United States

Imaging and manipulation of atomic-scale magnetism for future spintronic applications demands for a spin-sensitive technique with ultimate lateral resolution. Exploiting the tunneling effect between magnetic electrodes, as between a magnetic probe tip and a magnetic sample in a spin-polarized scanning tunneling microscopy (SP-STM) set up, has proven to be capable of resolving and switching magnetic structures down to the single atomic level. However, this approach disqualifies for many technical applications, since it requires tip-sample distances in the order of a few angstroms. For practical applications, technical feasible distances, like flying distances of read-write heads in current data storage devices, are in the range of a few nanometers. Electron tunneling over this distance is very unlikely and therefor not detectable. Spin-polarized vacuum states are unoccupied electronic states located nanometers apart from the underlying magnetic surface in vacuum [1]. In an SP-STM setup, these states can be addressed by spin-polarized electrons that tunnel resonantly from the magnetic tip via a vacuum state into the surface, resulting in a magnetic image [2]. As I will show in this talk, these states exhibit the same local spin quantization axis as the spin texture of the underlying sample surface, even when the spins are rotating on the atomic-scale [2]. Our SP-STM experiments at low temperatures on ultrathin films with non-collinear spin textures demonstrate that the spin-polarized resonant tunneling via the vacuum states allows for atomic-scale spin-sensitive imaging in real space at tip-sample distances of up to 8 nm [3]. Acting as mediators for the spin contrast across the nm-spaced vacuum gap, the vacuum states provide thereby a loophole from the hitherto existing dilemma of losing spatial resolution when increasing the tip-sample distance in a scanning probe setup. Experimental results will be presented and discussed in terms of the vacuum states’ spin-splitting and the magnetic contrast as a function of bias and tip-sample distance, as well as in terms of the atomic-scale nature of the resonant tunneling condition between the probe tip and the sample. While spin-polarized resonant tunnel currents in the low nA regime are used for non-perturbative imaging, injecting high spin-polarized resonant tunnel currents (~100 nA) via vacuum states considerably affect the underlying magnetism. As I will demonstrate in this talk, atomic-scale ferromagnets can be efficiently switched via these states, with the underlying current-induced mechanism being based on thermally-assisted spin-transfer torque mediated by the vacuum states [4]. Consequently, spin-polarized vacuum states can be utilized for the readout and manipulation of atomic-scale magnetic objects from nanometer distances. Spin-polarized resonant tunneling qualifies for a spin-sensitive read-write technique with ultimate lateral resolution, potentially opening a pathway towards future technical applications.References: [1] M. Donath, C. Math, M. Pickel, A.B. Schmidt, and M. Weinelt, Surf. Sci. 601, 5701 (2007). [2] A. Schlenhoff, S. Kovarik, S. Krause, and R. Wiesendanger, Phys. Rev. Lett. 123, 087202 (2019). [3] A. Schlenhoff, S. Kovarik, S. Krause, and R. Wiesendanger, Appl. Phys. Lett. 116, 122406 (2020). [4] A. Schlenhoff, S. Krause, A. Sonntag, and R. Wiesendanger, Phys. Rev. Lett. 109, 097602 (2012).

MMM 2020

Utilizing Vacuum States above Surfaces for Imaging and Manipulation of Atomic-Scale Magnetism INVITED

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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technical paper

