Rolling Motion of Rigid Skyrmion Crystallites Induced by Chiral Lattice Torque.

Magnetic skyrmions are topologically protected spin textures with emergent particle-like behaviors. Their dynamics under external stimuli is of great interest and importance for topological physics and spintronics applications alike. So far, skyrmions are only found to move linearly in response to a linear drive, following the conventional model treating them as isolated quasiparticles. Here, by performing time and spatially resolved resonant elastic X-ray scattering of the insulating chiral magnet Cu2OSeO3, we show that for finite-sized skyrmion crystallites, a purely linear temperature gradient not only propels the skyrmions but also induces continuous rotational motion through a chiral lattice torque. Consequently, a skyrmion crystallite undergoes a rolling motion under a small gradient, while both the rolling speed and the rotational sense can be controlled. Our findings offer a new degree of freedom for manipulating these quasiparticles toward device applications and underscore the fundamental phase difference between the condensed skyrmion lattice and isolated skyrmions.

Treatment of multiple-beam X-ray diffraction in energy-dependent measurements.

During X-ray diffraction experiments on single crystals, the diffracted beam intensities may be affected by multiple-beam X-ray diffraction (MBD). This effect is particularly frequent at higher X-ray energies and for larger unit cells. The appearance of this so-called Renninger effect often impairs the interpretation of diffracted intensities. This applies in particular to energy spectra analysed in resonant experiments, since during scans of the incident photon energy these conditions are necessarily met for specific X-ray energies. This effect can be addressed by carefully avoiding multiple-beam reflection conditions at a given X-ray energy and a given position in reciprocal space. However, areas which are (nearly) free of MBD are not always available. This article presents a universal concept of data acquisition and post-processing for resonant X-ray diffraction experiments. Our concept facilitates the reliable determination of kinematic (MBD-free) resonant diffraction intensities even at relatively high energies which, in turn, enables the study of higher absorption edges. This way, the applicability of resonant diffraction, e.g. to reveal the local atomic and electronic structure or chemical environment, is extended for a vast majority of crystalline materials. The potential of this approach compared with conventional data reduction is demonstrated by the measurements of the Ta L3 edge of well studied lithium tantalate LiTaO3.

Evolution of Emergent Monopoles into Magnetic Skyrmion Strings.

Topological defects are fundamental concepts in physics, but little is known about the transition between distinct types across different dimensionalities. In topological magnetism, as in field theory, the transition between 1D strings and 0D monopoles is a key process whose observation has remained elusive. Here, we introduce a novel mechanism that allows for the controlled stabilization of emergent monopoles and show that magnetic skyrmion strings can be folded into monopoles. Conversely, they act as seeds out of which the entire string structure can unfold, containing its complete information. In chiral magnets, this process can be observed by resonant elastic X-ray scattering when the objects are in proximity to a polarized ferromagnet, whereby a pure monopole lattice is emerging on the surface. Our experimental proof of the reversible evolution from monopole to string sheds new light on topological defects and establishes the emergent monopole lattice as a new 3D topological phase.

Axially Bound Magnetic Skyrmions: Glueing Topological Strings Across an Interface.

A major challenge in topological magnetism lies in the three-dimensional (3D) exploration of their magnetic textures. A recent focus has been the question of how 2D skyrmion sheets vertically stack to form distinct types of 3D topological strings. Being able to manipulate the vertical coupling should therefore provide a route to the engineering of topological states. Here, we present a new type of axially bound magnetic skyrmion string state in which the strings in two distinct materials are glued together across their interface. With quasi-tomographic resonant elastic X-ray scattering, the 3D skyrmion profiles before and after their binding across the interface were unambiguously determined and compared. Their attractive binding is accompanied by repulsive twisting; i.e., the coupled skyrmions mutually affect each other via a compensating twisting. This state exists in chiral magnet-magnetic thin film heterostructures, providing a new arena for the engineering of 3D topological phases.

Reciprocal space tomography of 3D skyrmion lattice order in a chiral magnet.

