  We explore the magnetic properties of isolated a-b planes of trinuclear
organometallic crystals, Mo3S7(dmit)3, in which an interplay of strong
electronic correlations and spin molecular-orbital coupling (SMOC) occurs. The
magnetic properties can be described by a XXZ+120, S=1 Heisenberg model on a
honeycomb lattice with single-spin anisotropy, D, which depends strongly on
SMOC. Based on ab initio estimates of SMOC in Mo3S7(dmit)3 crystals, we predict
that the honeycomb layers of Mo3S7(dmit)3 are Neel ordered. However, in
materials with a greater degree of magnetic frustration, Neel order can give
way to the large-D phase.
