Navigation on the energy surface of the noncollinear Alexander–Anderson model

Implementation of the multiple impurity, noncollinear Alexander-Anderson model is described in detail and an analytical expression given for the force which determines the orientation of the magnetic momenta as well as a corresponding magnetic force theorem. Applications to trimers of Cr, Mn and Fe adsorbed on a metal surface are described, including the energy surface as a function of the the angles specifying the orientation of the magnetic momenta and minimum energy paths for transitions between stable states, which necessarily involve noncollinear ordering. A simple model for the interaction of a magnetic STM tip with a Cr dimer on a surface is briefly described. A finite range approximation is also formulated, which simplifies the self-consistency calculations and results in linear scaling of the computational effort with the number of magnetic atoms in the system. The theoretical approach described here can be used to study magnetic systems with complex energy landscapes, including stable states and magnetic transitions in frustrated magnetic systems, over a range in length scale, from a few to several thousands of magnetic atoms.