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The effect of high tensile strain and low dimensionality on the magnetic and electronic properties of CaMnO3 ultrathin films, epitaxially grown on SrTiO3 substrates, are theoretically analyzed (Fig. 1). By means of ab initio calculations, we find that, both, the high strain produced by the substrate and the presence of the free surface contribute to the stabilization of an in-plane ferromagnetic coupling, giving rise to a non-zero net magnetic moment in the ultrathin films. Remarkably, the FM component of the magnetic structure is stabilized, not as a consequence of a direct electron doping, as it happens when substituting the divalent Ca by trivalent elements or in the presence of O vacancies, as reported in the past, but rather because of a self-doping charge redistribution due to, both, the strain and the absence of apical oxygens. A deeper analysis of this charge redistribution can be obtained from the partial densities of states (pDOS) depicted in Fig. 2, where we separate the contributions of different MnO2 planes. From the total density of states projected onto each layer, we can see that the oxygens located at the surface are the ones which loose part of their charge, and this charge is redistributed in the Mn atoms located in inner layers, and begin to occupy the dx2-y2 orbitals. The self-doping electrons of this eg states, allow the presence of the FM double exchange and the AAF magnetic structure with more FM pairs becomes more stable. As it can also be seen from Fig.2, coupled with this change in the magnetic order we find an insulator-metal transition triggered by the quantum confinement and the tensile epitaxial strain.

MMM 2020

Strain induced magnetic transition in CaMnO3 ultrathin films

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

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, which are chiral geometric spin textures with a non-trivial topology [1, 2], are shown to have the advantages of small size, low driven current density and robustness against external perturbations for potential applications in the next-generation spintronic devices. Generally, skyrmions are stabilized by the non-collinear Dzyaloshinskii–Moriya interaction (DMI), originates from the strong spin-orbit coupling (SOC) combined with the inversion symmetry breaking, the latter of which may be implemented with a heterostructure. We report the use of the heterostructure consisting of a high SOC topological insulator (TI) (BiSbTe) and the ferrimagnet (GdFeCo) to create the DMI and demonstrate the presence of skyrmions [3]. A sizable interfacial DMI coefficient (D = 35.5±0.25 μJ m-2) is obtained by the Brillouin-Light-Scattering spectrum from the topological surface states, as shown in Figure 1. Small sizes of skyrmions under 100 nm are observed by the scanning transmission X-ray microscopy (STXM) at room temperature, and the Néel-type spin spiral transition is verified by the line-scan spin profile of the single skyrmion. Furthermore, the ferrimagnet is shown to create the antiferromagnetic (AFM) skyrmions, for which the element-resolved STXM identifies the AFM-coupled Gd and FeCo skyrmion lattices, as shown in Figure 2, which promises the potential of vanishing skyrmion Hall effect and ultrafast skyrmion dynamics. This work demonstrates the Néel-type skyrmions at the topological interface, where small skyrmions combined the giant spin-orbit toque have potential applications for high-density and energy-efficient spintronic devices [4].References: [1] A. Fert, N. Reyren and V. Cros, Nature Reviews Materials 2 (7), 17031 (2017). [2] W. Jiang, G. Chen, K. Liu, J. Zang, S. G. E. te Velthuis and A. Hoffmann, Physics Reports 704, 1-49 (2017). [3] H. Wu, F. Groß, B. Dai, D. Lujan, S. A. Razavi, P. Zhang, Y. Liu, K. Sobotkiewich, J. Förster, M. Weigand, G. Schütz, X. Li, J. Gräfe, and K. L. Wang, Advanced Materials 2003380 (2020). [4] H. Wu, Y. Xu, P. Deng, Q. Pan, S. A. Razavi, K. Wong, L. Huang, B. Dai, Q. Shao, G. Yu, X. Han, J.-C. Rojas-Sánchez, S. Mangin and K. L. Wang, Advanced Materials 31 (35), 1901681 (2019).

