Surface anisotropy in a magnetic cylinder induced by the displacement of a vortex core

In this article we investigate the induction of a surface anisotropy due to the displacement of the vortex core in a cylindrical nanostructure. In fact, the effect of the displacement of the vortex core in the dipolar energy can be modeled simply as a surface anisotropy of the form E_s=K_s∫_Sm dS(n̂·m̂)²/2. Moreover, the surface anisotropy constant K_s is proportional to the cylinder in-plane demagnetizing factor in the direction of the core deviation, N_y(L/R), i.e., K_s=μ₀M₀ ²RN_y(L/R), where R and L are the radius and the thickness of the cylinder, respectively. Our results show that the term of the nontrivial dipolar energy caused by the charges in the cylinder mantle can be replaced by a simple integral E_s that increases the efficiency of the numerical calculations in the analytical study of the displacement of the vortex core in magnetic vortices.