Creation and annihilation of mobile fractional solitons in atomic chains

Localized modes in one-dimensional (1D) topological systems, such as Majonara modes in topological superconductors, are promising candidates for robust information processing. While theory predicts mobile integer and fractional topological solitons in 1D topological insulators, experiments so far have unveiled immobile, integer solitons only. Here we observe fractionalized phase defects moving along trimer silicon atomic chains formed along step edges of a vicinal silicon surface. By means of tunnelling microscopy, we identify local defects with phase shifts of 2π/3 and 4π/3 with their electronic states within the band gap and with their motions activated above 100 K. Theoretical calculations reveal the topological soliton origin of the phase defects with fractional charges of ±2e/3 and ±4e/3. Additionally, we create and annihilate individual solitons at desired locations by current pulses from the probe tip. Mobile and manipulable topological solitons may serve as robust, topologically protected information carriers in future information technology.

Complex free-space magnetic field textures induced by three-dimensional magnetic nanostructures

The design of complex, competing effects in magnetic systems—be it via the introduction of nonlinear interactions1–4, or the patterning of three-dimensional geometries5,6—is an emerging route to achieve new functionalities. In particular, through the design of three-dimensional geometries and curvature, intrastructure properties such as anisotropy and chirality, both geometry-induced and intrinsic, can be directly controlled, leading to a host of new physics and functionalities, such as three-dimensional chiral spin states7, ultrafast chiral domain wall dynamics8–10 and spin textures with new spin topologies7,11. Here, we advance beyond the control of intrastructure properties in three dimensions and tailor the magnetostatic coupling of neighbouring magnetic structures, an interstructure property that allows us to generate complex textures in the magnetic stray field. For this, we harness direct write nanofabrication techniques, creating intertwined nanomagnetic cobalt double helices, where curvature, torsion, chirality and magnetic coupling are jointly exploited. By reconstructing the three-dimensional vectorial magnetic state of the double helices with soft-X-ray magnetic laminography12,13, we identify the presence of a regular array of highly coupled locked domain wall pairs in neighbouring helices. Micromagnetic simulations reveal that the magnetization configuration leads to the formation of an array of complex textures in the magnetic induction, consisting of vortices in the magnetization and antivortices in free space, which together form an effective B field cross-tie wall14. The design and creation of complex three-dimensional magnetic field nanotextures opens new possibilities for smart materials15, unconventional computing2,16, particle trapping17,18 and magnetic imaging19.

Unveiling the three-dimensional magnetic texture of skyrmion tubes

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.