Free-energy landscapes in magnetic systems from metadynamics

The knowledge of the free-energy barriers separating different states is critically important for the assessment of the long-term stability of information stored in magnetic devices. This information, however, is not directly accessible by standard simulations of microscopic models because of the ubiquitous time-scale problem, related to the fact that the transitions among different free-energy minima are characteristic of rare events. Here, we show that by employing the metadynamics algorithm based on suitably chosen collective variables, namely, helicity and circulation, it is possible to reliably recover the free-energy landscape. We demonstrate the effectiveness of this approach on an example of a vortex nucleation process in a magnetic nanodot with lowered spatial symmetry. With the help of reconstructed free-energy surfaces, we show the origin of symmetry broken vortex nucleation, where one polarity of the nucleated vortex core is preferred, even though only an in-plane magnetic field is present.