  The recent observation of ferromagnetic order in two-dimensional (2D)
materials has initiated a booming interest in the subject of 2D magnetism. In
contrast to bulk materials, 2D materials can only exhibit magnetic order in the
presence of magnetic anisotropy. In the present work we have used the
Computational 2D Materials Database (C2DB) to search for new ferromagnetic 2D
materials using the spinwave gap as a simple descriptor that accounts for the
role of magnetic anisotropy. In addition to known compounds we find 12 novel
insulating materials that exhibit magnetic order at finite temperatures. For
these we evaluate the critical temperatures from classical Monte Carlo
simulations of a Heisenberg model with exchange and anisotropy parameters
obtained from first principles. Starting from 150 stable ferromagnetic 2D
materials we find five candidates that are predicted to have critical
temperatures exceeding that of CrI3. We also study the effect of Hubbard
corrections in the framework of DFT+U and find that the value of U can have a
crucial influence on the prediction of magnetic properties. Our work provides
new insight into 2D magnetism and identifies a new set of promising monolayers
for experimental investigation.
