Magnetic skyrmions are topologically nontrivial particles with a potential application as information elements in future spintronic device architectures 1, 2 . While they are commonly portrayed as two dimensional objects, in reality magnetic skyrmions are thought to exist as elongated, tube-like objects extending through the thickness of the sample 3, 4 . The study of this skyrmion tube (SkT) state is highly relevant for investigating skyrmion metastability 5 and for implementation in recently proposed magnonic computing 6 . However, direct experimental imaging of skyrmion tubes has yet to be reported. Here, we demonstrate the first real-space observation of skyrmion tubes in a lamella of FeGe using resonant magnetic x-ray imaging and comparative micromagnetic simulations, confirming their extended structure.The formation of these structures at the edge of the sample highlights the importance of confinement and edge effects in the stabilisation of the SkT state, opening the door to further investigations into this unexplored dimension of the skyrmion spin texture.Skyrmion states are typically stabilised by the interplay of the ferromagnetic exchange and Zeeman energies with the Dzyalohsinskii-Moriya Interaction (DMI) 7 . In ferromagnet/heavy metal multilayer thin films, interfacial DMI is induced by symmetry-breaking spin-orbit coupling at the interface between the layers, leading to the formation of Néel-type skyrmions [8][9][10] . Bulk DMI, arising due to the lack of centrosymmetry in the underlying crystal lattice, is responsible for the formation of Bloch-type skyrmions in a range of chiral ferromagnets [11][12][13][14][15] . In crystals of these bulk materials the skyrmion state is typically only at equilibrium in a limited range of applied magnetic field and temperature just below the Curie temperature, T c , forming a hexagonal skyrmion lattice (SkL) in a plane perpendicular to the applied magnetic field.2 Figure 1 | Visualisation of the skyrmion tube spin texture. Three dimensional visualisation of three magnetic skyrmion tubes from the micromagnetic simulations presented in this paper, illustrating their extended spin structure. The inset highlights the location of the magnetic Bloch point at the end of each skyrmion tube. 3The three dimensional visualisation in Fig. 1 depicts the extended spin structure of three magnetic skyrmion tubes. The dynamics of this skyrmion tube (SkT) state play an important role in the creation and annihilation of skyrmions. For example, metastable skyrmions, which are created beyond the equilibrium thermal range by rapid field cooling 16 , are thought to unwind into topologically trivial magnetic states through the motion of a magnetic Bloch point located at the end of each individual skyrmion tube 3, 5 . Real-space observation of this dimension of the SkT state and its associated dynamics requires an in-plane magnetic field applied perpendicular to the imaging axis. Electron imaging techniques such as Fresnel Lorentz Transmission Electron Microscopy (LTEM) 12, 13 , and elec...

Spin waves are excitations in ferromagnetic media that have been proposed as information carriers in hybrid spintronic devices with much lower operation power than conventional charge-based electronics. Their wave nature can be exploited in majority gates by using interference for computation. However, a scalable spin-wave majority gate that can be cointegrated alongside conventional electronics is still lacking. Here, we demonstrate a submicrometer inline spin-wave majority gate with fan-out. Time-resolved imaging of the magnetization dynamics by scanning transmission x-ray microscopy illustrates the device operation. All-electrical spin-wave spectroscopy further demonstrates majority gates with submicrometer dimensions, reconfigurable input and output ports, and frequency-division multiplexing. Challenges for hybrid spintronic computing systems based on spin-wave majority gates are discussed.

While the magnetic properties of nanoscaled antidot lattices in in-plane magnetized materials have widely been investigated, much less is known about the microscopic effect of hexagonal antidot lattice patterning on materials with perpendicular magnetic anisotropy. By using a combination of first-order reversal curve measurements, magnetic x-ray microscopy, and micromagnetic simulations we elucidate the microscopic origins of the switching field distributions that arise from the introduction of antidot lattices into out-of-plane magnetized GdFe thin films. Depending on the geometric parameters of the antidot lattice we find two regimes with different magnetization reversal processes. For small antidots, the reversal process is dominated by the exchange interaction and domain wall pinning at the antidots drives up the coercivity of the system. On the other hand, for large antidots the dipolar interaction is dominating which leads to fragmentation of the system into very small domains that can be envisaged as a basis for a bit patterned media.

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