@article{12725, author = {Arjun Rana and Chen-Ting Liao and Ezio Iacocca and Ji Zou and Minh Pham and Emma-Elizabeth Subramanian and Yuan Lo and Sinéad Ryan and Xingyuan Lu and Charles Bevis and Robert Karl Jr and Andrew Glaid and Young-Sang Yu and Pratibha Mahale and David Shapiro and Sadegh Yazdi and Thomas Mallouk and Stanley Osher and Henry Kapteyn and Vincent Crespi and John Badding and Yaroslav Tserkovnyak and Margaret Murnane and Jianwei Miao}, title = {Direct observation of 3D topological spin textures and their interactions using soft x-ray vector ptychography}, abstract = {Magnetic topological defects are energetically stable spin configurations characterized by symmetry breaking. Vortices and skyrmions are two well-known examples of 2D spin textures that have been actively studied for both fundamental interest and practical applications. However, experimental evidence of the 3D spin textures has been largely indirect or qualitative to date, due to the difficulty of quantitively characterizing them within nanoscale volumes. Here, we develop soft x-ray vector ptychography to quantitatively image the 3D magnetization vector field in a frustrated superlattice with 10 nm spatial resolution. By applying homotopy theory to the experimental data, we quantify the topological charge of hedgehogs and anti-hedgehogs as emergent magnetic monopoles and probe their interactions inside the frustrated superlattice. We also directly observe virtual hedgehogs and anti-hedgehogs created by magnetically inert voids. We expect that this new quantitative imaging method will open the door to study 3D topological spin textures in a broad class of magnetic materials. Our work also demonstrates that magnetically frustrated superlattices could be used as a new platform to investigate hedgehog interactions and dynamics and to exploit optimized geometries for information storage and transport applications.}, year = {2022}, journal = {Submitted}, url = {https://arxiv.org/abs/2104.12933}, }