  We suggest that the pseudo-scalar vacuum field (PSV) in the dark matter (DM)
sector of the Universe may be as important as the electromagnetic vacuum field
in the baryonic sector. In particular, the spin-spin interaction between the DM
fermions, mediated by PSV, may represent the strongest interaction between the
DM fermions due to the absence of the electric charge and the magnetic dipole
moment. Based on this assumption, we consider the influence of the spin-spin
interaction, mediated by PSV, on the spin precession of the DM fermions (e. g.
neutralino). In the secular approximation, we obtain the exact expression
describing the frequency of the precession and estimate the decoherence rate.
