  We show how low-energy electronic models derived from the first-principles
electronic structure calculations can help to rationalize the magnetic
properties of two lacunar spinel compounds GaM4S8 with light (M=V) and heavy
(M=Mo) transition-metal elements, which are responsible for different
spin-orbit interaction strength. In the model, each magnetic lattice point was
associated with the M4S4 molecule, and the model itself was formulated in the
basis of molecular Wannier functions constructed for three magnetic t2 bands.
The effects of rhombohedral distortion, spin-orbit interaction, band filling,
and the screening of Coulomb interactions in the t2 bands are discussed in
details. The electronic model is further treated in the superexchange
approximation, which allows us to derive an effective spin model for the energy
and electric polarization ($P$) depending on the relative orientation of spins
in the bonds, and study the properties of this model by means of classical
Monte Carlo simulations with the emphasis on the possible formation of the
skyrmionic phase. While isotropic exchange interactions clearly dominate in
GaV4S8, all types of interactions -- isotropic, antisymmetric, and symmetric
anisotropic -- are comparable in the case of GaMo4S8. Particularly, large
uniaxial exchange anisotropy has a profound effect on the properties of
GaMo4S8. On the one hand, it raises the Curie temperature by opening a gap in
the spectrum of magnon excitations. On the other hand, it strongly affects the
skyrmionic phase by playing the role of a molecular field, which facilitates
the formation of skyrmions, but makes them relatively insensitive to the
external magnetic field in the large part of the phase diagram. We predict
reversal of the magnetic dependence of $P$ in the case of GaMo4S8 caused by the
reversal of direction of the rhombohedral distortion.
