Skyrmions and Spin Waves in Magneto–Ferroelectric Superlattices

Abstract

We present in this paper the effects of Dzyaloshinskii–Moriya (DM) magneto–electric coupling between ferroelectric and magnetic interface atomic layers in a superlattice formed by alternate magnetic and ferroelectric films. We consider two cases: magnetic and ferroelectric films have the simple cubic lattice and the triangular lattice. In the two cases, magnetic films have Heisenberg spins interacting with each other via an exchange J and a DM interaction with the ferroelectric interface. The electrical polarizations of ±1 are assumed for the ferroelectric films. We determine the ground-state (GS) spin configuration in the magnetic film and study the phase transition in each case. In the simple cubic lattice case, in zero field, the GS is periodically non collinear (helical structure) and in an applied field 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 temperatures. 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 magneto–electric DM coupling and the applied magnetic field. Phase transition to the disordered phase is studied. In the case of the triangular lattice, we show the formation of skyrmions even in zero field and a skyrmion crystal in an applied field when the interface coupling between the ferroelectric film and the ferromagnetic film is rather strong. The skyrmion crystal is stable in a large region of the external magnetic field. The phase transition is studied.

Mechanism of Topology Change of Flat Magnetic Structures

“…Magnetic vortices, first discovered in [ 9 ], have been studied in sufficient detail in the last two decades [ 10 ], but to date, interest in them has decreased. At the same time, there are certain signals about their possible use in spintronic devices [ 11 , 12 ], but not on a large scale, as previously assumed.…”

Vector Arithmetic in the Triangular Grid

“…Although we work with continuous coordinate system which uses real numbers, our work is essential in discrete mathematics, especially, in digital geometry to work, e.g., with digital images on the triangular grid. We should also note that hexagonal, triangular, honeycomb and other related grid structures are used in various other fields, e.g., in networks [ 12 , 13 , 17 , 18 , 19 ], in fractional calculus [ 20 , 21 ], in 3D printing [ 22 ], in chemical and physical modelling [ 23 ] and simulations [ 24 , 25 ], and in city planning [ 26 ], where continuous transformations play also crucial roles, thus our result may be applied. Additionally to the above mentioned fields, triangular grid is applied in skeletonization and thinning algorithms [ 27 , 28 ], in discrete tomography [ 29 ] and in cartography.…”

Vortex structure in magnetic nanodots: Dipolar interaction, mobile spin model, phase transition and melting

“…The phenomenological Landau-Ginzburg model introduced by I. Dzyaloshinskii [25] was microscopically derived by T. Moriya [26]. The DM interaction has been shown to generate skyrmions in thin films [27][28][29] and in magneto-ferroelectric superlattices [30][31][32].…”