Creation and observation of topological magnetic monopoles and their interactions in a ferromagnetic meta-lattice

Topological magnetic monopoles, also known as hedgehogs or Bloch points, are three-dimensional (3D) nonlocal spin textures that are robust to thermal and quantum fluctuations due to their topology 1-4 . Understanding their properties is of both fundamental interest and practical applications 1-9 . However, it has been difficult to experimentally produce topological magnetic monopoles in a controlled manner and directly observe their 3D magnetization vector field and interactions at the nanoscale. Here, we report the creation of 138 stable topological magnetic monopoles at the specific sites of a ferromagnetic meta-lattice at room temperature. We further develop 3D soft x-ray vector ptychography to determine the magnetization vector and emergent magnetic field of the topological monopoles with a 3D spatial resolution of 10 nm. This spatial resolution is comparable to the magnetic exchange length of transition metals 10 , enabling us to probe monopole-monopole interactions. We find that the topological monopole pairs with positive and negative charges are separated by 18.3±1.6 nm, while the positively and negatively charged pairs are stabilized at comparatively longer distances of 36.1±2.4 nm and 43.1±2.0 nm, respectively. We also observe virtual topological monopoles created by magnetic voids in the meta-lattice. This work demonstrates that ferromagnetic meta-lattices could be used as a new platform to create and investigate the interactions and dynamics of topological magnetic monopoles. Furthermore, we expect that soft x-ray vector ptychography can be broadly applied to quantitatively image 3D vector fields in magnetic and anisotropic materials at the nanoscale.