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 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 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.
Highlights
Magnetic skyrmions are topological configurations of spin vortices [1,2]
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
Using the same method of Monte Carlo simulation and the same definitions of the magnetic and ferroelectric order parameters as for the case of simple cubic lattice, we have studied the phase transition in the magneto–ferroelectric superlattice with the triangular lattice
Summary
Magnetic skyrmions are topological configurations of spin vortices [1,2]. Skyrmions and vortices have drawn enormous attention due to their fundamental and practical importance [3,4,5,6,7,8].Skyrmions hold great promise as a basis for future digital technologies [9,10,11,12,13,14,15,16,17,18]. Magnetic skyrmions are topological configurations of spin vortices [1,2]. Skyrmions and vortices have drawn enormous attention due to their fundamental and practical importance [3,4,5,6,7,8]. Skyrmions hold great promise as a basis for future digital technologies [9,10,11,12,13,14,15,16,17,18]. Information flow in next-generation spintronic devices could be associated with metastable isolated skyrmions guided along magnetic stripes [19,20]. Skyrmions have been experimentally observed, created and manipulated in a number of material systems, including magnetic materials [4,6,7,10,22,23,24,25,26,27,28,29,30], multiferroic materials
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