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Ultrathin asymmetrically sandwiched ferromagnetic films support fast moving chiral magnetic domain walls and skyrmions [1,2]. This paves the way to the realization of prospective racetrack memory concept, the performance of which is determined by the static and dynamic micromagnetic parameters [3]. The necessity of having strong Dzyaloshinskii-Moriya interactions (DMI) and perpendicular magnetic anisotropy requires the utilization of ultrathin magnetic (~1 nm) layers, which compromized structural quality, that substantially enhances the magnetic damping for non-collinear magnetic textures. Here, we present the experimental and theoretical analysis of ultrathin Co films with asymmetric interfaces //CrO x /Co/Pt and estimation of their micromagnetic parameters based on the analysis of the temperature dependence of magnetization as well as imaging of the morphology of magnetic domain walls (DWs) in stripes. Namely, we show that the best fit to the magnetometry data up to room temperature is obtained within a quasi-2D model, accounting for the lowest transversal magnons [4]. The fit provides access to the exchange constant in asymmetric stackes which is found to be about 1 order of magnitude smaller compared to the bulk Co. The experimentally observed tilt of magnetic domain walls in stripes in statics can be explained based on two models: (I) A unidirectional tilt could appear in equilibrium as a result of the competition between the DMI and additional in-plane easy-axis anisotropy, which breaks the symmetry of the magnetic texture and introduce tilts [5]. (II) A static DW tilt could appear due to the spatial variation of magnetic parameters, which introduce pinning centers for moving tilted DWs driven by magnetic field and can fix them at remanence [6]. We found that the second model is in line with the experimental observations and allows to determine self-consistently the DW damping parameter and DMI constant for the particular layer stack. The DW damping is found to be about 0.1 and explained by the enhanced longitudinal relaxation mechanism. The latter is shown to much stronger tan the standard transversal relaxation and can be even stronger than the spin pumping contribution for the case of ultrathin ferromagnetic films [7]. References: [1] N. Nagaosa and Y. Tokura, “Topological properties and dynamics of magnetic skyrmions”, Nat. Nanotechnol. 8, 899 (2013). [2] A. Fert, N. Reyren, and V. Cros, “Magnetic skyrmions: advances in physics and potential applications”, Nat. Rev. Mater. 2, 17031 (2017). [3] C. Garg, S.-H. Yang, T. Phung, A. Pushp and S. S. P. Parkin, “Dramatic influence of curvature of nanowire on chiral domain wall velocity”, Sci. Adv. 3, e1602804 (2017). [4] I. A. Yastremsky, O. M. Volkov, M. Kopte, T. Kosub, S. Stienen, K. Lenz, J. Lindner, J. Fassbender, B. A. Ivanov and D. Makarov, “Thermodynamics and Exchange Sti ff ness of Asymmetrically Sandwiched Ultrathin Ferromagnetic Films with Perpendicular Anisotropy”, Phys. Rev. Appl. 12, 064038 (2019). [5] O. V. Pylypovskyi, V. P. Kravchuk, O. M. Volkov, J. Fassbender, D. D. Sheka and D. Makarov, “Unidirectional tilt of domain walls in equilibrium in biaxial stripes with Dzyaloshinskii–Moriya interaction”, J. Phys. D: Appl. Phys. 53, 395003 (2020). [6] O. M. Volkov, F. Kronast, C. Abert, E. Se. Oliveros Mata, T. Kosub, P. Makushko, D. Erb, O. V. Pylypovskyi, M.-A. Mawass, D. Sheka, S. Zhou, J. Fassbender and D. Makarov, “Domain-Wall Damping in Ultrathin Nanostripes with Dzyaloshinskii-Moriya Interaction”, Phys. Rev. Appl. 15, 034038 (2021). [7] I. A. Yastremsky, J. Fassbender, B. A. Ivanov, and D. Makarov, “Enhanced Longitudinal Relaxation of Magnetic Solitons in Ultrathin Films”, Phys. Rev. Appl. 17, L061002 (2022).

