Phase formation in hole- and electron-doped rare-earth nickelate single crystals

Figure 1a shows the as-grown LaNiO₃ boule together with the characterization by PXRD and a Laue diffraction image (Fig. 1e). The OFZ synthesis with a HKZ-type furnace of LaNiO₃ as well as PrNiO₃, La₃Ni₂O₇, and (La,Pr)₄Ni₃O₁₀ has been reported previously Guo et al. (2018); Wang et al. (2018a); Zhang et al. (2017b); Zheng et al. (2020); Dey et al. (2019); Puphal et al. (2023); Zheng et al. (2019); Liu et al. (2022); Zhang et al. (2020); Huangfu et al. (2020), although only a few details were given about the growth, phase diagram and the formation of secondary phases. As can be seen in Fig. 1a, the PXRD reveals the presence of a small amount of NiO in addition to the primary LaNiO₃ phase in a pulverized piece broken off from the boule. The emergence of secondary phases such as NiO will be discussed in detail for the other nickelate compounds in this study. In accord with previous studies on LaNiO₃, we refine the PXRD data in the rhombohedral space group $R\bar{3}c$, which also describes the structure of the doped La-based perovskites in our study (see Tab. 1, 2). As apparent from Laue diffraction (Fig. 1e), the growth direction of LaNiO₃ corresponds to the rhombohedral (110) direction. Under the application of a relatively strong force, the LaNiO₃ boule can be cleaved. The exposed surfaces are rough with small facets (Fig. 1c,d) that are mostly aligned in parallel to the (110) plane. The boule can also be cleaved along the orthogonal direction, which is displayed in Fig. 1d where the $(1\bar{1}0)$ direction points out of the picture while the $c$-axis lies in the horizontal plane (see also the corresponding sketch of the crystal structure in Fig. 1b).

Figures 2a,b diplay the boules and the PXRD patterns of our PrNiO₃ growth and the attempted growth of Pr₆Ni₅O₁₆. To achieve a boule of PrNiO₃ with a length of about 8 cm (see Fig. 2a), a continuous pressure of 300 bar was held for several days. The results of our PXRD analysis of PrNiO₃ and our other growths are summarized in Tab.  1, displaying the lattice constants and phase compositions in wt%. In agreement with previous studies, we refine the structure of PrNiO₃ in the orthorhombic space group $Pbnm$. In Fig. 2c we present the first phase diagram of NiO - PrO₂, which at the given pressure of 300 bar oxygen only contains four phases: NiO, PrNiO₃, Pr₄Ni₃O₁₀ and PrO₂.

Similarly to LaNiO₃ (Fig. 1b), we detect a minor amount of NiO in the stoichiometrically grown PrNiO₃ (Fig. 2b). Note that an admixture of NiO to the perovskite phase can become relevant after a topotactic reduction where ferromagnetic Ni forms which can dominate the signal in magnetic susceptibility measurements Ortiz et al. (2022). In cases of very small NiO admixture, its presence can be below the detection limit of standard laboratory PXRD. A method that allows to detect even subtle amounts of NiO inclusions is BSE imaging. In particular, unlike SE images that reflect the sample topography, BSE images reveal the spatial distribution of the elements. Figure 2d shows the simultaneously acquired SE and BSE images of a broken surface from the PrNiO₃ boule. In the latter image, NiO rich regions are clearly observed as the dark contrast.

In principle, the emergence of NiO rich regions should be alleviated in a growth from a precursor with Pr excess. However, we find that when varying the stoichiometry to a subtle Pr rich content, Pr₄Ni₃O₁₀ forms as an intergrown phase, especially in regions in proximity to the surface of the boule (see light contrast in the right panel of Fig. 2e). This occurs because impurity phases are usually pushed to the surface in an OFZ growth, as nucleation occurs in the core of the boule. Due to our external heating source the heat is only indirectly transported to the center resulting in a small gradient. Nonetheless this observation is in contrast to the pressure stability, as the center also sees the least pressure and Pr₄Ni₃O₁₀ is more stable at lower pressures.

