Similarities and differences between nickelate and cuprate films grown on a ${\mathrm{SrTiO}}_3$ substrate

The recent discovery of superconductivity in Sr-doped ${\mathrm{NdNiO}}_2$ films grown on ${\mathrm{SrTiO}}_3$ started a novel field within unconventional superconductivity. To understand the similarities and differences between nickelate and cuprate layers on the same ${\mathrm{SrTiO}}_3$ substrate, here based on the density functional theory we have systematically investigated the structural, electronic, and magnetic properties of ${\mathrm{NdNiO}}_2$/${\mathrm{SrTiO}}_3$ and ${\mathrm{CaCuO}}_2$/${\mathrm{SrTiO}}_3$ systems. Our results revealed a strong lattice reconstruction in the case of ${\mathrm{NdNiO}}_2$/${\mathrm{SrTiO}}_3$, resulting in a polar film, with the surface and interfacial ${\mathrm{NiO}}_2$ layers presenting opposite displacements. To avoid the “polar catastrophe,” the ${\mathrm{NiO}}_2$ surface to the vacuum reconstructs as well. However, for ${\mathrm{CaCuO}}_2$/${\mathrm{SrTiO}}_3$, the distortions of those same two ${\mathrm{CuO}}_2$ layers were in the same direction. In addition, we found this distortion to be approximately independent of the studied range of film thickness for the nickelate films. Furthermore, we also observed a two-dimensional electron gas at the interface between ${\mathrm{NdNiO}}_2$ and ${\mathrm{SrTiO}}_3$, caused by the polar discontinuity, in agreement with recent literature. For ${\mathrm{NdNiO}}_2$/${\mathrm{SrTiO}}_3$ the two-dimensional electron gas extends over several layers, while for ${\mathrm{CaCuO}}_2$/${\mathrm{SrTiO}}_3$ this electronic rearrangement is very localized at the interface between ${\mathrm{CaCuO}}_2$ and ${\mathrm{SrTiO}}_3$. The electronic reconstruction found at the interface involves a strong occupation of the Ti $3d_{xy}$ state. In both cases, there is a significant electronic charge transfer from the surface Ni or Cu layers to the Ti interface layer. The interfacial Ni and Cu layers are hole and electron doped, respectively. By introducing magnetism and electronic correlation, we observed that the $d_{3z^2-r^2}$ orbital of Ni becomes itinerant while the same orbital for Cu remains doubly occupied, establishing a clear two- vs one-orbital active framework for the description of these systems. Furthermore, we also observed a strong magnetic reconstruction at the ${\mathrm{NdNiO}}_2$ surface to vacuum layer where magnetism is basically suppressed.

Figure 1

(a) Schematic unrelaxed slab model of (${\mathrm{NNO})}_n$/(${\mathrm{STO})}_4$ with the following convention: orange, Nd or Ca; gray, Ni or Cu; red, O; green, Sr; blue, Ti. Here, we fixed $a=b=3.905$ Å. We considered two undistorted STO layers (namely, with atomic positions fixed) to simulate the effects of the rest of the STO substrate. Schematic relaxed slab model of (b) (${\mathrm{NNO})}_4$/(${\mathrm{STO})}_4$ and (c) (${\mathrm{CCO})}_4$/(${\mathrm{STO})}_4$. (d) Electron localization function of the relaxed superlattice for (${\mathrm{NNO})}_4$/(${\mathrm{STO})}_4$ and (${\mathrm{CCO})}_4$/(${\mathrm{STO})}_4$.

