Crystal Hartree-Fock calculations for ${\mathrm{La}}_2{\mathrm{NiO}}_4$ and ${\mathrm{La}}_2{\mathrm{CuO}}_4$

Ground-state properties of ${\mathrm{La}}_2{\mathrm{NiO}}_4$ and the isostructural compound ${\mathrm{La}}_2{\mathrm{CuO}}_4,$ the parent material of some high-$T_c$ superconductors, have been calculated using the Hartree-Fock approximation (HFA). To our knowledge, this is the first report in the literature in which calculations for these two materials are done for an infinite crystal using the HFA. The results show that both the nickelate and cuprate are antiferromagnetic (AFM) insulators, in agreement with experiments. The character of the highest occupied band in the cuprate is found to be in-plane O ${2p}_{x,y}$ strongly mixed with Cu ${3d}_{x^2{-y}^2},$ agreeing with the hypotheses of most Hubbard models for this problem. The spin densities show rather localized peaks with approximate cubic symmetry at Ni sites (due to two singly occupied $e_g$ orbitals) or approximate fourfold symmetry at Cu sites (due to $d_{x^2{-y}^2})$ and are small elsewhere. The corresponding form factor agrees rather closely with our earlier cluster calculations for the nickelate, while differing appreciably in the cuprate. We speculate on the reason for this. The results for the cuprate are consistent with magnetic neutron-scattering experiments: The shape of the form factor is in overall qualitative agreement with that measured on a sample of questionable stoichiometry; for a sample with presumably good stoichiometry, on which only one Bragg peak was measured, the absolute intensity is in remarkably good agreement with our calculated result. The latter includes the well-known correction for zero-point or quantum spin fluctuations. However, the shape of the form factor for the nickelate is in serious disagreement with experiment. We also calculated the energy splitting between AFM and ferromagnetic states, and, for both materials, found the corresponding Heisenberg exchange parameter J to be of the correct order of magnitude (about a factor of 3 smaller than the experimental values). The calculated J value for the cuprate is close to the result of a recent cluster Hartree-Fock calculation. We discuss the determination of J in density-functional theories, as well as in the HFA, in the Appendix.