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 Jr; Andrew J Glaid; Jeffrey Rable; Pratibha Mahale; Joel Hirst; Thomas Ostler; William Liu; Colum M O'Leary; Young-Sang Yu; Karen Bustillo; Hendrik 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

doi:10.1038/s41565-022-01311-0

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

Nat Nanotechnol. 2023 Mar;18(3):227-232. doi: 10.1038/s41565-022-01311-0. Epub 2023 Jan 23.

Authors

Arjun Rana^#^{1

2}, Chen-Ting Liao^#^{2

3}, Ezio Iacocca^{4

5}, Ji Zou¹, Minh Pham^{2

6}, Xingyuan Lu^{1

7}, Emma-Elizabeth Cating Subramanian^{2

3}, Yuan Hung Lo^{1

2}, Sinéad A Ryan^{2

3}, Charles S Bevis^{2

3}, Robert M Karl Jr^{2

3}, Andrew J Glaid⁸, Jeffrey Rable⁸, Pratibha Mahale^{8

9}, Joel Hirst¹⁰, Thomas Ostler^{10

11}, William Liu^{1

2}, Colum M O'Leary^{1

2}, Young-Sang Yu¹², Karen Bustillo¹³, Hendrik Ohldag¹², David A Shapiro¹², Sadegh Yazdi¹⁴, Thomas E Mallouk^{8

9}, Stanley J Osher^{2

6}, Henry C Kapteyn^{2

3}, Vincent H Crespi⁸, John V Badding⁸, Yaroslav Tserkovnyak¹, Margaret M Murnane^{2

3}, Jianwei Miao^{15

16}

Affiliations

¹ Department of Physics & Astronomy and California NanoSystems Institute, University of California, Los Angeles, Los Angeles, CA, USA.
² STROBE Science and Technology Center, University of Colorado and NIST, Boulder, CO, USA.
³ JILA and Department of Physics, University of Colorado and NIST, Boulder, CO, USA.
⁴ Department of Mathematics, Physics, and Electrical Engineering, Northumbria University, Newcastle upon Tyne, UK.
⁵ Center for Magnetism and Magnetic Nanostructures, University of Colorado, Colorado Springs, CO, USA.
⁶ Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, USA.
⁷ School of Physical Science and Technology, Soochow University, Suzhou, China.
⁸ Departments of Chemistry, Physics, Materials Science and Engineering and Materials Research Institute, Penn State University, University Park, PA, USA.
⁹ Department of Chemistry, University of Pennsylvania, Philadelphia, PA, USA.
¹⁰ Materials and Engineering Research Institute, Sheffield Hallam University, Sheffield, UK.
¹¹ Department of Physics and Mathematics, University of Hull, Hull, UK.
¹² Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
¹³ National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
¹⁴ Renewable and Sustainable Energy Institute, University of Colorado, Boulder, CO, USA.
¹⁵ Department of Physics & Astronomy and California NanoSystems Institute, University of California, Los Angeles, Los Angeles, CA, USA. miao@physics.ucla.edu.
¹⁶ STROBE Science and Technology Center, University of Colorado and NIST, Boulder, CO, USA. miao@physics.ucla.edu.

^# Contributed equally.

PMID: 36690739
DOI: 10.1038/s41565-022-01311-0

Abstract

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 protection^1-4. Although TMMs have been observed in skyrmion lattices^1,5, spinor Bose-Einstein condensates^6,7, chiral magnets⁸, vortex rings^2,9 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.