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Additive nanotechnology enable curvilinear and three-dimensional (3D) magnetic architectures with tunable topology and functionalities surpassing their planar counterparts. Here, we experimentally reveal that 3D soft magnetic wireframe structures resemble compact manifolds and accommodate magnetic textures of high order vorticity determined by the Euler characteristic, $\chi$. We demonstrate that self-standing magnetic tetrapods (homeomorphic to a sphere; $\chi=+2$) support six surface topological solitons, namely four vortices and two antivortices, with a total vorticity of +2 equal to its Euler characteristic. Alternatively, wireframe structures with one loop (homeomorphic to a torus; $\chi = 0$) possess equal number of vortices and antivortices, which is relevant for spin-wave splitters and 3D magnonics. Subsequent introduction of $N$ holes into the wireframe geometry (homeomorphic to an $N$-torus; $\chi < 0$) enables the accommodation of a virtually unlimited number of antivortices, which suggests their usefulness for non-conventional (e.g. reservoir) computation. Furthermore, complex stray-field topologies around these objects are of interest for superconducting electronics, particle trapping and biomedical applications.

Ultrathin asymmetric magnetic films are a prominent material science platform, which combines unique magnetic and electronic properties enabling prospective memory and logic spin-orbitronic devices. Here, we present the quantification mechanism to distinguish all static and dynamic micromagnetic parameters of the layer stack based on magnetometry [1] and quasi-static morphology experiments on domain wall equilibrium tilts [2]. The DW damping is found to be about 0.1 [2] and it is demonstrated to arise from a longitudinal relaxation being dominant among transversal mechanisms for ultrathin films [3]. [1] I. A. Yastremsky et al., Phys. Rev. Appl. 12, 064038 (2019). [2] O. M. Volkov et al., Phys. Rev. Appl. 15, 034038 (2021). [3] I. A. Yastremsky et al., Phys. Rev. Appl. 17, L061002 (2022).

In recent years, curvilinear nanomagnetism is attracting attention for the broad range of effects emerging in curved geometries that are appealing for the innovative developments in stretchable and magnetoelectric devices, microrobots, sensors, flexible magnetic memories and nanoelectronics [1-5]. These phenomena encompass a vast range of exchange- and Dzyaloshinskii-Moriya (DMI)- induced interactions that typically result in topological magnetization patterning in shells, chiral symmetry breaking, and pinning of domain walls [1-5]. Less attention has been paid though to the role of the curvilinear effects in the magnetization dynamics of domain walls in curved geometries [4]. From application perspectives, spin-orbit torques are appealing as an alternative way to achieve the manipulation of magnetic domain walls and magnetization [8] with the breakthrough of lower power consumption. Recent developments in ultra-thin planar asymmetric multilayered strips describe a method to extract DMI and damping estimations from the dynamical tilt of domain walls from static measurements [9]. Following a similar approach, here we provide first results in single 100 nm-wide thin periodically corrugated strips of CrOx/Co/Pt with thickness of 2 nm and average curvature of 0.06 nm-1, tailored for an enhanced exchange-induced DMI. The orientation of the corrugation is tuned from the parallel to the perpendicular direction of the strip axis in different strips. Our results indicate that curvature plays a crucial role in the pinning and tilting of domain walls through DMI-induced and exchange-induced effects. In particular, DMI-induced anisotropy leads the pinning mechanism, while its combination with exchange-induced effects enhances the domain wall tilt. This opens a perspective for quantification and design of curvature-induced effects with application prospects in current challenges of spin-based nanoelectronics [10]. [1] Denys Makarov, et al., Advanced Materials 34, 3 (2022) [2] De

In recent years, curvilinear magnetism is captivating due to the broad range of phenomena emerging in curved geometries that are appealing for developments in stretchable and magnetoelectric devices, microrobots, sensors, flexible memories and nanoelectronics [1-5]. These phenomena encompass exchange- and Dzyaloshinskii-Moriya (DMI)-induced interactions that typically result in topological magnetization patterning in thin shells, symmetry breaking, and pinning of domain walls [1-9]. Less attention is been paid though to the role of the curvilinear effects in the stray field, and in the magnetization dynamics [4]. For application development, spin-orbit torques provide an alternative way to manipulate magnetic domain walls and magnetization [10, 11] with reduced power consumption. Here we present first results in stray field calculation in curvilinear geometries, and domain wall tilts in single 100 nm wide 2 nm thin periodically corrugated strips of CrOx/Co/Pt with average curvature of 0.06 nm-1. References [1] D. Makarov, et al., Advanced Materials 34, 2101758 (2022) [2] D. Sheka, et al., Small 18, 2105219 (2022) [3] D. Sander et al., J. Phys. D: Appl. Phys. 50, 363001 (2017). [4] E. Y. Vedmedenko, et al., J. Phys. D. Appl. Phys. 53, 453001 (2020). [5] D. Makarov et al., Applied Physics Reviews 3, 011101 (2016). [6] E. Berganza et al., Sci. Rep. 12, 3426 (2022) [7] E. Berganza et al., Nanoscale 12, 18646 (2022) [8] J. A. Fernandez-Roldan et al., APL Materials 10, 111101 (2022) [9] J. A. Fernandez-Roldan et al., Sci Rep 9, 5130 (2019). [10] O. V. Pylypovskyi et al., Scientific Reports 6, 23316 (2016). [11] O. M. Volkov et al., Phys. Rev. Applied 15, 034038 (2021)

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 approa

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 t

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 contras

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 magneti

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).

