16-07E

We consider the spin-1/2 antiferromagnetic $XXZ$ Heisenberg model on a two-dimensional network of weakly coupled frustrated diamond chains, i.e., a spin model related to the celebrated azurite compound. Using the strong-coupling approach we construct an effective Hamiltonian which yields the low-temperature high-field properties of the spin system. We examine effects of interchain interactions on localized-magnon physics.