Polarizability of electrically induced magnetic vortex “atoms”

Electric field control of magnetic structures, particularly topological defects in magnetoelectric materials, draws a great attention, which has led to experimental success in creation and manipulation of single magnetic defects, such as skyrmions and domain walls. In this work we explore a scenario of electric field creation of another type of topological defects – magnetic vortices and antivortices. Because of interaction of magnetic and electric subsystems each magnetic vortex (antivortex) in magnetoelectric materials possesses quantized magnetic charge, responsible for interaction between vortices, and electric charge that couples them to electric field. This property of magnetic vortices makes possible their creation by electric fields. We show that the electric field, created by a cantilever tip, produces a “magnetic atom” with a localized spot of ordered vortices (“nucleus” of the atom) surrounded by antivortices (“electronic shells”). We analytically find the vortex density distribution profile and temperature dependence of polarizability of this structure and confirm it numerically by Monte Carlo simulation