For PrNiO₃, the growth direction corresponds to the orthorhombic (100) direction. Similarly to LaNiO₃, under the application of a relatively strong force, the PrNiO₃ boule can be cleaved. The exposed surfaces are rough with small facets that are mostly aligned in parallel to the (100) plane. The boule can also be cleaved along the orthogonal direction, where the $(010)$ direction points out of the plane and the (001) direction is the horizontal one. Notably, for both La- and Pr-compounds these cleaving patterns emerge even for the doped cases that will be discussed below.

Next, we turn to the synthesis of the $n=5$ Ruddlesden-Popper phase Pr₆Ni₅O₁₆ under 300 bar oxygen partial pressure. If successful, the compound could provide a perspective for topotactic reductions to the Pr₆Ni₅O₁₂ phase, in analogy to superconducting Nd₆Ni₅O₁₂ films Pan et al. (2021), and seems ideally suited for the high-pressure OFZ growth, as the pressure stability range should fall into the region accessible with the HKZ. However, instead of Pr₆Ni₅O₁₆, our PXRD characterization reveals a phase mixture of the perovskite and the $n=3$ phase Pr₄Ni₃O₁₀ (Fig. 2b), which are the phases that encompass the $n=5$ compound in the growth phase diagram. Similarly, we find in an attempted synthesis (not shown here) that also the $n=5$ variant La₃Eu₃Ni₅O₁₆ cannot be stabilized under 300 bar oxygen (see Tab. 1), in spite of the different ionic radii of La and Eu. This is distinct from other layered materials such as cuprates, where the mixing of ionic radii of the smaller rare earth ion with large Ba facilitates the stabilization of complex layered structures. Here we find that instead of the $n=5$, the $n=1$ and 3 Ruddlesden-Popper phases form. Hence, we conclude that at a given pressure of 300 bar, the synthesis of La- and Pr-based Ruddlesden-Popper phases higher than $n=3$ is likely unfeasible, as the existence of these phases is probably restricted to a very narrow range in pressure and composition space.

Electron-doping of PrNiO₃ can be achieved through substitution of the trivalent Pr ions by nominally tetravalent Ce ions. Here we carry out the OFZ growth at 280 and 300 bar oxygen partial pressure, respectively, aiming for 5% Ce doping of the perovskite phase. The upper panel in Fig. 3a shows the as-grown boules for 280 (top) and 300 bar (bottom). In comparison to the growth of the undoped compounds, a more homogeneous and viscous liquid forms during this growth, facilitating the growth of a long and homogeneous boule. In our characterization, the boules grown under 280 and 300 bar show similar phase formations, and hence we only focus on the latter in the following. Already for the small amount of 5% doping, a phase mixture between Ce-substituted PrNiO₃, (Pr,Ce)O₂, and NiO forms (see PXRD in Fig. 3a), presumably because the solubility limit of Ce is very low. The phase formation in different regions of the boule is best seen in BSE imaging, with Fig. 3b giving a wide-scale overview of the cross section of the boule along the growth direction.

In the OFZ growth, we are constantly feeding the weighed-in stoichiometry, thus when a solubility limit in growth is reached the seed crystal incorporates too little of the corresponding element. Hence this accumulates in the growth until an eutectic point (the minimum in the phase diagram, e.g 0.2 and 0.75 shown in Fig. 3c) in the phase diagram is reached. Here, the eutectic part freezes out and forms a layer of the eutectic stoichiometry (which contains a major part of the impurity phase). This eutectic can be seen in Fig. 3b, which shows a large crossection of the boule via BSE with elemental resolution. Here black lines are visible revealing these eutectic rings. Figure 3d shows a magnified version of these eutectic mixes, revealing three phases intergrown with each other. Note that for all subsequent BSE images in the other subchapters we only show the magnified versions of the eutectic parts in our boule and XRD focuses on these sections as well, but in all cases similar eutectic rings are formed and completely homogenous parts exist as well, similar to what is visible in Fig. 3b on the top right.

