Supplyment to the article"Magnetic field-tuned size and dual annihilation pathways of chiral magnetic bobbers"

However, the mechanisms controlling their size and the dynamics of their annihilation are still not fully understood. In this study, we present an analytical model that predicts the radius R of the CB as a function of the external magnetic field, the Dzyaloshinskii−Moriya interaction (DMI), the magnetic anisotropy, and the exchange interaction.

The micromagnetic simulations validate this model across a broad range of parameters. We also identify two mechanisms of annihilation of CBs: (i) a droplet-like instability that occurs under rapid changes in the magnetic field, which we describe using a proposed magnetic Weber number We and its critical field step scaling; and (ii) Bloch point depinning mechanism at interfaces, for which we determine the threshold magnetic field Bth for annihilation.