Cluster study of the neutron-scattering form factor for antiferromagnetic KNiF3 and NiO.

Abstract

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}$${)}^{4\mathrm{\ensuremath{-}}}$ and (${\mathrm{NiO}}_{6}$${)}^{10\mathrm{\ensuremath{-}}}$ 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 \ensuremath{\Vert}q\ensuremath{\Vert} (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.