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Four different spin structures of two electrons and of two holes situated onthe lowest Landau levels (LLLs) are taken into account to investigate possiblebound states of the two-dimensional magnetic biexciton formed of twomagnetoexcitons with opposite wave vectors and antiparallel dipole moments. Thesinglet and triplet states of the spins of two electrons and of two holesseparately, as well as of two para- and two ortho-magnetoexcitons areconsidered. The general expressions describing the binding energy of the boundstates and the normalization conditions characterized by the effective spinparameter for the corresponding wave functions are derived. The most favorableof the four considered spin configurations happened to be the triplet-tripletspin structure of two electrons and of two holes. In its frame a metastablebound state with activation barrier comparable with two ionization potentialsof the magnetoexciton is revealed .

Metastable bound states of the quasi-bimagnetoexcitons in the lowest Landau levels approximation