Fig. 5

Profile and stability of skyrmions in Rh/Co/Ir(111). a Domain wall profile (open symbols) and zero field skyrmion profile (filled symbols), i.e., z-component m_z of the local magnetic moment, obtained based on atomistic spin dynamics for Rh_hcp/Co/Ir(111). The dashed and solid lines are fits to the standard domain wall and skyrmion profile⁵⁷, respectively. Note that there are small deviations in both cases due to the exchange frustration. The insets show the domain wall and skyrmion spin structures on the two-dimensional atomic lattice. b Energy barrier protecting skyrmions in Rh_hcp/Co/Ir(111) against annihilation into the FM state as a function of applied magnetic field. The cross-over from the chimera collapse (green background) to the radial symmetric collapse (beige background) at 1 T is indicated. c Total energy and energy contributions for the chimera collapse from the different interactions (exchange, DMI, magneto-crystalline anisotropy energy (MAE)) at zero field versus the reaction coordinate along the minimum energy path from the initial isolated skyrmion (Sk) state to the final FM state for Rh_hcp/Co/Ir(111). Energies are summed over all atoms of the simulation box and are given relative to the energy of the isolated skyrmion state. The saddle point (SP) is indicated. To the right: exchange energy at the saddle point, E_SP, resolved with respect to the exchange interactions of different shells: J_1..10. d the same plot as in c for the radial symmetric collapse mechanism at a field of B = 1.2 T. e Images along the minimum energy path in c right before the SP (SP-1), at the SP, and just after the SP (SP+1). For all images of the minimum energy path see Supplementary Fig. 8. f Images along the minimum energy path in d for the radial symmetric collapse mechanism. Note that in e, f only a small part of the full simulation box which contained (70 × 70) spins is shown