Eigenmode following for direct entropy calculation and characterisation of magnetic systems

The effect of entropy can be crucial for magnetic skyrmions, and in some cases, its accurate prediction has been prevented by the limitations of the harmonic approximation. We present an eigenmode following method (EMF) that has been developed for the numerical scanning of the potential energy surface and the direct calculation of entropy and pre-exponential factors of transition rates. While the concepts of following eigenmodes and numerical direct entropy calculation have been known individually, their combination yields a new and general way of effective sampling of the energy surface for high-accuracy treatment of non-harmonic eigenmodes. For this, the EMF method requires iterative updates of the eigenpairs of the softest eigenmodes that need the most accurate modelling. In contrast to other methods, EMF does not move “uphill" or “downhill" in energy to find stationary points, but to obtain energy curves. By numerical integration of the Boltzmann factor along these curves, the partition functions of the following eigenmodes can be calculated without making assumptions of their form. We introduce the general theoretical background and algorithm of the EMF method before providing test calculations and relevant use cases in the framework of atomistic spin simulations with a focus on magnetic skyrmion collapse.