Figure 2

(a) Possible polar catastrophe illustration predicted for (${\mathrm{NdNiO}}_2{)}_n$/${\mathrm{SrTiO}}_3$. (b) The displacements along the $c$ axis for the four layers of Ni or Ti atoms corresponding to different superlattices (${\mathrm{NNO})}_n$/STO ($n=1$–8). In Fig. 1 the notation $\mathrm{\Delta }M$ ($M={\mathrm{Ni}}_1$, ${\mathrm{Ni}}_2$, ${\mathrm{Cu}}_1$, ${\mathrm{Cu}}_2$, ${\mathrm{Ti}}_1$, and ${\mathrm{Ti}}_2$) was introduced. (c) The charge transfer of Ni and Ti atoms for different (${\mathrm{NNO})}_n$/(${\mathrm{STO})}_4$ ($n=1$–8), compared with the corresponding bulk values. (d) The main displacements along the $c$ axis for Cu or Ti atoms for different (${\mathrm{CCO})}_n$/(${\mathrm{STO})}_4$ ($n=1$–8). (e) The charge transfer of Ni and Ti sites for different (${\mathrm{CCO})}_n$/(${\mathrm{STO})}_4$ ($n=1$–8), compared with corresponding bulk values. In (c) and (e) the subscript “int” (“sur”) denotes interface (surface). Note that the single $M{\mathrm{O}}_2$ ($M=\text{Ni}$ or Cu) layer is both interface and surface for the $n=1$ case.

Figure 3

(a–c) Electronic density of states (DOS) of each layer for the case (${\mathrm{NNO})}_4$/(${\mathrm{STO})}_4$, calculated via DFT. The Fermi level is shown with dashed vertical lines. Results presented are for (a) the unrelaxed slab model, (b) the relaxed atomic positions superlattice model, and (c) the $20\%$ hole-doped NNO model. For comparison, we also show (d) the DFT electronic DOS of each layer for the case (${\mathrm{CCO})}_4$/(${\mathrm{STO})}_4$ using the relaxed superstructure. The Fermi level is the dashed vertical line.

Figure 4

Projected Ti band structure of the ${\mathrm{SrTiO}}_3$ layers for the nonmagnetic state. The Fermi level is shown with dashed horizontal lines. The weight of each Ti orbital is represented by the thickness of the lines. Note the $d_{xy}$ orbital, particularly at $\mathrm{\Gamma }$, is starting to be occupied because it is below the Fermi level. The electrons populating this portion of the Ti band arise from the Ni or Cu oxide films which, thus, become hole doped. (a) NNO/STO for various layers [label convention in Fig. 1] and (b) CCO/STO for various layers. For comparison, in (c) we show the Ti bands of STO (bulk form) displaying the typical band-insulator gap and with an unoccupied $d_{xy}$ band, as discussed in the text.

Figure 5

Ni and Cu projected local DOS corresponding to the $e_{2\mathrm{g}}$ orbital of (${\mathrm{NNO})}_4$/(${\mathrm{STO})}_4$ and (${\mathrm{CCO})}_4$/(${\mathrm{STO})}_4$ assuming a G-AFM-type magnetic configuration. The Fermi level is indicated with dashed lines. Note that we only show the local DOS of one Ni or Cu site at each layer.

Figure 6

(a) Schematic crystal structure of $AB{\text{O}}_2$ (electronic density $n=9$) with the following convention: orange, Sr or Nd; gray, Cu or Ni; and red, O. DOS near the Fermi level using the nonmagnetic states for (b) ${\mathrm{CaCuO}}_2$ and (c) ${\mathrm{NdNiO}}_2$.

Figure 7

Projected band structures of (a) ${\mathrm{CaCuO}}_2$ and (b) ${\mathrm{NdNiO}}_2$ for the nonmagnetic state. The Fermi level is shown with horizontal dashed lines. The weight of each orbital is represented by the thickness of the lines. Fermi surface of (c) ${\mathrm{CaCuO}}_2$ and (d) ${\mathrm{NdNiO}}_2$.

Figure 8

Projected band structures of Ni and interface Ti for the case (${\mathrm{NNO})}_2$/(${\mathrm{STO})}_4$ using $a=b=3.905$ Å and $a=b=3.943$ Å, respectively. The Fermi level is shown with horizontal dashed lines. The weight of each orbital is represented by the thickness of the lines.

Figure 9

Schematic relaxed slab model of (${\mathrm{NNO})}_n$/(${\mathrm{STO})}_4$ for G-AFM order ($U_{\mathrm{eff}}$ = 4 eV) with the following convention: orange, Nd or Ca; gray, Ni or Cu; red, O; green, Sr; and blue, Ti. Here, we fixed $a=b=3.905$ Å. We considered two undistorted STO layers (namely, with atomic positions fixed) to simulate the effects of the rest of the STO substrate.