2016, Streubel, Robert, Fischer, Peter, Kronast, Florian, Kravchuk, Volodymyr P., Sheka, Denis D., Gaididei, Yuri, Schmidt, Oliver G., Makarov, Denys

Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii–Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.

2019, Korniienko, Anastasiia, Kravchuk, Volodymyr P., Pylypovskyi, Oleksandr V., Sheka, Denis D., van den Brink, Jeroen, Gaididei, Yuri

A new type of magnonic crystals, curvature induced ones, is realized in ferromagnetic nanowires with periodically deformed shape. A magnon band structure of such crystal is fully determined by its curvature: the developed theory is well confirmed by simulations. An application to nanoscale spintronic devices with the geometrically tunable parameters is proposed, namely, to filter elements.

2022, Zaiets, Oleksandr, Kravchuk, Volodymyr P., Pylypovskyi, Oleksandr V., Makarov, Denys, Sheka, Denis D.

Vertically stacked exchange coupled magnetic heterostructures of cylindrical geometry can host complex noncolinear magnetization patterns. By tuning the interlayer exchange coupling between a layer accommodating magnetic vortex state and an out-of-plane magnetized layer, one can efficiently realize new topological chiral textures such as cone state vortices and circular stripe domains. We study how the number of circular stripes can be controlled by both the interlayer exchange coupling and the sample geometrical parameters. By varying geometrical parameters, a continuous phase transition between the homogeneous state, cone state vortex, circular stripe domains, and the imprinted vortex takes place, which is analysed by full scale micromagnetic simulations. The analytical description provides an intuitive pictures of the magnetization textures in each of these phases. The possibility to realize switching between different states allows for engineering magnetic textures with possible applications in spintronic devices.

2020, Yershov, Kostiantyn V., Kravchuk, Volodymyr P., Sheka, Denis D., Rößler, Ulrich K.

Periodical equilibrium states of magnetization exist in chiral ferromagnetic films, if the constant of antisymmetric exchange (Dzyaloshinskii-Moriya interaction) exceeds some critical value. Here, we demonstrate that this critical value can be significantly modified in curved film. The competition between symmetric and antisymmetric exchange interactions in a curved film can lead to a new type of domain wall which is inclined with respect to the cylinder axis. The wall structure is intermediate between Bloch and N\'eel ones. The exact analytical solutions for phase boundary curves and the new domain wall are obtained.

2015, Pylypovskyi, Oleksandr V., Kravchuk, Volodymyr P., Sheka, Denis D., Makarov, Denys, Schmidt, Oliver G., Gaididei, Yuri

We show that the interaction of the magnetic subsystem of a curved magnet with the magnet curvature results in the coupling of a topologically nontrivial magnetization pattern and topology of the object. The mechanism of this coupling is explored and illustrated by an example of a ferromagnetic Möbius ring, where a topologically induced domain wall appears as a ground state in the case of strong easy-normal anisotropy. For the Möbius geometry, the curvilinear form of the exchange interaction produces an additional effective Dzyaloshinskii-like term which leads to the coupling of the magnetochirality of the domain wall and chirality of the Möbius ring. Two types of domain walls are found, transversal and longitudinal, which are oriented across and along the Möbius ring, respectively. In both cases, the effect of magnetochirality symmetry breaking is established. The dependence of the ground state of the Möbius ring on its geometrical parameters and on the value of the easy-normal anisotropy is explored numerically.

2016, Pylypovskyi, Oleksandr V., Sheka, Denis D., Kravchuk, Volodymyr P., Yershov, Kostiantyn V., Makarov, Denys, Gaididei, Yuri

Manipulation of the domain wall propagation in magnetic wires is a key practical task for a number of devices including racetrack memory and magnetic logic. Recently, curvilinear effects emerged as an efficient mean to impact substantially the statics and dynamics of magnetic textures. Here, we demonstrate that the curvilinear form of the exchange interaction of a magnetic helix results in an effective anisotropy term and Dzyaloshinskii–Moriya interaction with a complete set of Lifshitz invariants for a one-dimensional system. In contrast to their planar counterparts, the geometrically induced modifications of the static magnetic texture of the domain walls in magnetic helices offer unconventional means to control the wall dynamics relying on spin-orbit Rashba torque. The chiral symmetry breaking due to the Dzyaloshinskii–Moriya interaction leads to the opposite directions of the domain wall motion in left- or right-handed helices. Furthermore, for the magnetic helices, the emergent effective anisotropy term and Dzyaloshinskii–Moriya interaction can be attributed to the clear geometrical parameters like curvature and torsion offering intuitive understanding of the complex curvilinear effects in magnetism.