The interplay between geometry and topology of the order parameter is crucial properties in soft and condensed matter physics, including cell membranes [1], nematic crystals [2,3], superfluids [4], semiconductors [5], ferromagnets [6] and superconductors [7]. Until recently, in the case of magentism, the influence of the geometry on the magnetization vector fields was addressed primarily by the design of the sample boundaries, aiming to tailor anisotropy of the samples. With the development of novel fabrication techniques allowing to realize complex 3D architectures, not only boundary effects, but also local curvatures can be addressed rigorously for the case of ferromagnets and antiferromagnets. It is shown that curvature governs the appearance of geometry-induced chiral and anisotropic responses [6-8]. Here we provide experimental confirmations of the existence of local and non-local curvature-induced chiral interactions of the exchange and magnetostatic origin in conventional soft ferromagnetic materials. Namely, we will present the experimental validation of the appearance of exchange-driven Dzyaloshinskii-Moriya interaction interaction (DMI, local effect) for the case of conventional achiral yet geometrically curved magnetic materials [9,10]. This curvature induced DMI is predicted to stabilize skyrmions [11] and skyrmionium states [12]. Furthermore, we will address the impact of nonlocal magnetostatic interaction on the properties of curvilinear ferromagnets, which enables the stabilization of topological magnetic textures [13,14], realization of high-speed magnetic racetracks [15] and curvature-induced asymmetric spin-wave dispersions in nanotubes [16]. Furthermore, symmetry analysis demonstrates the possibility to generate a fundamentally new chiral symmetry breaking effect, which is essentially nonlocal [13]. Thus, geometric curvature of thin films and nanowires is envisioned as a toolbox to create artificial chiral nanostructures from achiral magnetic materials. References: [1] H. T. McMahon and J. L. Gallop “Membrane curvature and mechanisms of dynamic cell membrane remodelling”, Nature 438, 590 (2005). [2] T. Lopez-Leon, V. Koning, K. B. S. Devaiah, V. Vitelli and A. Fernandez-Nieves, “Frustrated nematic order in spherical geometries”, Nature Physics 7, 391 (2011). [3] G. Napoli, O. V. Pylypovskyi, D. D. Sheka and L. Vergori, “Nematic shells: new insights in topology- and curvature-induced e ff ects”, Soft Matter 17, 10322-10333 (2021). [4] H. Kuratsuji, “Stochastic theory of quantum vortex on a sphere”, Phys. Rev. E 85, 031150 (2012). [5] C. Ortix, Phys, “Quantum mechanics of a spin-orbit coupled electron constrained to a space curve”, Phys. Rev. B 91, 245412 (2015). [6] D. D. Sheka, O. V. Pylypovskyi, O. M. Volkov, K. V. Yershov, V. P. Kravchuk and D. Makarov, “Fundamentals of Curvilinear Ferromagnetism: Statics and Dynamics of Geometrically Curved Wires and Narrow Ribbons”, Small 18, 2105219 (2022). [7] D. Makarov, O. M. Volkov, A. Kakay, O. V. Pylypovskyi, B. Budinská and O. V. Dobrovolskiy, “New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures”, Adv. Mater. 34, 2101758 (2022). [8] Y. Gaididei, V. P. Kravchuk and D. D. Sheka, “Curvature Effects in Thin Magnetic Shells”, Phys. Rev. Lett. 112, 257203 (2014). [9] O. M. Volkov, D. D. Sheka, Y. Gaididei, V. P. Kravchuk, U. K. Rößler, J. Fassbender and D. Makarov, ”Mesoscale Dzyaloshinskii-Moriya interaction: geometrical tailoring of the magnetochirality”, Sci. Rep. 8, 866 (2018). [10] O. M. Volkov, A. Kákay, F. Kronast, I. Mönch, M.-A. Mawass, J. Fassbender and D. Makarov, “Experimental observation of exchange-driven chiral effects in curvilinear magnetism”, Phys. Rev. Lett. 123, 077201 (2019). [11] V. P. Kravchuk, D. D. Sheka, A. Kákay, O. M. Volkov, U. K. Rößler, J. van den Brink, D. Makarov and Y. Gaididei, “Multiplet of Skyrmion States on a Curvilinear Defect: Reconfigurable Skyrmion Lattices”, Phys. Rev. Lett. 120, 067201 (2018). [12] O. V. Pylypovskyi, D. Makarov, V. P. Kravchuk, Y. Gaididei, A. Saxena and D. D. Sheka, “Chiral Skyrmion and Skyrmionium States Engineered by the Gradient of Curvature”, Phys. Rev. Appl. 10, 064057 (2018). [13] D. D. Sheka, O. V. Pylypovskyi, P. Landeros, Y. Gaididei, A. Kákay and D. Makarov, “Nonlocal chiral symmetry breaking in curvilinear magnetic shells”, Commun. Phys. 3, 128 (2020). [14] C. Donnelly, A. Hierro-Rodrı́guez, C. Abert, K. Witte, L. Skoric, D. Sanz-Hernández, S. Finizio, F. Meng, S. McVitie, J. Raabe, D. Suess, R. Cowburn and A. Fernández-Pacheco, “Complex free-space magnetic field textures induced by three-dimensional magnetic nanostructures”, Nat. Nanotech. 17, 136–142 (2022). [15] M. Yan, A. Kákay, S. Gliga and R. Hertel, “Beating the Walker limit with massless domain walls in cylindrical nanowires”, Phys. Rev. Lett. 104, 057201 (2010). [16] J. A. Otálora, M. Yan, H. Schultheiss, R. Hertel and A. Kákay, “Curvature-induced asymmetric spin-wave dispersion”, Phys. Rev. Lett. 117, 227203 (2016).

Conventional magnetic nanoscale devices are based on planar thin films and straight racetracks hosting magnetic topological solitons. Recent progress in fabrication and characterization methods allows to realise and study of complex-shaped planar and three-dimensional (3D) architectures. In the planar case, boundaries of nanodots lead to the formation of inhomogeneous textures, such as vortices and antivortices. In 3D, the magnetostatic interaction favours a spatially inhomogeneous shape anisotropy, which acts as easy-axis anisotropy along wires or hard axis of anisotropy perpendicular to the film surface. These interactions track the sample geometry and enable curvature-induced symmetry-breaking effects, such as topology-induced magnetization patterning and emergent anisotropic and chiral responses of the Dzyaloshinskii-Moriya interaction (DMI) type [1,2]. Curvature-induced magnetic responses can be classified as being local or nonlocal. In ferromagnets, local effects stem from the exchange interaction and DMI. The curvature-induced DMI originates from exchange: it is linear in curvatures and has the symmetry of the interfacial DMI. Its strength can be comparable with typical values of the intrinsic DMI. This is experimentally confirmed by the stabilization of chiral domain walls (CDW) on the apex of a Permalloy parabola-shaped stripe [3]. The strength of the CDW depinning field gives an estimation for the curvature-induced DMI constant and can be tuned by the geometry. In contrast to curvature itself, also curvature gradients offer a possibility to pin CDW, which was studied with an example of a circular indentation with a conic cross-section profile. This geometry supports circular CDWs described by the forced skyrmion equation, where the effective force acts as the stabilizing factor for large-radius skyrmion and skyrmionium states [4]. The magnetostatic interaction is a source of novel curvature-induced chiral effects, which are essentially nonlocal, in contrast to the conventional DMI [5]. The effect emerges in shells with non-zero mean curvature due to the non-equivalence between the top and bottom surfaces of a geometrically curved shell. It is possible to show that the analysis of nonlocal effects in curvilinear shells can be more intuitive with a split of a conventional volume magnetostatic charge into two terms: (i) tangential charge, governed by the tangent to the sample's surface, and (ii) geometrical charge, given by the normal component of magnetization and the mean curvature. In addition to the shape anisotropy (local effect), four additional nonlocal terms appear, determined by the surface curvature. Three of them are zero for any magnetic texture in shells with the geometry of minimal surfaces. The fourth term becomes zero only for the special symmetries of magnetic textures. The impact of local and nonlocal chiral effects on magnetic textures in curvilinear architectures will be discussed in this presentation.

