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

Magnetic skyrmions, topologically stable spin textures, have attracted significant interest due to their potential applications in information storage and processing. They are typically stabilized by the Dzyaloshinskii-Moriya interaction in the presence of a magnetic field and can be manipulated by electric fields in magnetoelectric systems. Here we investigate, using Monte Carlo simulations, the behavior of skyrmions in a classical Heisenberg magnetoelectric model on the square lattice under combined magnetic and electric fields. We analyze spin and dipolar textures, structure factors, magnetization, chirality, and polarization for different field directions and magnitudes, identifying ferromagnetic, ferroelectric, spiral, skyrmion crystal, skyrmion gas, and bimeron phases, as well as the field-induced transitions between them. We find that the competition between electric and magnetic fields can destroy or transform skyrmion lattices into skyrmion-gas or bimeron phases. While magnetic fields induce chiral phases even in the presence of an electric field, electric fields strongly reshape the chiral region and deform skyrmion textures. This reciprocal influence between magnetic and electric orders reflects the intrinsic magnetoelectric coupling characteristic of multiferroic materials. Specifically, we observe the simultaneous sudden growth in magnetization with a switch-off in the polarization, typically observed in experiments. In this context, localized magnetoelectric entities, such as skyrmions carrying electric quadrupoles, exemplify the intertwined nature of spin and charge degrees of freedom, providing a microscopic basis for the control of topological states in ME systems and their potential use in spintronic applications.