From perovskite to infinite-layer nickelates: hole concentration from x-ray absorption

Abstract

The difficulty of determining cation concentrations and oxygen stoichiometry in infinite-layer nickelate thin films has so far prevented clear experimental identification of the nickel electron configuration in the superconducting phase. We used soft x-ray absorption spectroscopy to study the successive changes in PrNiO$_x$ thin films at various intermediate stages of topotactic reduction with $x=2-3$. By comparing the Ni-$L$ edge spectra to single and double cluster ligand-field calculations, we find that none of our samples exhibit a pure $d^9$ configuration. Our quantitative analysis using the charge sum rule shows that even when films are maximally reduced, the averaged number of nickel $3d$ holes is 1.35. Superconducting samples have even higher values, calling into question the previously assumed limit of hole doping. Concomitant changes in the oxygen $K$-edge absorption spectra upon reduction indicate the presence of oxygen $2p$ holes, even in the most reduced films. Overall, our results suggest a complex interplay of hole doping mechanisms resulting from self-doping effects and oxygen non-stoichiometry.

Figures (18)

• Figure 1: Structure of (a) perovskite $R$NiO$_3$Garcia1992, (b) metastable, intermediate phase $R$NiO$_{2.5}$ with ordered oxygen vacancies Alonso1997, and (c) infinite-layer nickelates $R$NiO$_2$Crespin2005. Panels (d-g) show the Ni-$3d$ orbital energies for the two sets of $D_{4h}$ ligand fields used in the model calculations together with their nominal hole spin occupation for the different Ni configurations considered in the single cluster calculations. (h-k) Resulting spectra $I_{\rm XAS}\propto f"/ {\rm Energy}$, where $f"$ is the imaginary part of the scattering factor that was obtained from single cluster ligand-field calculations for the four different configurations sketched in (d-g). Each top panel show the individual spectra for in-plane ($x$) and out-of-plane ($z$) polarization of the incoming x-rays, together with the polarization averaged spectrum calculated by $I_{\rm av} = (2I_x + I_z)/3$. The bottom panels show the linear dichroism defined as $I_x-I_z$. The energy values have been shifted for $d^8$ by 857.1 eV to match the experimental data and for $d^7$ ($d^9$) additionally by +1 (-1) eV according to reference data Wang2000. Note that the spectra satisfy the charge sum rule, i.e. the integral of the polarization-averaged spectrum is proportional to the number of $3d$ holes. For better visualization we plot the height of the legend symbols for $I_{\rm pol. av.}$ and $I_{x-z}$ proportional to the mathematical integral of the shaded areas.
• Figure 2: Ni-$L$ edge XAS for in-plane ($x$) and out-of-plane ($z$) polarization for MBE-grown PNO on NGO at several intermediate reduction steps (left column), characterized by the given $c$, and, in the middle and right column, PNO on STO with STO capping comparing superconducting ("sc") PLD samples (right column) and non-superconducting MBE samples (middle column) obtained by two different reduction procedures (see text for details). All spectra have been post-edge normalized at 889 eV.
• Figure 3: Results from the charge sum rule analysis comparing the values of the integrated area over the $L_{3,2}$ region (845-880 eV) for the different samples as a function of out-of-plane Ni-Ni distance $c$. The colored point symbols show the results of the different pieces of MBE-1. The gray point was obtained from data measured on a NiO reference crystal. The filled, blue squares belong to samples of MBE-2. The dark yellow cross is obtained from analyzing published data of a MBE-grown NdNiO$_2$ film Parzyck2024a. The four unfilled markers correspond to the PLD-grown samples, where the hexagon indicates the result for a similar sample measured in Ref. Sahib2025. As reference values to calculate the $3d$ occupation, we used cluster calculations for NiO and the MBE-1 sample with $c$=3.77Å, as well as the zero for the $d10$ state, which leads to a proportionality factor of 0.0977 holes per unit of integral. For details on how the errors were estimated, see Methods section.
• Figure 4: The polarization dependent Ni-$L$ spectra and dichroism of the MBE-1 sample piece with $c=3.77$ Å can be well described by a double cluster calculation with both sites in a Ni 3$d^8$ high-spin configuration and some coupling between the sites.
• Figure 5: Results of the sum rule analysis, in which the number of $d$ holes, as determined from the integrated spectra, is plotted against the formal Ni oxidation state from zero to II. The number of $d$ holes is calculated as 10 minus the number of $d$ electrons from Fig. \ref{['Fig_SumRule_vsC']}. The two reference values from the 3.77Å sample and NiO (circles with crosses inside) were set to Ni(II) and used to determine the proportionality relation indicated by a straight line passing through the origin. The values of all other samples were placed on the line according to their $h_{3d}$ values (left vertical axis). For the oxygen reduced nickelates a low covalence and almost no charge transfer from O to Ni is assumed Li2021, therefore the number of $d$ holes can be translated into an oxygen content (right vertical axis). The light teal area shows where the dome of Pr$_{1-x}$Sr$_x$NiO$_2$ liesOsada2020 with a proportionality factor of one since previous papers calculated the number of $d$ electrons/holes from the formal stoichiometry Pan2022. The red diamonds show the results of our single cluster calculations for $d^8$ HS and $d^8$ LS (II) and the $d^9$ (I) configuration.