Atomically thin, magnetic materials have gained a lot of attention since 2017, when the first 2D ferromagnet was reported [1]. This breakthrough has triggered research on 2D magnetic materials [2]. They are not only important from a fundamental point of view -to understand the theory of magnetism in reduced dimensions-, but also for technological applications. However, probing the magnetic order of the 2D systems by conventional magnetic experimental setups is very challenging. On the other hand, it is well known, that even in the single layer limit, semiconducting two-dimensional materials strongly absorb light. Therefore, optical spectroscopy is a good method for their characterization. In order to shed light on the intriguing phenomena of 2D magnetism, we present comprehensive theoretical investigations of the optical properties of the van der Waals layered material MnPS3, which is one important example from the large family of transition metal phosphorus trisulfide (MPS3) [3]. Our study reveals, that the interband absorption spectrum, which is proportional to the imaginary part of the dielectric function, is very similar for different possible magnetic states of MnPS3. On the other hand, the calculated effective masses of electrons and holes exhibit an anisotropic behaviour and they strongly depend on the magnetic order. Aforementioned properties are reflected in the binding energy of excitons in the studied systems. The impact of the magnetic order on electronic band gap is also revealed, and indirect character of electronic band gap is confirmed as the groundstate of bulk system. Our results demonstrate that the magnetic order of 2D materials can be indirectly inferred via optical measurements. The study was accomplished thanks to the funds allotted by the National Science Centre, Poland within the framework of the research project ‘SONATA12’ no. UMO-2016/23/D/ST3/03446. Access to computing facilities of TU Dresden ZIH for the project ”TransPheMat”, PL-Grid Polish Infrastructure for Supporting Computational Science in the European Research Space, and of the Interdisciplinary Center of Modeling (ICM), University of Warsaw are gratefully acknowledgedReferences: [1] B. Huan et al., Nature 546, p. 270-273 (2017) [2] M. Gibertini et al., Nat. Nanot. vol. 14, p. 408 (2019). [3] R. Brec, Solid State Ionics vol. 22, p. 3-30 (1986).

Controlling magnetic properties of the van der Waals crystal MnPS3 via the absorption spectrum.

Magneto-optical (MO) devices based on the Faraday effect are widely used for optical communication and optical sensing. Due to their weak MO effect in the optical frequency range, the size of MO devices is typically in the range of 10~1000 wavelengths, limiting their application in integrated photonic systems. Currently, most studies for enhancing the Faraday effect are based on surface plasmon resonance.1, 2 However, due to the Ohmic loss of metals, these structures are optically lossy. Therefore, all dielectric nanostructures provide an alternative route to achieve high Faraday rotation and high transparency simultaneously.3,4 Here, we report theoretical and experimental study on enhanced Faraday effect in all dielectric MO metasurfaces based on Si/Ce:YIG nanostructures. The device is composed of a 2D periodic array of amorphous Si nanodisks patterned on Ce:YIG/YIG oxide thin film stacks grown on silica. By adjusting the geometric parameters, magnetic dipole and electric dipole Mie resonance modes can be excited in the Si disks. Thanks to the high refractive index of Ce:YIG/YIG, the modes are also strongly confined in the Ce:YIG/YIG layers. The transmission spectrum is simulated using the finite element time-domain difference method, which agrees excellently with experimental results. The Faraday rotation spectrum of the sample was measured using a home-made microscale Faraday rotation characterization set-up, which shows obvious enhancement peaks in the vicinity of each resonance. The MO response of the Ce:YIG thin film deposited on the same silica substrate is also presented as a reference. With the transmission close to 40%, we achieved 2.3-fold Faraday rotation enhancement compared to bare Ce:YIG thin films. Our device shows effective MO enhancement in the sub-wavelength scale, which is promising for applications such as free space non-reciprocal photonic devices and MO imaging.References: 1. Liu, M. and Zhang, X., Nature Photonics., Vol. 7, p.430-431 (2013) 2. Armelles, G. and Cebollada, A., Advanced Optical Materials., Vol. 1, p.10-35 (2013) 3. Christofi, A., Kawaguchi, Y. and Alu, A., Optics Letters, Vol. 43, p.1838-1841 (2018) 4. Royer, F., Varghese, B. and Gamet, E., ACS omega, Vol. 5, p.2886-2892 (2020)

