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Calculations of stable and metastable magnetic states as well as minimumenergy paths for transitions between states are carried out using anoncollinear extension of the multiple-impurity Alexander-Anderson model and amagnetic force theorem which is derived and used to evaluate the total energygradient with respect to orientation of magnetic moments -- an important toolfor efficient navigation on the energy surface. By using this force theorem,the search for stable and metastable magnetic states as well as minimum energypaths revealing the mechanism and activation energy of transitions can becarried out efficiently. For Fe monolayer on W(110) surface, the model givesmagnetic moment as well as exchange coupling between nearest and next-nearestneighbors that are in good agreement with previous density functional theorycalculations. When applied to nanoscale Fe islands on this surface, themagnetic moment is predicted to be 10\% larger for atoms at the island rim,explaining in part an experimentally observed trend in the energy barrier formagnetization reversal in small islands. Surprisingly, the magnetic moment ofthe atoms does not change much along the minimum energy path for thetransitions, which for islands containing more than 15 atom rows along either$[001]$ or $[1\bar{1}0]$ directions involves the formation of a thin, temporarydomain wall. A noncollinear magnetic state is identified in a $7\times 7$atomic row Fe island where the magnetic moments are arranged in an antivortexconfiguration with the central ones pointing out of the $(110)$ plane. Thisillustrates how the model can describe complicated exchange interactions eventhough it contains only a few parameters. The minimum energy path between thisantivortex state and the collinear ground state is also calculated and thethermal stability of the antivortex state estimated.

physical review. b, condensed matter and materials physics

Calculations of magnetic states and minimum energy paths of transitions  using a noncollinear extension of the Alexander-Anderson model and a magnetic  force theorem