Duplication, Collapse, and Escape of Magnetic Skyrmions Revealed Using a Systematic Saddle Point Search Method

Abstract

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 ...

Spirit : Multifunctional framework for atomistic spin simulations

“…As is shown in Ref. 13, the covariant second derivatives, valid at all points of the phase space, can be calculated using a projector-based approach. 64 The corresponding 2N × 2N Hessian matrix can be represented as…”

“…The test of a larger and far more complex system has been given in Ref. 13, where the minimum mode following method revealed the existence of a skyrmion duplication mechanism. By defining the force field in the above way, previously unknown transition mechanisms can be found and subsequently used in the calculation of lifetimes.…”

“…10. Together with such a GUI, Spirit unifies various computational methods that are commonly applied to atomistic (and in part also to micromagnetic) simulations: Monte Carlo and Landau Lifshitz Gilbert (LLG) dynamics, 11 the geodesic nudged elastic band (GNEB) method 12 , minimum mode following 13 (MMF), harmonic transition-state theory 14 (HTST), and the visualization of eigenmodes. All of these methods are quite distinct, but complementary in nature.…”

Multiple minimum-energy paths and scenarios of unwinding transitions in chiral nematic liquid crystals

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Efficient optimization method for finding minimum energy paths of magnetic transitions

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