  We analyze the magnetic form factor of Cu$^{2+}$ in low-dimensional quantum
magnets by taking the metal-ligand hybridization into account explicitly. In
this analysis we use the form of magnetic Wannier orbitals, derived from the
first-principles calculations, and identify the contributions of different
atomic sites. Having performed local density approximation calculations for
cuprates with different types of ligand atoms, we discuss the influence of the
on-site Coulomb correlations on the structure of the magnetic orbital. The
typical composition of Wannier functions for copper oxides, chlorides and
bromides is defined and related to features of the magnetic form factor. We
propose easy-to-use approximations of the partial orbital contributions to the
magnetic form factor in order to give a microscopic explanation for the results
obtained in previous first-principles studies.
