Skyrmions exhibit topologically nontrivial spin textures [1] and can be motioned by comparably small spin-polarized currents [2]. This renders them promising for the use as information carriers in future magnetic data storage and processing technologies, referred to as Skyrmionics. To better understand the physics of Skyrmions, a detailed knowledge of the real space magnetic structure of these spin solitons is mandatory. We have therefore studied the 3D magnetic textures of Skyrmion tubes (SkTs) using in-line and off-axis electron holography (EH). While the orientation of the in-plane magnetic induction B obtained from a Fe0.95Co0.05Ge nanoplate using in-line EH shows the expected hexagonal vortex-like pattern (Fig. 1), a thorough quantitative analysis implies that the underlying 3D texture deviates from that of homogeneously extended Bloch Skyrmions [3]. Low temperature holographic vector field electron tomography (VFET [4]) in an external magnetic field was therefore used to quantitatively reconstruct the full 3D magnetic texture of SkTs in an FeGe needle [5]. The resulting high-resolution 3D magnetic images (Fig. 2) reveal various previously unseen details of the SkTs. Our findings include the occurrence of local deviations from a homogeneous Bloch character within the tubes. They highlight the collapse of the Skyrmion texture upon approaching the surfaces of the needle, provide evidence for the coexistence of longitudinal and transverse Skyrmion textures, and reveal an axial modulation of the SkTs that is found to be strongly correlated among neighboring tubes in the needle. Based on the quantitative 3D magnetic induction data, we have calculated spatially resolved energy density maps across the SkTs that provide experimental evidence for the energetic stabilization of these magnetic solitons through an energy gain due to the Dzyaloshinskii-Moryia interaction, which overcompensates the exchange energy in the tube centers.

![](https://assets.underline.io/uploads/markdown_image/1/image/95d4498ede230bdf211fb866fabb1ce2.jpg)

Orientation map of the projected in-plane component of the magnetic induction in the hexagonal Skyrmion lattice of a Fe0.95Co0.05Ge nanoplate.

![](https://assets.underline.io/uploads/markdown_image/1/image/a445af1acb5f54ffe8123e81a66772df.jpg)

Morphology of an FeGe needle (left) and direction of the 3D magnetic induction B (right) as determined from holographic VFET experiments.

Unravelling the details of the magnetic texture of skyrmion tubes in three dimensions

The increasing exploration of nanomagnetism into the third dimension lead to the discovery of novel frustration mechanisms and ensuing magnetic configurations and textures, many with unprecedented properties [1]. The fundamental understanding of these configurations and the interactions stabilizing them requires a quantitative microscopy technique revealing 3D magnetic structures with a spatial resolution below characteristic magnetic length scales pertaining to a given problem. In our contribution we introduce holographic vector-field electron tomography (VFET), a combination of off-axis electron holography (EH) and electron tomography in the transmission electron microscope (TEM), facilitating sub-10 nanometer spatial resolution [2, 3]. Off-axis EH utilizes an interferometric setup to determine the phase shift of an electron wave that passed through the sample. The Aharonov-Bohm phase shift of ferro-magnetic samples is proportional to projections of both electric potential (mainly mean inner potential) and magnetic flux density (B-field), which allows to reconstruct them in 3D from a tilt series of 2D phase images by tomographic methods [2]. The principle and workflow of holographic VFET is illustrated in Fig. 1. In addition to the comprehensive workflow of recording and reconstructing the 3D data, crucial steps of alignment and image processing, e.g., precise displacement correction of 2D projections and 3D tomograms, phase unwrapping, denoising, etc. are addressed. Fig. 2 shows two examples, how holographic VFET is applied to reveal 3D magnetic configurations in nanoscale magnetic materials. In Figs. 2a,b, we present 3D remanent states in a Co-rich CoNi cylindrical nanowire (NW) with a diameter of 70 nm and the hcp c-axis oriented almost perpendicular to the NW axis [4]. We observed two different remanent states after the application of an external saturation field of 2 T perpendicular (Fig. 2a) and parallel (Fig. 2b) to the NW axis. The external field direction perpendicular to both the wire axis and the magnetocrystalline easy axis resulted in a transverse-vortex chain configuration, whereas a field direction parallel to the wire axis produced longitudinal vortex domains with their cores aligned along the applied field, but with alternately opposite chirality. Micromagnetic simulations confirm our findings and enable us to understand the origin of the observed complex magnetic states, in particular, reveal a large influence of the NW morphology on the remanent state. In Fig. 2c, the first 3D reconstruction of Bloch-Skyrmions in a FeGe needle-shaped FIB sample taken at 90K temperature is depicted. The reconstructed textures provide insights into a variety of previously unseen local deviations from a homogeneous Bloch character within the skyrmion tubes (SkTs), details of the collapse of the skyrmion texture at surfaces, and a correlated modulation of the SkT in FeGe along their tube axes. [5]

**References:**

[1] A. Fernandez-Pacheco et al., Nat Commun 8, p.15756 (2017) [2] D. Wolf et al., Chem Mater 27, p. 6771 (2015) [3] D. Wolf et al., Comm Phys 2, p. 87 (2019) [4] I.M. Andersen et al., submitted (2021) [5] D. Wolf et al., to be submitted (2021) [6] DW and AL have received funding from the European Research Council (ERC) under the Horizon 2020 research and innovation program of the European Union (grant agreement number 715620). AL, and SS acknowledge financial support through the Priority Program SPP2137 of the German Research Foundation (DFG) within projects LU-2261/2-1 and RE-1164/6-1.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d41934af339cca9f9876429c2fd07a66.jpg)
Principle and workflow of holographic vector-field electron tomography (VFET) in the transmission electron microscope (adapted from Ref. [3]). (1) Modulation of electron waves by magnetic sample, (2) Interference of modulated object wave with unmodulated reference wave by an electrostatic biprism building up an electron hologram, (3) Reconstruction of hologram yielding amplitude and phase shift of object wave, (4) Acquisition of two tilt series around two tilt axes, X and Y, providing two (ideally 360°) phase tilt series, (5/6) Calculation of half the sum/difference of opposite projections (green/red arrow) resulting in electric/magnetic phase tilt series, (7) 3D reconstruction of electric potential from electric phase tilt series, (8) 3D Reconstruction of the two magnetic B-field components Bx (By) from the derivatives in y (x) - direction of the magnetic phase tilt series, (9) Computation of Bz component by solving divB=0.


