Infinite-layer $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_2$: ${\mathrm{Ni}}^{1+}$ is not ${\mathrm{Cu}}^{2+}$

The Ni ion in $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_2$ has the same formal ionic configuration $3d^9$ as does Cu in isostructural $\mathrm{Ca}\mathrm{Cu}{\mathrm{O}}_2$, but it is reported to be nonmagnetic and probably metallic whereas $\mathrm{Ca}\mathrm{Cu}{\mathrm{O}}_2$ is a magnetic insulator. From ab initio calculations we trace its individualistic behavior to (1) reduced $3d–2p$ mixing due to an increase of the separation of site energies $({\epsilon }_d–{\epsilon }_p)$ of at least $2\mathrm{eV}$, and (2) important $\mathrm{Ni}3d(3z^2-r^2)$ mixing with $\mathrm{La}5d(3z^2–r^2)$ states that leads to Fermi surface pockets of $\mathrm{La}5d$ character that hole dope the $\mathrm{Ni}3d$ band. Correlation effects do not appear to be large in $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_2$. However, ad hoc increase of the intra-atomic repulsion on the Ni site (using the $\mathrm{LDA}+\mathrm{U}$ method) is found to lead to a correlated state: (i) the transition metal $d(x^2-y^2)$ and $d(3z^2-r^2)$ states undergo consecutive Mott transitions; (ii) their moments are antialigned leading (ideally) to a “singlet” ion in which there are two polarized orbitals; and (iii) mixing of the upper Hubbard $3d(3z^2–r^2)$ band with the $\mathrm{La}5d\left(xy\right)$ states leaves considerable transition metal $3d$ character in a band pinned to the Fermi level. The magnetic configuration is more indicative of a ${\mathrm{Ni}}^{2+}$ ion in this limit, although the actual charge changes little with $U$.

Figure 1

(Color online) Crystal structure of $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_2$, isostructural to $\mathrm{Ca}\mathrm{Cu}{\mathrm{O}}_2$. Ni ions are in the origin and La ions in the center of the unit cell. It has no axial oxygens.

Figure 2

LDA paramagnetic band structure of $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_2$. The $\mathrm{Ni}3d(x^2-y^2)$ band crosses the Fermi level (zero energy) very much as occurs in cuprates (see Fig. 3). The $\mathrm{La}4f$ bands lie on $2.5–3.0\mathrm{eV}$. The $\mathrm{La}5d(3z^2–r^2)$ band drops below $E_F$ at $\Gamma$ and $A$.

Figure 3

“Fatband” representation of $\mathrm{Ni}3d(x^2–y^2)$ in LDA. This band appears at first very two-dimensional, but is not because (1) the saddle point at $X(0,\pi ∕a,0)$ is not midway between the $\Gamma$ and $M(\pi ∕a,\pi ∕a,0)$ energies, and (2) $k_z$ dispersion between the $X$ and $R(0,\pi ∕a,\pi ∕c)$. The dispersions along the $X–R$ and $M–A$ lines (not shown in this figure) are simple cosine-like and dispersionless, respectively.

Figure 4

(Color online) Paramagnetic Fermi surface in the local density approximation. In the center (not visible), i.e., $\Gamma$, there is a sphere [a radius $0.25(\pi ∕a)$] having $d(3z^2-r^2)$ character of Ni and La. The cylinder with radius $0.8(\pi ∕a)$ contains $\mathrm{Ni}d(x^2-y^2)$ holes, whereas another sphere [a radius $0.4(\pi ∕a)$] at each corner contains $\mathrm{Ni}d\left(zx\right)$ electrons.

Figure 5

LDA band structures of $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_2$, graphed on the same energy scale. Top panel: paramagnetic; bottom panel: antiferromagnetic. The $\mathrm{Ni}3d$ bands lie above $-3\mathrm{eV}$ and are disjointed from the $\mathrm{O}2p$ bands (not shown) which begin just below $-3\mathrm{eV}$. The antiferromagnetism introduces the gap in the $\mathrm{Ni}dp\sigma$ band midway between $\Gamma$ and $M$ in the range $0–1\mathrm{eV}$. The symmetry points are given such as $(0,0,x)$ for $\Gamma \left(Z\right)$, $(1∕2,1∕2,x)$ for $X\left(R\right)$ and $(1,0,x)$ for $M\left(A\right)$. $x$ is zero for the first symbols and 1 for the symbols in parentheses.

Figure 6

Behavior of the Ni magnetic moment vs the interaction strength $U$ in antiferromagnetic $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_2$.

Figure 7

(Color online) Change of the $\mathrm{Ni}3d(3z^2–r^2)$ and $3d(x^2–y^2)$ densities of states as on-site Coulomb interaction $U$ increases. One can easily identify a splitting (“Mott transition”) of the $3d(x^2–y^2)$ states occurring near $U=0$, and the light (green) lines outline their path with increasing $U$ (majority is solid, minority is dashed). A distinct Mott transition involving oppositely directed moment of the $3d(3z^2–r^2)$ states is outlined with the dark (purple) lines. This moment is oppositely directed. The conceptual picture is also complicated by the splitting even at $U=0$ which persists in the majority states, leaving a band at $E_F$ with strong $\mathrm{Ni}3d(3z^2–r^2)$ character as well as the expected upper Hubbard band at $4\mathrm{eV}$.

Figure 8

Isocontour plot of the spin density of the “singlet” Ni ion $(U=8\mathrm{eV})$ when there is an $x^2–y^2$ hole with spin up and a $3z^2–r^2$ hole with spin down. Dark and light surfaces denote isocontours of equal magnitude but opposite sign.

Figure 9

(Color online) Comparison of LDA projected paramagnetic DOS $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_2$ (upper panel) and $\mathrm{Ca}\mathrm{Cu}{\mathrm{O}}_2$ (lower panel). Note the separation of the $\mathrm{Ni}3d$ states from the $\mathrm{O}2p$ states in the upper panel, which does not occur for the more strongly hybridized cuprate.