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Microscopic analysis of the magnetic form factor in low-dimensional cuprates

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.