Electronic structure and magnetism in sodium nickelate: Density-functional and model studies

Abstract

The electronic structure and magnetism in $\mathrm{Na}\mathrm{Ni}{\mathrm{O}}_{2}$ are studied from density-functional calculations and by solving model Hamiltonians, suggested from the density-functional results, to understand the magnetic exchange. The density-functional calculations within the LSDA approximation yield a layered antiferromagnetic solution with ferro-orbital ordering of the $\mathrm{Ni}(d)$ orbitals arising from the Jahn-Teller distortion around the ${\mathrm{Ni}}^{3+}$ ion in agreement with the orbital ordering inferred from neutron diffraction. The weak ferromagnetic interaction within the layer $({J}_{F}\ensuremath{\approx}1\phantom{\rule{0.3em}{0ex}}\mathrm{meV})$ is caused by the 90\ifmmode^\circ\else\textdegree\fi{} Ni-O-Ni exchange following the Goodenough-Kanamori-Anderson rules, while the weaker antiferromagnetic interaction between the layers $({J}_{AF}\ensuremath{\approx}\ensuremath{-}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{meV})$ is mediated via a long Ni-O-Na-O-Ni superexchange path. In order to shed light on the differences between $\mathrm{Na}\mathrm{Ni}{\mathrm{O}}_{2}$ and $\mathrm{Li}\mathrm{Ni}{\mathrm{O}}_{2}$, which show very different magnetic behaviors in spite of the similarity of their crystal structures, we examine the effect of the coupling of the alkali atom (Na) motion to the electronic degrees of freedom on the interlayer exchange ${J}_{AF}$. A model Hamiltonian is proposed and solved by exact diagonalization and by using the variational Lang-Firsov method. We find that reducing the mass by going from Na to Li does reduce the strength of the magnetic exchange, but only by a small amount, so that the difference in mass alone cannot describe the differences in magnetic behavior between the two compounds. It is suggested that other electronic effects such as differences in orbital ordering could be responsible for the difference in magnetism between $\mathrm{Na}\mathrm{Ni}{\mathrm{O}}_{2}$ and $\mathrm{Li}\mathrm{Ni}{\mathrm{O}}_{2}$.