It is commonly assumed that surfaces modify the properties of stable materials within the top few atomic layers of a bulk specimen only. Exploiting the polarization dependence of resonant elastic X-ray scattering to go beyond conventional diffraction and imaging techniques, we have determined the depth dependence of the full 3D spin structure of skyrmions-that is, topologically nontrivial whirls of the magnetization-below the surface of a bulk sample of Cu2OSeO3 We found that the skyrmions change exponentially from pure Néel- to pure Bloch-twisting over a distance of several hundred nanometers between the surface and the bulk, respectively. Though qualitatively consistent with theory, the strength of the Néel-twisting at the surface and the length scale of the variation observed experimentally exceed material-specific modeling substantially. In view of the exceptionally complete quantitative theoretical account of the magnetic rigidities and associated static and dynamic properties of skyrmions in Cu2OSeO3 and related materials, we conclude that subtle changes of the materials properties must exist at distances up to several hundred atomic layers into the bulk, which originate in the presence of the surface. This has far-reaching implications for the creation of skyrmions in surface-dominated systems and identifies, more generally, surface-induced gradual variations deep within a bulk material and their impact on tailored functionalities as an unchartered scientific territory.

Mode-Resolved Detection of Magnetization Dynamics Using X-ray Diffractive Ferromagnetic Resonance.

Collective spin excitations of ordered magnetic structures offer great potential for the development of novel spintronic devices. The present approach relies on micromagnetic models to explain the origins of dynamic modes observed by ferromagnetic resonance (FMR) studies, since experimental tools to directly reveal the origins of the complex dynamic behavior are lacking. Here we demonstrate a new approach which combines resonant magnetic X-ray diffraction with FMR, thereby allowing for a reconstruction of the real-space spin dynamics of the system. This new diffractive FMR technique builds on X-ray detected FMR that allows for element-selective dynamic studies, giving unique access to specific wave components of static and dynamic coupling in magnetic heterostructures. In combination with diffraction, FMR is elevated to the level of a modal spectroscopy technique, potentially opening new pathways for the development of spintronic devices.

Multidomain Skyrmion Lattice State in Cu2OSeO3.

Magnetic skyrmions in chiral magnets are nanoscale, topologically protected magnetization swirls that are promising candidates for spintronics memory carriers. Therefore, observing and manipulating the skyrmion state on the surface level of the materials are of great importance for future applications. Here, we report a controlled way of creating a multidomain skyrmion state near the surface of a Cu2OSeO3 single crystal, observed by soft resonant elastic X-ray scattering. This technique is an ideal tool to probe the magnetic order at the L3 edge of 3d metal compounds giving an average depth sensitivity of ∼50 nm. The single-domain 6-fold-symmetric skyrmion lattice can be broken up into domains, overcoming the propagation directions imposed by the cubic anisotropy by applying the magnetic field in directions deviating from the major cubic axes. Our findings open the door to a new way to manipulate and engineer the skyrmion state locally on the surface or on the level of individual skyrmions, which will enable applications in the future.

inserexs: reflection choice software for resonant elastic X-ray scattering.

This paper presents inserexs, an open-source computer program that aims to pre-evaluate the different reflections for resonant elastic X-ray scattering (REXS) diffraction experiments. REXS is an extremely versatile technique that can provide positional and occupational information about the atoms present in a crystal. inserexs was conceived to help REXS experimentalists know beforehand which reflections to choose to determine a parameter of interest. Prior work has already proven this to be useful in the determination of atomic positions in oxide thin films. inserexs allows generalization to any given system and aims to popularize resonant diffraction as an alternative technique to improve the resolution of crystalline structures.

Anatomy of Skyrmionic Textures in Magnetic Multilayers.

Room temperature magnetic skyrmions in magnetic multilayers are considered as information carriers for future spintronic applications. Currently, a detailed understanding of the skyrmion stabilization mechanisms is still lacking in these systems. To gain more insight, it is first and foremost essential to determine the full real-space spin configuration. Here, two advanced X-ray techniques are applied, based on magnetic circular dichroism, to investigate the spin textures of skyrmions in [Ta/CoFeB/MgO]n multilayers. First, by using ptychography, a high-resolution diffraction imaging technique, the 2D out-of-plane spin profile of skyrmions with a spatial resolution of 10 nm is determined. Second, by performing circular dichroism in resonant elastic X-ray scattering, it is demonstrated that the chirality of the magnetic structure undergoes a depth-dependent evolution. This suggests that the skyrmion structure is a complex 3D structure rather than an identical planar texture throughout the layer stack. The analyses of the spin textures confirm the theoretical predictions that the dipole-dipole interactions together with the external magnetic field play an important role in stabilizing sub-100 nm diameter skyrmions and the hybrid structure of the skyrmion domain wall. This combined X-ray-based approach opens the door for in-depth studies of magnetic skyrmion systems, which allows for precise engineering of optimized skyrmion heterostructures.