Antiferromagnetically-coupled skyrmion lattices in topological insulator/ferrimagnet heterostructures

Magnetic skyrmions are topologically stable configuration with particle-like properties. Due to their efficient current-induced manipulation, they could act as carrier of information in futur devices. They where initially observed at low temperature and by applying an intense magnetic field in bulk materials exhibiting broken inversion symmetry[1-2] and in epitaxial ultrathin films with interfacial Dzyaloshinskii-Moriya interaction[3-4]. An intense research effort during the past few years has led to their stabilization at room temperature[5] but still by applying an external magnetic field. A promising strategy to overcome this last obstacle is to exploit the interlayer exchange coupling in magnetic heterostructure to produce an internal effective magnetic field Bint[6-7]. Here, we demonstrate that magnetic skyrmions with a mean diameter around 60 nm can be stabilized at room temperature and zero external magnetic field in an exchange-biased Pt/Co/Ni80Fe20/Ir20Mn80 multilayerstack[8]. This is achieved through an advanced optimization of the multilayer-stack composition in order to balance the different magnetic energies controlling the skyrmion size and stability. Magnetic imaging is performed both with magnetic force microscopy and scanning nitrogen-vacancy magnetometry, the latter providing unambiguous measurements at zero external magnetic field. Simulation of the PL quenching image are also achieved and the results, in agreement with experimental data, allows us to extract informations such as skyrmion's size. These results establish exchange-biased multilayer stacks as a promising platform toward the effective realization of memory and logic devices based on magnetic skyrmions.References: [1] S. Mühlbauer et al., Science323, 915 (2009) [2] X. Z. Yu et al., Nature (London) 465, 901 (2010) [3] S. Heinze et al., Nature Phys.7, 713 (2011) [4] N. Romming et al., Science341, 636 (2013) [5] W. Jiang et al., Science349, 283 (2015) [6] G. Chen et al., Appl. Phys. Lett.106, 242404 (2015) [7] Y. Guang et al., Nat. Commun.11, 949 (2020) [8] K. Gaurav Rana et al., Phys. Rev. Applied 13, 044079 (2020)

Room-Temperature Skyrmions at Zero Field in Exchange-Biased Ultrathin Films

Skyrmions induced by the Dzyaloshinskii–Moriya (DM) interaction have the great potential for spintronic applications, owing to emergent electromagnetic phenomena, and ultra-low current driven motion. Although near room temperature skyrmions were reported for B20-type FeGe (ferromagnetic Curie temperature TC = 278 K)1, β-Mn type CoxZnyMnz (TC = 420 K)2 and tetragonal Heusler Mn1.4Pt1-yRhySn (TC = 390 K)3, their skyrmion size were found to be relatively large around 100 nm. It is of particular importance to develop new materials that exhibited skyrmions with small skyrmion sizes at and above room temperature. In this study, we focused on β-Mn type nitride A2Mo3N, because skyrmion phase was observed at 100 K by Lorenz transmission electron microscopy (LTEM) in FexCo1.5-xRh0.5Mo3N (x = 0.3 and 0.5)4. We prepared the epitaxial A2Mo3N films and investigated the effects of multi doping of A site on magnetic properties as well as the appearance of skyrmion phases. A series of A2Mo3N (A = Fe, Pd, Ni, Pt,) epitaxial thin films was fabricated on c-plane sapphire substrates with the (110) orientation by reactive magnetron sputtering. The skyrmion phase in a 50 nm thick film with Fe1.68Pd0.32Mo3N was determined by topological Hall effect (THE) and LTEM imaging. Topological Hall resistivity ρTH induced by skyrmions at 4 K and 300 K are shown in Fig. 1 as a function of applied magnetic field. Enormous ρTH at 4 K indicates the dense skyrmion phase, and reduced ρTH at 300 K indicates the isolated skyrmion phase with sign reversal, which is considered to be induced by the temperature-dependent electronic state. LTEM images of single skyrmion at 90 K and 300 K are shown in Fig. 2. Small size skyrmion (ca. 60 nm) was observed unaffected by the temperature. These results indicate that β-Mn-type A2Mo3N has a great potential and is a candidate as a host of new kind of skyrmion, which may help us to understand the fundamental mechanisms of DM interaction in the skyrmion.References: [1] P. Upadhyaya et al., Phys. Rev. B 92, 134411 (2015). [2] Y. Tokunaga et al., Nat. Commun. 6, 7638 (2015). [3] V. Kumar et al., Phys. Rev. B 101, 014424 (2020). [4] W. Li et al. Phys. Rev. B 93, 060409(R) (2016).

