# Dzyaloshinskii-Moriya Interaction in Magneto-Ferroelectric Superlattices: Spin Waves and Skyrmions

## TL;DR

This paper investigates how Dzyaloshinskii-Moriya interactions influence spin configurations, spin waves, and skyrmion formation in magneto-ferroelectric superlattices, revealing their impact on magnetic and electric properties.

## Contribution

It introduces a comprehensive study of DM magnetoelectric coupling effects on spin structures and excitations in superlattices, combining ground-state analysis, spin wave theory, and Monte Carlo simulations.

## Key findings

- Non-collinear ground states in zero field
- Skyrmions appear under applied magnetic field
- DM interaction significantly alters spin wave modes

## Abstract

We study in this paper effects of Dzyaloshinskii-Moriya (DM) magnetoelectric coupling between ferroelectric and magnetic layers in a superlattice formed by alternate magnetic and ferroelectric films.Magnetic films are films of simple cubic lattice with Heisenberg spins interacting with each other via an exchange $J$ and a DM interaction with the ferroelectric interface. Electrical polarizations of $\pm{1}$ are assigned at simple cubic lattice sites in the ferroelectric films.We determine the ground-state (GS) spin configuration in the magnetic film. In zero field, the GS is periodically non collinear and in an applied field $\mathbf H$ perpendicular to the layers, it shows the existence of skyrmions at the interface. Using the Green's function method we study the spin waves (SW) excited in a monolayer and also in a bilayer sandwiched between ferroelectric films, in zero field. We show that the DM interaction strongly affects the long-wave length SW mode. We calculate also the magnetization at low temperature $T$. We use next Monte Carlo simulations to calculate various physical quantities at finite temperatures such as the critical temperature, the layer magnetization and the layer polarization, as functions of the magnetoelectric DM coupling and the applied magnetic field.Phase transition to the disordered phase is studied in detail.