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.

中文翻译：

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磁-铁电超晶格中的 Skyrmions 和自旋波

我们在本文中介绍了由交替的磁性和铁电薄膜形成的超晶格中铁电和磁性界面原子层之间的 Dzyaloshinskii-Moriya (DM) 磁电耦合的影响。我们考虑两种情况：磁性和铁电薄膜具有简单的立方晶格和三角形晶格。在这两种情况下，磁性薄膜的海森堡自旋通过交换 J 和 DM 与铁电界面的相互作用相互作用。假设铁电薄膜的极化为±1。我们确定磁性薄膜中的基态 (GS) 自旋配置并研究每种情况下的相变。在简单的立方晶格情况下，在零场中，GS 周期性地不共线（螺旋结构），并且在垂直于层的外加场 H 中，它表明界面处存在斯格明子。我们使用格林函数方法研究了在零场中在单层和夹在铁电薄膜之间的双层中激发的自旋波 (SW)。我们表明 DM 相互作用强烈影响长波长 SW 模式。我们还计算了低温下的磁化强度。我们使用接下来的蒙特卡罗模拟来计算有限温度下的各种物理量，例如临界温度、层磁化强度和层极化，作为磁电 DM 耦合和外加磁场的函数。研究了向无序相的相变。在三角形格子的情况下，我们展示了当铁电膜和铁磁膜之间的界面耦合相当强时，即使在零场中也会形成斯格明子和在外加场中形成斯格明子晶体。斯格明子晶体在外磁场的大范围内是稳定的。研究相变。