Magnetic skyrmions in epitaxial thin films of A2Mo3N with the filled β-Mn-type structure

Magnetic skyrmions are localized magnetic textures in magnetic films, behaving as particles and topologically different from the uniform ferromagnetic state, which have been identified to be extremely promising for applications, as well as of fundamental interest [1]. The magnetism community has provided a great effort in the last years to stabilize them at room temperature, most often by designing magnetic and heavy-metal multilayers combining perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI) [2]. The DMI promotes a unique chirality of the skyrmionic spin textures and, combined with spin-orbit torques generated in the heavy-metal layer(s), allows efficient current-induced motion of skyrmions [3]. However, recent observations have revealed that multilayered skyrmions are prone to present a hybrid chirality, due to the competition between dipolar interaction and DMI, which can negatively influence their current-induced motion [4] and also their size and stability [6]. We will discuss how those effects can be reduce thanks to synthetic antiferromagnets (SAF) based systems that allow the stabilisation of smaller antiferromagnetic skyrmions, due to the cancellation of the long range dipolar effects [7]. We will mainly focus on Pt/Co/Ru and Pt/CoFeB/Ru based systems and present the optimization process that has been done on the thicknesses of the different layer in order to maximize the antiferromagnetic RKKY coupling without cancelling the perpendicular magnetic anisotropy, needed to stabilize skyrmions. Those optimizations enabled for example the observation at room temperature of spin spiral, predicted by micromagnetic simulations, by reaching an effective anisotropy close to zero. We will then describe how, combined to a bias layer structure, multi-repeats SAF can host antiferromagnetic skyrmions and present their observation by MFM techniques without needs to go under vacuum. Those observations will also be completed by NV center microscopy images. The ANR grant TOPSky TOPSKY (ANR-17-CE24-0025), the SESAME Ile de France IMAGeSPIN (EX039175), the DARPA TEE program grant (MIPR#HR0011831554) and EU grant SKYTOP (H2020 FET Proactive 824123) are acknowledged for their financial support.References: [1] A. Fert, N. Reyren, V. Cros, Nat. Rev. Mat. 2 (2017), 17031. [2] C. Moreau-Luchaire et al, Nat. Nanotech, 11 (2016), 444 ; S. Woo et al, Nat. Mater. 15 (2016), 501 ; A. Soumyanarayanan et al, Nat. Mater. 16 (2017), 898 ; A. Hrabec et al, Nat. Comm. 8 (2017), 15765. [3] K. Litzius et al, Nat. Phys. 13 (2017), 170 ; S. Woo et al, Nat. Comm. 8 (2017), 15573. [4] W. Legrand et al, Sci. Adv. 4 (2018), eaat0415 ; Y. Dovzhenko et al, Nat. Comm. 9 (2018), 2712. [5] F. Büttner et al, Sci. Rep., 8 (2018), 4464 ; A. Bernand-Mantel et al, SciPost Phys. 4 (2018), 027. [6] W. Legrand et al, Phys. Rev. Applied 10 (2018), 064042. [7] W. Legrand et al, Nat. Mater. 19 (2019), 34–42.

Room-temperature magnetic imaging of antiferromagnetic skyrmions in multi-repeats synthetic antiferromagnets

Magnetic skyrmions [1] are promising candidates for next-generation spintronic devices. Their solitonic and chiral nature allows an efficient current-induced motion up to high velocities [2]. A fine tuning of their chirality would enable highly-manipulable magnetic skyrmions, which paves the way for new functionalities in spintronic memory, logic and neuromorphic devices [3,4]. This gives great importance to the control of the interfacial Dzyaloshinskii-Moriya interaction (iDMI) [5,6] strength and sign, at the origin of magnetic skyrmions and their chirality. In this study, we directly demonstrate magnetic skyrmion’s chirality switching in a Ta/FeCoB/TaOx trilayer. In fact, by varying the thickness of FeCoB and the oxidation state at the FeCoB/TaOx interface, we are able to obtain different regions in which magnetic skyrmions are right-handed (iDMI>0) or left-handed (iDMI<0) (resp. regions #4 and #2 on Fig.1). This material-dependent chirality switching brings a new degree of freedom to the exciting physics of magnetic skyrmions. For the first time, we show that the iDMI sign crossover in the different regions, as measured by Brillouin-Light-Scattering (BLS), is accompanied by a change of skyrmion chirality, as confirmed by the opposite direction of current-induced motion of magnetic skyrmions (See Fig. 2). Notably, between the two regions of opposite iDMI sign we have found, as expected, a region where iDMI∼0. In this region, the control of the iDMI with an electric field [7] may lead to a voltage-induced chirality switching, which hasn’t been observed yet. This all-electrical control of magnetic skyrmions represents a cornerstone towards power efficient spintronic devices and multidirectional logic functionnalities.References: [1] A. N. Bogdanov and D. A. Yablonskii, J. Exp. Theor. Phys., Vol. 95, p101−103 (1989) [2] W. Jiang, P. Upadhyaya and W. Zhang et al., Science, Vol. 349 (2015) [3] X. Zhang, Y. Zhou and K. M. Song et al., J. Phys.: Condens. Matter, Vol. 32 (2020) [4] A. Fert, N. Reyren and V. Cros et al., Nat. Rev. Mater., Vol. 2 (2017) [5] I. E. Dzyaloshinskii, Sov. Phys. JETP, Vol. 5 (1957) [6] T. Moriya, Phys. Rev., Vol. 120 (1960) [7] T. Srivastava, M. Schott and R. Juge et al., Nano. Lett, Vol. 18 (2018)

