Searching for activated transitions in complex magnetic systems

The process of finding activated transitions in localized spin systems with continuous degrees of freedom is developed based on a magnetic variant of the activation-relaxation technique. In addition to the description of the method and the relevant local properties of the magnetic energy landscape, a criterion to efficiently recognize failed attempts and an expression for the step magnitude to control the convergence are proposed irrespective of the physical system under study. The present implementation is validated on two translational symmetric systems with isotropic exchange interactions. Then, in one example, diffusion processes of a skyrmion vacancy and a skyrmion interstitial are revealed for a skyrmion system on a square spin lattice. In another example, the set of activation events about a metastable state of a two-dimensional dipolar spin glass is investigated and the corresponding energy barrier distribution is found. Detailed inspection of the transition states reveals the participation of nearest-neighbor pairs affording a simplified analytical understanding.