Ultrafast Demagnetization Dominates Fluence Dependence of Magnetic Scattering at Co $M$ Edges

We systematically study the fluence dependence of the resonant scattering cross-section from magnetic domains in Co/Pd-based multilayers. Samples are probed with single extreme ultraviolet (XUV) pulses of femtosecond duration tuned to the Co $M_{3,2}$ absorption resonances using the FERMI@Elettra free-electron laser. We report quantitative data over 3 orders of magnitude in fluence, covering $16\mathrm{mJ}/{\mathrm{cm}}^2/\mathrm{pulse}$ to $10000\mathrm{mJ}/{\mathrm{cm}}^2/\mathrm{pulse}$ with pulse lengths of 70 fs and 120 fs. A progressive quenching of the diffraction cross-section with fluence is observed. Compression of the same pulse energy into a shorter pulse—implying an increased XUV peak electric field—results in a reduced quenching of the resonant diffraction at the Co $M_{3,2}$ edge. We conclude that the quenching effect observed for resonant scattering involving the short-lived Co 3p core vacancies is noncoherent in nature. This finding is in contrast to previous reports investigating resonant scattering involving the longer-lived Co 2p states, where stimulated emission has been found to be important. A phenomenological model based on XUV-induced ultrafast demagnetization is able to reproduce our entire set of experimental data and is found to be consistent with independent magneto-optical measurements of the demagnetization dynamics on the same samples.

Figure 1

Sample layout and experiment design. (a) Magnetic force microscopy image of a $5\mu \mathrm{m}\times 5\mu \mathrm{m}$ sample area. Blue and red colors indicate opposite magnetization directions perpendicular to the sample plane. (b) Schematic cross-section of the structured sample membrane and sketch of the experiment. The cross-section shows the etched silicon-nitride membrane with the artificial grating structure and the magnetic multilayer. The focused FEL pulse (blue line) with a pulse length of 70 fs or 120 fs first hits the silicon-nitride membrane with the artificial grating structure. A CCD detector 50 mm downstream of the sample records the XMCD small-angle scattering (SAS) signal. The cross-shaped beamstop protects the detector from the intense directly transmitted light. (c) Representative XMCD-SAS pattern. $I_{\mathrm{mag}}$ and $I_{\mathrm{gr}}$ denote the SAS contributions of the magnetic domain pattern and the milled grating, respectively. White outlines mark the regions in which the respective signals are integrated.

Figure 2

Fluence dependence of the relative XMCD-SAS cross-section $S$ for two different x-ray pulse lengths (circles), shown as a function of the single-shot pulse energy (a) and normalized per unit time within the pulse, i.e., divided by the pulse duration (FWHM) (b) [15]. The black diamond symbols indicate the characterization fluence of $(16\pm 4)\mathrm{mJ}/{\mathrm{cm}}^2/\mathrm{pulse}$ used in the experiments. Solid lines show the results of a simulation taking only ultrafast demagnetization during the pulse into account. The shaded areas mark the uncertainty of this model, which is predominantly given by the confidence with which the FEL pulse lengths are calculated from machine parameters [15].

Figure 3

Magnetization after an optical excitation measured by time-resolved MOKE on the same sample as used in the XUV experiment. The measurement is performed on the sample substrate, i.e., next to a silicon-nitride membrane. Solid lines are double-exponential fits to the data that yield the demagnetization time constant of ${\tau }_m=(113\pm 9)\mathrm{fs}$ for all pump fluences. For comparison, the temporal pulse envelope of the single shots used in the FEL experiment are indicated as dashed and dotted lines (70 fs and 120 fs, respectively). Note that these lines do not reflect the optical pump and probe pulses of 50 fs pulse duration used in the MOKE experiment.