Hartree-Fock study of charge-ordered states in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ and ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_4$

Charge ordering in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_{x}M{\mathrm{O}}_4$ ($M=\mathrm{Cu}$ and Ni) has been studied by means of unrestricted Hartree-Fock calculations. The present calculations show that, while the vertical charge stripes along the (1,0) direction of the ${\mathrm{CuO}}_2$ square plane are favored in the cuprates with a charge-transfer energy Δ $\sim 2\mathrm{eV},$ the diagonal stripes are stable in the nickelates with Δ $\sim 4\mathrm{eV}.$ It has been found that the metal-centered and oxygen-centered stripes are nearly degenerate in energy both in the cuprates and in the nickelates. In the metal-centered diagonal stripe of the nickelates, the coupling between ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Ni}}^{3+}$ is calculated to be ferromagnetic. The stabilization of the various charge-ordered states by the elongation and tilting of the $M{\mathrm{O}}_6$ octahedra has also been studied.