Abstract
Magnetic skyrmions are stable topological solitons with complex non-coplanar spin structures. Their nanoscopic size and the low electric currents required to control their motion has opened a new field of research, skyrmionics, that aims for the usage of skyrmions as information carriers. Further advances in skyrmionics call for a thorough understanding of their three-dimensional (3D) spin texture, skyrmion–skyrmion interactions and the coupling to surfaces and interfaces, which crucially affect skyrmion stability and mobility. Here, we quantitatively reconstruct the 3D magnetic texture of Bloch skyrmions with sub-10-nanometre resolution using holographic vector-field electron tomography. The reconstructed textures reveal local deviations from a homogeneous Bloch character within the skyrmion tubes, details of the collapse of the skyrmion texture at surfaces and a correlated modulation of the skyrmion tubes in FeGe along their tube axes. Additionally, we confirm the fundamental principles of skyrmion formation through an evaluation of the 3D magnetic energy density across these magnetic solitons.
Highlights
As multidimensional solitons, skyrmions[1] are localized in two dimensions, which requires a definite mechanism through additional frustrating magnetic couplings for their stabilization[2] and application, for example, for advanced magnetic memories[3,4,5]
In three-dimensional (3D) bulk materials or thicker films, the skyrmions are extended string-like objects; in the simplest formation they are homogeneously continued as skyrmion tubes (SkTs) preserving translational invariance along their axis
Already from the earliest observations of skyrmionic phases in films of chiral helimagnets[16,17], it is known that their phase diagrams massively deviate from those of bulk materials. 3D surface twists can stabilize SkTs in thin films[10,11,18] and 3D modulations of SkTs embedded in a conical host phase may introduce an attractive interaction between these tubes19. 3D SkT modulations affect emergent electric and magnetic fields acting on spin-polarized electrons and magnons[20], which results in unusual transport phenomena[21] on top of the normal topological Hall effect in static and current-driven skyrmion crystals[22,23,24,25]
Summary
We used low-temperature holographic VFET in combination with the spatial stabilization of the specimen’s magnetic state by an external magnetic field to reconstruct the full vector-field B of the skyrmionic spin texture in FeGe in all three dimensions at nanometre resolution. We observed a substantial bending and twisting of these axes that was locally correlated with the occurrence of pronounced edge states, in directions that were affected by confinements. These deformations appeared at length scales, where harmonic modulations were promoted by the DM interaction. Online content Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41565-021-01031-x
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