Enhanced Magneto-Optical Effect in Ce:YIG Based All Dielectric Metasurfaces

Observation of All-Optical Switching (AOS) of magnetization in ferrimagnetic GdFeCo alloys, using ultrashort circularly polarized laser pulses [1], triggered a renewed interest in ferrimagnetic rare Earth-transition metal (RE-TM) alloys [1-5]. Tb-containing ferrimagnetic alloys exhibit all-optical helicity-dependent switching (AO-HDS), and have strong perpendicular magnetic anisotropy, a result of a high spin-orbit coupling in Tb [6]. In this work we study the magnetic properties and AOS performance of amorphous TbCo alloys, prepared by a DC magnetron sputtering (for more details see [7]). We measured μ0Hc using polar magneto-optical Kerr effect (MOKE), and investigated the AOS behaviour using a pump-probe based static magneto-optical imaging setup. We show that AO-HDS is possible in TbxCo100−x for certain compositions (x=24-30 at.%) and thicknesses (Fig. 1), if the laser pulse parameters such as pump fluence, are optimized, and the number of pulses in one burst is at least 50-100. Samples with the compositions out of this range show only helicity-independent thermal demagnetization. We also performed ab initio calculations of the inverse Faraday effect to explain the cumulative nature of the multi-shot AO-HDS switching. It is triggered by circularly polarized laser light, inducing a helicity dependent magnetic moment in the Co atoms of the alloys (Fig. 2). This study shows that ferrimagnetic TbCo films can exhibit AO-HDS in a certain compositional range and laser pulse parameters, with a minimal amount of shots.References: 1. C. D. Stanciu et al Phys. Rev. Lett. 99, 047601 (2007) 2. B. Hebler et al, Frontiers in Materials 3, 8 (2016). 3. S. Alebrand et al Applied Physics Letters101,162408 (2012). 4. S. Mangin et al, Nature Materials 13, 286 (2014). 5. C. H. Lambert et al, Science 345, 1337 (2014) 6. R. Moreno et al, Phys. Rev. B 96, 014409 (2017). 7. A. Ciuciulkaite et al. arXiv:2002.07544

Design of TbxCo100-x for All Optical Switching of Magnetization

On-chip optical isolators are key components in photonic integrated circuits (PICs). In recent years, passive magneto-optical (MO) isolators based on nonreciprocal phase shift (NRPS) have been widely studied [1]. Micro-ring and Mach-Zehnder interferometer (MZI) isolators have achieved considerable progress on silicon on insulator (SOI) platforms [2, 3]. As a different material platform, silicon nitride (SiN) based PICs show much lower propagation loss, which are highly promising for telecommunication, data communication and sensing applications [4, 5]. However, high performance MO isolators have not been demonstrated on SiN, which is fundamentally limited by the low Faraday rotation and weak NRPS for MO thin films grown on SiN waveguides. Here, we report high-performance integrated MO isolators on SiN platforms for both TM and TE polarizations using cerium doped yttrium iron garnet (Ce: YIG) thin films deposited by pulsed laser deposition (PLD). By increasing the Ce solubility up to 40% [6], Ce:YIG thin films grown on SiN show high Faraday rotation up to -5500 deg/cm at 1550 nm wavelength, which is 83% higher than previously reported Ce1Y2Fe5O12 thin films [7, 8]. Based on these materials, broadband SiN MZI isolators are designed and fabricated. The TM isolators show 24 dB isolation and 4 dB insertion loss around 1567 nm wavelength, with a footprint of 0.9×0.25 mm2. For TE isolators, a maximum isolation ratio of 28 dB with insertion loss of 7.5 dB is observed at 1565 nm wavelength. These devices have exceeded the performance of their counterparts on SOI [7]. Our work demonstrates that high performance MO thin films and optical isolators can be monolithically integrated on SiN PICs.References: [1] Bi L, H.J. and Jiang P, Nature Photonics., Vol. 5, p.758 (2011) [2] Shoji Y, F.A. and M. T, IEEE Journal of Selected Topics in Quantum Electronics., Vol. 22, p.264-270 (2016) [3] Pintus P, H.D. and Morton P A, Journal of Lightwave Technology., Vol. 37, p.1463-1473 (2019) [4] Baets R, S.A.Z and Clemmen S, Optical Fiber Communication Conference., p. Th3J-1 (2016) [5] Gaeta A L, Lipson M and Kippenberg T J, Nature Photonics., Vol. 13, p.158-169 (2019) [6] Zhang Y, Wang C T and Liang X, Journal of Alloys and Compounds., Vol. 703, p.591-599 (2017) [7] Zhang Y, Du Q and Wang C, Optica., Vol. 6, pp.473-478 (2019) [8] Du Q, Wang C and Zhang Y, ACS Photonics., Vol. 5, p.5010-5016 (2018)

Waveguide Integrated Broadband Magneto-Optical Isolators on Silicon Nitride Platforms

