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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.
The concept of a topological Kondo insulator (TKI) has been brought forward as a new class of topological insulators in which non-trivial surface states reside in the bulk Kondo band gap at low temperature due to the strong spin-orbit coupling [1-3].
The electrodynamics of topological insulators (TIs) is described by modified Maxwells equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupl
Vanadium dioxide (VO2) is a model system that has been used to understand closely-occurring multiband electronic (Mott) and structural (Peierls) transitions for over half a century due to continued scientific and technological interests. Among the ma
We report the simultaneous measurement of the structural and electronic components of the metal-insulator transition of VO$_2$ using electron and photoelectron spectroscopies and microscopies. We show that these evolve over different temperature scal
We present an in-depth classification of the topological phases and Majorana fermion (MF) excitations that arise from the bulk interplay between unconventional multiband spin-singlet superconductivity and various magnetic textures. We focus on magnet