Nonetheless, the matrix is a perovskite phase as the Laue diffraction images from broken surfaces of the boule (not shown here) can be indexed in space group $Pbnm$, which suggests that large grains of Ce-substituted PrNiO₃ have crystallized in our boule, although BSE imaging reveals that the other two phases are intergrown in these grains (Figs. 3b,d). Importantly, we do not detect any traces of higher order Ruddlesden-Popper phases, such as Pr₄Ni₃O₁₀, which is in contrast to the Pr-excess growth of the undoped compound shown in Fig. 2e. Instead, we observe already the formation of (Pr,Ce)O₂ which is an endmember of the growth phase diagram. Hence, we propose the modified growth phase diagram shown in Fig. 3c for a Ce-mixed pseudo binary composition.

Next, we focus on the electron-doping of LaNiO₃. As a first attempt we attempted to synthesize crystals of composition La_0.8Ce_0.2NiO₃, which according to prior work on infinite-layer thin films is optimal for superconductivity, but observed that the growth was not very stable as can be seen in the image of the grown boule in Fig. 4a. Large crystals could not be extracted from the growth and we find a low wt% of the perovskite phase (see Tab. 2). Thus, we go for lower substitutions and we obtain large single-crystals with millimeter dimensions (as shown in Fig. 4a) for the nominal compositions La_0.95Ce_0.05NiO₃ and La_0.91Ce_0.09NiO₃. For the La-based compounds, we observe that already small Ce-substitution levels lead to the emergence of a competing phase, which in this case is the pyrochlore phase La₂Ce₂O₇. The presence of this secondary phase is detected in the PXRD patterns (Figs. 4b,c) and the BSE image (Fig. 4e), revealing that La₂Ce₂O₇ is embedded in the single crystalline perovskite matrix as eutectic rings together with NiO. Hence, Ce-substitution of the perovskite phase is challenging, although small crystals of (La,Pr)_1-xCe_xNiO₃ surrounded by regions of secondary phases can be realized in the boule.

A different route to achieve electron-doping can be the substitution by tetravalent Zr ions. Such doping was recently proposed theoretically for the topotactically reduced $n=2$ compound La_2.4Zr_0.6Ni₂O₆ Worm et al. (2022) where superconducting behavior is expected according to the nominal valence of Ni. As a first step, we attempt to synthesize this material at a moderate pressure of 14 bar oxygen. While such pressure was sufficient to synthesize the non-substituted $n=2$ compound La₃Ni₂O₇ Liu et al. (2022), we find for the Zr-doped variant that a phase mixture between the perovskite and the double-perovskite phase La₂NiZrO₆ forms (see Tab. 2). As the $n=\infty$ phase is typically stable starting with 30 bar Zhang et al. (2017b), we reduce the pressure and attempt a synthesis at 2.5-4.5 bar (see Tab. 2). In this case, however, we obtain a mixture of the $n=0$ and $n=\infty$ phases, finally proving the destabilization of higher order Ruddlesden-Popper phases with electron doping.

As a next step, we focus on the synthesis of the perovskite phase and test the maximally possible Zr substitution content. To this end, we prepare a ”gradient rod” that is composed of sections with different substitution levels of Zr. The prepared sections correspond to 5%, 8.75%, 12.5%, 16.75%, and 20% Zr (Fig. 5a). During the growth, we observe that all substitutions help to stabilize the melt, while secondary phases emerge for 8.75% and higher substitutions. Notably, the growth conditions are stable even in the case of evolving phase mixtures. However, no large single-crystals form in these attempts due to the shrinking sizes of the perovskite domains, as evidenced in the BSE images, seen in the decrease of a single contrast matrix (see Figs. 5f, g). A rudimentary proposal for the pseudo-binary phase diagram is shown in Fig. 5h, which notably only provides points in the center, where our PXRD characterization (exemplary PXRD patterns in Figs. 5b,c) reveal the formation of the pure perovskite and perovskite double-perovskite mixtures at higher doping levels, respectively.

