Thermal Stability of Metastable Magnetic Skyrmions

Abstract

Magnetic skyrmions are two-dimensional, localized, particle-like, topologically non-trivial magnetic spin textures. In recent years, they have attracted a lot of interest as potential candidates for novel spintronics applications. Isolated skyrmions are metastable excitations of the ferromagnetic ground state. They are separated from it by an activation energy, which may be overcome at finite temperature under the effect of thermal fluctuations. In this thesis, we study the thermal stability of metastable magnetic skyrmions on the two-dimensional square lattice, for which we use an atomistic spin model. This task is firstly carried out via a numerical implementation of Langer's statistical theory for the decay of metastable states. The paths of minimum energy that lead to the skyrmion annihilation are computed via the geodesic nudged elastic band method. The transition state at the barrier top, which is a saddle point (SP), is precisely identified by a climbing image algorithm. We focus on chiral magnetic skyrmions and we look at two types of annihilation mechanisms: collapse, in which the skryrmion progressively shrinks in size until it annihilates, and escape through a boundary. We find that the thermally significant modes are the modes localized to the skyrmion, in contrast to the rest of the collective spin-wave modes, which extend to the entire lattice and contribute weakly. Important variations of the attempt frequency over several orders of magnitude are found, depending on the mechanism and on the value of the external magnetic field. They originate from strong entropic effects which come from the difference in configurational entropy between the metastable skyrmion state and the saddle point. In the cases we studied, the configurational entropy decreases at the SP (Delta S < 0), which results in lowered attempt frequencies, and enhanced skyrmion stability. We refer to this effect as entropic narrowing in the SP region. The strong entropic contribution mainly originates from the skyrmion's internal modes, and is generally more pronounced for collapse mechanisms. Next, we use forward flux sampling (FFS) to compute skyrmion collapse rates as a function of the applied field, and compare them with the previous results from Langer's theory. This is an important step, because the use of Langer's theory is based on many assumptions. We obtain a good agreement between both methods, thus confirming the strong dependence of the attempt frequency on the external field. While in magnetism, it is common practice to only focus on activation barriers and assume a characteristic value of the prefactor in the gigahertz regime, we conclude that due to a strong entropic contribution, internal energy barriers are not enough in order to correctly predict the lifetime of magnetic skyrmions, and it is essential to also evaluate a rate prefactor. Lastly, we look at paths to annihilation of first- and second-order skyrmions and antiskyrmions on the frustrated square lattice. Frustrated exchange has been found to arise from interface effects in certain systems where nanoscale interface skyrmions have been observed. We find that, in certain regions of parameter space, the annihilation of skyrmionic solutions no longer occurs through an isotropic type of collapse, and instead involves the injection of the opposite topological charge into the system, by means of the nucleation of merons and antimerons. Alternatively, the second-order (anti)skyrmion may split into a bound (anti)skyrmion pair, which involves no change in the total topological charge.