Static and Dynamics of Topological Defects in Magnetic Dots

A Taylor expansion of dipole-dipole interaction in 2D systems defines a Landau-like local dipolar interaction in spin derivative field. The lowest order of this interaction gives the dipolar anisotropy. The next non-zero order is responsible for the appearance of magnetic vortices and hyperbolic defects. The following non-zero orders indicate the occurrence of higher topological defects such as double circle and of modulations. The arrangement of self-screened topological defects is discussed in agreement with the Monte Carlo simulations and experimental observations. Excited localized modes associated with these defects are classified.