This dataset contains the numerical data for our publication "Curvilinear spin-wave dynamics beyond the thin-shell approximation: Magnetic nanotubes as a case study" published in Physical Review B. The data consists of dispersion, magnetization ground states and mode profiles of spin waves in vortex-state magnetic nanotubes of different thicknesses, and has been calculated with the TetraX micromagnetic modeling package. All calculations are described within each subfolder by a jupyter notebook.

Asymmetric ultrathin magnetic thin films represent intriguing materil platforms, which support emerging fundamentals effects, such as skyrmion and topological [1] Hall effects and fast motion of chiral magnetic non-collinear textures [2], that underlie prospective memory and logic devices based on spin-orbit torques. Such asymmetric stacks can provide strong perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interactions (DMI), which is necessary for the sabilization of chiral non-collinear magnetic textures. As the performance of spin-orbitronic devices is determined by the static and dynamic micromagnetic parameters [3], it is crucial to determine all internal micromagnetic parameters for the particular layer combination and sample geometry. In particular, the speed of a domain wall (DW) based racetrack is determined by the DMI constant, $D$, and the DW damping parameter, $\alpha$. The necessity of having strong DMI requires the utilization of ultrathin magnetic (~1 nm) layers, which implies polycrystalinity and compromized structural quality, that substantially enhances the magnetic damping compared to bulk. Accessing this parameters typically requires dynamic experiments, whose interpretations are cumbersome due to the creep regime. Here, we present the experimental and theoretical investigation of tilted DWs in perpendicularly magnetized asymmetric //CrOx/Co/Pt layer stacks with the surface-induced DMI. We will discuss two possible theoretical mechanism for the appearance of titled DWs: (I) A unidirectional tilt could appear in equilibrium as a result of the competition between the DMI and additional in-plane easy-axis anisotropy, which breaks the symmetry of the magnetic texture and introduce tilts [4]. (II) A static DW tilt could appear due to the spatial variation of magnetic parameters, which introduce pinning centers for DWs [5]. A moving DW can be trapped in a tilted state after the external driving field is off. Based on these theoretical approaches, we perform a statistical analysis of the DW tilt angles obtained in staticts after the external magnetic field used for the sample demagnetization was off. We found that the second approach confirms the experimental observations and allows to determine self-consistently the range of DW damping parameters and DMI constants for the particular layer stack. Using two reference fields, which provide two characteristic tilt angles, allow us to retrieve the range of DMI strength $D \geq 0.8$ mJ/m2 and DW damping parameters $\alpha \geq 0.1$. The upper limit for the DMI constant agrees with an independent transport-based measurement giving $D=0.90 \pm 0.13$ mJ/m2, which further refines our estimate of the damping parameter $\alpha=0.13 \pm 0.02$. Thus, the combination of the proposed method with standard metrological techniques opens up opportunities for the quantification of both static and dynamic micromagnetic parameters based on static measurements of the DW morphology. [1] N. Nagaosa and Y. Tokura, “Topological properties and dynamics of magnetic skyrmions”, Nat. Nanotechnol. 8, 899 (2013). [2] A. Fert, N. Reyren, and V. Cros, “Magnetic skyrmions: advances in physics and potential applications”, Nat. Rev. Mater. 2, 17031 (2017). [3] C. Garg, S.-H. Yang, T. Phung, A. Pushp and S. S. P. Parkin, “Dramatic influence of curvature of nanowire on chiral domain wall velocity”, Sci. Adv. 3, e1602804 (2017). [4] O. V. Pylypovskyi, V. P. Kravchuk, O. M. Volkov, J. Fassbender, D. D. Sheka and D. Makarov, “Unidirectional tilt of domain walls in equilibrium in biaxial stripes with Dzyaloshinskii–Moriya interaction”, J. Phys. D: Appl. Phys. 53, 395003 (2020). [5] O. M. Volkov, F. Kronast, C. Abert, E. Se. Oliveros Mata, T. Kosub, P. Makushko, D. Erb, O. V. Pylypovskyi, M.-A. Mawass, D. Sheka, S. Zhou, J. Fassbender and D. Makarov, “Domain-Wall Damping in Ultrathin Nanostripes with Dzyaloshinskii-Moriya Interaction”, Phys. Rev. Appl. 15, 034038 (2021).

Curvilinear magnetic objects are in focus of intensive research due to the possibility to obtain new fundamental effects and stabilize topologically non-trivial magnetic textures at the nanoscale [1]. In geometrically-broken magnetic objects all energy functionals, that contains spatial derivatives, e.g. exchange, magnetostatic and intrinsic Dzyaloshinskii-Moriya (DMI) interactions, are reshaping in a way of appearance additional curvature-induced chiral and anisotropy terms. These novel chiral magnetic responses arise in the physical space, by introducing bends and twists to magnetic architectures even of conventional materials. We address both experimentally and theoretically the appearance of curvature-induced exchange effects in parabolic nanostripes with different geometrical parameters [2]. We show that a pinning of transversal domain wall at the parabolic apex is originated due to the presence of local curvature-induced DMI that creates a subsequent pinning potential. Measuring the depinning field enables to quantify the effective exchange-driven DMI interaction constant. In its turn, the interplay between the intrinsic and exchange-induced DMI paves the way to a mesoscale DMI, whose symmetry and strength depend both on the geometrical and material parameters [3]. Developing this concept we propose a novel approach towards artificial ME materials with helimagnetic nanohelices embedded in a piezoelectric matrix [4]. By applying an electric field, small geometrical changes of pitch and radius could lead to the phase transition from a homogeneously magnetized state (full average magnetic moment) to a periodical one (zero average magnetic moment). [1] R. Streubel et. al., J. Phys. D: Appl. Phys. 49,363001 (2016). [2] O. Volkov et al.. Phys. Rev. Lett. 123, 077201 (2019). [3] O. Volkov et al., Sci. Rep. 8, 866 (2018). [4] O. Volkov et al., J. Phys. D: Appl. Phys. 52, 345001 (2019).

