GC-03 - Theoretical Study of theTransport of Skyrmions at Room Temperature in Granular Racetracks

Abstract: Magnetic skyrmions are whirling magnetic structures that can be found on certain magnetic materials [1]. They are promising candidates to become the next generation of information carriers as well as basic elements in ultradense magnetic memories, logic devices or computational systems due to their small size and high mobility. Skyrmions can be stabilized in ferromagnetic ultrathin films with the aid of interfacial Dzyaloshinskii-Moriya (iDM) interaction with a heavy-metal substrate. The same mechanism allows the formation of skyrmions in multilayers with alternate ferromagnets and heavy-metals. The experimental finding of room-temperature skyrmions has boosted the potentiality of skyrmions for applications and, in consequence, the study of their current-driving dynamics at non-zero temperatures.Skyrmionic racetracks are considered one of the most reliable systems to transport skyrmions using the spin-orbit torque produced by a spin-polarized current fed in a heavy-metal substrate. The racetrack borders create a confining potential whose intensity determines the limit speed that a skyrmion can achieve inside a track without being annihilated at the border.As temperature increases, the topological protection of skyrmions is reduced, however, in some systems it is possible to stabilize and transport them. Apart from compromising stability, temperature can turn skyrmion dynamics into stochastic. As temperature increases the dispersion of the skyrmions position becomes larger, behaving like a Brownian particle. This stochastic motion sets new conditions and restrictions on the applicability of racetracks. In particular some binary questions like: Will the skyrmion be annihilated at the edge of the racetrack?, now become probabilistic questions: Which is the probability of a skyrmion to be annihilated at the edge of the racetrack?To address this kind of questions, a deterministic approach has been developed to study the dynamics of skyrmions at non-zero temperatures [2]. By solving the Fokker-Planck equation (FPE) for a skyrmion we can directly determine the probability of finding a skyrmion for a given time and position. In [2], the dynamics of a skyrmion when approaching a pinning potential and when driven along a racetrack was studied. In this work we present a natural continuation to that study: the granularity of the ferromagnet is taken into account while the skyrmion is moving along a racetrack.When nanomagnetic systems are studied from a theoretical point of view, usually we do not consider the granularity of the ferromagnetic materials that form the system, neglecting the influence of the polycrystalline structure and the presence of defects. However, in experiments we cannot avoid them. The granularity and defects difficult the motion of skyrmions at low velocities setting an unpinning velocity, adding an additional ingredient to the transport of skyrmions: they can be pinned in some point of the track [3].We simulate the granularity of the material setting a random array of pining potentials with random (within a range) intensities. We study how the probability of a skyrmion to reach the end of track of length without being trapped or annihilated (success probability) changes as we vary the density of pining potentials, which is proportional to the density of crystal grains, and the intensity of the pining potentials, which is proportional to the difference of the magnetic properties between grains.In Fig.1 and Fig.2 we show different snapshots for the density of probability of a skyrmion being on a given position, in a simulation where 100 pin potentials are placed randomly. In Fig.2 the average intensity of the pining potentials is higher than in Fig. 1. We can observe in Fig. 1 that the probability of success is close to 1, indicating that the skyrmion will survive to its travel along the track without getting pinned. However, in Fig.2 we observe that there is a considerable probability that the skyrmion gets pined and does not reach the end of the track.In order to build real devices, we need to ensure that the probability of success is as close to 1 as possible. We study how this success probability depends on the skyrmion speed, and granularity of the track at room temperature, finding that the granularity can even help in some cases. References: [1] Albert Fert, Vincent Cros, João Sampaio, Nat. Nanotechnology, 8, 152–156(2013)[2] Josep Castell-Queralt, Leonardo González-Gómez, Carles Navau, Phys. Rev. B 101, 140404(R) (2020)[3] Barton L. Brown, Uwe C. Täuber, and Michel Pleimling, Phys. Rev. B, 100, 024410 (2019) Images: https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/c29d136d6432c1a8980e5c1679287717.jpg Snapshots of the time evolution of the probability density of finding a skyrmion at a certain position. The corresponding snapshot times are, from left to right, 1.5/3/4.5/7.8/13.5 ns. The track length is 1 mm. There are 100 pining sites randomly distributed on the track with moderate intensity. The success probability is close to 1 (higher than when we have no granularity), with a small probability of being annihilated at the edge of the track or being trapped. https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/01ca6d0e939f9fbbd60fcf1caf2580f6.jpg Snapshots of the time evolution of the probability density of finding a skyrmion at a certain position. The corresponding snapshot times are, from left to right, 0.6/1.8/3.9/9/15 ns. The track length is 1 mm. There are 100 pining sites randomly distributed on the track with high intensity. The success probability is close to 0 since the trapping probability of the skyrmion is close to 1 (the skyrmion would be most likely trapped at some pinning site).