Identification of mechanisms of magnetic transitions using an efficient method for converging on first order saddle points
arxiv(2024)
Abstract
A method for locating first order saddle points on the energy surface of
magnetic systems is described and several applications presented. The starting
point of the iterative algorithm involved in the method can be anywhere, even
close to a local energy minimum representing an initial state of a magnetic
system and, in contrast to chain-of-states methods, the final state need not be
specified. Convergence on the saddle points is guided by a negative energy
gradient whose component along the minimum mode of the system is inverted,
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 evaluation of the
Hessian itself. The efficient implementation of the method and its linear
scaling with the system size make it applicable to large systems. 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.
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