The skyrmion racetrack is a promising concept for future information technology. There, binary bits are carried by nanoscale spin swirls–skyrmions–driven along magnetic strips. Stability of the skyrmions is a critical issue for realising this technology. Here we demonstrate that the racetrack skyrmion lifetime can be calculated from first principles as a function of temperature, magnetic field and track width. Our method combines harmonic transition state theory extended to include Goldstone modes, with an atomistic spin Hamiltonian parametrized from density functional theory calculations. We demonstrate that two annihilation mechanisms contribute to the skyrmion stability: At low external magnetic field, escape through the track boundary prevails, but a crossover field exists, above which the collapse in the interior becomes dominant. Considering a Pd/Fe bilayer on an Ir(111) substrate as a well-established model system, the calculated skyrmion lifetime is found to be consistent with reported experimental measurements. Our simulations also show that the Arrhenius pre-exponential factor of escape depends only weakly on the external magnetic field, whereas the pre-exponential factor for collapse is strongly field dependent. Our results open the door for predictive simulations, free from empirical parameters, to aid the design of skyrmion-based information technology.

Chiral magnets are an emerging class of topological matter harboring localized and topologically protected vortex-like magnetic textures called skyrmions, which are currently under intense scrutiny as an entity for information storage and processing. Here, on the level of micromagnetics we rigorously show that chiral magnets can not only host skyrmions but also antiskyrmions as least energy configurations over all non-trivial homotopy classes. We derive practical criteria for their occurrence and coexistence with skyrmions that can be fulfilled by (110)-oriented interfaces depending on the electronic structure. Relating the electronic structure to an atomistic spin-lattice model by means of density functional calculations and minimizing the energy on a mesoscopic scale by applying spin-relaxation methods, we propose a double layer of Fe grown on a W(110) substrate as a practical example. We conjecture that ultra-thin magnetic films grown on semiconductor or heavy metal substrates with C 2v symmetry are prototype classes of materials hosting magnetic antiskyrmions.

The Spirit framework is designed for atomic scale spin simulations of magnetic systems of arbitrary geometry and magnetic structure, providing a graphical user interface with powerful visualizations and an easy to use scripting interface. An extended Heisenberg type spin-lattice Hamiltonian including competing exchange interactions between neighbors at arbitrary distance, higher-order exchange, Dzyaloshinskii-Moriya and dipole-dipole interactions is used to describe the energetics of a system of classical spins localised at atom positions. A variety of common simulations methods are implemented including Monte Carlo and various time evolution algorithms based on the Landau-Lifshitz-Gilbert equation of motion, which can be used to determine static ground state and metastable spin configurations, sample equilibrium and finite temperature thermodynamical properties of magnetic materials and nanostructures or calculate dynamical trajectories including spin torques induced by stochastic temperature or electric current. Methods for finding the mechanism and rate of thermally assisted transitions include the geodesic nudged elastic band method, which can be applied when both initial and final states are specified, and the minimum mode following method when only the initial state is given. The lifetime of magnetic states and rate of transitions can be evaluated within the harmonic approximation of transition-state theory. The framework offers performant CPU and GPU parallelizations. All methods are verified and applications to several systems, such as vortices, domain walls, skyrmions and bobbers are described.

Various transitions that a magnetic skyrmion can undergo are found in calculations using a method for climbing up the energy surface and converging onto first order saddle points. In addition to collapse and escape through a boundary, the method identifies a transition where the skyrmion divides and forms two skyrmions. The activation energy for this duplication process can be similar to that of collapse and escape. A tilting of the external magnetic field for a certain time interval is found to induce the duplication process in a dynamical simulation. Such a process could turn out to be an important avenue for the creation of skyrmions in future magnetic devices.Localized, non-collinear magnetic states are receiving a great deal of attention, where skyrmions have come under special focus. Along with interesting transport properties, skyrmions exhibit particle-like behaviour and carry a topological charge enhancing their stability with respect to uniform ferromagnetic background. In addition to the interest in their intriguing properties, they have been suggested as a basis for technological applications e.g. data storage or even data processing devices [1, 2]. A racetrack design of a memory device has been outlined where a spin polarized current drives a chain of skyrmions past a reading device [3, 4]. The effect of temperature and external magnetic field on the stability of the skyrmions need to be studied, as well as ways to generate and manipulate them. The effect of defects is also an important consideration [5, 6]. Two mechanisms for the annihilation of skyrmions have been characterized by theoretical calculations of atomic scale systems: Collapse of a skyrmion to form ferromagnetic state [7][8][9][10][11] and escape of a skyrmion through the boundary of the magnetic domain [9][10][11][12]. The effect of a non-magnetic impurity has also been calculated [11]. By using harmonic transition state theory for magnetic systems [14,15], the lifetime of skyrmions has been estimated [11,12]. Parameter values obtained from density functional theory [13] are found to give results that are consistent with experimental observations [16,17]. The challenge is to design materials where magnetic skyrmions are small enough while being sufficiently stable at ambient temperature, and to develop methods for manipulating them.Theoretical calculations can help accelerate this development by identifying the various possible transformations that a skyrmion can undergo at a finite temperature on a laboratory time scale. This can be achieved by the use of rate theory where the major challenge is to find the relevant transition mechanisms. If the final state of a transition is specified, in addition to the initial state, the geodesic nudged elastic band (GNEB) method [7,18] can be used to find the minimum energy path of the transition and, thereby, the activation energy which is the highest rise in energy along the path. However, the final states of possible transitions are not always known. Another category of methods for identifying ...

