Analytical and Monte Carlo study of two antidots in magnetic nanodisks   with vortex-like magnetization
  How stable vortex-like magnetization in magnetic nanodisks with small aspect ratio ($L/R<<1$) is affected by two antidots is investigated analytically and by Monte Carlo simulations. For suitable ranges of the physical parameters this vortex presents bistable states when pinned around the antidots. The hysteresis loop obtained shows a central loop associated to the pinning mechanism of the vortex at the antidots. Our results agree qualitatively well with those provided by experiments and micromagnetic simulations. 
A.R. Pereira, A.R. Moura, W.A. Moura-Melo, D.F. Carneiro, S.A. Leonel,   and P.Z. Coura