TY - JOUR
T1 - Three-dimensional topological magnetic monopoles and their interactions in a ferromagnetic meta-lattice
AU - Rana, Arjun
AU - Liao, Chen Ting
AU - Iacocca, Ezio
AU - Zou, Ji
AU - Pham, Minh
AU - Lu, Xingyuan
AU - Subramanian, Emma Elizabeth Cating
AU - Lo, Yuan Hung
AU - Ryan, Sinéad A.
AU - Bevis, Charles S.
AU - Karl, Robert M.
AU - Glaid, Andrew J.
AU - Rable, Jeffrey
AU - Mahale, Pratibha
AU - Hirst, Joel
AU - Ostler, Thomas
AU - Liu, William
AU - O’Leary, Colum M.
AU - Yu, Young Sang
AU - Bustillo, Karen
AU - Ohldag, Hendrik
AU - Shapiro, David A.
AU - Yazdi, Sadegh
AU - Mallouk, Thomas E.
AU - Osher, Stanley J.
AU - Kapteyn, Henry C.
AU - Crespi, Vincent H.
AU - Badding, John V.
AU - Tserkovnyak, Yaroslav
AU - Murnane, Margaret M.
AU - Miao, Jianwei
N1 - Funding information: We thank R. Dunin-Borkowski and J. E. Han for stimulating discussions and Y. Yuan and Y. Yang for help with data analysis. This work was primarily supported by STROBE: a National Science Foundation Science and Technology Center under award DMR1548924. J.M. and A.R. acknowledge support by the US Department of Energy, Office of Science, Basic Energy Sciences, Division of Materials Sciences and Engineering under award number DE-SC0010378 for the contribution to the development of vector ptycho-tomography. J.M. thanks partial support by the Army Research Office MURI Program under grant number W911NF-18-1-0431. M.M.M. and H.C.K. acknowledge partial support by the US Department of Energy, Office of Science, Basic Energy Sciences X-Ray Scattering Program Award DE-SC0002002 and DARPA TEE Award D18AC00017 for the data acquisition and analysis. Y.T. and J.Z. were supported by the US Department of Energy, Office of Basic Energy Sciences under grant number DE-SC0012190. E.I. acknowledges the College of Letters, Arts, and Sciences at UCCS for start-up support. Soft X-ray ptycho-tomography experiments were performed at COSMIC and used resources of the Advanced Light Source, which is a US Department of Energy Office of Science User Facility under contract number DE-AC02- 05CH11231. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
PY - 2023/3/1
Y1 - 2023/3/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85146649017&partnerID=8YFLogxK
U2 - 10.1038/s41565-022-01311-0
DO - 10.1038/s41565-022-01311-0
M3 - Letter
AN - SCOPUS:85146649017
SN - 1748-3387
VL - 18
SP - 227
EP - 232
JO - Nature Nanotechnology
JF - Nature Nanotechnology
IS - 3
ER -