The recent convergence of chiral molecules with metal halide perovskite frameworks gives rise to an interesting family of chiral systems: two-dimensional, chiral hybrid organic-inorganic perovskites (2D-chiral-HOIPs). While possessing photovoltaic properties of traditional HOIPs, this class of materials is endowed with chirality through its organic ligands in which the degeneracy of the electron spin in charge transport is broken, i.e., the Chirality-Induced Spin Selectivity (CISS) effect manifests, making it a promising platform to bridge opto-spintronic studies and the CISS effect. In this work, 2D-chiral-HOIP/NiFe heterostructures are studied by means of the magneto-optical Kerr effect using a Sagnac interferometer. Upon illumination of the HOIPs, the Kerr signal at the HOIP / NiFe interface changes, and a linear dependence of the response on the magnetic field is observed. The sign of the slope was found to depend on the chirality of the HOIPs. The results demonstrate the utility of chiral HOIP materials for chiral Opto-spintronic applications. D.S. acknowledges the support from National Science Foundation ECCS 1936527. D.H.W. acknowledges the support of the Department of Energy (Grant No. ER46430). Work at Utah is supported by US Department of Energy (Grant No. DE-FG02-04ER46148). F.L. acknowledges NERSC and CHPC at the University of Utah for providing the computing resources.

Magneto-Optical Detection of Photoinduced Magnetism via Chirality Induced Spin Selectivity in 2D Chiral Hybrid Organic-Inorganic Perovskites

High-gyrotropy rare-earth iron garnets with low losses enable the realization of integrated optical isolators for laser-on-chip silicon photonics [1]. However, integrated isolators with magneto-optical materials have always required an external magnetic field. Novel waveguide isolator designs with Ce:TbIG can operate in the remnant magnetization state and overcome the magnetic field requirement [2,3]. Further magnetless design optimizations and device downscaling require a deeper understanding of the magnetic properties of the material in the bulk and at the interface. Here, sputter-deposited Ce:TbIG thin films with large Faraday rotation (∼-3500°/cm) are shown to have a near-ideal stoichiometry of Ce0.5Tb2.5Fe4.75O12 with a rare-earth to iron ratio (Ce+Tb/Fe) of 0.57. Magnetometry revealed a 44nm magnetic dead layer (MDL) at the garnet-silicon interface that can be detrimental to waveguide photonics relying on evanescent tail interaction. However, the large Faraday rotation (independent of film thickness) compensates for gyrotropy loss due to the MDL, Figure 1(a). The effective anisotropy of Ce:TbIG on Si is also important, but calculations using bulk thermal mismatch overestimate the effective anisotropy. X-ray diffraction measurements yield highly accurate measurements of strain that show anisotropy favors an in-plane magnetization in agreement with the positive magnetostriction of Ce:TbIG, Figure 1(b). Upon doping TbIG with Ce, a slight decrease in compensation temperature occurs which points to preferential rare-earth occupation in dodecahedral sites and an absence of cation redistribution between different lattice sites [4]. The high Faraday rotation, large remanent ratio, large coercivity, and preferential in-plane magnetization enable Ce:TbIG to be an in-plane latched garnet, immune to stray fields with magnetization collinear to the direction of light propagation.References: [1] K. Srinivasan and B. J. H. Stadler, Opt. Mater. Express, Vol. 8, p. 3307 (2018). [2] K. Srinivasan et al., ACS Photonics, Vol. 6, pp. 2455–2461 (2019). [3] C. Zhang et al., Sci. Rep., Vol. 7, pp. 1–8 (2017). [4] K. Srinivasan et al., Adv. Funct. Mater., Vol. 30, p. 2000409 (2020).

Interfacial and Bulk Magnetic Properties of Stoichiometric Cerium Doped Terbium Iron Garnet Polycrystalline Thin Films

