The mechanism and activation energy for the annihilation of a magnetic skyrmion is studied by finding the minimum energy path for the transition in a system described by a Heisenberg-type Hamiltonian extended to include dipole-dipole, Dzyaloshinskii-Moriya, and anisotropy interactions so as to represent a Co monolayer on a Pt(111) surface. The annihilation mechanism involves isotropic shrinking of the skyrmion and slow increase of the energy until the transition state is reached after which the energy drops abruptly as the ferromagnetic final state forms. The maximum energy along the minimum energy path, which gives an estimate of the activation energy within the harmonic approximation of transition state theory, is found to be in excellent agreement with direct Langevin dynamics simulations at relatively high temperature carried out by Rohart et al. [Phys. Rev. B 93, 214412 (2016)2469-995010.1103/PhysRevB.93.214412]. The dipole-dipole interaction, the computationally most demanding term in the Hamiltonian, is found to be important but its effect on the stability of the skyrmion and shape of the transition path can be mimicked accurately by reducing the anisotropy constant in the Hamiltonian.
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