TY - JOUR AU - Arjun Rana AU - Chen-Ting Liao AU - Ezio Iacocca AU - Ji Zou AU - Minh Pham AU - Emma-Elizabeth Subramanian AU - Yuan Lo AU - Sinéad Ryan AU - Xingyuan Lu AU - Charles Bevis AU - Robert Karl Jr AU - Andrew Glaid AU - Young-Sang Yu AU - Pratibha Mahale AU - David Shapiro AU - Sadegh Yazdi AU - Thomas Mallouk AU - Stanley Osher AU - Henry Kapteyn AU - Vincent Crespi AU - John Badding AU - Yaroslav Tserkovnyak AU - Margaret Murnane AU - Jianwei Miao AB - 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. BT - Submitted N2 - 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. PY - 2022 T2 - Submitted TI - Direct observation of 3D topological spin textures and their interactions using soft x-ray vector ptychography UR - https://arxiv.org/abs/2104.12933 ER -