Cluster study of the neutron-scattering form factor for antiferromagnetic ${\mathrm{KNiF}}_3$ and NiO

Motivated by difficulties in understanding the magnetism of the insulating parent of high-${\mathit{T}}_{\mathit{c}}$ supeconductors, we have studied the less covalent, and thus simpler, antiferromagnetic (AF) insulators NiO and ${\mathrm{KNiF}}_3$. We also consider the apparently covalent material ${\mathrm{La}}_2$${\mathrm{NiO}}_4$, which is closely related to the high-${\mathit{T}}_{\mathit{c}}$ superconductor parent ${\mathrm{La}}_2$${\mathrm{CuO}}_4$. Despite many studies of ${\mathrm{KNiF}}_3$ and NiO via cluster calculations, we found that a satisfactory ab initio cluster theory of the neutron form factor is lacking. We have carried out such a calculation in the unrestricted Hartree-Fock (UHF) approximation, taking the basic cluster as (${\mathrm{NiF}}_6$${)}^{4\mathrm{-}}$ and (${\mathrm{NiO}}_6$${)}^{10\mathrm{-}}$ for ${\mathrm{KNiF}}_3$ and NiO, respectively, treating the remaining lattice in the point-charge model. We show that correlation effects and Pauli repulsion corrections to the point charges are negligible in these cases. After correcting for the zero-point spin fluctuations, the UHF form factor agrees well with experiment in ${\mathrm{KNiF}}_3$, where the absolute value of the form factor is known for small scattering vectors q. The UHF calculations agree satisfactorily with the relative form factor data for NiO, which cover a large range of ‖q‖ (the absolute experimental values are not available); the agreement in shape includes the variations with q due to asphericity of the spin density. We also found that the UHF results on ${\mathrm{La}}_2$${\mathrm{NiO}}_4$, obtained by using similar methods, disagree sharply with experiment.