We study planar ferromagnetic spin-chain systems with weak antiferromagnetic
inter-chain interaction and dipole-dipole interaction. The ground state depends
sensitively on the relative strengths of antiferromagnetic exchange and dipole
energies kappa=J'a^2c/(g_L\mu_B)^2. For increasing values of \kappa, the ground
state changes from a ferromagnetic via a collinear antiferromagnetic and an
incommensurate phase to a 120^o structure for very large antiferromagnetic
energy. Investigation of the magnetic phase diagram of the collinear phase, as
realized in CsNiF_3, shows that the structure of the spin order depends
sensitivly on the direction of the magnetic field in the hexagonal plane. For
certain angular domains of the field incommensurate phases appear which are
separated by commensurate phases. When rotating the field, the wave vector
characterizing the structure changes continuously in the incommensurate phase,
whereas in the commensurate phase the wave vector is locked to a fixed value
describing a two-sublattice structure. This is a result of the competition
between the exchange and the dipole-dipole interaction.Comment: 12 pages, ReVTeX, 13 figures, to be published in Z. Physi