Phase transitions in bilayer systems of weakly coupled ferromagnetic films

Abstract

The interaction between magnetic films with strong perpendicular magnetic anisotropy is of considerable interest due to applications in nanotechnology, spintronics, and data storage. These systems exhibit a variety of magnetic ordering patterns and phase transitions arising from the competition between intralayer exchange and dipolar interactions and interlayer exchange coupling. In this work, we investigate a ferromagnetic bilayer system consisting of two-dimensional films separated by a nonmagnetic spacer, in the absence of an external magnetic field. The system is modeled using the Ising model with short-range ferromagnetic exchange and dipolar interactions within each layer, together with a ferromagnetic interlayer coupling. The intralayer exchange constants are set to J1=1 and J2=1.5, while the dipolar interaction is identical in both layers, g1=g2=1. Weak interlayer couplings, J3=0.1 and J3=0.2, are considered. Under these conditions, the ground state is characterized by alternating stripe domains with widths h=1 and h=2 in layers 1 and 2, respectively. At higher temperatures, a tetragonal liquid (TL) phase emerges, characterized by mutually perpendicular stripe domains without orientational or positional order, before eventually reaching the paramagnetic phase. Monte Carlo simulations were performed using both the Wang–Landau (WL) and the Metropolis sampling under the short-time dynamics technique (STD) framework. The WL method was employed to address the main features of the phase transitions. STD was used to analyze the early-time evolution of the orientational order parameter from both ordered and disordered initial configurations, allowing the critical temperatures and critical exponents of the transitions to be determined. This approach is particularly useful for systems with long-range dipolar interactions, where long relaxation times and finite-size effects can hinder conventional equilibrium methods. Our results characterize the phase behavior of the coupled bilayer and reveal the influence of weak interlayer coupling on the ordering and critical properties of the system.

Keywords: magnetic bilayer anisotropic systems; phase transitions; weak coupling effect