Additionally, we explore the phase formation for the growth of La_0.8Zr_0.2NiO₃ at various oxygen partial pressures ranging from 15, 25, 35 to 150 bar (not shown here). We find that for a stable growth of the perovskite phase at least 35 bar pressure is required. Above this pressure, however, we do not detect significant changes in the phase formation, nor the incorporated Zr-substitution content. These results indicate that the solubility limit of Zr in nickelates lies around 8%, which is also confirmed by a detailed EDS analysis (see Appendix B), where even for crystals from a growth with a nominally higher Zr substitution the detected content in the perovskite matrix does not exceed 8%. The formed double-perovskite phase can be considered as an impurity phase where Zr substitutes half of the Ni site, instead of the desired substitution of the La sites. Hence, one might suspect that Zr generally substitutes the Ni site, even for low Zr admixtures. However, our Rietveld refinement of the perovskite phase reveals that in this phase Zr solely occupies the La site. Moreover, we observe a solubility limit of approximately 8% also for substitutions with elements other than Zr (see below).

Motivated by these insights, we next carry out the growth of crystals with much lower Zr substitution content and optimized growth parameters. Pictures of the corresponding La_0.98Zr_0.02NiO₃ and La_0.95Zr_0.05NiO₃ boules are shown in Fig. 6. From the boules, we extract large and high-quality perovskite crystals, as confirmed by PXRD (Figs. 6a,b) and BSE imaging (Fig. 6d), as well as EDS analysis (see Appendix B).

Hole-doping of perovskite nickelates can be achieved through the substitution with divalent ions such as Ca and Sr. In a previous high-pressure flux growth, the synthesis of small Ca-substituted LaNiO₃ single-crystals was achieved Puphal et al. (2021), with 8% Ca content determined by XRD refinement, whereas EDS indicated a higher level of 12% in cleaved pieces. In an attempt to realize larger Ca-substituted crystals with the floating zone technique under oxygen pressures ranging from 200-300 bar, we perform growths with nominal compositions La_0.8Ca_0.2NiO₃ and Pr_0.8Ca_0.2NiO₃. However, we find that only the $n=1$ Ruddlesden-Popper phases La_1.6Ca_0.4NiO₄ and Pr_1.6Ca_0.4NiO₄ as well as NiO form for such high substitution levels (not shown here). Since our floating zone growth with Zr revealed a solubility limit around 8% (Fig. 5e), we next attempt the growth of La_0.92Sr_0.08NiO₃. However, we find that connecting the corresponding feed and seed rods at 300 bar pressure is unfeasible, due to a heavy oxidization and freezing of the melt. To circumvent these issues we start the growth at a lower pressure and by sequentially increasing it up to 300 bar a stable growth is achieved. The results of the growth are presented in Tab. 2.

To confirm the anticipated the solubility limit of Sr of 8%, we subsequently attempt the growth of La_0.84Sr_0.16NiO₃. Unlike in the 8% case, a direct connection at 300 bar pressure is possible, highlighting that an increase in pressure is necessary to stabilize the higher nominal Ni^3.16+ oxidation state compared to Ni^3.08+ in La_0.92Sr_0.08NiO₃. Figure 7a shows the PXRD of pulverized pieces broken off from different parts of the boule. As expected for the growth of hole-doped compounds where extreme oxygen pressures are required, a concentration gradient is observed towards the center of the boule (see inset in Fig. 7a). In particular, we find that the fraction of the desired perovskite phase decreases towards the center of the boule, which is in accord with an increasing oxygen deficiency reported in previous floating zone growths of LaNiO₃ Zheng et al. (2020). The wt% and lattice constants from three different regions of the boule are summarized in Tab. 2.

