The generalized force method, previously developed for an isotropic inhomogeneous ionosphere, exploits the knowledge about the character of the extrema of the phase distance-where high ionospheric rays correspond to minima and low rays to saddle points-to systematically find all relevant rays between fixed points, thereby enabling efficient global point-to-point ray tracing. In this article, the generalized force approach is extended to magneto-active, anisotropic ionosphere by locating minima and saddle points of a more general phase distance functional where trial functions include both the candidate ray path geometry and the orientation of the wavefront. For both O and X modes, the rays are found using an optimization algorithm guided by the generalized force whose definition depends on the ray type. The generalized force method, implemented in the form of computer software, is applied to problems of oblique sounding in realistic ionosphere described by NeQuick2 and IGRF13 models. The results of the ionogram simulations demonstrate the method's ability to solve routine problems of ionospheric ray tracing and show its potential in solving various inverse problems, as well as in verifying and correcting models of the ionosphere.

An efficient and scalable implementation of a method for locating first-order saddle points on the energy surface of a magnetic system is presented, along with several applications in which the mechanisms of various magnetic transitions are identified. The starting point for the iterative search algorithm can be anywhere, even close to a local energy minimum representing an initial state of the system, and the final state need not be specified. Convergence on a saddle point is obtained by inverting the component of the gradient along the minimum mode, thereby effectively transforming the neighborhood of the saddle point to that of a local minimum. The method requires only the lowest two eigenvalues and corresponding eigenvectors of the Hessian of the system's energy and they are found using a quasi-Newton limited-memory Broyden-Fletcher-Goldfarb-Shanno solver for the minimization of the Rayleigh quotient without explicit evaluation of the Hessian. The method is applicable to large systems, as it does not introduce additional scaling overhead to the computational complexity determined by the interactions present in the system. Applications are presented to transitions in systems that reveal significant complexity of coexisting magnetic states, such as skyrmions, skyrmion bags, skyrmion tubes, chiral bobbers, and globules. The identification of new metastable three-dimensional (3D) textures, such as magnetic bobbers with extended equilibrium distance between the base and the terminating Bloch point, and magnetic globules appearing as isolated states in 3D due to magnetostatic interactions, demonstrates the usefulness of the method for the characterization of complex energy surfaces of magnetic systems. When combined with rate theory within the harmonic approximation, the method can be used for simulations of the long timescale dynamics of complex magnetic systems characterized by multiple metastable states.

We present an optimal field-free protocol for current-induced switching of a perpendicularly magnetized ferromagnetic insulator nanoelement on the surface of a topological insulator. The time dependence of in-plane components of the surface current, which drives the magnetization reversal via the Dirac spin-orbit torque with minimal Joule heating, is derived analytically as a function of the switching time and material properties. Our analysis identifies that energy-efficient switching is achieved for vanishing damping-like torque. The optimal reversal time that balances switching speed and energy efficiency is determined. When we compare topological insulators to heavy-metal systems, we find similar switching costs for the optimal ratio between the spin-orbit torque coefficients. However, topological insulators offer the advantage of tunable material properties. Finally, we propose a robust and efficient simplified switching protocol using a down-chirped rotating current pulse, tailored to realistic ferromagnetic/topological insulator systems.

Topological magnetic solitons, such as skyrmions, exhibit intriguing particle-like properties that make them attractive for fundamental research and practical applications. While many magnetic systems can host skyrmions as statically stable configurations, chiral magnets stand out for their ability to accommodate a wide diversity of skyrmions with arbitrary topological charges and varied morphologies. Despite extensive investigation, a complete understanding of chiral magnetic skyrmions has remained elusive. We present a classification of all chiral skyrmions, demonstrating three classes based on their response to external magnetic field pulses: stationary, translating, and rotating. We highlight the role of magnetic texture symmetry in this classification. Skyrmions with varied dynamics offer avenues for exploring phenomena like skyrmion-skyrmion scattering that might be crucial for future applications.

The potential for manipulating characteristics of skyrmions in a CrI₃ monolayer using circularly polarised light is explored. The effective skyrmion-light interaction is mediated by bright excitons whose magnetization is selectively influenced by the polarization of photons. The light-induced skyrmion dynamics is illustrated by the dependencies of the skyrmion size and the skyrmion lifetime on the intensity and polarization of the incident light pulse. Two-dimensional magnets hosting excitons thus represent a promising platform for the control of topological magnetic structures by light.

Energy-efficient switching of nanoscale magnets requires application of a time-varying magnetic field characterized by microwave frequency. At finite temperatures, even weak thermal fluctuations induce perturbations in the magnetization that can accumulate in time, disrupt the phase locking between the magnetization and the applied field, and eventually compromise magnetization switching. It is demonstrated here that the magnetization reversal is mostly disturbed by unstable perturbations arising in a certain domain of the configuration space of a nanomagnet. The instabilities can be suppressed and the probability of magnetization switching enhanced by applying an additional stimulus such as a weak longitudinal magnetic field that ensures bounded dynamics of the perturbations. Application of the stabilizing longitudinal field to a uniaxial nanomagnet makes it possible to reach a desired probability of magnetization switching even at elevated temperatures. The principle of suppressing instabilities provides a general approach to enhancing thermal stability of magnetization dynamics.

Bright excitons in ferromagnetic monolayers of CrI₃ efficiently interact with lattice magnetization, which makes all-optical resonant magnetization control possible in this material. Using the combination of ab initio simulations within the Bethe-Salpeter approach, semiconductor Bloch equations, and Landau-Lifshitz equations, we construct a microscopic theory of this effect. By solving numerically the resulting set of coupled equations describing the dynamics of atomic spins and spins of the excitons, we demonstrate the possibility of tunable control of the macroscopic magnetization of a sample.

Novel 2D material CrI3 reveals unique combination of 2D ferromagnetism and robust excitonic response. We demonstrate that the possibility of the formation of magnetic topological defects, such as Neel skyrmions, together with large excitonic Zeeman splitting, leads to giant scattering asymmetry, which is the necessary prerequisite for the excitonic anomalous Hall effect. In addition, the diamagnetic effect breaks the inversion symmetry, and in certain cases can result in exciton localization on the skyrmion. This enables the formation of magnetoexcitonic quantum dots with tunable parameters.

Magnetic skyrmions have raised high hopes for future spintronic devices. For many applications, it would be of great advantage to have more than one metastable particle-like texture available. The coexistence of skyrmions and antiskyrmions has been proposed in inversion-symmetric magnets with exchange frustration. However, so far only model systems have been studied and the lifetime of coexisting metastable topological spin structures has not been obtained. Here, we predict that skyrmions and antiskyrmions with diameters below 10 nm can coexist at zero magnetic field in a Rh/Co bilayer on the Ir(111) surface—an experimentally feasible system. We show that the lifetimes of metastable skyrmions and antiskyrmions in the ferromagnetic ground state are above one hour for temperatures up to 75 and 48 K, respectively. The entropic contribution to the nucleation and annihilation rates differs for skyrmions and antiskyrmions. This opens the route to the thermally activated creation of coexisting skyrmions and antiskyrmions in frustrated magnets with Dzyaloshinskii–Moriya interaction.