Interplay of electric and magnetic fields in skyrmion phases of the classical Heisenberg model on a square lattice

Magnetic skyrmions are topologically stable spin textures that can be stabilized by Dzyaloshinskii-Moriya interaction and manipulated by external fields, making them promising for lowdissipation spintronic applications. In magnetoelectric materials, electric fields provide an additional control mechanism through spin-polarization coupling. Here we investigate, using classical Monte Carlo simulations, the combined effects of magnetic and electric fields on skyrmion phases in a ferromagnetic Heisenberg model on the square lattice with Dzyaloshinskii-Moriya interaction and magnetoelectric coupling via the d-p hybridization mechanism. We analyze spin and dipolar textures, structure factors, magnetization, polarization, and scalar chirality for different field orientations and strengths, identifying ferromagnetic, ferroelectric, spiral, skyrmion crystal, skyrmion gas, and bimeron phases, as well as the field-driven transitions between them. We show that electric fields strongly reshape the stability region and internal structure of chiral phases, inducing skyrmion deformation, transmutation into bimerons, and shifts of the chiral window in magnetic field. Concomitant changes in magnetization and polarization across phase boundaries reflect the intrinsic magnetoelectric coupling characteristic of type-II multiferroics. Our results highlight the role of localized magnetoelectric entities, such as skyrmions carrying electric quadrupolar textures, in mediating electric-field control of topological magnetic states, providing a microscopic framework relevant to multiferroic skyrmion-host materials.