![](https://assets.underline.io/uploads/markdown_image/1/image/5510c31e0fc0dc100ad286c0cc5a0e09.jpg)
Holographic VFET of magnetic nanostructures. (a,b) Volume rendering of the By component of the reconstructed magnetic induction B of two remanent magnetic states (a) and (b) in a Co-rich CoNi nanowire (70 nm diameter) after external field HSat applied perpendicular (a) and parallel (b) to the wire axis. The magnified regions with vectors slices show transverse vortex chains in (a) and longitudinal vortex domains of alternating chirality separated by a domain wall in (b). (c) Volume rendering of the in-plane components Bx, By according to the colorwheel and iso-surface of the mean inner potential reconstruction highlighting the FeGe FIB-prepared specimen shape (grey, bottom half only). The magnified views visualize a single skyrmion tube (SkT) in which the three vectors slices plot the 3D spin texture inside the SkT at different z-heights.

3D Mapping of Magnetic Nanotextures with Nanometer Resolution Using Holographic Vector-Field Electron Tomography

Interfacial electrochemical effects on magnetism, often also named magneto-ionic effects, are an emerging room-temperature and low-voltage approach in the research area of voltage control of magnetism [1]. In magneto-ionic systems, the magnetic layer is gated via a solid or liquid electrolyte and the applied voltage triggers ion migration and interfacial redox reactions, which impact the magnetic properties. In contrast to multiferroic systems and capacitive electronic charging, magneto-ionic concepts make significant magnetic property changes possible at room temperature and without the need for strain mediation [2], [3]. Since the mechanism is based on electrochemical charge transfer at the electrode/electrolyte interface, the morphology and the composition may be key to the magneto-ionic efficiency. We report magneto-ionic manipulation of ultrathin films in extended and stripe geometry and 3D nanoplatelet structures. In situ magnetic transport measurements are used in this study to determine and analyze the magneto-ionic effect. For FeOOH nanoplatelets, the application of a low voltage via liquid electrolyte gating yields an ON switching of magnetization (deduced from changes of the anomalous Hall resistance, see Figure 1a) [4]. The transformation proceeds via voltage-induced dissolution/redeposition, with the initially paramagnetic FeOOH structure as iron ion reservoir. The time-dependency of the reduction reaction enables the non-volatile setting of magnetic layers with different total magnetic moments. A large reversible magneto-ionic change of magnetization of up to 15% is achieved in the resulting iron films, which is explained by the enhanced roughness of the iron films obtained from the nanoplatelet structure. For thin Fe3O4/Fe films in stripe geometry, we achieved a tunable magnetoresistance by electrolytic gating (Figure 1b) [5]. Here, the tuning mechanism relies on voltage-triggered redox reactions, which locally affect the Fe3O4 regions. In the low-magnetic-field region (&lt;1 T), a crossover from positive to negative magnetoresistance is achieved by a voltage change of only 1.72 V. We will further present first results on the impact of the composition in iron triad magneto-ionic systems on magnetic properties by going beyond iron structures. The proposed approach is promising for the development of energy-efficient magnetic switches, sensors, and magnetic actuation, and may offer new avenues in magnetoelectronic devices.

**References:**

[1] K. Leistner, Current Opinion in Electrochemistry Vol. 25, p. 100636 (2021) [2] C. Navarro-Senent et al., APL Materials, Vol. 7, p. 030701 (2019) [3] K. Duschek et al., J. Mater. Chem. C, Vol. 6, p. 8411 (2018) [4] M. Nichterwitz et al., J. Phys. D: Appl. Phys., Vol. 53, p. 084001 (2020) [5] M. Nichterwitz et al., ACS Appl. Electron. Mater., Vol. 2, p. 2543 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e678a85b2d151bfa98d2f7b3f748549d.jpg)
Fig. 1 (a) electric “ON” switching of magnetism via electrolytic gating of FeOOH nanoplatelets. Magnetization curves as measured by anomalous Hall effect (AHE) after reduction at −1.27 V for different reduction times. The inset shows the cross-sectional REM image of a FeOOH pristine sample. (Adapted from [4]). (b) Voltage-control of the magnitude and the sign of magnetoresistance (MR) of FeOx/Fe nanocomposite thin films by electrolytic gating in LiOH. The inset shows a cross-sectional HR-TEM image of the pristine iron oxide-iron nanocomposite film. (Adapted from [5]).

 Magneto-ionic effect in iron triad nanostructures with different shapes and composition

**Session chair:** Aisha Aqeel, University of Munich



GOG - Fundamental Interactions in Skyrmions and Novel Phases

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Unravelling the details of the magnetic texture of skyrmion tubes in three dimensions

3D Mapping of Magnetic Nanotextures with Nanometer Resolution Using Holographic Vector-Field Electron Tomography

Magneto-ionic effect in iron triad nanostructures with different shapes and composition

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