  Four different spin structures of two electrons and of two holes situated on
the lowest Landau levels (LLLs) are taken into account to investigate possible
bound states of the two-dimensional magnetic biexciton formed of two
magnetoexcitons with opposite wave vectors and antiparallel dipole moments. The
singlet and triplet states of the spins of two electrons and of two holes
separately, as well as of two para- and two ortho-magnetoexcitons are
considered. The general expressions describing the binding energy of the bound
states and the normalization conditions characterized by the effective spin
parameter for the corresponding wave functions are derived. The most favorable
of the four considered spin configurations happened to be the triplet-triplet
spin structure of two electrons and of two holes. In its frame a metastable
bound state with activation barrier comparable with two ionization potentials
of the magnetoexciton is revealed .
