Quantifying the topology of magnetic Skyrmions in three dimensions

abstract

Magnetic Skyrmions have so far been treated as two-dimensional spin structures characterized by a topological winding number. However, in real systems with the finite thickness of the device material being larger than the magnetic exchange length, the Skyrmion spin texture extends into the third dimension and cannot be assumed as homogeneous. Using soft x-ray laminography we reconstruct with about 20 nm spatial (voxel) size the full three-dimensional spin texture of a Skyrmion in an 800 nm diameter and 95 nm thin disk patterned into a 30×[Ir/Co/Pt] multilayered film. A quantitative analysis finds that the evolution of the radial profile of the topological Skyrmion number is non-uniform across the thickness of the disk. Estimates of the micromagnetic energy densities suggest that the changes in topological profile are related to non-uniform competing energetic interactions. Our results provide a foundation for nanoscale metrology for spintronics devices using topology as a design parameter.

experimental methods

The soft x-ray magnetic laminography experiments were conducted at the PolLux beamline of the Swiss Light Source (SLS) at PSI in Villigen/Switzerland. A rotation series at 45 degrees sample incident angle to the x-ray beam was taken over 56 rotation angles covering 360 degrees with data taken over a 12 hour period. Three laminography data sets were recorded at the L3 edge of Co (around 778 eV x-ray photon energy) with both positive, and negative circular polarization, as well as linear horizontal polarization. All three images are necessary at each rotation angle. The two circular polarization images allow  to quantitatively derive the x-ray magnetic circular dichroism (XMCD) signal, whereas  the linearly-polarized X-ray image enables removing additional nonlinear structural background signals not accounted for with the typical dichroism , as well as unwanted asymmetries in the degree of circular polarization of the beam produced by the PolLux bending magnet. The step size in the horizontal and vertical direction was 20nm. This step size effectively oversamples the diffraction limited resolution which is 42.7nm as calculated from end-station geometry and optics of the 35 nm zone plate used during the experiment. Oversample scans were not taken due to the long acquisition times required for this technique.

file structure

Data was collected over six days of beamtime from 2022-20-14 to 2022-10-10. Each folder contains the data taken on that day. The files in each folder are .hdf5 files containing metadata and images. The file names are of the form Sample_Image_2022-10-DD_index.hdf5.

data structure

The hdf5 file structure contains the microscopy images and metadata. Metadata contains the comprehesive parameters of the microscope with hundreded of fields. The micrsoscope images are photon counts arranged in MATLAB format .mat files. Each index is a pixel in the STXM raster pattern. The data and metadata needed to produce the results reported here can be found in the fields for step size, zone plate geometry, rotation angle, and azimuthal angle. The hdf5 adresses for these parameters are:

photon count image (counts): '/entry1/counter0/data'

step size (nm): '/entry1/instrument/zone_plate/geometry/translation/distances'

zone plate geometry (microns): '/entry1/instrument/zone_plate/outer_diameter'

rotation angle (degrees): '/entry1/sample/rotation_angle'

azimuthal angle (degrees): '/entry1/collection/sample_azimuthal_angle''

data analysis

The three-dimensional reconstruction was produced using the open source 3-D magnetic vector tomogram software availiable under and open source license at https://zenodo.org/records/1324335 reported in Donnelly et al., "Tomographic reconstruction of a three-dimensional magnetization vector field", New Journal of Physics (2018)