Chirality Switch of Magnetic Skyrmion in Ta/FeCoB/TaOx Trilayers

Praseodymium Iron Boron (PrFeB) thin film has recently attracted considerable attention for the potential magnetic property, which can alternate for currently NdFeB magnetic materials. The super low spin-reorientation temperature (about 4.2 K), huge uniaxial magnetocrystalline anisotropy (Ku), large coercivity (Hc), high saturation magnetization (Ms), and large energy products (BHmax) are the great properties that make PrFeB become a promising candidate in application of magnetic recording media nowadays. It is known that there is the body-centered tetragonal (BCT) structure of Pr2Fe14B phase mainly existing in PrFeB thin films to strengthen perpendicular magnetic anisotropy (PMA). The small lattice mismatch (δ) between Pr2Fe14B (00l) texture with [100] direction and BCC(110) texture underlayer with [110] and [001] directions makes the easy axis [001] perpendicular to the film plane. In this study, the Pr-Fe-B films with PMA were fabricated without underlayer on biased substrate by Pr25Fe65B10 alloy target. The substrate temperature was kept at 650oC and the bias was adjusted from -150 V to +100 V during sputtering hard magnetic Pr-Fe-B films. Then, Si3N4 cover layer was deposited at room temperature (RT). The deposited films were characterized for structural and magnetic properties by employing appropriate techniques. Effect of the substrate bias voltage on physical properties of thin film was systematically investigated. From our results, the squareness of the Pr-Fe-B film was enhanced significantly, because an epitaxial growth was initiated from applying substrate bias continuously through the Pr-Fe-B magnetic layer with the range of voltage from -50 to +50 V. Applying positive substrate bias changed atomic mobility, the Pr, Fe, and B atoms may diffuse chaotically in the magnetic layer. Consequently, an epitaxial barrier of the Pr-Fe-B alloy was broken among the elements in the magnetic layer, affected the deposition rates, improved the magnetic performance, and epitaxial growth of Pr-Fe-B thin films.

Strengthen the Magnetic Properties of Pr-Fe-B Thin Films by Biased Substrate

We report on magnetoresistance studies in La0.67Sr0.33MnO3 (LSMO) thin film on LaAlO3 by strain engineering at the interface. For this we investigate the magnetization and transport properties of compressively strained ferromagnetic LSMO films. We patterned Hall bars of the LSMO films and measure the longitudinal resistance in a 4-probe configuration applying a dc current bias. We systematically characterize the magnetic anisotropy of the thin films by varying temperature, applied magnetic field and the angle between current and field. The temperature and angular dependence of the longitudinal magnetoresistance for an in plane magnetic configuration explicitly shows three distinctly different magnetic phases. We observe a fourfold symmetry in the angular dependence of the magnetoresistance, for the temperature range between 10 to 125 K, indicating a biaxial anisotropy in the plane parallel to the (110) and (1-10) directions of thin film. Increasing the temperature further shows the presence of a second magnetic phase between 125 K to 250 K characterized by a twofold in-plane angle dependent magnetoresistance signal. We postulate that the fourfold symmetry is driven by magneto crystalline anisotropy whereas the twofold symmetry arises due to conventional anisotropic magnetoresistance. On increasing the temperature further, the thin film transit to a paramagnetic insulating phase. We show that the temperature variation of the angular dependence of the magnetoresistance is an important approach to study the different anisotropy induced in such strained thin oxide films and can complement torque based magnetometry studies.

Temperature dependence of the anisotropic magnetoresistance of compressively strained thin films of La2/3Sr1/3MnO3 on LaAlO3

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).

Real-Space Imaging of Confined Magnetic Skyrmion Tubes INVITED

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).

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