Sharafullin Ildus F, Diep Hung T
Institute of Physics and Technology, Bashkir State University, 32, Validy str, Ufa 450076, Russia.
Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, CNRS, UMR 8089, 2 Avenue Adolphe Chauvin, CEDEX, 95302 Cergy-Pontoise, France.
Entropy (Basel). 2020 Aug 4;22(8):862. doi: 10.3390/e22080862.
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 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.
在本文中，我们展示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）磁电耦合效应。我们考虑两种情况：磁性和铁电薄膜具有简单立方晶格和三角晶格。在这两种情况下，磁性薄膜具有通过交换相互作用以及与铁电界面的DM相互作用而相互作用的海森堡自旋。假设铁电薄膜的电极化强度为±1。我们确定磁性薄膜中的基态（GS）自旋构型，并研究每种情况下的相变。在简单立方晶格情况下，在零场中，基态是周期性非共线的（螺旋结构），在垂直于层的外加磁场H中，它在界面处显示出斯格明子的存在。使用格林函数方法，我们研究了在零场下单层以及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。接下来，我们使用蒙特卡罗模拟来计算有限温度下的各种物理量，如临界温度、层磁化强度和层极化强度，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。在三角晶格的情况下，我们表明即使在零场中也会形成斯格明子，并且当铁电薄膜和铁磁薄膜之间的界面耦合相当强时，在外加磁场中会形成斯格明子晶体。斯格明子晶体在较大的外磁场区域内是稳定的。研究了相变。
