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

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

*Corresponding author for this work

Research output: Contribution to journalLetterpeer-review

19 Citations (Scopus)


Topological magnetic monopoles (TMMs), also known as hedgehogs or Bloch points, are three-dimensional (3D) non-local 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, and 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.

Original languageEnglish
Pages (from-to)227-232
Number of pages6
JournalNature Nanotechnology
Issue number3
Early online date23 Jan 2023
Publication statusPublished - 1 Mar 2023


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