Quantifying the topology of a skyrmion in 3D with soft x-ray laminography*

The push into three dimensions is of growing interest in basic nanomagnetism research with high relevance for future spintronics devices. A spin texture is a three dimensional vector-valued structure which is the result of competition between fundamental energetic interactions and defines the emergent properties of the system including real-space topology (Skyrmion number) and transport behavior responsible for device functionality. A complete description of this microstate requires knowledge of the three components of the magnetization vector covering the volume of the sample in three spatial dimensions. Soft x-ray laminography using magnetic circular dichroism (XMCD) as a contrast mechanism is a three-dimensional imaging technique for magnetic systems which can resolve this information at the nanoscale. The physical information contained in such a [Mx(x, y, z) , My(x, y, z) , Mz(x, y, z)] dataset categorically surpasses what it is possible to quantify with typical Mz(x,y) image data.

In this study a magnetic 30×[Ir/Co/Pt] DMI 800 nm diameter nanodisk is imaged with x-ray laminography at the Pollux end station of the Swiss Light Source. From this data we quantitatively measure the topological profile of a skyrmion and its chirality over the full 90 nm thickness of the sample. From the vector data the relative energy densities of the different micromagnetic energies are derived. The skyrmion topological profile and energetic densities are found to vary across the thickness of the disk demonstrating that the structure of magnetic skyrmions in repeating multilayer systems is more complex that what can be accommodated in a simple two-dimensional framework. Our results provide the foundation for nanoscale magnetic metrology for future tailored spintronics devices using topology as a design parameter, and have the potential to reverse-engineer a spin Hamiltonian from macroscopic data, tying theory more closely to experiment.