  We report the magnetic and electronic properties of the bilayer ruthenate
Sr$_3$Ru$_2$O$_7$ upon Fe substitution for Ru. We find that
Sr$_3$(Ru$_{1-x}$Fe$_x$)$_2$O$_7$ shows a spin-glass-like phase below 4 K for
$x$ = 0.01 and commensurate E-type antiferromagnetically ordered insulating
ground state characterized by the propagation vector $q_c$ = (0.25 0.25 0) for
$x$ $\geq$ 0.03, respectively, in contrast to the paramagnetic metallic state
in the parent compound with strong spin fluctuations occurring at wave vectors
$q$ = (0.09 0 0) and (0.25 0 0). The observed antiferromagnetic ordering is
quasi-two-dimensional with very short correlation length along the $c$ axis, a
feature similar to the Mn-doped Sr$_3$Ru$_2$O$_7$. Our results suggest that
this ordered ground state is associated with the intrinsic magnetic instability
in the pristine compound, which can be readily tipped by the local magnetic
coupling between the 3$d$ orbitals of the magnetic dopants and Ru 4$d$
orbitals.
