60 61 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 2 0 / 2 1 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 2 0 / 2 1 Imaging the vertical dimension ofmagnetic skyrmions Related publication: BirchM.T., Cortés-Ortuño D.,Turnbull L. A.,WilsonM. N., Groß F.,Träger N., Laurenson A., Bukin N., Moody S. H.,WeigandM., Schütz G., Popescu H., Fan R., Steadman P.,Verezhak J. A.T., Balakrishnan G., Loudon J. C.,Twitchett-Harrison A. C., Hovorka O., Fangohr H., Ogrin F.Y., Gräfe J. &Hatton P. D. Real-space imaging of confinedmagnetic skyrmion tubes. Nat. Commun. 11 , 1726 (2020). DOI: 10.1038/s41467-020-15474-8 Publication keywords: Skyrmions; Imaging; Diffraction M agnetic skyrmions are hedgehog-like particles that can be found in some magnetic materials. They are typically portrayed as two-dimensional whirl-like objects, but in reality, skyrmion lattices have a vertical, tube-like structure. The limitations of most magnetic imaging techniques meant that scientists had not observed this three-dimensional structure. Imaging the three- dimensional structure of the skyrmions is important for understanding the stability of skyrmions. A team of researchers used I10: Beamline for Advanced Dichroism Experiments (BLADE) to performmagnetic diffraction measurements on a thin slice of skyrmionmaterial, approximately ~100 nanometres thick. They needed low energy X-rays to probe the magnetic state of the sample, and the experiment had to be performed under vacuum. Using the beamline’s soft X-ray diffractometer, Reflectivity and Advanced Scattering from Ordered Regimes (RASOR), allowed them to perform the experiment while controlling the temperature of the sample and applying external magnetic fields. With these results, the team could determine at what temperatures and applied magnetic fields the magnetic skyrmions exist within the sample. This information allowed them to acquire images of skyrmions’ vertical structure at X-ray imaging beamlines at SOLEIL and BESSY II. And by imaging their vertical structure, they were able to study the nanoscale mechanisms that govern the formation and destruction of skyrmions. Skyrmions have potential applications in future electronic devices. The computers and smartphones of the future may use skyrmions to store data. Understanding the stability of skyrmions is essential so that the data is not lost when the skyrmion device is turned off. This research is, therefore, a crucial step towards realising this goal. Magnetic skyrmions, nanoscopic whirls composed of magnetic spins 1 , are promising candidates for information elements in future low-power data storage and logic devices 2 . For such applications, enhancing the skyrmion stability is vital: any data encoded in the form of skyrmions must remain unchanged when the device is powered off 3 . This stability is determined by the dynamics which govern skyrmion destruction. While they are commonly portrayed as two-dimensional objects arranged in a hexagonal lattice, in reality skyrmion lattices exist as extended tube-like objects in three-dimensions (Fig. 1). This vertical dimension holds the key to understanding skyrmion annihilation: a skyrmion tube is destroyed when it breaks in half, forming magnetic singularities known as Bloch points at the break locations 4,5 . The subsequent motion of these Bloch points unwinds the skyrmion tube along its length (Fig. 1). Due to the limitations of commonly used magnetic imaging techniques, images of skyrmion tubes, and thus true understanding of skyrmion annihilation dynamics, have remained elusive. In a work recently published in Nature Communications , such limitations were overcome using a combination of X-ray diffraction and X-ray imaging to acquire the first direct observations of magnetic skyrmion tubes. Before commencing imaging experiments, it was vital to determine the magnetic phase diagram of the FeGe lamella sample. Various magnetic states compete with the skyrmion state. At low applied magnetic fields, a helical state is realised, i.e. a spiral arrangement of magnetic spins (Fig. 2a) with uncompensated moments. When applying a magnetic field out of the plane of the sample, the skyrmion state is formed, with skyrmions arranging into a hexagonal lattice (Fig. 2b). In contrast, when an in-plane magnetic field is applied, the conical state is formed, which differs from the helical state because the spins are tilted towards the applied field direction (Fig. 2c). One would also expect skyrmion tubes to form with their cylindrical axes in the plane of the sample in this field configuration. Small angle X-ray scattering (SAXS) experiments were carried out using the RASOR diffractometer at the beamline I10 at Diamond Light Source. The X-ray beamwas directed through the FeGe lamella, with