Skyrmion phases in ground state of magnetoelectric bilayer induced by planar Dzyaloshinskii-Moriya interaction

Composite multiferroic films allow the existence of a wide range of stable magnetic skyrmion structures in the phase diagram, which can be used to create next-generation ultra-dense memory units. In this paper, we investigate the processes of formation of skyrmion lattice phases and continuously distributed skyrmion phases in the ground state of a magnetoelectric film consisting of a magnetic layer surrounded by two ferroelectric layers with a triangular lattice and Dzyaloshinskii-Moriya interfacial magnetoelectric interaction. The ground state is calculated using an artificial neural network, which approximates the ground state of the film as a function of macroscopic parameters. The proposed method for calculating the ground state has a number of advantages compared to classic gradient descent and allows one to construct a phase diagram of the dependence of the topological charge on the parameters of magnetic and magnetoelectric interaction. Using a combined method including gradient descent and an artificial neural network, we have mapped the phase diagram of the skyrmion topological charge for different combinations of exchange and magnetoelectric interaction parameters. Using a neural network to predict first approximations of the ground states allowed us to avoid the excessive computational costs required in the case of direct gradient descent with random initialization for the system of 3600 interdependent nonlinear equations for each spin and dipole component.

1. State assignment of Russian Federation for the implementation of scientific research by laboratories - 075-03-2021-193/5