Curvilinear magnetism is the emerging field in micromagnetism which studies influences of external geometry and its topology on magnetic vector fields [1]. Much attention was paid to fundamental theoretical investigations of curvature-induced effects for local [2,3] and non-local magnetic interactions [4], which results in the prediction of various magnetochiral effects [2,5], topologically-induced magnetic patterns [5,6], stabilization of individual skyrmions [7,8] and skyrmion lattices [9] on curvilinear defects. Recently, we provided the very first experimental confirmation and quantitative assessment of the existence of the curvature-induced chiral interaction of exchange origin in a conventional soft ferromagnetic material [10]. In its turn, the interplay between the intrinsic and exchange-induced Dzyaloshinskii-Moriya interaction (DMI) paves the way to a mesoscale DMI [3], whose symmetry and strength depends both on the geometrical and material parameters of the magnetic system. Extending this concept we proposed a novel approach towards artificial magnetoelectric materials with helimagnetic nanohelices embedded in a piezoelectric matrix [11], where electric field could control magnetic states through the utilization of curvature-induced effects. [1] R. Streubel et. al., J. Phys. D: Appl. Phys. 49,363001 (2016). [2] Y. Gaididei et al., Phys. Rev. Lett. 112, 257203 (2014). [3] O. Volkov et al., Sci. Rep. 8, 866 (2018). [4] D. D. Sheka et al., Commun. Phys. 3, 128 (2020). [5] V. P. Kravchuk et al., Phys. Rev. B 85, 144433 (2012). [6] O. V. Pylypovskyi et al., Phys. Rev. Lett. 114, 197204 (2015). [7] V. P. Kravchuk et al., Phys. Rev. B 94, 144402 (2016). [8] O. V. Pylypovskyi et al., Physical Review Applied 10, 064057 (2018). [9] V. P. Kravchuk et al., Phys. Rev. Lett. 120, 067201 (2018). [10] O. M. Volkov et al., Phys. Rev. Lett. 123, 077201 (2019). [11] O. M. Volkov et al., J. Phys. D: Appl. Phys. 52, 345001 (2019).

Structural inversion symmetry breaking in low-dimensional magnetic systems determines their electronic and magnetic properties at interfaces [1,2]. Asymmetrically sandwiched magnetic films can provide strong perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interactions (DMI), which is necessary for prospective memory and logic devices based on chiral non-collinear magnetic textures, e.g. skyrmions [3,4], skyrmion bubbles and chiral domain walls (DWs) [5]. The device performance is determined by the static and dynamic micromagnetic parameters [6,7]. In particular, the speed of a DW-based racetrack memory is defined by both the strength of the external driving, e.g. magnetic field or spin-polarized current, and internal magnetic parameters, e.g. the DMI constant and damping parameter [6,7]. The necessity of having a strong DMI in asymmetrically sandwiched magnetic structures requires the utilization of ultrathin (in the range of 1 nm) magnetic films, which implies the polycrystalinity and compromized structural quality of the layer stack. Structural imperfections in addition to the spin-pumping mechanism [8,9], that arises due to the proximity of a ferromagnetic material with a heavy-metal, lead to a substantial enhancement of the magnetic damping parameter of ultrathin films compared to bulk. Accessing this parameter typically requires dynamic experiments on the motion of DWs in confined geometries, which are usually done in the creep regime due to the pronounced pinning. Here, we demonstrate both experimentally and theoretically the presence of tilted DWs in statics in perpendicularly magnetized asymmetric //CrOx/Co/Pt layer stacks with surface-induced DMI, Fig. 1. We show that in such systems there are two possible theoretical mechanism for the appearance of titled DWs: (I) A unidirectional tilt could appear in equilibrium as a result of the competition between the DMI and additional in-plane easy-axis anisotropy, which breaks the symmetry of the magnetic texture and introduce tilts [10]. (II) A static DW tilt could appear due to the spatial variation of magnetic parameters, which introduce pinning centers for DWs. A moving DW can be trapped in a tilted state after the external driving field is off. Based on these theoretical approaches, we perform a statistical analysis of the DW tilt angles obtained in staticts after the external magnetic field used for the sample demagnetization was off. We found that the second approach corresponds better to the experimental observations and allows to determine self-consistently the range of DW damping parameters and DMI constants for the particular layer stack. Using two reference fields, which provide two characteristic tilt angles, allow us to retrieve the range of DMI strength mJ/m2 and DW damping parameters . The upper limit for the DMI constant agrees with an independent transport-based measurement giving mJ/m2, which further refines our estimate of the damping parameter . This value lies in a typical DW damping range for the Co-based asymmetrical layer stacks, that are obtained from dynamic experiments [11,12]. Thus, the combination of the proposed method with standard metrological techniques opens up opportunities for the quantification of both static and dynamic micromagnetic parameters based on static measurements of the DW morphology. [1] A. Fert, N. Reyren, and V. Cros, Nature Reviews Materials 2, 17031 (2017). [2] R. Wiesendanger, Nature Reviews Materials 1, 16044 (2016). [3] A. N. Bogdanov and D. A. Yablonskiı̆, Zh. Eksp. Teor. Fiz. 95, 178 (1989). [4] S. Woo, K. Litzius, B. Krüger, et al., Nature Materials 15, 501 (2016). [5] S. Emori, U. Bauer, S.-M. Ahn, et al., Nature Materials 12, 611 (2013). [6] C. Garg, S.-H. Yang, T. Phung, et al., Science Advances 3, e1602804 (2017). [7] S. Parkin and S.-H. Yang, Nature Nanotechnology 10, 195 (2015). [8] Y. Tserkovnyak, A. Brataas, G. E. W. Bauer, et al., Reviews of Modern Physics 77, 1375 (2005). [9] A. Brataas, Y. Tserkovnyak, and G. E. W. Bauer, Physical Review Letters 101, 037207 (2008). [10] O. V. Pylypovskyi, V. P. Kravchuk, O. M. Volkov, et al., Journal of Physics D: Applied Physics 53, 395003 (2020). [11] J.-M. L. Beaujour, J. H. Lee, A. D. Kent, et al., Physical Review B 74 (2006). [12] A. J. Schellekens, L. Deen, D. Wang, et al., Applied Physics Letters 102, 082405 (2013).