a CCD placed downstream to collect the resulting diffraction pattern. By tuning the energy of the X-rays to an absorption edge of the Fe atoms within the sample, the diffraction peaks arising from the ordered magnetic structures were resonantly enhanced. Representative diffraction patterns for the helical, skyrmion lattice and conical states were measured (Fig. 2d-f), revealing twofold or sixfold symmetry around the central main beam. By performing such diffraction experiments as a function of temperature and applied magnetic field, magnetic phase diagrams for both out-of-plane and in-plane magnetic fields were determined (Fig. 2g and h, respectively). Magnetically-sensitive imagingwas performed using X-ray holography and scanning transmission X-ray microscopy (STXM) techniques, at the SEXTANTS MagneticMaterials Group Beamline I10 beamline at SOLEIL and the MAXYMUS instrument at BESSY II respectively. An example microscopy image of the skyrmion lattice state for an out-of-plane field is shown (Fig. 3a).The result agrees well with the simulated image created frommicromagnetic simulations of a skyrmion lattice state (Fig.3b).The images highlight that X-ray imaging provides magnetic contrast parallel or anti-parallel to the X-ray beam. We then investigated the possibility of observing skyrmion tubes with the field applied in-plane. When observed from the side, an individual skyrmion tube is expected to exhibit both light and dark contrast, as the spins point in opposing directions either side of the skyrmion core. We observed such a contrast pattern in the corner of the FeGe lamella, showing three pairs of horizontal stripes (bottom left of Fig. 3c), which have the appearance of three skyrmion tubes (horizontal stripes) embedded within the surrounding conical state (vertical stripes). Tovalidatetheidentityofthesestructuresasskyrmiontubes,complimentary micromagnetic simulations of skyrmion tubes within a conical state background were performed. The resulting simulated image (Fig. 3d), shows remarkable agreement to the experimental data. A three-dimensional visualisation of the simulated magnetic state (Fig. 3e), reveals the skyrmion tube structures. Future experiments will allow us to observe these skyrmion tubes unwinding under different external stimuli, such as by the application of electric currents. The combination of diffraction techniques performed at Diamond and the imaging techniques carried out at SOLEIL and BESSY II was vital to the success of this project. Furthermore, initial development of the SAXS technique at Diamond enabled us to expand our research into X-ray holography and microscopy techniques. In the future, we look forward to the possibility of performing such imaging experiments in the UK, utilising the flagship coherent soft X-ray imaging and diffraction beamline which was recently proposed for the Diamond-II upgrade. Figure 1: Three-dimensional visualisation of three magnetic skyrmion tubes, depicting the Bloch-point annihilation mechanism. The orientation of the applied magnetic field, H, is indicated. Figure 2: (a-c) Visualisations of the Helical (H), skyrmion lattice (SkL), and conical (C) states; (d-f), Corresponding SAXS diffraction patterns acquired after zero-field cooling (ZFC) or field cooling (FC) to 100 K at different applied magnetic fields H; (g-h) Magnetic phase diagrams determined for out-of-plane and in-plane fields respectively. The helical rotation transition region between H and C is labelled T. The zero field cooling and field cooling paths are illustrated. Figure 3: STXM (a,c) and simulated (b,d) images of the skyrmion lattice (a,b) and skyrmion tube (c,d) states; (e) Three-dimensional visualisation of skyrmion tubes within a conical structure from the micromagnetic simulation. References: 1. Mühlbauer S. et al. Skyrmion lattice in a chiral magnet. Science. 323 , 915–919 (2009). DOI: 10.1126/science.1166767 2. Nagaosa N. et al. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8 , 899–911 (2013). DOI: 10.1038/ nnano.2013.243 3. Yu X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465 , 901–904 (2010). DOI: 10.1038/nature09124 4. Milde P. et al. Unwinding of a skyrmion lattice by magnetic monopoles. Science (80-. ). 340 , 1076–1080 (2013). DOI: 10.1126/science.1234657 5. Kagawa F. et al. Current-induced viscoelastic topological unwinding of metastable skyrmion strings. Nat. Commun. 8 , 1332 (2017). DOI: 10.1038/s41467-017-01353-2 Funding acknowledgement: EPSRC grants: EP/M028771/1 and EP/N032128/1. Beamline proposals: Diamond Light Source (SI20866-2), SOLEIL (20180679) and BESSY II (181- 06589ST). Corresponding authors: Prof. Peter Hatton, Durham University,
[email protected] ; Dr Max Birch, Max Planck Institute for Intelligent Systems,
[email protected]