New Horizons of Micromagnetism: Electric Field Control of Topological Magnetic Structures

In magnetoelectric media, besides conventional micromagnetic interactions, such as exhange stiffnes, magnetic anisotropy, and magnetostatic interaction, an additional term should be added into the thermodynamic potential, which is proportional to the electric field and spatial derivatives of the magnetization vector. This inhomogeneous magnetoelectric interaction leads to the energy modulation in domain boundaries, manifesting as electrostatic attraction or repulsion of magnetic domain walls to the electrode, their refraction in the vicinity of the stripe electrode, as well as electric field-induced magnetic bubble domain nucleation. At the submicron level, the inhomogeneous magnetoelectric interaction enables electric field control of Bloch lines, the inhomogeneities inside the domain walls, and supports the vortex state of magnetization and skyrmions.