Two-dimensional (2D) materials have attracted interest in many applications, and have emerged as a unique family of nano-materials in physics and materials science. The ability to control the electronic states of two-dimensional (2D) materials is expected to lead to new physical phenomena and device concepts. Graphene is one of the most interesting 2D materials because of its unique band structure leading to electrons behaving like massless particles. There is a large number of materials composed of layers coupled by weak van der Waals forces, which allow for easy layer separation and arbitrary stacking of these. Even more recently, 2D materials with magnetism have been discovered. FM order has been found to exist even in an atomically thin layer in CrI3 [1]. Key property here is the magnetic anisotropy, and among layered systems one can find representatives whose magnetism is described more or less accurately by either the Heisenberg, Ising, or XY model.

In layered vdW magnets the exchange coupling between layers is rather weak and can be relatively easily modified. Regime of weak interlayer coupling represents transition between the more explored cases of isotropic bulk-like magnets and the ideal 2D limit (monolayer) [2]. Here we examine general features of finite temperature magnetic order in this regime by atomistic spin dynamics methods, employing stochastic LLG equation for spin system. The method is applied to systems with honeycomb lattice, where also the most well-known 2D magnet example – CrI3 - belongs. We study how is the ordering temperature affected by interlayer coupling and other properties in these systems, and how much this solution differs from the mean-field approach results.

References
[1] B. Huang, et al., Nature 546 (2017) 270
[2] Torelli and Olsen, 2D Mater. 6 (2019) 015028