Since the discoveries of robust two-dimensional ferromagnetism in CrI₃ [1] and Cr₂Ge₂Te₆ [2], many research interests have focused on thermal stabilities of magnetism on van der Waals monolayers. In this work, we investigated the thermal evolutions of classical spins on 2D ferromagnetic honeycomb monolayers during simulated cooling and/or annealing by using the Monte Carlo method. Using the Heisenberg Hamiltonian with parameters proposed for CrI₃ [3], we closely reproduce the experimentally observed temperature- and in-plane magnetic field-dependences of the magnetization including the size of the Curie temperature [1]. We also find that in zero-field cooling CrI₃ monolayers exhibit multiple domains with high densities of domain walls. We will present how the domains behave as the temperature or magnetic field is changed.

[1] B. Huang, et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit, Nature 546.7657 (2017)
[2] C. Gong, et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals, Nature 546. 265 (2017)
[3] L. Chen, J.-H. Chung, B. Gao, T. Chen, M.B. Stone, A.I. Kolesnikov, Q. Huang, and P. Dai, 1 (2018).