Optical properties of $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_3$ films tuned from compressive to tensile strain

Materials with strong electronic correlations host remarkable—and technologically relevant—phenomena such as magnetism, superconductivity, and metal-insulator transitions. Harnessing and controlling these effects is a major challenge, on which key advances are being made through lattice and strain engineering in thin films and heterostructures, leveraging the complex interplay between electronic and structural degrees of freedom. Here we show that the electronic structure of $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_3$ can be tuned by means of lattice engineering. We use different substrates to induce compressive and tensile biaxial epitaxial strain in $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_3$ thin films. Our measurements reveal systematic changes of the optical spectrum as a function of strain and, notably, an increase of the low-frequency free carrier weight as tensile strain is applied. Using density functional theory (DFT) calculations, we show that this apparently counterintuitive effect is due to a change of orientation of the oxygen octahedra. The calculations also reveal drastic changes of the electronic structure under strain, associated with a Fermi surface Lifshitz transition. We provide an online applet to explore these effects. The experimental value of integrated spectral weight below 2 eV is significantly (up to a factor of 3) smaller than the DFT results, indicating a transfer of spectral weight from the infrared to energies above 2 eV. The suppression of the free carrier weight and the transfer of spectral weight to high energies together indicate a correlation-induced band narrowing and free carrier mass enhancement due to electronic correlations. Our findings provide a promising avenue for the tuning and control of quantum materials employing lattice engineering.

Figure 1

Full set of optical data at 10 K of five $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_3$ film/substrate combinations at different strains, and simultaneous Drude Lorentz fits to the full data set of each film/substrate combination $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_3$ on $\mathrm{Y}\mathrm{Al}{\mathrm{O}}_3\left(\mathrm{Y}\mathrm{N}\mathrm{O}\right), \mathrm{Nd}\mathrm{Al}{\mathrm{O}}_3\left(\mathrm{N}\mathrm{A}\mathrm{O}\right), \mathrm{La}\mathrm{Al}{\mathrm{O}}_3\left(\mathrm{L}\mathrm{A}\mathrm{O}\right), \mathrm{Nd}\mathrm{Ga}{\mathrm{O}}_3\left(\mathrm{N}\mathrm{G}\mathrm{O}\right), \mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3\left(\mathrm{S}\mathrm{T}\mathrm{O}\right)$. Blue dots and curves represent the bare substrate; red dots and curves represent the film/substrate combination. (a)–(d) $\mathrm{\Psi }\left(\omega \right)$ of the terahertz ellipsometry measurements. THz ellipsometric data were collected with an angle of incidence of ${65}^{\circ }$ (${60}^{\circ }$ for $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_3/\mathrm{Y}\mathrm{Al}{\mathrm{O}}_3$). (e)–(h) Transmission in terahertz range. (i)–(m) Infrared reflectivity measurements. (n)–(r) $\mathrm{\Psi }\left(\omega \right)$ angle of the visible ellipsometry measurements. (s)–(w) $\mathrm{\Delta }\left(\omega \right)$ angle of the visible ellipsometry measurements. Visible light ellipsometric data were collected with an angle of incidence of ${68}^{\circ }$.

Figure 2

(a) Optical conductivity spectra at 10 K of $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_3$ films at different substrate-induced in-plane strains indicated in the legend. These spectra roughly fall in two groups: Negative-strain spectra (red, orange, and green curves) display a clear peak at 0.8 eV separated from the Drude peak by a minimum at 0.5 eV. Positive-strain spectra (blue and brown curves) show a weak maximum, almost a shoulder, at approximately 0.65 eV. (b) Optical conductivity spectra calculated with density functional theory (DFT) of $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_3$ films for in-plane strains indicated in the legend and assuming a fixed scattering rate $\hslash /\tau =60$ meV.

Figure 3

Position of the maximum of the peak of the optical conductivity at $\sim 1$ eV, in experiments and in DFT calculations. An overall decrease of the peak position is observed as strain is varied from the most compressive to the most tensile.

Figure 4

(a)–(e) Optical spectral weight $W$ as a function of frequency from experiment at 10 K and DFT calculations for each strain value. (f) Experimental (closed symbols) and DFT (open symbols) evolution of the free carrier spectral weight $W\left({\mathrm{\Omega }}_D\right)$ of $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_3$ films as a function of strain. For the theoretical values of $-3.99\%$ strain the calculated crystal structure is $I4/mcm$; for all other strain values the structure converged to $C2/c$. The error bar applies to all experimental points and was determined by repeating the Kramers-Kronig analysis after multiplying the reflectivity with $1\pm 0.05$. (g) Strain dependence of the effective mass according to Eq. (2).

