15-03U

We consider the spin-$\frac{1}{2}$ antiferromagnetic $XXZ$  Heisenberg model on the frustrated diamond spin chain in the $z$- or $x$-aligned external magnetic field. We investigate magnetization process of the frustrated diamond spin chain using the effective models found in the strong-coupling approximation for the case of the Heisenberg interaction anisotropy parameter $\Delta>1$. The theory is used to explain the experimental data for natural mineral azurite ${\rm Cu_{3}(CO_{3})_{2}(OH)_{2}}$.