The optical control of magnetism offers an attractive possibility to manipulate small magnetic domains for prospective memory devices on ultrashort time scales. Here, we report on the local deterministic transformation of the magnetic domain pattern from stripes to bubbles in out-of-plane magnetized Co/Pt multilayers controlled only by the helicity of ultrashort laser pulses. Relying on the experimentally determined average size of stripe domains and the magnetic layer thickness, we calculate the temperature and characteristic fields at which the stripe-bubble transformation occurs. Furthermore, we demonstrate that in the narrow range of the laser power, the helicity induces a drag on domain walls.

The chemically ordered B2 Fe50Rh50 alloy is antiferromagnetic. By inducing chemical disorder its structure can be changed to the ferromagnetic A2 structure. Following the laser writing method published here [1] we used a pulsed laser to induce ferromagnetism locally in Fe50Rh50 thin films of 10, 20, and 30nm thickness. XMCD measurements on the laser-treated region revealed the formation of an annulus of FM contrast and a non-FM center. Transmission electron microscopy (TEM) on a section through the annulus found the FM region to be A2 and the enclosed non-contrast region of the fcc A1 structure. The surrounding untreated region remained in the B2 structure.

Curvature effects in magnetism offer appealing possibilities to obtain new magnetic textures at the nanoscale due to the interplay between exchange and magnetostatic interactions. Experimentally and theoretically, curvature driven changes of static magnetic properties in parabolic nanostripes have been addressed here. The shape of a parabolic stripe is tuned to cover broad range of widths and curvatures allowing to construct a phase diagram of magnetic equilibrium states. For this, joint experimental, i.e., soft X-ray imaging, and theoretical studies are carried out. Analytical calculations in the framework, when non-local magnetostatic effects are neglected, coincide with the experimental and simulation results in a broad range of parameters. The results give confidence in the applicability of the existing theoretical framework for further analytical considerations of equilibrium magnetization states of curvilinear nanomagnets.

Dzyaloshinskii-Moriya interaction (DMI) is a key ingredient which allows to obtain chiral non-collinear magnetic textures, e.g. chiral domain walls and skyrmions. The conventional spin-orbit induced DMI emerges in gyrotropic crystals or at the interfaces. Therefore, tailoring of DMI is done by optimizing materials. A viable alternative to the material screening approach relies on the use of geometrically broken symmetries of conventional materials, where local geometrical curvatures generate effective exchange-induced DMI. Here, we provide the very first experimental confirmation of the existence of the curvature-induced DMI in a Permalloy parabolic nanostripe. By analyzing the evolution of transversal domain wall (DW) [1] under the influence of external field we correlate the depinning field of the DW with the curvature-induced DMI field. We put forth a framework to analyze this field and assess the strength of the effective DMI. [1] O. Volkov et. al, Physica Status Solidi – Rapid Research Letters, 1800309 (2018).

Curvilinear magnetic objects are in the focus of intensive research due to the possibility to obtain new fundamental effects and stabilize topologically non-trivial magnetic textures at the nanoscale [1]. The physics in these systems is driven by the interplay between exchange and magnetostatic interactions, which contain spatial derivatives in their energy functionals. This makes both interactions sensitive to the appearance of bends and twists in the physical space. Here, we address experimentally and theoretically curvature-induced effects in parabolic nanostripes with different geometrical parameters [2]. We show that two different magnetic states can appear: the homogeneous magnetic distribution along the parabolic stripe and a state with a transversal domain wall pinned at the vertex of the parabola. The analytical calculation, based on local magnetostatic model, showed its validity and applicability in a wide range of geometrical parameters. [1] R. Streubel et al., J. Phys. D: Applied Physics 49, 363001 (2016). [2] O. Volkov et al., Physica Status Solidi – Rapid Research Letters, 1800309 (2018).

Magnetic storage and logic devices based on magnetic domain wall motion rely on the precise and synchronous displacement of multiple domain walls. The conventional approach using magnetic fields does not allow for the synchronous motion of multiple domains. As an alternative method, synchronous current-induced domain wall motion was studied, but the required high-current densities prevent widespread use in devices. Here we demonstrate a radically different approach: we use out-of-plane magnetic field pulses to move in-plane domains, thus combining field-induced magnetization dynamics with the ability to move neighbouring domain walls in the same direction. Micromagnetic simulations suggest that synchronous permanent displacement of multiple magnetic walls can be achieved by using transverse domain walls with identical chirality combined with regular pinning sites and an asymmetric pulse. By performing scanning transmission X-ray microscopy, we are able to experimentally demonstrate in-plane magnetized domain wall motion due to out-of-plane magnetic field pulses.