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The recent observations of ferromagnetic order in several two-dimensional(2D) materials have generated an enormous interest in the physical mechanismsunderlying 2D magnetism. In the present prospective article we show thatDensity Functional Theory (DFT) combined with either classical Monte Carlosimulations or renormalized spin-wave theory can predict Curie temperatures forferromagnetic insulators that are in quantitative agreement with experiment.The case of materials with in-plane anisotropy is then discussed and it isargued that finite size effects may lead to observable magnetic order inmacroscopic samples even if long range magnetic order is forbidden by theMermin-Wagner theorem.

mrs communications

Theory and simulations of critical temperatures in CrI3 and other 2D  materials: Easy-axis magnetic order and easy-plane Kosterlitz-Thouless  transitions