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The recent observation of ferromagnetic order in two-dimensional (2D)materials has initiated a booming interest in the subject of 2D magnetism. Incontrast to bulk materials, 2D materials can only exhibit magnetic order in thepresence of magnetic anisotropy. In the present work we have used theComputational 2D Materials Database (C2DB) to search for new ferromagnetic 2Dmaterials using the spinwave gap as a simple descriptor that accounts for therole of magnetic anisotropy. In addition to known compounds we find 12 novelinsulating materials that exhibit magnetic order at finite temperatures. Forthese we evaluate the critical temperatures from classical Monte Carlosimulations of a Heisenberg model with exchange and anisotropy parametersobtained from first principles. Starting from 150 stable ferromagnetic 2Dmaterials we find five candidates that are predicted to have criticaltemperatures exceeding that of CrI3. We also study the effect of Hubbardcorrections in the framework of DFT+U and find that the value of U can have acrucial influence on the prediction of magnetic properties. Our work providesnew insight into 2D magnetism and identifies a new set of promising monolayersfor experimental investigation.

High throughput computational screening for 2D ferromagnetic materials: the critical role of anisotropy and local correlations