As a secondary phase in the PXRD, we detect the $n=1$ Ruddlesden-Popper phase, which is also evidenced in the BSE imaging as a light color (Figs. 7b,c). As can be seen especially in Figs. 7b,c, in the center of the boule the grains of the perovskite phase are immersed in a matrix of the $n=1$ Ruddlesden-Popper phase and NiO (Fig. 7b), whereas the situation is reversed in the outer regions, where the Ruddlesden-Popper phase and NiO form small inclusions in the perovskite phase (Fig. 7c). Such an intergrowth behavior appears to be a general characteristic for all investigated substitutions above 8% and points towards the existence of a general solubility limit in perovskite nickelates independent of the dopant species. In contrast, substitution levels far above 8% have been reported for thin film perovskite nickelates Lee et al. (2020), which might be facilitated by the epitaxial strain provided by the substrate.

Nevertheless, our EDS analysis (see Appendix B) performed locally on grains with the perovskite phase indicates that the Zr and Sr contents can reach values between 12 and 13% (see Tab. 2), which is comparable to the highest value detected by EDS in high-pressure flux grown Ca-substituted LaNiO₃ single-crystals Puphal et al. (2021). These values are substantially higher 8%, but it is possible that the EDS analysis includes a systematic overestimation of these dopants. In contrast, for the rare-earth element Ce, where the EDS analysis is based on the $M$ instead of the $K$-line, we find a maximum of 7(1)% substitution (Tab. 2), which is compatible with a solubility limit of 8%. In conclusion, complementary studies with analyses methods other than EDS are desirable to determine the maximum substitution content of Zr and Sr realizable in optical floating zone grown perovskite nickelates.

Recent investigations into the effects of hole- and electron-doping on perovskite nickelates have primarily utilized thin film samples Song et al. (2023); Patel et al. (2022). In electron-doped Nd_1-xCe_xNiO₃, films, a suppression of the metal-to-insulator transition of NdNiO₃ was reported, favoring a shift towards a metal-to-metal transition for Ce doping levels as subtle as 2.5% Song et al. (2023). In the following, we explore similar effects in our (Pr,Ce)NiO₃ crystals.

Figure 8 presents a comparative analysis of the electronic and magnetic properties of our undoped and Ce-doped PrNiO₃ crystals. Note that the crystals have been cut into oriented pieces and annealed in a high gas pressure autoclave at 600^∘C under an oxygen partial pressure of 600 bar for 5 days, followed by a rapid cooling down to room temperature. This methodical approach ensures the exclusion of the influences of oxygen deficiency on the measured properties. Figure 8a displays the expected sharp metal-to-insulator transition over several orders of magnitude in the resistivity in the undoped PrNiO₃ single-crystal around 128 K, consistent with previous literature Zheng et al. (2019). For our single crystals with a nominal composition of Pr_0.95Ce_0.05NiO₃, EDS indicates a lower realized Ce substitution level of around 2(1)%. We observe a metal-to-metal transition around 116 K in Fig. 8b. This change from a metal-to-insulator to a metal-to-metal transition is qualitatively similar to that in Nd_1-xCe_xNiO₃ films Song et al. (2023).

In the magnetic susceptibility, anomalies with hysteretic behavior occur at similar temperatures as the metal-to-insulator and metal-to-metal transition in PrNiO₃ and (Pr,Ce)NiO₃, respectively (Figs. 8c,d). These anomalies indicate the presence of an antiferromagnetic transition Zheng et al. (2019). Above the transition, the susceptibility can be well described by a Curie-Weiß law $\chi$ = $\frac{C}{T-\theta_{W}}$, which yields the Curie constant $C=2.20(6)$ emu K/mol Oe${}^{-1}=27.6(7)\cdot 10^{-6}$m³K/mol and $\theta_{W}=-91(1)$ K for (Pr,Ce)NiO₃. This is well comparable to undoped PrNiO₃ with a Curie constant $C=2.38(1)$ emu K/mol Oe${}^{-1}=29.9(1)\cdot 10^{-6}$m³K/mol and $\theta_{W}=-99(1)$ K. We note that the magnetic signal of our (Pr,Ce)NiO₃ sample contains a contribution from the intergrown (Pr,Ce)O₂ phase, which exhibits an antiferromagnetic transition at 12 K whose signature can be seen both in the resistivity and susceptibility (Figs. 8b,d).