Magnetic singularities, also known as magnetic monopoles or Bloch points, represent intriguing phenomena in nanomagnetism. We show that a pair of coupled Bloch points may appear as a localized, stable state in cubic chiral magnets. Detailed analysis is presented of the stability of such objects in the interior of crystals and in geometrically confined systems.

While chiral magnetic skyrmions have been attracting significant attention in the past years, recently, a new type of a chiral particle emerging in thin films − a chiral bobber − has been theoretically predicted and experimentally observed. Here, based on theoretical arguments, we uncover that these novel chiral states possess inherent transport fingerprints that allow for their unambiguous electrical detection in systems comprising several types of chiral states. We reveal that unique transport and orbital characteristics of bobbers root in the non-trivial magnetization distribution in the vicinity of the Bloch points, and demonstrate that tuning the details of the Bloch point topology can be used to drastically alter the emergent response properties of chiral bobbers to external fields, which bears great potential for spintronics applications and cognitive computing.Nowadays, chiral magnetic skyrmions are believed to serve as one of the fundamental blocks for future magnetic technologies, such as racetrack memories [1] or artificial neurons [2][3][4]. These fascinating topologically protected chiral particles can be characterized with the quantized flux of the "emergent" magnetic field B em ∼n · (∂ xn × ∂ yn ) (i.e. the density of topological charge) due to the spatially non-trivial distribution of spinsn(x, y). They also display a number of dynamical effects which make them promising potential bits for efficient creation and manipulation by external fields [1,5]. One of the most crucial aspects for the implementation of skyrmionic devices is the ability to distinguish the emergence and dynamics of skyrmions by referring to electronic transport measurements, which are normally associated with the topological Hall effect arising from the presence of B em [6,7]. On the other hand, it was recently predicted theoretically and subsequently confirmed experimentally [8], that in thin films of chiral magnets an intricate interplay of external fields, temperature and exchange interactions can result in the formation of novel chiral particles -chiral bobbers [9]. In contrast to skyrmions that form in tubes [10], chiral bobbers are localized at the surface and manifestly incorporate a so-called Bloch point (BP) into their structure. These are characterized by fast non-adiabatic changes of the local magnetization around them.The experimental discovery of bobbers [8] represents an important milestone in magnetism. While earlier it was assumed that in chiral magnets there is only one type of particlelike objects − skyrmions − the work by Zheng and co-authors shows that the physics of quasiparticles in chiral magnets is significantly richer, and at least two types of particles with different physical properties may coexist in the same sample. Similar to elementary particles such magnetic quasiparticles may interact with each other with attractive or repelling forces controlled by the strength of the external magnetic field. The discovery of a new type of magnetic quasiparticle opens the vista for new research aiming to invest...

The early state of spinodal decomposition was studied by small angle neutron scattering in the critical mixture of the isotopic blend deutero-polystyrene/polystyrene (d-PS/PS) of equal molecular volume of 1.42×106 cm3/mol in a temperature range 12 K≤‖Tc−T‖≤82 K. This process can be described by the relaxation between two static structure factors, S(Q) representing the equilibrium values of the system in the mixed state and at the temperature where phase separation occurs. The time evolution of the relaxation process is described by the dynamical structure factor, L(Q,t) which depends on the dynamic properties of the mixture. It will be shown that the static structure factor of a mixed system can also be determined in the unstable two-phase region during the early state of spinodal decomposition. Consistent values for the Flory–Huggins parameter were found in comparison with a lower molecular d-PS/PS sample and, therefore, a lower critical temperature which was even smaller than the phase separation temperatures of the present system. The observed time evolution of the fluctuation modes is nonexponential. Therefore, it was originally supposed that internal modes of the coil come into play. The analysis of the data with an ansatz by Akcasu, which takes internal modes into account showed, however, that the phase separation in the experimental range of wave number and time is dominated by the centre of mass diffusion as in the C–H–C case and the nonexponential behavior was attributed to a time dependent increase of the ‘‘range’’ of the Onsager coefficient. A range of the Onsager coefficient larger than the radius of gyration of a single coil is predicted in case of entangled polymers. However, no time dependence was predicted so far. The evaluated diffusion constants follow an Arrhenius behavior and are consistent with earlier studies. They show a D0∝N−2 scaling consistent with reptation. A further result is the observation of a second order peak in the structure factor already in the early times of spinodal decomposition. So far, this was only attributed to the late state of spinodal decomposition.

The current development to employ magnetic skyrmions in novel spintronic device designs has led to a demand for room temperature-stable skyrmions of ever smaller size. We present extensive studies on skyrmion stability in atomistic magnetic systems in two-and three-dimensional geometries. We show that for materials described by the same micromagnetic parameters, the variation of the atomistic exchange between different neighbors, the stacking order, and the number of layers of the atomic lattice can significantly influence the rate of the thermally activated decay of a skyrmion. These factors alone are important considerations, but it is shown that their combination can open up novel avenues of materials design in the search for sub-10 nm skyrmions, as their lifetime can be extended by several orders of magnitude.