Breathing Modes of a Magnetic Skyrmion on a Defective Surface

Abstract

Due to the tiny size of magnetic skyrmions with their unique topological robustness [1], they hold the promise of low-energy and high-density memory devices. To utilize the magnetic skyrmions for future spintronic devices, their atomistic nature should be studied because this topological spin structures formed physically on the atomic sites in the monolayer-scaled-thickness thin films. I.e., it is indispensable that the magnetic skyrmions are influenced by the surface roughness and the thermal fluctuation. To address those atomistic effects on the skyrmions, we adopt a numerical method based on atomic-scaled micromagnetic model. In this work, we focused on the effect of atomistic defects on the dynamics of skyrmions, particularly, the breathing mode. As a model system, monolayer Co nanodisk with 60 nm diameter was used. We assumed that the Co film has simple cubic (SC) structure with the lattice constant of 2.5 Å and the interfacial Dzyaloshinskii-Moriya interaction (DMI) appears only at the bottom surface [3][4]. The DMI is considered as the tensor form of magnetic interaction between neighbor spins. To explore the effect of roughness, we assumed that the vacancies are formed randomly on the top surfaces of the Co film with various number of vacancies. Figure 1(a) reveals clearly that the size of skyrmion in a steady state is affected sensitively by the surface roughness; the vacancies shrink the skyrmion. As shown in Fig. 1(b), the breathing mode is affected dramatically with the roughness. While its eigenfrequency was enhanced with increasing the roughness, its amplitude and the quality factor decreases. This reveals that the atomistic defects can weaken significantly the topological robustness