Corrigendum to "Spin structure relation to phase contrast imaging of isolated magnetic Bloch and Néel skyrmions" [Ultramicroscopy 212 (2020) 112973].

Several errors are present in the text and Fig. 3 of the article Ultramicroscopy 212 (2020) 112973. This includes minor confusions concerning the skyrmion helicities and a wrong orientation of a color wheel that represents the electron phase gradient direction. Further, the presented correction factors for finite probe sizes were based on an erratic simulation which is now corrected. This leads to different error values for the measured skyrmion size. These flaws do not affect the main message of the paper which is the relation of the skyrmion structure with the electron phase at all. They only affect the small section of the proof of principle skyrmion size measurement where aberrations were included.

Spin structure relation to phase contrast imaging of isolated magnetic Bloch and Néel skyrmions.

Magnetic skyrmions are promising candidates for future storage devices with a large data density. A great variety of materials have been found that host skyrmions up to the room-temperature regime. Lorentz microscopy, usually performed in a transmission electron microscope (TEM), is one of the most important tools for characterizing skyrmion samples in real space. Using numerical calculations, this work relates the phase contrast in a TEM to the actual magnetization profile of an isolated Néel or Bloch skyrmion, the two most common skyrmion types. Within the framework of the used skyrmion model, the results are independent of skyrmion size and wall width and scale with sample thickness for purely magnetic specimens. Simple rules are provided to extract the actual skyrmion configuration of pure Bloch or Néel skyrmions without the need of simulations. Furthermore, first differential phase contrast (DPC) measurements on Néel skyrmions that meet experimental expectations are presented and showcase the described principles. The work is relevant for material sciences where it enables the engineering of skyrmion profiles via convenient characterization.

Dynamical Defects in Rotating Magnetic Skyrmion Lattices.

The chiral magnet Cu_{2}OSeO_{3} hosts a Skyrmion lattice that may be equivalently described as a superposition of plane waves or a lattice of particlelike topological objects. A thermal gradient may break up the Skyrmion lattice and induce rotating domains, raising the question of which of these scenarios better describes the violent dynamics at the domain boundaries. Here, we show that in an inhomogeneous temperature gradient caused by illumination in a Lorentz transmission electron microscope different parts of the Skyrmion lattice can be set into motion with different angular velocities. Tracking the time dependence, we show that the constant rearrangement of domain walls is governed by dynamic 5-7 defects arranging into lines. An analysis of the associated defect density is described by Frank's equation and agrees well with classical 2D Monte Carlo simulations. Fluctuations of boundaries show a surgelike rearrangement of Skyrmion clusters driven by defect rearrangement consistent with simulations treating Skyrmions as point particles. Our findings underline the particle character of the Skyrmion.

True single domain and configuration-assisted switching of submicron Permalloy dots observed by electron holography.

The switching behavior of submicron circular Permalloy nanomagnets has been investigated. Electron holography provides a magnetic resolution of down to 10 nm. This allows us to observe in detail the switching and to measure the induction within single nanodots with diameters down to 150 nm at a thickness of 6 nm. Particles of these dimensions show a single domain state during the whole switching process which takes place at external fields of only a few 100 A/m. For larger or thicker particles the magnetization reversal runs via the formation of a C state or an intermediate vortex state.

Direct observation of switching processes in permalloy rings with lorentz microscopy.

To achieve a deeper understanding of the switching process of magnetic Permalloy rings, Lorentz electron microscopy (LTEM) is used for the first time to image the magnetic configuration of such rings under applied external field conditions. Because of the exceptionally high lateral resolution we find two clearly distiguishable wall configurations present in the so-called "onion state." Furthermore, we show that a bias field present during a remagnetization cycle prevents the rings from transforming into a flux closure state, in which case remagnetization is a pure domain wall motion process.

Recording of single-particle hysteresis loops with differential phase contrast microscopy.

The magnetic behaviour of laterally patterned structures on a micrometer or nanometer scale in external magnetic fields can be described by their hysteresis loops. However, it is very difficult to record the hysteresis loop of a single (sub-) micron-sized particle. Furthermore, extensive calculations are necessary in order to interpret the shape of the loop and to conclude the micromagnetic domain configuration in the sample from the hysteresis loop only. We have developed a technique which yields both the hysteresis loop and the magnetic domain structure simultaneously. This method uses differential phase contrast microscopy and a microscope with remote control capability for the automatic recording of a single-particle hysteresis loop.

Polarization decorrelation in optical fibers with randomly varying elliptical birefringence.

Polarization decorrelation in single-mode fibers with randomly varying elliptical birefringence is studied. It is found that the effects of ellipticity on the polarization decorrelation length depend on the relative sizes of the beat length and the autocorrelation length of the birefringence fluctuations in the fiber. However, the evolution of the differential group delay remains unaffected by ellipticity.

Development of a specimen holder for in situ generation of pure in-plane magnetic fields in a transmission electron microscope.

As the development of quantised storage media progresses, detailed knowledge is required about the magnetisation reversal behaviour of sub-micron sized magnetic structures in external magnetic fields. Using the Lorentz mode of transmission electron microscopy (LTEM) the magnetic microstructure of thin film samples can be imaged with high spatial resolution. A novel approach for in situ magnetising experiments is described which combines the development of a custom-made sample holder which generates two orthogonal in-plane components of magnetic field in the specimen plane with the benefit of computer-controlled variation of the field. We present a specimen stage suitable for a Philips CM30 Twin/LTEM, which allows the generation of well-defined magnetic in-plane fields in the TEM.

Mapping the chemistry in nanostructured materials by energy-filtering transmission electron microscopy (EFTEM).

Energy-filtered transmission electron microscopy (EFTEM) can be used to acquire elemental distribution maps at high lateral resolution within short acquisition times, which makes it quite efficient for a detailed characterization of nanostructures, as illustrated with examples concerning a nanostructured substituted La-based cermet compound and a nanoscale multilayer. In the first example, we show how phases in a rapidly cooled substituted LaNi5 can be visualized by recording jump ratio images. Secondly, EFTEM was capable of imaging individual nanoscale layers in a magnetic multilayer consisting of 2 nm terbium and 3 nm iron.

Comparative study of pulse interactions in optical fiber transmission systems with different modulation formats.

We compare nonlinear channel interactions in classical soliton, periodically-stationary dispersion-managed soliton (DMS), and chirped-return-to-zero (CRZ) systems. We studied multichannel systems with a single pulse in each channel and a more general case with multiple bit streams in each channel. First, we find that in classical soliton systems, the distortions are reversible, while in the DMS and CRZ systems they are not. Second, we find that the classical soliton system shows no increase in the degradation as the number of channels increases, while both the DMS and CRZ systems do show an increase in the degradation.