Whereas theoretical investigations have revealed the significant influence of magnetic surface and edge states on Skyrmonic spin texture in chiral magnets, experimental studies of such chiral states remain elusive. Here, we study chiral edge states in an FeGe nanostripe experimentally using off-axis electron holography. Our results reveal the magnetic-field-driven formation of chiral edge states and their penetration lengths at 95 and 240 K. We determine values of saturation magnetization $M_S$ by analyzing the projected in-plane magnetization distributions of helices and Skyrmions. Values of $M_S$ inferred for Skyrmions are lower by a few percent than those for helices. We attribute this difference to the presence of chiral surface states, which are predicted theoretically in a three-dimensional Skyrmion model. Our experiments provide direct quantitative measurements of magnetic chiral boundary states and highlight the applicability of state-of-the-art electron holography for the study of complex spin textures in nanostructures.

In two-dimensional van der Waals magnets, the presence of magnetic orders, strong spin–orbit coupling, and asymmetry at interfaces is the key ingredient for hosting noncollinear spin textures. Here, we investigate the characteristics and evolution of magnetic domain structures in thin Fe₃GeTe₂ nanolayers as a function of temperature, applied magnetic field, and specimen thickness using advanced magnetic electron microscopy. Specifically, electron holography analyses reveal the spin configurations of Bloch-type, zero-field-stabilized magnetic bubbles in 20-nm-thick Fe₃GeTe₂ nanolayers at cryogenic temperature. In situ Lorentz transmission electron microscopy measurements further provide detailed magnetic phase diagrams of noncollinear spin textures, including magnetic spirals and bubbles in Fe₃GeTe₂ as a function of temperature, applied magnetic field, and specimen thickness. We further estimate the micromagnetic parameters of Fe₃GeTe₂, such as anisotropy energy density and magnetization at specific specimen temperature using the critical thicknesses measured from Lorentz microscopy measurements. Our experimental results of magnetic domain structures in Fe₃GeTe₂ nanolayers reveal that due to their intrinsic highly uniaxial magnetocrystalline anisotropy, a very thin film of tens of nanometers of Fe₃GeTe₂ can support the spontaneous and stable formation of zero-field magnetic bubbles.

Electron diffraction techniques in transmission electron microscopy (TEM) have been successfully employed for determining the unit-cell parameters of crystal phases, albeit they exhibit a limited accuracy compared with X-ray or neutron diffraction, and they often involve a tedious measurement procedure. Here, a new package for determining unit-cell parameters from a single electron diffraction pattern has been developed. The essence of the package is to reconstruct a 3D reciprocal primitive cell from a single electron diffraction pattern containing both zero-order Laue zone and high-order Laue zone reflections. Subsequently, the primitive cell can be reduced to the Niggli cell which, in turn, can be converted into the unit cell. Using both simulated and experimental patterns, we detail the working procedure and address some effects of experimental conditions (diffraction distortions, misorientation of the zone axis and the use of high-index zone axis) on the robustness and accuracy of the software developed. The feasibility of unit-cell determination of the TiO₂nanorod using this package is also demonstrated. Should the parallel-beam, nano-beam and convergent-beam modes of the TEM be used flexibly, the software can determine unit-cell parameters of unknown-structure crystallites (typically >50 nm).

Magnetic skyrmions are vortex-like spin structures that are of great interest scientifically and for applications in low-power magnetic memories. The nanometer size and complex spin structure require high-resolution and quantitative experimental methods to study the physical properties of skyrmions. Here, we illustrate how Lorentz TEM and off-axis electron holography can be used to study the spin textures of magnetic skyrmions in the noncentrosymmetric B20-type helimagnet FeGe as a function of temperature and applied magnetic field. By reversing the magnetic field inside the microscope, the switching mechanism of the skyrmion lattice at 240 K is followed, showing a transition of the skyrmion lattice to the helical structure before the anti-skyrmion lattice is formed