokes–Poincaré parameter) has been experimentally determined or extrapolated from an experimentally determined value (see Table II).^48,50 Since the samples are identical, and the spectra have been normalized to a unified measuring condition, the XMCD values determined for FL23 allow an assessment of $S3$ for the FLASH2 measurements by scaling the PM3  $S3$ value by the ratio XMCD_FL23/XMCD_PM3. The such obtained $S3$ values of the FLASH2 circular polarization for the individual L-resonance energies are given in the bottom row of Table II. We note that for Fe $L2$⁠, Co $L3$⁠, and Ni $L3$⁠, the scaling results in mean values and even uncertainty intervals are greater than 100%. We assign this to the imperfect normalization of the FL23 data mentioned earlier, which leads to additional uncertainties not included in the error bars for XMCD_FL23; the latter only describe the scatter in spectra. We, therefore, capped the values and error bars given in Table II at 100%; the negative uncertainties are those of the uncapped values.

Essentially, we find $S3$ values consistent with almost 100% circular polarization as expected. The apparently small value for Co $L2$ of 86% is probably due to the relatively large experimental error (see earlier). The differing values for Co $L3$ and $L2$⁠, however, could as well stem from a non-synchronous gap change of the Apple-III afterburner and the main FLASH2 undulator during the energy scans. This is a matter of undulator parameters calibration and will be improved in the future.

To demonstrate the feasibility of ultrafast dynamics magnetic studies with circular polarization, we present the ultrafast element specific XMCD transient of Fe in the FeNi sample after laser excitation. Due to the 20 laser pulses in each pulse train, which arrived before the first pulse of the FEL pulse train (intensity build-up, see Sec. III), a considerable nearly constant heating of the samples was observed leading to a significant reduction of the sample base magnetization and XMCD. Even liquid nitrogen cooling of the samples could not remove this effect. Yet, a compromise had to be found for the pump-laser fluence, minimizing the heating while dynamically inducing a significant demagnetization.

The effective temporal resolution of this measurement results from various contributions (see Table III): the laser and the x-ray pulse widths and the jitter/drift in the FEL-laser synchronization. The latter contributions can partially be corrected for by measurements of BAM and LAM (see Sec. III). Additional temporal broadening can arise from the beamline monochromator, which was used in the single grating mode. Here, the x-ray pulse elongation depends on how many grating grooves are illuminated by the x-ray beam and can vary between 100 and 200 fs depending on the beamline alignment. Summing up all the contributions, the temporal resolution for our experiment was expected to be in a range between 170 and 270 fs.

Here, a double exponential function, which mimics the magnetic dynamics, is convolved with a Gaussian function, $G(t,Δτ)$⁠, taking into account the experimental time resolution $Δτ$ (FWHM). $τd$ is the time constant for the demagnetization, and $τr$ is a second time constant modeling the recovery. $t0$ denotes the time of simultaneous arrival of pump and probe pulse. $H(t−t0)$ is the Heaviside function $(H(t−t0)=0$ if $t<t0$ and $H(t−t0)=1$ if $t>t0)$⁠.

Except the demagnetization time, $τd$⁠, which was kept fixed at 250 fs, we left all other parameters free in the fitting process. This yields a time resolution $Δτ$ of 150  $±$ 30 fs, which overlaps with the lower limit of the temporal resolution estimated earlier.

We have successfully used ultrashort circularly polarized soft x-ray pulses at the FLASH2 facility in the photon energy range 700–860 eV. The degree of circular polarization is found to be consistent with almost 100%. This photon energy range covers the $L3,2$-edges of the 3d elemental magnets Fe and Co and the $L3$-edge of Ni, which are highly relevant for the field of ultrafast magnetization dynamics. After further accelerator commissioning, the available photon energy range will also cover the Ni $L2$-edge (870 eV). With the envisaged improvements to the pump-laser system to make the pulse energies in the train more uniform, a higher repetition rate pump laser, and improved overall temporal resolution, FLASH will offer even more interesting research possibilities for ultrafast spin dynamics experiments on 3d transition metals.

We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out at the beamline FL23 at FLASH2. Beamtime was allocated for proposals F-20211728 EC and F-20220710. The statics reference measurements were carried out at the PM3 scattering instrument at the BESSY II electron storage ring operated by the Helmholtz-Zentrum Berlin für Materialien und Energie; we would like to thank Torsten Kachel for the experimental support. This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through TRR 227 “Ultrafast Spin Dynamics,” Project ID 328545488 (projects A01, A02, and A03) and by the Bundesministerium für Bildung und Forschung (BMBF) through the project “Spinflash” (05K22KE2).

The authors have no conflicts to disclose.

S. Marotzke: Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). D. Gupta: Formal analysis (equal); Investigation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). R.-P. Wang: Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Writing – review & editing (equal). M. Pavelka: Investigation (equal); Writing – review & editing (equal). S. Dziarzhytski: Investigation (equal); Methodology (equal); Writing – review & editing (equal). C. von Korff Schmising: Conceptualization (equal); Investigation (equal); Resources (equal); Writing – review & editing (equal). S. Jana: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). N. Thielemann-Kühn: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). T. Amrhein: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). M. Weinelt: Funding acquisition (equal); Investigation (equal); Writing – review & editing (equal). I. Vaskivskyi: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). R. Knut: Investigation (equal); Writing – review & editing (equal). D. Engel: Resources (lead); Writing – review & editing (equal). M. Braune: Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). M. Ilchen: Methodology (equal); Writing – review & editing (equal). S. Savio: Methodology (equal); Writing – review & editing (equal). T. Otto: Methodology (equal); Writing – review & editing (equal). K. Tiedtke: Methodology (equal); Writing – review & editing (equal). V. Scheppe: Methodology (equal); Writing – review & editing (equal). J. Rönsch-Schulenberg: Methodology (equal); Writing – review & editing (equal). E. Schneidmiller: Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). C. Schüßler-Langeheine: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). H. A. Dürr: Investigation (equal); Writing – review & editing (equal). M. Beye: Conceptualization (equal); Formal analysis (equal); Investigation (equal). Methodology (equal); Project administration (equal); Software (equal); Writing – review & editing (equal). G. Brenner: Conceptualization (equal); Investigation (equal); Methodology (equal); Project administration (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). N. Pontius: Conceptualization (lead); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (equal).

The data that support the findings of this study are openly available in Zenodo at https://doi.org/10.5281/zenodo.15076836, Ref. 54.