  Ba$_2$Cu$_3$O$_4$Cl$_2$ has two inter-penetrating square Cu sublattices, one
with square root 2 times the in-plane spacing of the other. Isotropic magnetic
interactions between the two sublattices are completely frustrated. Quantum
fluctuations resolve the intrinsic degeneracy in the ordering direction of the
more weakly coupled sublattice in favor of collinear ordering. We present
neutron scattering and magnetization studies of the magnetic structure when the
Cu ions are substituted with Co. The Co spins create new magnetic interactions
between the two sublattices. The ordering behavior of both Cu sublattices is
retained largely unmodified. Between the phase transitions of the two
sublattices spin-glass behavior is observed. Magnetization results show a
strong enhancement to the ferromagnetic aspect of the magnetic structure. The
combination of glassy behavior and large moments strongly suggest that the Co
moments induce the formation of local canted states.
