Skyrmion-Excited Spin-Wave Fractal Networks.

Magnetic skyrmions exhibit unique, technologically relevant pseudo-particle behaviors which arise from their topological protection, including well-defined, 3D dynamic modes that occur at microwave frequencies. During dynamic excitation, spin waves are ejected into the interstitial regions between skyrmions, creating the magnetic equivalent of a turbulent sea. However, since the spin waves in these systems have a well-defined length scale, and the skyrmions are on an ordered lattice, ordered structures from spin-wave interference can precipitate from the chaos. This work uses small-angle neutron scattering (SANS) to capture the dynamics in hybrid skyrmions and investigate the spin-wave structure. Performing simultaneous ferromagnetic resonance and SANS, the diffraction pattern shows a large increase in low-angle scattering intensity, which is present only in the resonance condition. This scattering pattern is best fit using a mass fractal model, which suggests the spin waves form a long-range fractal network. The fractal structure is constructed of fundamental units with a size that encodes the spin-wave emissions and are constrained by the skyrmion lattice. These results offer critical insights into the nanoscale dynamics of skyrmions, identify a new dynamic spin-wave fractal structure, and demonstrate SANS as a unique tool to probe high-speed dynamics.

Direct Demonstration of Topological Stability of Magnetic Skyrmions via Topology Manipulation.

Topological protection precludes a continuous deformation between topologically inequivalent configurations in a continuum. Motivated by this concept, magnetic skyrmions, topologically nontrivial spin textures, are expected to exhibit topological stability, thereby offering a prospect as a nanometer-scale nonvolatile information carrier. In real materials, however, atomic spins are configured as not continuous but discrete distributions, which raises a fundamental question if the topological stability is indeed preserved for real magnetic skyrmions. Answering this question necessitates a direct comparison between topologically nontrivial and trivial spin textures, but the direct comparison in one sample under the same magnetic fields has been challenging. Here we report how to selectively achieve either a skyrmion state or a topologically trivial bubble state in a single specimen and thereby experimentally show how robust the skyrmion structure is in comparison with the bubbles. We demonstrate that topologically nontrivial magnetic skyrmions show longer lifetimes than trivial bubble structures, evidencing the topological stability in a real discrete system. Our work corroborates the physical importance of the topology in the magnetic materials, which has hitherto been suggested by mathematical arguments, providing an important step toward ever-dense and more-stable magnetic devices.

Streamlined approach to mapping the magnetic induction of skyrmionic materials.

Recently, Lorentz transmission electron microscopy (LTEM) has helped researchers advance the emerging field of magnetic skyrmions. These magnetic quasi-particles, composed of topologically non-trivial magnetization textures, have a large potential for application as information carriers in low-power memory and logic devices. LTEM is one of a very few techniques for direct, real-space imaging of magnetic features at the nanoscale. For Fresnel-contrast LTEM, the transport of intensity equation (TIE) is the tool of choice for quantitative reconstruction of the local magnetic induction through the sample thickness. Typically, this analysis requires collection of at least three images. Here, we show that for uniform, thin, magnetic films, which includes many skyrmionic samples, the magnetic induction can be quantitatively determined from a single defocused image using a simplified TIE approach.