Confinement-induced metal-to-insulator transition in strained LaNiO${}_3$/LaAlO${}_3$ superlattices

Using density functional theory calculations including a Hubbard $U$ term we explore the effect of strain and confinement on the electronic ground state of superlattices containing the band insulator LaAlO${}_3$ and the correlated metal LaNiO${}_3$. Besides a suppression of holes at the apical oxygen, a central feature is the asymmetric response to strain in single unit cell superlattices: For tensile strain a band gap opens due to charge disproportionation at the Ni sites with two distinct magnetic moments of 1.45${\mu }_{\mathrm{B}}$ and 0.71${\mu }_{\mathrm{B}}$. Under compressive stain, charge disproportionation is nearly quenched and the band gap collapses due to overlap of $d_{3z^2-r^2}$ bands through a semimetallic state. This asymmetry in the electronic behavior is associated with the difference in octahedral distortions and rotations under tensile and compressive strain. The ligand hole density and the metallic state are quickly restored with increasing thickness of the (LaAlO${}_3$)${}_n$/(LaNiO${}_3$)${}_n$ superlattice from $n=1$ to $n=3$.

Figure 1

Bulk LaNiO${}_3$. (a) Projected density of states of Ni $3d$ character (black dotted line) obtained within GGA $+$ $U$ ($U=4$ eV and $J=0.7$ eV). Positive (negative) values correspond to majority (minority) spin. Note that $d_{3z^2-r^2}$ (green line) and $d_{x^2-y^2}$ orbitals (orange dashed line) are degenerate in bulk LNO. (b) Electron density distribution of the unoccupied states integrated between $E_{\mathrm{F}}$ and $E_{\mathrm{F}}+2.5$ eV. La and O ions are denoted by purple and red spheres, respectively.

Figure 2

Band structure obtained within GGA $+$ $U$ of bulk LaNiO${}_3$ along the high-symmetry lines $\Gamma (0,0,0)–Z(0,0,\pi )–A(\pi ,0,\pi )–R(\pi ,\pi ,\pi )–Z(0,0,\pi )$ using a $\sqrt{2}a\times \sqrt{2}a\times 2a$ unit cell with $a$ being the lattice parameter of the pseudocubic cell. In (a) and (b) the $d_{3z^2-r^2}$ and $d_{x^2-y^2}$ character is emphasized by green triangles and light orange circles, respectively.

Figure 3

Total density of states for (LAO)${}_1$/(LNO)${}_1$ for the case of tensile (STO) (solid line, gray area), (DSO) (long-dashed blue line) and compressive strain (LAO) (short-dashed cyan line). Additionally, the DOS of monoclinic bulk LNO is shown with a red line. The inset shows a zoom-in around the Fermi level displaying the opening of a band gap for (LAO)${}_1$/(LNO)${}_1$ under tensile strain.

Figure 4

Projected density of states (PDOS) of Ni $3d$ states (black dotted line), $d_{3z^2-r^2}$ (green line) and $d_{x^2-y^2}$ orbitals (orange dashed line) in (LAO)${}_1$/(LNO)${}_1$ for (a) compressive (LAO) and (b) tensile (STO) strain. The lower panels show the PDOS of basal (orange dashed line) and apical (green line) oxygens. Note the charge disproportionation at the Ni sites and the reduced density at the apical oxygen sites.

Figure 5

Majority spin band structure of (LAO)${}_1$/(LNO)${}_1$ under compressive strain ($a_{\mathrm{LAO}}$). Note the reduced dispersion of the $d_{3z^2-r^2}$ band (green triangles) compared to bulk LNO caused by confinement and the opposite effect for the $d_{x^2-y^2}$ band (orange circles) due to the reduction of the in-plane lattice parameter.

Figure 6

Majority spin band structure of (LAO)${}_1$/(LNO)${}_1$ under tensile (STO) strain. $d_{3z^2-r^2}$ and $d_{x^2-y^2}$ character is emphasized by green triangles and orange circles, respectively. The direct band gap opens at A with a valence band maximum (VBM) of predominantly Ni1 character and conduction band minimum (CBM) with mostly Ni2 contribution.

Figure 7

Electron density distribution of the unoccupied states integrated between $E_{\mathrm{F}}$ and $E_{\mathrm{F}}+2.5$ eV in (LAO)${}_1$/(LNO)${}_1$ for (a) compressive (LAO) and (b) tensile (STO) strain. Note the reduction in hole density on the apical oxygen between Ni and Al, as well as the charge disproportionation at the Ni sites for tensile strain. La, O, and Al ions are shown in purple, red, and light gray, respectively.

Figure 8

(a) Projected density of states (PDOS) of $3d$ states for Ni at interface (IF) and in the central layer (IF-1) in (LaAlO${}_3$)${}_3$/(LaNiO${}_3$)${}_3$ for tensile (STO) strain. Total $3d$, $d_{3z^2-r^2}$, and $d_{x^2-y^2}$ character are denoted by black dotted, green, and orange dashed line, respectively. (b) Electron density distribution of unoccupied states (yellow) integrated between $E_{\mathrm{F}}$ and $E_{\mathrm{F}}+2.5$ eV. Note that only half of the simulation cell is shown. For color coding see Fig. 7.

Figure 9

Majority spin band structure of (LaAlO${}_3$)${}_3$/(LaNiO${}_3$)${}_3$ for tensile (STO) strain. Note the splitting of $d_{3z^2-r^2}$bands (green triangles) of Ni in the interface (IF) and (IF-1) layer, respectively. $d_{x^2-y^2}$ bands are emphasized by orange circles.

Figure 10

Strain dependence of the in-plane (red squares) and out-of-plane (blue circles) (a) bond angles and (b) Ni-O bond lengths in (LaAlO${}_3$)${}_1$/(LaNiO${}_3$)${}_1$; (c) NiO${}_6$ octahedral rotation ($\theta$) and tilt ($\phi$) angles, and (d) Glazer's rotation angles $\alpha$ and $\gamma$. The symbols at $0\%$ strain represent the bulk LNO values.