The susceptibility curves in Figs. 8c,d are expected to be dominated by the paramagnetic signal of the Pr${}^{3}+$ cations. Nevertheless, the effective moment is extracted using $\mu_{eff}=\sqrt{3kC/N\mu_{B}^{2}}=2.828\sqrt{C}$. Assuming the effective paramagnetic moment of non-disproportionated Ni³⁺ LS ($\mu_{eff}=1.73\mu_{B}=\sqrt{3kC/N\mu_{B}^{2}}$), $C_{Ni^{3+}}$ is estimated to be $0.375$ emu K/mol. Subsequently, if we consider $C=C_{Ni}+C_{Pr}$, $\mu_{eff}$ of Pr is calculated to be 3.82 $\mu_{B}$ which is only slightly larger than the expected moment of 3.5 $\mu_{B}$ and the reported one for PrNiO₃ Klein et al. (2021).

Next, we characterize the physical properties of a selection of La-based compounds. To this end, we analyze large crystals of LaNiO₃, La_0.95Zr_0.05NiO₃, and La_0.91Ce_0.09NiO₃ by Laue diffraction and cut them into rectangular pieces with the $(1\bar{1}0)$ direction pointing out of the plane, while the $c$-axis and (110) direction lie in the horizontal plane (Fig. 9a). Subsequently, the surfaces of the shaped and oriented crystals are polished using a 1 $\mu$m grain size. The crystals are then annealed in a high gas pressure autoclave at 600^∘C under an oxygen partial pressure of 600 bar for 5 days, followed by quick cooling to room temperature. We find that oxygen annealing is required to alleviate the oxygen deficiency of the as-grown crystals, which induces antiferromagnetic orderZeng et al. (2020). Figure 9b) shows the resistivity of the annealed crystals measured along the $c$ axis. The high quality of our single-crystals is reflected in the large residual resistivity ratio (RRR) of LaNiO₃, with a value of 19, exceeding previously reported values Zhang et al. (2017b); Zheng et al. (2020); Dey et al. (2019); Tomioka et al. (2021); Puphal et al. (2023). The RRR value of the Zr-substituted crystal is found to be 3, and that of the Ce-substituted crystal is 43. The slope of the resistivity curve of all three crystals is similar, with Fermi-liquid behavior at temperatures below 100 K and a $T^{1.5}$ scaling behavior at higher temperatures. This is consistent with earlier reports of OFZ grown perovskite nickelates Zhang et al. (2017b); Guo et al. (2018). While the Ce substitution lowers the overall resistivity, as expected for electron doping, Zr substitution appears to show the opposite effect.

Due to the metallic nature, the magnetic properties of LaNiO₃ are not as simple as following the expected Curie laws, unlike PrNiO₃. Pure LaNiO₃ has complex magnetic correlations that can not be described by simple Pauli paramagnetism Wang et al. (2018a). A Stoner enhanced maximum (highlighted by an arrow) is observed in LaNiO₃ centered around 220 K (Fig. 9c), which cannot by described by simple Pauli paramagnetism. Zr doping leads to a complete suppression of this observed maximum in the magnetic susceptibility. As a result, the full temperature range of the susceptibility of the Zr doped compound can be captured by a Curie-Weiß fit, with $C=1.504(3)\cdot 10^{-3}$ emu K/mol Oe${}^{-1}=1.89(4)\cdot 10^{-8}$ m³K/mol and $\theta_{W}=-2.2(1)$ K. As discussed above, we take $C_{Zr}$ to be $C-0.375$. This results in $\mu_{eff}=3\mu_{B}$ which is comparable to an expected moment $\mu_{Zr^{2+}}=2.8\mu_{B}$ of a $J=2$ state, suggesting a magnetic Zr contribution. Notably, on the other hand we observe a similar Stoner enhanced maximum and a somewhat lower Curie tail for Ce substitution. In La_0.91Ce_0.09NiO₃, however, a considerable mass fraction is La₂Ce₂O₇. La₂Ce₂O₇ is solely diamagnetic and results in a small contribution in the susceptibility. Thus for the Ce doped crystal, the real mass of the perovskite phase was considered, determined from PXRD via Rietveld refinement.

