  As experimentally well established, YBa_2Cu_3O_6 is an antiferromagnet with
the magnetic moments lying on the Cu sites. Starting from this experimental
result and the assumption, that nearest-neighbor Cu atoms within a layer have
exactly antiparallel magnetic moments, the orientation of the magnetic moments
has been determined within a nonadiabatic extension of the Heisenberg model of
magnetism, called nonadiabatic Heisenberg model. Within this group-theoretical
model there exist four stable magnetic structures in YBa_2Cu_3O_6, two of them
are obviously identical with the high- and low-temperature structure
established experimentally. However, not all the magnetic moments which appear
to be antiparallel in neutron-scattering experiments are exactly antiparallel
within this group-theoretical model. Furthermore, within this model the
magnetic moments are not exactly perpendicular to the orthorhombic c axis.
