  In this work we conduct a numerical search of non-trivial mechanisms, leading
to new tendencies towards long-range ferromagnetic ordering in two-dimensional
materials. For this purpose we employ an original variant of pairwise
infinitesimal spin rotations technique to establish the magnetic transition
temperature as the rigid function of basic crystal's parameters. It favored the
numerical optimization of this function using modified genetic algorithm,
designed to harvest local extrema. It resulted in revealing the moderate
metallicity, accompanied by essential orbital anisotropy, as the prime
configuration, which provides the most favoring conditions to ferromagnetic
ordering, related to double-exchange and superexchange mechanisms.