Skyrmions represent a class of chiral magnetic textures with unique properties relevant for spintronic and spin-orbitronic applications [1]. Geometrical curvature can be used as an efficient mean to tailor chiral and anisotropic responses of thin ferromagnetic shells [2-4]. This was recently confirmed by quantifying the strength of the Dzyaloshinskii-Moriya interaction (DMI) in curved nanostripes [5]. Furthermore, there are numerous predictions of the stabilization of curvature-driven of small-radius skyrmions in spherical shells [6] and an appearance of skyrmion lattices as the ground state in intrinsically chiral curvilinear thin films [7]. Here, we demonstrate a new pathway of stabilizing Neel skyrmion and skyrmionium states relying on the gradient of curvature using a magnetic thin film hosting a circular nanoindentation [8]. These skyrmion states can be formed in a material even without an intrinsic DMI. We propose a physical picture of this effect, which is related to the pinning of a chiral magnetic domain wall at the bend of a nanoindentation. Geometry of the film is described by two principal curvatures k1(r), describing film geometry in radial direction, and k2(r) inversely proportional to the distance from origin. In this respect, the spatial inhomogeneity of the curvature-induced DMI governing by k1(r) is responsible for the stabilization of the skyrmion state. The lateral dimensions of the stabilized chiral magnetic textures are varied in a broad range by engineering the size of the nanoindentation. We describe the stability condition of skyrmion states. Furthermore, on the fundamental side, we put forth a general analytical framework allowing us to map a complex problem of the description of a magnetic texture at a surface of revolution to a standard planar problem with modified constants of DMI and magnetic anisotropy. In this respect, our model predicts a new mechanism of pinning of magnetic domain walls in planar ferromagnetic films with intrinsic DMI on inhomogeneities of the DMI. [1] A. Fert, N. Reyren, V. Cros, Nat. Rev. Mater., Vol. 2, 17031 (2017) [2] R. Streubel, P. Fischer, F. Kronast et al., J. Phys. D: Appl. Phys. Vol. 49, 363001 (2016) [3] O. Pylypovskyi, V. Kravchuk, D. Sheka et al., Phys. Rev. Lett. Vol. 114, 197204 (2015) [4] Y. Gaididei, A. Goussev, V. Kravchuk et al., J. Phys. A: Mat. and Theor. Vol. 50, 385401 (2017) [5] Volkov, Kakay, Kronast et al., Phys. Rev. Lett. Vol. 123, 077201 (2019) [6] V. Kravchuk, U. K. Röβler, O. M. Volkov et al., Phys. Rev. B. 94, 144402 (2016) [7] V. Kravchuk, D. Sheka, A. Kákay et al., Phys. Rev. Lett. Vol. 120, 067201 (2018) [8] O. Pylypovskyi, D. Makarov, V. Kravchuk et al., Phys. Rev. Appl. Vol. 10, 064057 (2018)

Spectrum of spin eigenmodes localized on a ferromagnetic skyrmion pinned by a geometrical defect (bump) of magnetic films is studied theoretically. By means of direct numerical solution of the corresponding eigenvalue problem and finite element micromagnetic simulations we demonstrate, that the curvature can induce localized modes with higher azimuthal and radial quantum numbers, which are absent for planar skyrmions (for the same parameters). The eigenfrequencies of all modes, except the breathing and gyromodes decreases with increasing curvature. Due to the translational symmetry break, the zero translational mode of the skyrmion gains a finite frequency and forms the gyromode, which describes the uniform rotation of skyrmions around the equilibrium position. In order to treat the gyromotion analytically we developed a Thiele-like collective variable approach. We show that Neel skyrmions in curvilinear films experience a driving force originating from the gradient of the mean curvature. The gyrofrequency of the pinned skyrmion is proportional to the second derivative of the mean curvature at the point of equilibrium.

The efficiency of manipulation of domain walls and skyrmions in ferromagnetic racetracks with perpendicular anisotropy determines perspectives of development of data storage and logic devices relying on spintronic and spin-orbitronic concepts [1, 2]. The domain wall dynamics is dependent on its orientation with respect to the racetrack axis. In-plane fields [3], edge roughness [4] and current [5] result in the domain wall tilt in samples, possessing Dzyaloshinskii-Moriya interaction (DMI). Here, we show theoretically, that the tilt can appear in equilibrium and describe the domain wall dynamics under the action of external field. We consider a thin biaxial stripe with DMI of interfacial type [6]. The main easy axis of anisotropy is perpendicular to the plane, and the direction of the second easy axis lies in the stripe plane under the angle α to the stripe axis. While the shape anisotropy results in α = 0, a general case α ≠ 0 can appear under the influence of other effects, e.g crystalline structure [7]. While the second easy axis defines the preferable in-plane magnetization within the domain wall, the DMI forces the domain wall being perpendicular to the magnetization gradient. The competition between these two energy contributions and the domain wall tension results in the unidirectional tilt of the whole domain wall. If the DMI is weak enough, there is an additional metastable domain wall state, tilted into the opposite direction. The symmetry break is observed not only for static magnetization texture, but also in the domain wall dynamics under the action of external magnetic field. The domain wall reveals fast and slow motion regimes for the opposite signs of A. The maximum of the Walker field and Walker velicities is determined by the angle A of the second easy axis anisotropy and does not coincide with a shape-induced anisotropy direction A=0. The domain wall possesses the switch of the magnetization direction inside the domain wall in the slow motion regime, which results in the faster motion. [1] K.-S. Ryu, L. Thomas, S.-H. Yang et al., Nat. Nanotech., Vol. 8, 527 (2013) [2] O. Pylypovskyi, D. Sheka, V. Kravchuk et al., Sci. Rep. Vol. 6, 23316 (2016) [3] C. Muratov, V. Slastikov, A. Kolesnikov et al., Phys. Rev. B. Vol. 96, 134417 (2017) [4] E. Martinez, S. Emori, N. Perez et al. J. Appl. Phys. Vol. 115, 213909 (2014) [5] O. Boulle, S. Rohart, L. Buda-Prejbeanu et al., Phys. Rev. Lett. Vol. 111, 217203 (2013) [6] O. Pylypovskyi, V. Kravchuk, O. Volkov et al., J. Phys. D. (2020), DOI:10.1088/1361-6463/ab95bd [7] M. Heide, G. Bihlmayer, S. Blügel, Pys. Rev. B, Vol. 78, p. 140403 (2008).

