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Open AccessArticle

Skyrmions and Spin Waves in Magneto–Ferroelectric Superlattices

by 1,† and 2,*,†
1
Institute of Physics and Technology, Bashkir State University, 32, Validy str, Ufa 450076, Russia
2
Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, CNRS, UMR 8089, 2 Avenue Adolphe Chauvin, CEDEX, 95302 Cergy-Pontoise, France
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2020, 22(8), 862; https://doi.org/10.3390/e22080862
Received: 8 July 2020 / Revised: 29 July 2020 / Accepted: 1 August 2020 / Published: 4 August 2020
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. View Full-Text
Keywords: superlattice; magneto–ferroelectric coupling; spin waves; skyrmions; phase transition; Green’s function theory; Monte Carlo simulation superlattice; magneto–ferroelectric coupling; spin waves; skyrmions; phase transition; Green’s function theory; Monte Carlo simulation
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MDPI and ACS Style

Sharafullin, I.F.; Diep, H.T. Skyrmions and Spin Waves in Magneto–Ferroelectric Superlattices. Entropy 2020, 22, 862. https://doi.org/10.3390/e22080862

AMA Style

Sharafullin IF, Diep HT. Skyrmions and Spin Waves in Magneto–Ferroelectric Superlattices. Entropy. 2020; 22(8):862. https://doi.org/10.3390/e22080862

Chicago/Turabian Style

Sharafullin, Ildus F.; Diep, Hung T. 2020. "Skyrmions and Spin Waves in Magneto–Ferroelectric Superlattices" Entropy 22, no. 8: 862. https://doi.org/10.3390/e22080862

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