The magnetic fields of spiral galaxies have been extensively observed, particular by Rainer Beck and collaborators (e.g., Braun et al. 2010) using Faraday rotation. In NGC 6946 (Beck 2007), the field structure is uniform in the interarm regions, probably from the combing action of shear with little disruption from star formation. It is more chaotic in the arms, and even weaker on average in the arms than the interarms because of the strong random component in the arms. The total field strength in the arms should be higher than in the interarms because of compression from the spirals, but this higher field strength might not be seen with rotation measures if the field direction fluctuates on small scales.
Gravitational instabilities in spiral arm gas are enhanced by the lack of shear and the magnetic field (Elmegreen 1987), which tends to run parallel to the arms in the direction of the unstable flow. This field removes angular momentum from a growing condensation, as mentioned in Lecture 1. Kim & Ostriker (2001) have dubbed this the Magneto-Jeans instability, and modeled it numerically. Gas collapses along spiral arms into giant cloud complexes, aided by the parallel magnetic field. The dense gas then emerges downstream from the arms as interarm feathers.