  We construct stationary global configurations of both aligned and unaligned
logarithmic spiral perturbations in a composite disc system of stellar and
isopedically magnetized gaseous singular isothermal discs (SIDs) coupled by
gravity. The thin gaseous SID is threaded across by a vertical magnetic field
B_z with a constant ratio of the surface gas mass density to B_z. There exist
two classes of stationary magnetohydrodynamic (MHD) solutions with in-phase and
out-of-phase density perturbations. For both aligned and unaligned cases with
azimuthal periodicities |m|\geq 2 (m is an integer), there may be two, one, and
no solution situations, depending on the chosen parameters. For the transition
criteria from an axisymmetric equilibrium to aligned secular bar-like
instabilities, the corresponding T/|W| ratio can be much lower than the
oft-quoted value of T/|W|\sim 0.14, where T is the total rotational kinetic
energy and W is the total gravitational potential energy plus the magnetic
energy. The T/|W| ratios for the two sets of solutions in different ranges are
separated by m/(4m+4). For the unaligned cases, we study marginal stabilities
for axisymmetric (m=0) and non-axisymmetric (m\neq 0) disturbances. The
gravitational influence of an axisymmetric dark matter halo on the background
is also examined. The global analytical solutions and their properties are
valuable for testing and benchmarking numerical MHD codes. Our model analysis
contains more realistic elements and offers useful insights into the structures
and dynamics of disc galaxies consisting of stars and magnetized interstellar
medium. In the presence of star burst activities, supernovae, hypernovae,
superbubbles etc., our open magnetic field geometry in disc galaxies bears
strong implications on circumnuclear and spiral galactic winds.
