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

Abstract

Topological magnetic monopoles, also known as hedgehogs or Bloch points, are threedimensional (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 xray 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 metalattices 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.

Soft x-ray vector ptycho-tomography: a new quantitative vector nanoimaging method for spin textures in 3D

“…To showcase the method, we demonstrated the creation and observation of topological magnetic monopoles (TMMs) and their interactions in a nanoscale magnetic metamaterial 3,9,10 . More than 100 stable TMMs are created in a frustrated ferromagnetic meta-lattice.…”

Accurate real space iterative reconstruction (RESIRE) algorithm for tomography

“…Numerical simulations of a biological vesicle and experimental results of an aragonite coral sample and an amorphous thin film have shown that RESIRE outperforms FBP, SIRT, and GENFIRE with less peripheral noise, more easily detectable boundaries and features, and reduced missing wedge effects. As the power of RESIRE has been demonstrated with the successful reconstructions of amorphous solids and 3D vector ptychography of magnetic materials 45,46 , we expect that RESIRE can be applied to a wide range of imaging modalities in different disciplines, such as AET 1,3,[5][6][7][8][9][10] , coherent diffractive imaging [16][17][18][19][20][21][22][23][24][25][26][27][28]62,63 , cryo-electron tomography 14,15 , x-ray absorption and phase contrast imaging 2,42,[64][65][66][67][68] , and medical computed tomography 30,34,41…”

Magnetostatic interaction between Bloch point nanospheres

“…In such a case, the dipolar term does not contribute to stabilizing hedgehog-like BPs. Consequently, this kind of BP can only be stabilized in the absence of dipolar energy and under certain specific conditions 52 , 53 . On the other hand, because does not contribute to a global factor in the magnetostatic field inside the sphere, even spherically symmetric BPs generate a dipolar field inside the nanoparticle.…”