Irreversible transformation of ferromagnetic ordered stripe domains in single-shot infrared-pump/resonant-x-ray-scattering-probe experiments

The evolution of a magnetic domain structure upon excitation by an intense, femtosecond infrared (IR) laser pulse has been investigated using single-shot based time-resolved resonant x-ray scattering at the x-ray free electron laser LCLS. A well-ordered stripe domain pattern as present in a thin CoPd alloy film has been used as a prototype magnetic domain structure for this study. The fluence of the IR laser pump pulse was sufficient to lead to an almost complete quenching of the magnetization within the ultrafast demagnetization process taking place within the first few hundreds of femtoseconds following the IR laser pump pulse excitation. On longer time scales this excitation gave rise to subsequent irreversible transformations of the magnetic domain structure. Under our specific experimental conditions, it took about 2 ns before the magnetization started to recover. After about 5 ns the previously ordered stripe domain structure had evolved into a disordered labyrinth domain structure. Surprisingly, we observe after about 7 ns the occurrence of a partially ordered stripe domain structure reoriented into a novel direction. It is this domain structure in which the sample's magnetization stabilizes as revealed by scattering patterns recorded long after the initial pump-probe cycle. Using micromagnetic simulations we can explain this observation based on changes of the magnetic anisotropy going along with heat dissipation in the film.

Figure 1

Sketch of the experimental setup. Each CoPd alloy membrane is illuminated with a single-shot IR pump and a single x-ray probe pulse. A post-characterization is performed with a single x-ray probe pulse at a delay of $t=1\min$. The small-angle x-ray diffraction pattern of the magnetic domains is recorded on a CCD detector. (a) Magnetic force microscopy (MFM) image of the prepared stripe domains with an average domain size of 71 nm. (b) Corresponding small-angle x-ray scattering pattern with scattering vector $q$ and azimuthal angle Φ. (c) The radial intensity distribution $I\left(q\right)$ defines the degree of homogeneity in the domain width. (d) The azimuthal angle intensity distribution $I\left(\Phi \right)$ defines the degree of alignment of the domains in the plane of the film. The intensity distribution $I\left(\Phi \right)$ defines the quantitative orientation anisotropy constant $K^{\to }$ which is 0.98 in the prepared state before excitation by the pump laser pulse (b).

Figure 2

(a)–(c) IR-pump x-ray probe diffraction patterns for different delay times $t=2.5,5.5$, and $7\mathrm{ns}$. (a) The almost complete loss of the magnetic scattering intensity $(1\mathrm{ps}<t<3\mathrm{ns})$ is observed after an intense single IR laser pulse. (b) Partial recovery of the magnetic scattering intensity at $t=5.5\mathrm{ns}$ showing that disordered labyrinth domains are formed and that partially ordered stripes are recovered aligned along the initial direction. (c) New partially ordered stripes are observed at $t=7\mathrm{ns}$ with a 60° rotation of the stripe alignment direction. (d) Azimuthal intensity distributions $I\left(\Phi \right)$ for different single-shot pump-probe delays. A new preferential orientation direction is observed at $t\ge 7\mathrm{ns}$ as evident from the superposition of a scattering ring and two Bragg spots. The new magnetic phase order is characterized by an orientation anisotropy of $K^{\to }=0.25\pm 0.15$.

Figure 3

(a) Post-characterization azimuthal angle intensity distribution $I\left(\Phi \right)$ for all investigated films at room temperature. The new angular distribution (with the preferred axis rotated by −60 deg) is found independent of the pump-probe delay used during the experiment. (b) Scattering pattern of the final state observed for the film used in the pump-probe experiment with a pump-probe delay of $t=7\mathrm{ns}$. (c) Magnetic force microscopy (MFM) image at room temperature recorded in a section of the area exposed to the IR pulse of the aforementioned sample. (d) The Fourier transformation of the MFM image (blue markers) reveals an anisotropic, preferential orientation of the magnetic domain structure, which is in perfect agreement with the one characterized by the azimuthal line cut of the post-characterization image of the same sample (orange line).

Figure 4

Evolution of the domain wall profiles with the temperature. (a) Worm domains at 300 K (anisotropy constant $K=5\times {10}^6\mathrm{J}/{\mathrm{m}}^3$) and (b) worm domains at elevated temperature $(K=1.6\times {10}^5\mathrm{J}/{\mathrm{m}}^3)$. (c) Domain wall profiles extracted along the red line in images (a) and (b). The black profile line is extracted from (a) and the red line from image (b). The magnetization amplitudes are normalized to those in image (a). The larger extension of the wall size is observed at elevated temperature. The image size is $0.5\times 0.5\mu {\mathrm{m}}^2$. The spatial resolution of the simulation is 5 nm.

Figure 5

Micromagnetic simulations investigating domain dynamics following the Landau-Gilbert time-dependent evolution. (a) The starting configuration analog to the recovery of the magnetization at $t=5.5\mathrm{ns}$ [see Fig. 2]. (b) and (c) Simulated temporal evolution in the presence of an in-plane anisotropy field of $100\mu \mathrm{T}$ (red arrows). (d)–(f) Analogous simulation of the temporal evolution of the labyrinth domains obtained without in-plane anisotropy field. The size of the images is $1\times 1\mu {\mathrm{m}}^2$ and the resolution is 5 nm. The red circles limit the center of the calculated images to avoid boundary effects. Inside the circle the magnetic domains are found to be aligned preferentially parallel to the external magnetic field (the direction is given by the red arrows).

Figure 6

Dynamic of the orientation anisotropy $K^{\to }\left(t\right)$ characterizing the dynamics of the partially ordered domain structure. All data points are derived from the experimental data. The large dispersion of the data points is related to the lateral instability of the x-ray pulses modifying the thermal recovery and the magnetic anisotropy of the film. The dashed curve is given as a guide for the eyes. The gray and yellow colors highlight the observed angular redistribution of the intensity along the resonant scattering rings from $\Phi =0^{\circ }$ to $\Phi =-{60}^{\circ }$ corresponding to the preferential reorientation of the domains along the in-plane direction from $\Phi =0^{\circ }$ to $\Phi =+{30}^{\circ }$. As the time interval during which the film is at low magnetic anisotropy is short (between $t\sim 5\mathrm{ns}$ and $t\sim 10\mathrm{ns}$), the orientation anisotropy is only partial. The error bars for $K^{\to }\left(t\right)$ are given by the standard deviation of the experimental data points.