Skyrmions attract a special attention for spintronic and spinorbitronic devices by their unique static and dynamic properties [1]. The interplay between geometry and magnetization texture gives additional degrees of freedom in control of such topologically nontrivial patterns via geometry-induced anisotropy and Dzyaloshinskii-Moria interaction (DMI) in materials with easy-normal anisotropy [2-5]. It is sufficient for appearance of skyrmions and skyrmion lattices as a ground state on small curvilinear defects [6]. Here, we propose a new way to stabilize skyrmions and control their size via curvature gradient in a nanoindentation even without intrinsic DMI [7]. Our mathematical formalism also allows to describe planar films with inhomogeneous distribution of material parameters. We consider a thin membrane with easy-normal anisotropy and circular nanoindentation of a conic frustrum shape with inner and outer radii R and R , respectively. This geometry can be described by two principal curvatures, k and k , providing the whole information about geometry in the given point of the membrane. While k (r) is inversely proportional to the distance from origin r, k (r) has sharp peaks in points of the bend of the membrane. To compare textures in curved membranes and flat films we propose a projection of a surface of revolution to a plane, which reconstructs a skyrmion equation. The energy of the magnetic texture in projected coordinates obtains a curvature-modified anisotropy and two DMI terms, related to principal curvatures. In contrast to the planar case, the corresponding skyrmion equation is characterized not only by DMI coefficients itself, but also their spatial derivatives playing a role of the external driving force, proportional to d(k + k )/dr. The main consequences of the driving force are: (i) the ground state cannot be strictly normal to the membrane with nonconstant curvature; (ii) a gradient of k can result in stabilization of the Neel skyrmion of radius R or R (Fig. 1). Skyrmions, stabilized at the inner and outer bends, have the opposite chiralities. If the difference between R and R is large enough, both skyrmions can coexist forming a skyrmionium state with zero total winding number. In the limiting case of sharp bends, the minimal angle α of the indentation side for stabilizing topologically nontrivial textures equals 4L/R radians, with R being either R or R (α = 0 corresponds to a flat film) and L being a magnetic length. Numerical analysis of skyrmion stability is performed in a wide range of geometrical parameters (Fig. 2). It is shown that the strength and spatial localization of the DMI coefficient, associated with k , plays the main role in the pinning of topologically nontrivial textures and pinning strength is estimated to be hundredths of Kelvin for typical parameters of Co/Pt multilayers. In conclusion, we propose a mathematical framework which allows us to describe magnetic nanomembranes with rotational symmetry and planar films with circular distribution of material parameters using the same apparatus. It uncovers two mechanisms of skyrmion stabilization, namely DMI-driven [8] and DMI gradient-driven [7]. The first one does not require the curvature gradients and lead to formation of small-radius skyrmions, while the second allows stabilization of large-radius skyrmions and skyrmionium states of the geometrically defined size. References: [1] A. Fert, N. Reyren, V. Cros, Nat. Rev. Mater., Vol. 2, 17031 (2017); [2] R. Streubel, P. Fischer, F. Kronast et al., J. Phys. D: Appl. Phys. Vol. 49, 363001 (2016); [3] O. Pylypovskyi, V. Kravchuk, D. Sheka et al., Phys. Rev. Lett. Vol. 114, 197204 (2015); [4] Y. Gaididei, V. Kravchuk, D. Sheka, Phys. Rev. Lett. Vol. 112, 257203 (2014); [5] Y. Gaididei, A. Goussev, V. Kravchuk et al., J. Phys. A: Mat. and Theor. Vol. 50, 385401 (2017); [6] V. Kravchuk, D. Sheka, A. Kákay et al., Phys. Rev. Lett. Vol. 120, 067201 (2018); [7] O. Pylypovskyi, D. Makarov, V. Kravchuk et al., Phys. Rev. Appl. Vol. 10, 064057 (2018); [8] V. Kravchuk, U. Roessler, O. Volkov et al., Phys. Rev. B, Vol. 94, 144402 (2016).

