Identification of mechanisms of magnetic transitions using an efficient method for converging on first order saddle points

Abstract

A method for locating first order saddle points on the energy surface of a magnetic system is described and several applications presented where the mechanism of various magnetic transitions is identified. The starting point for the iterative search algorithm can be anywhere, even close to a local energy minimum representing an initial state of the system, and the final state need not be specified. Convergence on a saddle point is obtained by inverting the component of the gradient along the minimum mode, thereby effectively transforming the neighbourhood of the saddle point to that of a local minimum. The method requires only the lowest two eigenvalues and corresponding eigenvectors of the Hessian of the system's energy and they are found using a quasi-Newton limited-memory Broyden-Fletcher-Goldfarb-Shanno solver for the minimization of the Rayleigh quotient without explicit evaluation of the Hessian. The method is applicable to large systems as the computational effort scales linearly with system size. Applications are presented to transitions in systems that reveal significant complexity of co-existing magnetic states, such as skyrmions, skyrmion bags, skyrmion tubes, chiral bobbers, and globules. When combined with rate theory within the harmonic approximation, the method can be used for simulations of the long timescale dynamics of complex magnetic systems characterized by multiple metastable states.