To further characterize our samples and determine the oxidation states of the substituted ions, we investigate freshly cleaved surfaces of selected single crystals using XPS. Specifically, this technique offers insights into the effectiveness of the intended charge carrier doping. Due to the significant overlap and complex multi-component structures of the La 3$d$ and Ni 2$p$ core-level spectra, we will concentrate on a qualitative analysis in the following.

An overview of all XPS spectra across a wide binding energy range is displayed in Fig. 10a. In Fig. 10b, the peaks at 854.8 and 851.2 eV correspond to La 3$d_{3/2}$, while the doublet at 837.9 and 834.6 eV can be identified as La 3$d_{5/2}$, indicating the La³⁺ oxidation state. The La 3$d_{3/2}$ and Ni 2$p_{1/2}$ peaks overlap Mickevičius et al. (2006), and the Ni 2$p_{3/2}$ peak is accompanied by a satellite line, which is positioned approximately 6–7 eV higher in binding energies. The Ni 2$p_{1/2}$ peak follows at 872.3 eV.

Figure 10c focuses on the XPS of La_0.91Ce_0.09NiO₃. Ce 3$d$ is known to exhibit a very complex multiplet splitting, resulting in several peaks. Notably, the multiplet structure observed in our La_0.91Ce_0.09NiO₃ spectrum matches the characteristic spectrum of Ce⁴⁺ in CeO₂ Pfau, Schierbaum, and Göpel (1996), thereby confirming the presence of carrier doping in this system since Ce⁴⁺ is replacing La³⁺ sites. In contrast, Ce³⁺ would give rise to two doublets at 880.9 eV / 885.2 eV and 899.1 eV / 903.4 eV Bêche et al. (2008), which we do not observe.

In the case of the presence of Zr⁴⁺ in electron-doped La_1-xZr_xNiO₃, the corresponding peak of the Zr 3$d_{5/2}$ binding energy is expected around 182 eV Lackner et al. (2019). However, we observe two Zr 3d_5/2 doublets, corresponding to binding energies of 181.1 eV and 180 eV, clearly indicating a lower Zr valency, and likely even a mixed valence state (see reference data from ZrO₂ in Fig. 10d). This suggests that the anticipated electron doping might not have occurred in this system, which is consistent with the increase in resistivity observed in the Zr-substituted crystal, as opposed to the decrease in resistivity in the Ce-substituted crystal (Fig. 9b). Nevertheless, we cannot rule out that the shape of the spectrum in Fig. 10d is strongly influenced by surface effects, as in the case of Sr-doping, which is described below.

Lastly, we explore the possibility of achieving hole-doping by incorporating Sr²⁺ ions in La_0.92Sr_0.08NiO₃. Previous works have suggested that hole doping is realized in Sr-substituted nickelate thin films Li et al. (2019); Zeng et al. (2020); Lee et al. (2020); Gao et al. (2021); Osada et al. (2021), but no direct evidence of the Sr²⁺ valence state has been reported so far, to the best of our knowledge. In the XPS of our La_0.92Sr_0.08NiO₃ crystal, we find that the Sr 3$d$ multiplet exhibits several overlapping peaks (Fig. 10e), in particular the 3$d_{5/2}$ peaks at 131.8 eV and 133.8 eV, and the 3$d_{3/2}$ peaks at 133.6 eV and 135.6 eV. These peaks differ from the simpler 3$d$ doublet at 134.3 eV and 132.5 eV of Sr²⁺ in SrTiO₃ Vasquez (1992). Yet, our observed peak structure is closely similar to that of the Sr ions in La_0.4Sr_0.6CoO₃Wang et al. (2018b). In the cobaltate, the two doublets were ascribed to distinct surface and lattice Sr sites, due to the formation of SrO and Sr(OH)₂ on the surface. Such a scenario could apply similarly to the Sr ions in our nickelate sample.