Efficient manipulations of chiral textures like domain walls and skyrmions are crucial for the development of prospective spintronic devices [1-2]. Domain walls moving in stripes with perpendicular anisotropy and Dzyaloshinskii-Moriya interaction (DMI) exhibit a tilt resulting in a decrease of their maximal velocity [3]. Beside the direct current influence [3], the tilt is usually caused by in-plane fields [4] or an edge roughness [5]. In this work, we show that the domain wall tilt can appear as a result of competition of the in-plane anisotropy and DMI. We also describe the field-driven dynamics of the tilted domain wall. We consider an infinitely long biaxial stripe with interfacing DMI (Fig. 1) and biaxial anisotropy. The first easy axis of anisotropy is perpendicular to the stripe plane and the second easy axis lies within the stripe plane and makes an angle α with the stripe axis. The shape anisotropy forces α=0, while α≠0 can appear due to other effects, e.g. exchange bias from underlying antiferromagnet. The second anisotropy rotates the in-plane magnetization inside the domain wall according to the in-plane easy axis direction. The optimum of the DMI energy is reached when the magnetization rotates perpendicularly to the domain wall plane. In stripes the energy balance between these two energy terms and the energy of the domain wall tension results in a unidirectional tilt by angle χ of the domain wall plane (χ=0 corresponds to the domain wall perpendicular to the stripe), determined by α. There is a metastable state of the wall, tilted into the opposite direction in a certain range of anisotropy and DMI values. This is related to the symmetry break between the two opposite directions of the magnetization rotation inside the domain wall due to the presence of a weak DMI. Furthermore, the dynamics of the domain wall in the presence of a biaxial anisotropy and DMI exhibits a symmetry break with respect to the magnetic field and the easy axis direction A. The domain wall reveals fast and slow motion regimes for the opposite signs of α. The slow regime is characterized by a smaller Walker field b and switch of the magnetization direction inside the domain wall in a certain field below b . The latter results in an increase of the domain wall speed. The velocity of the domain wall is inversely proportional to cos χ. The maximum of the Walker field corresponds to α≠0 (Fig. 2). In conclusion, we describe a unidirectional tilt of a domain wall in a biaxial stripe with DMI, which appears at equilibrium without external magnetic field and demonstrate the enhancement of the Walker field and velocity [6]. The domain wall dynamics reveal fast and slow regimes depending on the orientation of the easy axis of the in-plane anisotropy and the applied magnetic field. References: [1] K.-S. Ryu, L. Thomas, S.-H. Yang et al., Nat. Nanotech., Vol. 8, 527 (2013); [2] O. Pylypovskyi, D. Sheka, V. Kravchuk et al., Sci. Rep. Vol. 6, 23316 (2016); [3] O. Boulle, S. Rohart, L. Buda-Prejbeanu et al., Phys. Rev. Lett. Vol. 111, 217203 (2013); [4] C. Muratov, V. Slastikov, A. Kolesnikov et al., Phys. Rev. B. Vol. 96, 134417 (2017); [5] E. Martinez, S. Emori, N. Perez et al. J. Appl. Phys. Vol. 115, 213909 (2014); [6] O. Pylypovskyi, V. Kravchuk, O. Volkov et al., ArXiv, 2001.03408 (2020)

The orientation of a chiral magnetic domain wall in a racetrack determines its dynamical properties. In equilibrium, magnetic domain walls are expected to be oriented perpendicular to the stripe axis. We demonstrate the appearance of a unidirectional domain wall tilt in an out-of-plane magnetized stripes with biaxial anisotropy (the firsrt easy axis is perpendicular to the plane and the second one is tilted with respect to the stripe axis) and interfacial Dzyaloshinskii--Moriya interaction (DMI). The tilt is a result of the interplay between the in-plane easy-axis anisotropy and DMI. We show that the additional anisotropy and DMI prefer different domain wall structure: anisotropy links the magnetization azimuthal angle inside the domain wall with the stripe main axis in contrast to DMI, which prefers the magnetization perpendicular to the domain wall plane. Their balance with the energy gain due to domain wall extension defines the equilibrium magnetization and domain wall tilt angles. We demonstrate that the Walker field and the corresponding Walker velocity of the domain wall can be enhanced in the system supporting tilted walls.

Magnetic crystals with broken chiral symmetry possess intrinsic spinorbit driven Dzyaloshinskii-Moriya interaction (DMI). Geometrically broken symmetry in curvilinear magnetic systems also leads to the appearance of extrinsic to the crystal exchange driven effective DMI [1,2]. The interplay between the intrinsic and geometrical-induced DMI paves the way to a mesoscale DMI, whose symmetry and strength depend on the geometrical and material parameters [3]. We demonstrate this approach on the example of a helix with intrinsic DMI. Adjusting the helical geometry allows to create new artificial chiral nanostructures with defined properties from standard magnetic materials. For instance, we propose a novel approach towards artificial magnetoelectric materials, whose state is controlled by means of the geometry. [1] Y. Gaididei et. al, Phys. Rev. Lett. 112, 257203 (2014). [2] R. Streubel et. al, J. Phys. D: Applied Physics 49, 363001 (2016). [3] O. Volkov et. al, Scientific Reports 8, 866 (2018).

The magnetic vortex core in a nanodot can be switched by an alternating transversal magnetic field. We propose a simple collective coordinate model, which describes the comprehensive vortex core dynamics, including the resonant behavior, weakly nonlinear regimes, and reversal dynamics. A chaotic dynamics of the vortex polarity is predicted. All analytical results are confirmed by micromagnetic simulations., Полярнiсть магнiтного вихору в наноточцi може бути перемкнена пiд дiєю змiнного магнiтного поля, прикладеного перпендикулярно до осi наночастинки. В данiй роботi запропоновано просту модель на основi колективних змiнних, яка описує складну динамiку вихрового осердя, включаючирезонансну поведiнку, слабконелiнiйний режим та динамiку перемикань. Передбачено наявнiсть хаотичної динамiки. Всi аналiтичнi результати пiдтверджено мiкромагнiтними моделюваннями.

International audience; The study of pre-equilibrium emitted particles is an useful tool to examine nuclear clustering; in order to study how possible cluster structures affect nuclear reactions, the NUCL-EX collaboration (INFN, Italy) is carrying out an extensive research campaign on pre-equilibrium emission of light charged particles from hot nuclei. In this framework, the reactions 16O + 30Si, 18O + 28Si and 19F + 27Al at 7 MeV/u have been measured at the GARFIELD+RCo array in Legnaro National Laboratories. After a general introduction on the experimental campaign, this contribution will focus on the analysis results obtained so far; effects related to the entrance channel and to the colliding ions cluster nature are emphasized through differences between the theoretical predictions and the experimental data.

