Transformation of a skyrmionium to a skyrmion through the thermal annihilation of the inner skyrmion

Abstract

Skyrmioniums are doughnutlike topological spin textures in chiral magnets, which are able to move with zero skyrmion Hall effect. The annihilation of a skyrmionium involves the topological transition through singularity formation at the continuum level. Here we analytically and numerically study a type of thermal annihilation of a skyrmionium under the framework of micromagnetism. The skyrmionium initially exists in an ultrathin ferromagnetic film in the exchange-dominated regime and is stabilized under a uniform perpendicular magnetic field. The thermal annihilation of the "skyrmion"inside the skyrmionium results in the transformation of the skyrmionium to a skyrmion. We derive an analytical formula in the Arrhenius form describing the annihilation rate of this process. We find that the analytical solutions agree well with the micromagnetic simulation results. Besides, from the large deviation point of view, we derive the dynamical path for the collapse of a skyrmionium. Our results are useful for understanding the thermal stability of skyrmioniums and may lead to spintronic applications based on the thermal manipulation of skyrmioniums.