  The natural mineral azurite Cu$_3$(CO$_3$)$_2$(OH)$_2$ is a frustrated magnet
displaying unusual and controversially discussed magnetic behavior. Motivated
by the lack of a unified description for this system, we perform a theoretical
study based on density functional theory as well as state-of-the-art numerical
many-body calculations. We propose an effective generalized spin-1/2 diamond
chain model which provides a consistent description of experiments:
low-temperature magnetization, inelastic neutron scattering, nuclear magnetic
resonance measurements, magnetic susceptibility as well as new specific heat
measurements. With this study we demonstrate that the balanced combination of
first principles with powerful many-body methods successfully describes the
behavior of this frustrated material.