Figure 5

Calculated DFT optical conductivity (a) below and (b) above 0.5 eV of tetragonal structures without oxygen-octahedra rotations and tilts (red) compared to the fully distorted structures (blue) at $-2.3\%$ (dashed), 0.0% (solid), and $+2.4\%$ (dotted) strains assuming a fixed scattering rate of $\hslash /\tau =60$ meV.

Figure 6

(a) Calculated strain dependence of the in-plane (red) and out-of-plane (blue) DC conductivity using a fixed scattering rate of $\hslash /\tau =60$ meV. (b) Wannier model effective in-plane $t_{ab}$ (red) and out-of-plane $t_c$ (blue) hopping amplitudes, and (c) on-site energies of the $d_{z^2}$ (blue) and $d_{x^2-y^2}$ (red) Wannier orbitals.

Figure 7

(a) Rotation of the oxygen octahedra along the $x$ and $y$ axis (corresponding to out-of-plane tilts $\alpha$ and $\beta$) and along the $z$ axis (corresponding to the in-plane rotation angle $\gamma$) extracted from the relaxed DFT crystal structures. Note that the values of $\alpha$ and $\beta$ are very close. (b) Unit cell of $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_3$ and illustration of the tilt axes. (c) Evolution of the intra-$e_g$ crystal-field splitting, evaluated from the projected DFT density of states as a function of strain. (d) Calculated ratio of the in-plane to out-of-plane hopping amplitudes as a function of strain (see Appendix pp2).

Figure 8

DFT Fermi surface for 5 values of strain (columns). Each row corresponds to a different value of the out-of-plane momentum $k_z$ (in units of $\pi /c$). The Lifshitz transition is manifest when a small compressive (see $k_z=0.5$) or tensile (see $k_z=0.0$) strain is applied. Along each Fermi surface sheet, the magnitude of the in-plane Fermi velocity $v_x^2+v_y^2$ is color coded, demonstrating the overall increase of the in-plane velocity under tensile strain.

Figure 9

Temperature-dependent part of the DC resistivity, $\rho \left(T\right)-{\rho }_0$, of the five $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_3$ film/substrate combinations $\mathrm{Y}\mathrm{Al}{\mathrm{O}}_3$ ($-3.34\%$), $\mathrm{Nd}\mathrm{Al}{\mathrm{O}}_3$ ($-2.55\%$), $\mathrm{La}\mathrm{Al}{\mathrm{O}}_3$ ($-1.28\%$), $\mathrm{Nd}\mathrm{Ga}{\mathrm{O}}_3$ ($+0.68\%$), $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ ($+1.75\%$), where ${\rho }_0$ is the residual resistivity. The values of ${\rho }_0$ are 167, 48, 48, 68, and $50\mu \mathrm{\Omega }\mathrm{cm}$ for $\mathrm{Y}\mathrm{Al}{\mathrm{O}}_3, \mathrm{Nd}\mathrm{Al}{\mathrm{O}}_3, \mathrm{La}\mathrm{Al}{\mathrm{O}}_3, \mathrm{Nd}\mathrm{Ga}{\mathrm{O}}_3$, and $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$, respectively.

Figure 10

Fermi surface of the unstrained tetragonal structure without octahedral rotations and tilts calculated with DFT and a subsequent Wannier model construction (middle column). The second and fourth columns show the Fermi surface of the same model, but with the crystal-field splitting ${\mathrm{\Delta }}_c$ of $-2.3\%$ and $+2.4\%$ tetragonal structures, respectively. The first and last columns show the effect of scaling the hopping ratio $t_{ab}/t_c$ by 0.8 and 1.2 in addition to the modified ${\mathrm{\Delta }}_c$. Each row corresponds to a different value of the out-of-plane momentum $k_z$ (in units of $\pi /c$). Along each Fermi surface sheet the magnitude of the in-plane Fermi velocity $v_x^2+v_y^2$ is color coded. Note that the additional sheets visible in Fig. 8 are Fermi surface reconstructions due to a two-Ni-atom (twice as large) unit cell.

Figure 11

(a)–(c), DFT density of states projected on $d_{z^2}$ (blue) and $d_{x^2-y^2}$ (red) orbitals. (d)–(f) Energy momentum dispersion along the trajectory shown in the inset of (a), with orbital character for three different strain values: $-4.0\%$ [(a), (d)], 0.0% [(b), (e)], $+3.2\%$ [(c), (f)].