Employing soft x-ray resonant magnetic scattering to study domain sizes and anisotropy in Co/Pd multilayers

It is demonstrated that the magnetic diffraction pattern of the isotropic disordered maze pattern is well described utilizing a gamma distribution of domain sizes in a one-dimensional model. From the analysis, the mean domain size and the shape parameter of the distribution are obtained. The model reveals an average domain size that is significantly different from the value that is determined from the peak position of the structure factor in reciprocal space. As a proof of principle, a wedge-shaped $({\mathrm{Co}}_{t\AA }/{\mathrm{Pd}}_{10\AA }{)}_8$ multilayer film, that covers the thickness range of the spin-reorientation transition, has been used. By means of soft x-ray resonant magnetic scattering (XRMS) and imaging techniques the thickness-driven evolution of the magnetic properties of the cobalt layers is explored. It is shown that minute changes of the domain pattern concerning domain size and geometry can be investigated and analyzed due to the high sensitivity and lateral resolution of the XRMS technique. The latter allows for the determination of the magnetic anisotropies of the cobalt layers within a thickness range of a few angstroms.

Figure 1

(a) Layout of the XRMS experiment at the P04 beamline of Petra III. The beam coming from the left passes through a pinhole with a diameter of 40 μm, and is scattered at the sample. The scattering pattern is recorded by a CCD camera. The direct beam is blocked by a beam stop. Optionally a second pinhole and a photodiode can be placed before and behind the sample to record absorption. (b) Sketch of the Co/Pd sample system.

Figure 2

(a) The XMCD asymmetry along the wedge at the Co $L_3$ edge (778 eV) calculated from the transmitted intensities with left- and right- circular polarization. (b) Co thickness calculated from absorption profiles with opposite helicities at 778 eV (black lines) and calibrated with an EDAX profile along the wedge (red line).

Figure 3

(a) Scanning transmission x-ray microscopy (STXM) image at $h\nu =778\mathrm{eV}$ showing the domain size evolution with increasing Co thickness. (b) X-ray scattering patterns of magnetic domains. The rectangular structure in the center is used to mask out the superimposed projection image of the membrane window. Yellow dashed-line circles indicate the maximum of the structure factor for each Co thickness. (c) Intensity profiles extracted from the diffraction pattern via radial integration (colored symbols). We observe a shift of the peak position $Q_{max}$ (black horizontal arrow), as well as a decrease of the scattering intensity and an increase of peak width. Above a total Co thickness of $t_{\mathrm{Critical}}=58.5\pm 0.4\AA$ the peak positions stay constant in $Q$ while the intensity continues to drop (black vertical arrow). The solid lines are simulated intensity profiles resulting from a FFT of a one-dimensional domain pattern with gamma-distributed domain sizes.

Figure 4

Comparison of the domain size distribution of a maze pattern from a Nd-Fe-B sample extracted from line profiles (black circles) with the probability density function of a gamma distribution (blue circles) fitted to the data. The inset shows a part of a Kerr image from this sample. The domain size distribution and the Kerr image have been taken from Fig. 2 in Ref. [43] (Courtesy of Dr. Juliane Thielsch and Dr. Thomas G. Woodcock). A good agreement of both curves is apparent. The increasing frequencies at very small domain sizes occur from wavy domain walls specific to the system (see Ref. [43]). Only in the range between 2 and 3 times the mean domain size deviations are present.

Figure 5

(a) Relation between the domain size $D_{\mathrm{gamma}}=\vartheta k$ versus $D_{Q_{\max }}=\pi /Q_{max}$. Values from the intensity profiles fitted to the experimental data are given by blue circles. The orange and green dashed lines show the dependences for two different $k$ values and the black solid line illustrates the Gaussian distribution. (b) Intensity profile extracted from the diffraction pattern at $t_{\mathrm{Co},\mathrm{total}}=54.6\pm 0.4\AA$ (open symbols) and the corresponding simulated intensity profile (blue solid line) obtained by a FFT of a one-dimensional domain pattern of gamma-distributed domain sizes. A histogram of this distribution is shown in the inset. A shape parameter of $k=4$ and an average domain size of $D_{\mathrm{gamma}}=73\mathrm{nm}$ are used as input parameters.

Figure 6

Intensity profile at $t_{\mathrm{Co},\mathrm{total}}=54.6\AA$ normalized to the peak maximum and position $Q_{max}$ (blue open symbols). For comparison a normalized intensity profile at $t_{\mathrm{Co},\mathrm{total}}=59.5\AA$ is plotted (red open symbols). The widths of both structure factors are different, indicating structural changes of the domain pattern at $t_{\mathrm{Critical}}$. The simulated data indicate a change of the shape parameter of the gamma distribution from $k=4$ to 3.3 (red and blue lines). The inset shows the normalized intensity profiles in the thickness range of $t_{\mathrm{Co},\mathrm{total}}=50.3$ to 57.7 Å. Every second profile is plotted for the sake of better representation. The black curve displays the normalized simulated intensity profile with a shape parameter $k=4$ which is denoted as a universal curve for all profiles.

Figure 7

$K_{1,\mathrm{eff}}{t}_{\mathrm{Co},\mathrm{single}}$ versus Co thickness of the Co/Pd multilayer. The values for $K_{1,\mathrm{eff}}{t}_{\mathrm{Co},\mathrm{single}}>0$ (blue dots) are calculated using the analytical expression in Ref. [25] (see text), and a linear fit is shown. The values for $K_{1,\mathrm{eff}}{t}_{\mathrm{Co},\mathrm{single}}<0$ are calculated using the integrated scattering intensities and the expression for the canting angle [Eq. (4)].