Strain and composition dependence of orbital polarization in nickel oxide superlattices

A combined analysis of x-ray absorption and resonant reflectivity data was used to obtain the orbital polarization profiles of superlattices composed of four-unit-cell-thick layers of metallic LaNiO${}_3$ and layers of insulating $RX$O${}_3$ ($R=\text{La}$, Gd, Dy and $X=\text{Al}$, Ga, Sc), grown on substrates that impose either compressive or tensile strain. This superlattice geometry allowed us to partly separate the influence of epitaxial strain from interfacial effects controlled by the chemical composition of the insulating blocking layers. Our quantitative analysis reveals orbital polarizations up to 25$\%$. We further show that strain is the most effective control parameter, whereas the influence of the chemical composition of the blocking layers is comparatively small.

Figure 1

(a)–(f) XAS spectra (FY shifted by $+$1.5 for clarity) measured with linearly polarized light. Dotted grey lines show the results of Lorentzian fits to the tail of the La $M_4$ lines. The normalized difference spectra $[I_x\left(E\right)-I_z\left(E\right)]/\left[\frac{1}{3}(2I_x+I_z)\right]$ are shown directly below the corresponding spectra, together with the results of the cluster calculation. (g) Hole ratio $X_{\mathrm{av}}$ obtained via the sum rule (1) and (h) crystal field splitting $\Delta e_g$ obtained from the cluster calculation vs the in-plane lattice constant $a_{\mathrm{SL}}$ (see the Appendix) of LNO-LAO on LSAO (), LNO-LAO on YAO (), LNO-LAO on STO (Ref. 9; ), LNO-DSO on STO (), LNO-LGO on STO (), LNO-DSO on DSO (), and LNO-GSO on GSO (). (i) Sketch of the measurement geometry.

Figure 2

(Top) Polarization-dependent XAS spectra (TEY and FY) after subtraction of the La $M_4$ line (Lorentzian fit) together with the spectra obtained from our cluster calculation ($\gamma =0.6$, $\delta =0.4$, and $\Delta e_g=300$ meV). All spectra are normalized by their polarization-averaged integral [$A=(2I_x+I_z)/3$]. (Bottom) Normalized difference spectra $[I_x\left(E\right)-I_z\left(E\right)]/A$. The results of the cluster calculation are shown for $\gamma =0.6$, $\delta =0.4$, and different values of $\Delta e_g$, ranging from 0 to 300 meV.

Figure 3

Band structure (left) and Wannier orbitals (right) of bulk LaNiO${}_3$ (space group R$\overline{3}$c, Ref. 25): (a) downfolded to atomic-like Ni-$d$ and O-$p$ orbitals and (b) Wannier orbitals obtained by downfolding the antibonding Ni-$d$ O-$p$ bands to extended Ni-$\mathrm{d}$${}_{eg}$ orbitals, explicitly including covalency. The difference in phase of the wave functions is depicted by red and blue colors. The color coding for the band structure is as follows: red corresponds to Ni $e_g$, blue to Ni $t_{2g}$ and green to O $p$ character of the bands. The calculations were performed using the Stuttgart-NMTO code.[26, 27]

Figure 4

Reflectivity as a function of $q_z$ for the (a) LNO-LAO on LSAO, (b) LNO-DSO on STO, (c) LNO-LGO on STO, (d) LNO-DSO on DSO, and (e) LNO-GSO on GSO superlattice. The $q_z$ values at (002), chosen for the constant $q_z$ shown in Fig. 3 of the main text, are marked by green vertical lines and correspond to values of (a) 0.3880, (b) 0.4146, (c) 0.4120, (d) 0.4035, and (e) 0.4055 Å${}^{-1}$.

Figure 5

Experimental and simulated constant-$q_z$ energy scans at the (002) superlattice peak of (a) LNO-LAO on LSAO, (b) LNO-DSO on STO, (c) LNO-LGO on STO, (d) LNO-DSO on DSO, and (e) LNO-GSO on GSO. The experimentally obtained normalized difference [$I_{\sigma }\left(E\right)-I_{\pi }\left(E\right)]/[I_{\sigma }\left(E\right)+I_{\pi }\left(E\right)$] is shown directly below the corresponding spectrum together with the simulated one. The obtained layer-resolved orbital polarizations within the LNO layer stack, $P_B$ (interface layer) and $P_A$ (inner layers), are stated in each panel.

Figure 6

Averaged ($P_{\mathrm{av}}$) and layer-resolved ($P_A$, $P_B$) orbital polarizations obtained from the combined analysis of XAS and reflectivity as a function of the in-plane lattice constant $a_{\mathrm{SL}}$ measured by x-ray diffraction. (Inset) ratio $P_B/P_A$ vs the lattice constant ratio $c_{\mathrm{LNO}}/a_{\mathrm{LNO}}$ (full squares) with $c_{\mathrm{LNO}}=2c_{\mathrm{SL}}-c_{RX\mathrm{O}}$ and $a_{\mathrm{LNO}}=a_{\mathrm{SL}}$ and vs the size of the $X$ cation $r_X$ (Ref. 36; open stars) for superlattices under tensile strain. The $c$-axis lattice parameter of $RX$O was obtained from the Poisson ratio: $c_{RX\mathrm{O}}=\frac{2\nu }{\nu -1}(a_{\mathrm{SL}}-a_{RX\mathrm{O}}^{\mathrm{bulk}})+a_{RX\mathrm{O}}^{\mathrm{bulk}}$ using $\nu =0.26$.[37]

Figure 7

Ex situ atomic force microscopy pictures of the specimen surfaces before (left) and after (right) deposition for (a) LNO-DSO on DSO and (b) LNO-DSO on STO.

Figure 8

Reciprocal space maps around the pseudocubic (103) peak position for (4//4) u.c. SLs with composition (a) LNO-LAO on LSAO, (b) LNO-LAO on YAO, (c) LNO-DSO on STO, (d) LNO-LGO on STO, (e) LNO-DSO on DSO, and (f) LNO-GSO on GSO. The measurements were done using Cu $K_{\alpha }$ radiation ($E=8048$ eV).