  (Abridged) We investigate the growth of spiral-arm substructure in vertically
stratified, self-gravitating, galactic gas disks, using local numerical MHD
simulations. Our new models extend our previous 2D studies (Kim & Ostriker
2002), which showed that a magnetized spiral shock in a thin disk can undergo
magneto-Jeans instability (MJI), resulting in interarm spur structures and
massive fragments. Similar spur features have recently been seen in
high-resolution observations of several galaxies. Here, we consider two sets of
numerical models: 2D models that use a thick-disk gravitational kernel, and 3D
runs with explicit vertical stratification. When disks are sufficiently
magnetized and self-gravitating, the result in both sorts of models is the
growth of spiral-arm substructure similar to that in our previous razor-thin
models. Reduced self-gravity in thick disks increases the spur spacing to ~10
times the Jeans length at the arm peak. Bound clouds that form from spur
fragmentation have masses ~(1-3)x10^7 Msun each, a factor ~3-8 times larger
than in razor-thin models with the same gas surface density and stellar spiral
arm strength. We find that unmagnetized or weakly magnetized 2D models are
unstable to the wiggle instability (WI) previously identified by Wada & Koda
(2004), and proposed as a potential spur- and clump-forming mechanism.
However,our fully 3D models do not show this effect. Non-steady motions and
strong vertical shear prevent coherent vortical structures from forming,
evidently suppressing the WI that appears in 2D (isothermal) runs. We also find
no clear traces of Parker instability in the nonlinear spiral arm substructures
that emerge (in self-gravitating models), although conceivably Parker modes may
help seed the MJI at early stages since azimuthal wavelengths are similar.