International audience; The study of pre-equilibrium (or fast) emitted particles is a useful tool to examine nuclear clustering; to study how possible cluster structures affect nuclear reactions, the NUCL-EX Collaboration (INFN, Italy) is carrying out an extensive research campaign on pre-equilibrium emission of light charged particles from hot nuclei. In this framework, the reactions 16O + 30Si, 18O + 28Si and 19F + 27Al at 7 MeV/u have been measured at the GARFIELD+RCo array in Legnaro National Laboratories. After a general introduction on the experimental campaign, this contribution will focus on the analysis results obtained so far; effects related to the entrance channel and to the colliding ions cluster nature are emphasized through differences between the theoretical predictions and the experimental data.

Crystals with broken inversion symmetry can host fundamentally appealing and technologically relevant periodical or localized chiral magnetic textures. The type of the texture as well as its magnetochiral properties are determined by the intrinsic Dzyaloshinskii-Moriya interaction (DMI), which is a material property and can hardly be changed. Here we put forth a method to create new artificial chiral nanoscale objects with tunable magnetochiral properties from standard magnetic materials by using geometrical manipulations. We introduce a mesoscale Dzyaloshinskii-Moriya interaction that combines the intrinsic spin-orbit- and extrinsic curvature-driven DMI terms and depends both on the material and geometrical parameters. The vector of the mesoscale DMI determines magnetochiral properties of any curved magnetic system with broken inversion symmetry. The strength and orientation of this vector can be changed by properly choosing the geometry. For a specific example of nanosized magnetic helix, the same material system with different geometrical parameters can acquire one of three zero-temperature magnetic phases, namely, phase with a quasitangential magnetization state, phase with a periodical state and one intermediate phase with a periodical domain wall state. The difference between equilibrium magnetization states for magnetic nanohelices with opposite geometrical chiralities put forth on a new simple measuring method of the DMI constant. Our approach paves the way towards the realization of a new class of nanoscale spintronic and spinorbitronic devices with the geometrically tunable magnetochirality.

Dynamics of topological magnetic textures are typically induced externally by, e.g., magnetic fields or spin/charge currents. Here, we demonstrate the effect of the internal-to-the-system geometry-induced motion of a domain wall in a curved nanostripe. Being driven by a gradient of the curvature of a stripe with biaxial anisotropy, transversal domain walls acquire remarkably high velocities of up to 100m/s and do not exhibit any Walker-type speed limit. We pinpoint that the inhomogeneous distribution of the curvature-induced Dzyaloshinskii-Moriya interaction is a driving force for the motion of a domain wall. Although we showcase our approach on the specific Euler spiral geometry, the approach is general and can be applied to a wide class of geometries.

Curvilinear nanomagnets can support magnetic skyrmions stabilized at a local curvature without any intrinsic chiral interactions. Here, we propose an alternative mechanism to stabilize chiral Neel skyrmion states relying on the gradient of curvature. We illustrate our approach with an example of a magnetic thin film with perpendicular magnetic anisotropy shaped as a circular indentation. We show that in addition to the topologically trivial ground state, there are two skyrmion states with winding numbers +/- 1 and a skyrmionium state with a winding number 0. These chiral states are formed due to the pinning of a chiral magnetic domain wall at a bend of the nanoindentation due to spatial inhomogeneity of the curvature-induced Dzyaloshinskii-Moriya interaction. The latter emerges due to the gradient of the local curvature at the bend. While the chirality of the skyrmion is determined by the sign of the local curvature, its radius can be varied in a broad range by engineering the position of the bend with respect to the center of the nanoindentation. We propose a general method, which enables us to reduce the magnetic problem for any surface of revolution to the common planar problem by means of proper modification of constants of anisotropy and Dzyaloshinskii-Moriya interaction.

The correlations between mass distributions of the binary fragments, total kinetic energy (TKE), and neutron multiplicity have been investigated for the reaction Ti-50+Pb-208 at 294 MeV bombarding energy. Although this reaction has been used to synthesize the Rf (Z = 104) superheavy element, a complete study of its fragmentation dynamics is still not available in the literature. In this work, average neutron multiplicities were extracted as a function of different fragment mass splits and TKE windows. A weak increase of the prescission neutron multiplicity is observed going from asymmetric to symmetric mass splits. A fission delay time of 4.5 x 10(-20) s has been extracted for the symmetric fission. The neutron multiplicity extracted for the symmetric mass split was used to derive the average number of neutrons emitted in the spontaneous fission of (258)Rf. The extrapolated value of 4.7 +/- 1.4 is found to be consistent with systematics of spontaneous and neutron-induced fission in heavy nuclei and with the results of previous works for superheavy nuclei with Z = 116 and Z = 124.

The EUROnu project has studied three possible options for future, high intensity neutrino oscillation facilities in Europe. The first is a Super Beam, in which the neutrinos come from the decay of pions created by bombarding targets with a 4 MW proton beam from the CERN High Power Superconducting Proton Linac. The far detector for this facility is the 500 kt MEMPHYS water Cherenkov, located in the Frejus tunnel. The second facility is the Neutrino Factory, in which the neutrinos come from the decay of mu(+) and mu(-) beams in a storage ring. The far detector in this case is a 100 kt magnetized iron neutrino detector at a baseline of 2000 km. The third option is a Beta Beam, in which the neutrinos come from the decay of beta emitting isotopes, in particular He-6 and Ne-18, also stored in a ring. The far detector is also the MEMPHYS detector in the Frejus tunnel. EUROnu has undertaken conceptual designs of these facilities and studied the performance of the detectors. Based on this, it has determined the physics reach of each facility, in particular for the measurement of CP violation in the lepton sector, and estimated the cost of construction. These have demonstrated that the best facility to build is the Neutrino Factory. However, if a powerful proton driver is constructed for another purpose or if the MEMPHYS detector is built for astroparticle physics, the Super Beam also becomes very attractive., We acknowledge the financial support of the European Community under the European Commission Framework Program 7 Design Study: EUROnu, Project No. 212372 and from the National Science Fund of Bulgaria under Contract No. 02-149/07.10.2009