We are presenting some results of our experiments image of formation using a device in which light is scattered by a thin film of ferrofluid subjected to an external magnetic field and comparing them with the effect of optical vortex [1-7]. When the light passes through this thin layer of ferrofluid, we can observe directly, with the naked eye, the formation of interesting luminous patterns. In addition to this, we can also observe the effects of light polarization in this system using a polariscope. Some interesting applications of this type of device include optical switches, or the simulation of atmospheric optics known as jumping laser dogs, just to cite few of them. Another potential application is characterizing and controlling the quality of compound magnets observing the patterns formed in this type of Hele-Shaw cell filled with ferrofluids, known as Ferrocell. Using polarized light, the pattern formation curiously resembles the nodal lines of the transverse electric and magnetic modes observed in optical resonant cavities, associated with the hypergeometric polynomials [6], such as Hermite-Gauss, Laguerre-Gauss, and Ince-Gauss polynomials. In this analogy, the magnetic field has an equivalent role of the Gaussian irradiance distribution, and the light source is a very flat lamp normal to z, which nearly corresponds to a plane wave with constant flux set up to the z-axis, analogous to a standing wave in the optical cavity. In this work, we are exploring the analogy between our experiment with the mode conversion in a laser cavity with our system, because mode convergion requires Hermite-Gaussian (HG) modes, which can easily be made inside the laser cavity and in our experiment using polarized light.References: 1) A. Tufaile, T. A. Vanderelli, A. P. B. Tufaile, Journal of Applied Mathematics and Physics 4, 1977-1988 (2016). 2) A. Tufaile, T. A. Vanderelli, A. P. B. Tufaile, Advances in Condensed Matter Physics 2017, Article ID 2583717 (2017). 3) Y. Shen, X. Wang , Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong and X. Yuan, Light Science & Applications 8, 90 (2019). 4) A. Tufaile, A. P. B. Tufaile, T. A. Vanderelli, M. Snyder, Proceedings of Frontiers in Optics/Laser Science, JTu3A.17 (2019) 5) A.P.B Tufaile, T.A. Vanderelli, R. Amorim, A. Tufaile, Proceedings of the 12th Conference on Light and Color in Nature, 24–25 (2016). 6) A. Tufaile, T. A. Vanderelli, M. Snyder, A. P. B. Tufaile, Condens. Matter 2019, 4, 35. 7) A. Tufaile, T. A. Vanderelli, M. Snyder, A. P. B. Tufaile, Controlling Light Diffraction with Magnetic Nanostructures; TechConnect Briefs: Boston, MA, USA; ISBN 978-009988782-8-7, (2019).

Optical Vortex and Ferrocell: A Comparative Study

Magnetic field pulser generates magnetic field by driving current through an inductor. These pulsers have numerous applications based on the output magnetic field intensity and switching time. For communication systems, the pulser is central for an all-optical switching platform employing the theory of Faraday rotation [1]. In medical field, the pulser is used to perform transcranial magnetic stimulation to provide safer, noninvasive treatment for certain mental disorders [2]. Another application area is portable magnetic resonance systems where the pulser initiates magnetic resonance [3]. These are just some of the many fields where magnetic field pulsers have found applicability over the years. Recent developments in transistor technologies have enabled production of transistors with higher power and superfast switching. Among these is the introduction of gallium nitride (GaN) based transistors. Compared to silicon-based transistors, GaN transistors have higher electron mobility, a property which allows smaller size for a given on-resistance and breakdown voltage. GaN transistor also offers high drain current and extremely fast switching speed [4]. These are all desirable properties for a switch in the magnetic field pulser design. This investigation will explore the application of GaN transistor in a pulser design. Based on the advantages of GaN transistor, the investigation looks towards creating a pulser capable of producing magnetic field of 500 Gauss with a rise/fall time of less than 500 nanoseconds. This investigation will surpass findings from prior studies to build a pulser targeted for magneto-optic switching [5] applications. A preliminary result as seen in Figure 1 shows that at the same maximum current level, the GaN transistor displays steeper rise and fall when compared to a Si transistor. This result further highlights the potential of GaN transistor as the switching device where rapid switching is preferable.References: [1] J. W. Tioh, M. Mina, and R. J. Weber, “All-optical integrated switch utilizing Faraday rotation,” IEEE Trans. Magn., vol. 46, no. 6, pp. 2474–2477, Jun. 2010. [2] J. Selvaraj, P. Rastogi, N. P. Gaunkar, R. L. Hadimani, and M. Mina, “Transcranial magnetic stimulation: Design of a stimulator and a focused coil for the application of small animals,” IEEE Transactions on Magnetics, no. 99, pp. 1–5, 2018. [3] N. P. Gaunkar, J. Selvaraj, W.-S. Theh, R. Weber, and M. Mina, “Pulsed magnetic field generation suited for low-field unilateral nuclear magnetic resonance systems,” AIP Advances, vol. 8, no. 5, p. 056814, 2018. [4] L. F. Eastman and U. K. Mishra, "The toughest transistor yet [GaN transistors]," IEEE Spectrum, vol. 39, no. 5, pp. 28-33, May 2002, doi: 10.1109/6.999791. [5] J.W. Pritchard, M. Mina, and R.J. Weber, “Magnetic Field Generator Design for Magneto-Optic Switching Applications,” IEEE Transactions on Magnetics, Vol. 49, No. 7, pp. 4242-4244, 2013.

