  The magnetic properties of Cs$_2$Cu$_3$CeF$_{12}$ were investigated through
magnetization and specific heat measurements. Cs$_2$Cu$_3$CeF$_{12}$ is
composed of a buckled kagome lattice of Cu$^{2+}$, which is stacked along the b
axis. The exchange network in the buckled kagome lattice is strongly
anisotropic. Consequently, Cs$_2$Cu$_3$CeF$_{12}$ can be divided into two
subsystems: alternating Heisenberg chains with strong antiferromagnetic
exchange interactions and dangling spins. The dangling spins couple with one
another via effective exchange interactions, which are mediated by chain spins.
The dangling spins are further divided into two subsystems, DS1 and DS2. The
dangling spins in DS1 undergo three-dimensional ferromagnetic ordering at 3.14
K, while those in DS2 remain paramagnetic down to 0.35 K. The effective
interaction between the DS1 spins is approximately expressed by the
ferromagnetic $XXZ$ model with the $z$ direction parallel to the
crystallographic c axis. A magnetic phase diagram for $H {\parallel} c$ was
obtained and was analyzed within the framework of the molecular field
approximation. With increasing magnetic field, the dangling spins are polarized
and the magnetization curve exhibits a wide plateau at one-third of the
saturation magnetization.
