Ab initiostudy of ground and excited states of NiO(100) monolayer

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Abstract
Ab initio periodic Hartree-Fock calculations are reported of ground and d d excited states of an unsupported NiO(100) monolayer in the ferromagnetic, ferrimagnetic, antiferromagnetic and fully frustrated spin alignments as a function of the lattice constant. The ground state is found to be highly ionic and insulating with a minimum energy lattice constant of 4.0 Å. The Ni(d8 ) configuration is [(xz )2 (yz )2 (xy )2 (z 2 )1 (x 2 -y 2 )1 ], as found previously for the bulk, despite the reduced dimensionality leading to a reduction in the number of nearest neighbours and difference in the ligand-field ordering. The valence band DOS resembles closely that of the bulk with a majority weight of O(p) states at the upper edge leading to a charge-transfer system. The Ni d states occur ~1 eV below the O(p) band and are dispersed over ~4.5 eV in three distinct sub-bands. The relative stability of the four spin alignments is antiferromagnetic > ferrimagnetic > ferromagnetic > fully frustrated, with differences in energy of 10.779 meV, 10.017 meV and 1.675 meV respectively at 4.0 Å. Values of -0.84 meV and -10.78 meV can be deduced for the direct spin-spin, Ed , and superexchange, Ese , interaction energies respectively, which compare with values of -1.5 meV and -7.0 meV found previously for the bulk at a lattice constant of 4.265 Å. Ese is found to decrease rapidly to -3.66 meV at 4.5 Å, unlike Ed which remains fairly constant. This reduction in Ese is attributed largely to the increase in the band gap of the monolayer compared with the bulk. For the ferromagnetic spin alignment at 4.0 Å variationally converged solutions have been obtained for the one-electron dxy dz 2 , dxy dx 2 -y 2 and spin-forbidden dx 2 -y 2 dz 2 excited states and the two-electron dxy /dyz dz 2 /dx 2 -y 2 excited state with excitation energies of 1.16 eV, 1.09 eV, 1.84 eV and 1.79 eV respectively. These are close to values that have been deduced from optical and EEL spectra and high-level cluster calculations. Converged solutions for the dxy dz 2 excited state in the ferromagnetic alignment have been obtained for the concentration range 1-4 excited states per 2 × 2 unit cell and in the other spin alignments for complete excitation at lattice constants from 3.9 to 5.0 Å. These show dxy dz 2 excitations, and by implication other d d excitations, to be highly local with an interaction energy of xy dz 2 excited state leads to values of Ed , the direct spin-spin coupling energy, which are an order of magnitude greater than the ground state values and appreciably in excess of the bulk value. Ese , on the other hand, remains approximately the same. The first ionized state is found to be essentially d8 , as it is in the bulk, with strong localization of the hole in a p orbital of a single O atom and retention of the local Ni moments. By direct analogy with the changes in the oxygen k -edge spectrum of Lix Ni1-x O the band gap in the NiO(100) monolayer is estimated to be ~5.3 eV from the gap between the hole band and the conduction band edge. The first electron addition state is found to be essentially d9 [(dz 2 )2 ]. The energy of the single charge-transfer excitonic state of a 2 × 2 unit cell is estimated to be to be ~5.6 eV, in close agreement with the band gap deduced from the DOS of the first ionized state.