  Cool weakly ionized gaseous rotating disk, are considered by many models as
the origin of the evolution of protoplanetary clouds. Instabilities against
perturbations in such disks play an important role in the theory of the
formation of stars and planets. Thus, a hierarchy of successive fragmentations
into smaller and smaller pieces as a part of the Kant-Laplace theory of
formation of the planetary system remains valid also for contemporary
cosmogony. Traditionally, axisymmetric magnetohydrodynamic (MHD), and recently
Hall-MHD instabilities have been thoroughly studied as providers of an
efficient mechanism for radial transfer of angular momentum, and of density
radial stratification. In the current work, the Hall instability against
nonaxisymmetric perturbations in compressible rotating fluids in external
magnetic field is proposed as a viable mechanism for the azimuthal
fragmentation of the protoplanetary disk and thus perhaps initiating the road
to planet formation. The Hall instability is excited due to the combined effect
of the radial stratification of the disk and the Hall electric field, and its
growth rate is of the order of the rotation period.