GaN Based High Strength Magnetic Field Pulser

Magnetic domain wall (DW) Skyrmions are 360° transitions of the internal magnetization in a Dzyaloshinskii DW. These structures are analogous to vertical Bloch lines (VBLs), which were once considered for magnetic memory storage. Although they have been predicted theoretically [1], DW skyrmions have only recently been observed experimentally [2]. Here we performed a systematic study of multiple iterations of [Pt/(Co/Ni)M/Ir]N multi-layers to formulate a phase diagram of magnetic excitations related to domain wall substructures, including DW skyrmions, via Lorentz transmission electron microscopy (LTEM). [Pt/(Co/Ni)M/Ir]N multi-layers were deposited by magnetron sputtering onto Si3N4 TEM membranes [3]. LTEM was performed using an aberration-corrected FEI Titan G2 80-300. In low DMI samples, VBLs are formed over all thicknesses, but are only seen to form pile-ups (i.e. n-π VBLs) in the case of ultrathin samples. We attribute this to the formation of hybrid DWs in thicker samples where the magnetization varies along the z-axis, thereby, creating low energy paths to annihiliation of 2π VBLs. Likewise, only pure Dzyaloshinskii DWs are observed in thicker samples with high DMI. It is only for lower thicknesses in this strong DMI regime that DW skyrmions are observed. Like their VBL counterparts, DW Skyrmions are found to have a pinning effect on the domain wall as seen through the in-situ application of a perpendicular magnetic field. The stability and dynamic response of DW skyrmions are examined further via micromagnetics. The energy barrier to annihilation was calculated using M3 [4] and a GNEB method and is observed to decrease with increased DMI strength. Most notably an energy barrier to annihilation of >60 kBT was found for D<1.0 mJ/m2 at room temperature giving confidence in the stability of DW Skyrmions for use in magnetic memory devices. Details regarding their dynamic response to electric current will be discussed. [5]References: [1] R. Cheng, M. Li, A. Sapkota, A. Rai, et al., Phys. Rev. B, Vol. 99, p. 184412 (2019). [2] M. Li, A. Sapkota, A. Rai, et al., ArXiV: 2004.07888 (2020). [3] M. Li, D. Lau, M. De Graef, and V. Sokalski, Phys. Rev. Mater., Vol. 3, p. 064409, (2019). [4] Micromagnetic Code M3: http://magneticslab.ua.edu/micromagnetics-code.html. [5] This research is supported by the Defense Advanced Research Project Agency (DARPA) program on Topological Excitations in Electronics (TEE) under grant number D18AP00011. The authors also acknowledge use of the Materials Characterization Facility at Carnegie Mellon University supported by grant MCF-677785.

Domain Wall Skyrmions: Examining Domain Wall Substructures in [Pt/(Co/Ni)M/Ir]N Multi-Layers

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 host material, as seen in Fig. 1 [3]. These structures are theorised to exhibit Bloch points, responsible for the topological unwinding of skyrmions [4]. The study of this skyrmion tube state (SkT) is vital for furthering the understanding of skyrmion formation and dynamics for future applications. However, direct experimental imaging of skyrmion tubes has yet to be reported. Here, we demonstrate the real-space observation of skyrmion tubes in a lamella of FeGe using resonant magnetic x-ray imaging and comparative micromagnetic simulations, the horizontal stripes seen in Fig. 2, confirming their extended structure [5]. 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 investigation into this unexplored dimension of the skyrmion spin texture.References: [1] Rößler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797 (2006). [2] Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899 (2013). [3] Seki, S. et al. Propagation dynamics of spin excitations along skyrmion strings. Nat. Commun. 11, 256 (2020). [4] Milde, P. et al. Unwinding of a skyrmion lattice by magnetic monopoles. Science 340, 1076 (2013). [5] Birch, M. et al. Real-space imaging of confined magnetic skyrmion tubes. Nat. Commun. 11, 1726 (2020).

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Utilizing Vacuum States above Surfaces for Imaging and Manipulation of Atomic-Scale Magnetism INVITED

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