Three-dimensional topological magnetic monopoles and their interactions in a ferromagnetic meta-lattice

Rana, Arjun; Liao, Chen-Ting; Iacocca, Ezio; Zou, Ji; Pham, Minh; Lu, Xingyuan; Cating Subramanian, Emma-Elizabeth; Hung Lo, Yuan; Ryan, Sinéad A.; Bevis, Charles S.; Karl Jr, Robert M.; Glaid, Andrew J.; Rable, Jeffrey; Mahale, Pratibha; Hirst, Joel; Ostler, Thomas; Liu, William; O’Leary, Colum M.; Yu, Young-Sang; Bustillo, Karen; Ohldag, Hendrik; Shapiro, David A.; Yazdi, Sadegh; Mallouk, Thomas E.; Osher, Stanley J.; Kapteyn, Henry C.; Crespi, Vincent H.; Badding, John V.; Tserkovnyak, Yaroslav; Murnane, Margaret M.; Miao, Jianwei

Abstract

Topological magnetic monopoles (TMMs), also known as hedgehogs or Bloch points, are three-dimensional (3D) nonlocal spin textures that are robust to thermal and quantum fluctuations due to the topology protection1-4. Although TMMs have been observed in skyrmion lattices1,5, spinor Bose–Einstein condensates6,7, chiral magnets8, vortex rings2,9, and vortex cores10, it has been difficult to directly measure the 3D magnetization vector field of TMMs and probe their interactions at the nanoscale. Here, we report the creation of 138 stable TMMs at the specific sites of a ferromagnetic meta-lattice at room temperature. We further develop soft x-ray vector ptycho-tomography to determine the magnetization vector and emergent magnetic field of the TMMs with a 3D spatial resolution of 10 nm. This spatial resolution is comparable to the magnetic exchange length of transition metals11, enabling us to probe monopole-monopole interactions. We find that the TMM and anti-TMM pairs are separated by 18.3±1.6 nm, while the TMM and TMM, anti-TMM and anti-TMM pairs are stabilized at comparatively longer distances of 36.1±2.4 nm and 43.1±2.0 nm, respectively. We also observe virtual TMMs created by magnetic voids in the meta-lattice. This work demonstrates that ferromagnetic meta-lattices could be used as a platform to create and investigate the interactions and dynamics of TMMs. Furthermore, we expect that soft x-ray vector ptycho-tomography can be broadly applied to quantitatively image 3D vector fields in magnetic and anisotropic materials at the nanoscale.

Citation

Rana, A., Liao, C.-T., Iacocca, E., Zou, J., Pham, M., Lu, X., Cating Subramanian, E.-E., Hung Lo, Y., Ryan, S. A., Bevis, C. S., Karl Jr, R. M., Glaid, A. J., Rable, J., Mahale, P., Hirst, J., Ostler, T., Liu, W., O’Leary, C. M., Yu, Y.-S., Bustillo, K., …Miao, J. (2023). Three-dimensional topological magnetic monopoles and their interactions in a ferromagnetic meta-lattice. Nature nanotechnology, 18, 227–232. https://doi.org/10.1038/s41565-022-01311-0

• Journal Article Type: Letter
• Acceptance Date: Dec 13, 2022
• Online Publication Date: Jan 23, 2023
• Publication Date: 2023
• Deposit Date: Feb 27, 2023
• Publicly Available Date: Jul 24, 2023
• Journal: Nature nanotechnology
• Print ISSN: 1748-3387
• Publisher: Nature Publishing Group
• Peer Reviewed: Peer Reviewed
• Volume: 18
• Pages: 227–232
• DOI: https://doi.org/10.1038/s41565-022-01311-0
• Keywords: Imaging techniques; Magnetic properties and materials; Topological matter
• Public URL: https://hull-repository.worktribe.com/output/4152865
• Additional Information: This is currently under embargo - see email from senior editor at Nature Nanotechnology below in the notes. Publication is not expected for around another 6/7 weeks or more.