  Here we report on the effect of rare earth Gd-doping on the magnetic
properties and magnetotransport of GaN two-dimensional electron gasses (2DEGs).
Samples are grown by plasma-assisted molecular beam epitaxy and consist of
AlN/GaN heterostructures where Gd is delta-doped within a polarization-induced
2DEG. Ferromagnetism is observed in these Gd-doped 2DEGs with a Curie
temperature above room temperature and an anisotropic spontaneous magnetization
preferring an out-of-plane (c-axis) orientation. At magnetic fields up to 50
kOe, the magnetization remains smaller for in-plane configuration than for
out-of-plane, which is indicative of exchange coupled spins locked along the
polar c-axis. The sample with the lowest Gd concentration (2.3 $\times$
$10^{14}$ cm$^{-2}$) exhibits a saturation magnetization of 41.1
$\mu_B/Gd^{3+}$ at 5 K revealing that the Gd ion spins (7 ${\mu}_B$) alone do
not account for the magnetization. Surprisingly, control samples grown without
any Gd display inconsistent magnetic properties; in some control samples weak
ferromagnetism is observed and in others paramagnetism. The ferromagnetic 2DEGs
do not exhibit the anomalous Hall effect; the Hall resistance varies
non-linearly with the magnetic field, but does not track the magnetization
indicating the lack of coupling between the ferromagnetic phase and the
conduction band electrons within the 2DEG.
