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Electronic structure of stripe ordered La$_{2-x}$Sr$_{x}$NiO$_{4}$ isinvestigated. The system with x=1/3 is insulator, in LSDA+U calculations, andshows charge and spin stripe, consistent with the experimental results. Highlycorrelated system of x=1/2 is studied by using exact diagonalization ofmulti-orbital many body Hamiltonian derived from LDA calculations and includingon-site and inter-site Coulomb interactions. The fluctuation of the residualspin on Ni$^{3+}$ (hole) site couples with the charge fluctuation betweenNi$^{3+}$ and Ni$^{2+}$ states and this correlation lowers the total energy.The resultant ground state is insulator with charge and spin stripe of theenergy gap 0.9eV, consistent with observed one. The on-site Coulomb interactionstabilizes integral valency of each Ni ion (Ni$^{3+}$ and Ni$^{2+}$), but doesnot induce the charge order. Two quantities, inter-site Coulomb interaction andanisotropy of hopping integrals, play an important role to form the charge andspin stripe order in a system of x=1/2.

Charge and spin stripe in La$_{2-x}$Sr$_{x}$NiO$_{4}$ (x=1/3,1/2)