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

The Ruddlesden–Popper (RP) nickelates R_n+1Ni_nO_3n+1 (R = rare-earth ion) with the perovskite (n = ∞) or perovskite-derived crystal structures (n ≠ ∞) are prototypical quantum materials,¹ showing a plethora of electronic, orbital, and magnetic phases already without charge carrier doping.^2–6 The perovskite-derived phases with n = 1–3 have been actively studied since the 1980s.⁷ To synthesize the perovskite phase RNiO₃, high pressure is required to stabilize the Ni³⁺ oxidation state and the distorted crystal structure, where the octahedral tilt angles are determined by the radius of the R ion. The least distorted perovskite nickelate LaNiO₃ was first synthesized in 1957,⁸ whereas nickelates with R other than La were realized in 1991.⁹ The RNiO₃ compounds have been of long-standing interest due to their sharp metal-to-insulator transition^10–12 and magnetic ground state with an unconventional spin spiral.^13,14 Additionally, the metal-to-insulator transition is accompanied by an orthorhombic to monoclinic structural phase transition.¹² The transition temperatures of these phases decrease as the size of the R ion increases. One exception is the compound with the largest anion, LaNiO₃, which exhibits a rhombohedral structure and remains metallic and paramagnetic down to the lowest temperatures, provided that the oxygen content is stoichiometric.^15,16

Upon hole- or electron-doping of the Ruddlesden–Popper nickelate, new electronic phases can emerge,^17–22 along with potential functional properties.^23,24 In RNiO₃ powders, hole- and electron doping up to 10% has been achieved through the substitution of the R ion by divalent Sr/Ca and tetravalent Th/Ce ions, respectively.^25–28 Typically, the powder synthesis is carried out under high external oxygen gas pressures.⁹ Recent studies have reported substitutions in powders as high as 40%.²⁹ However, further investigations are needed to determine if such high substitution concentrations are homogeneously incorporated into the microstructure of the RNiO₃ powder grains.

Since 2019, the field has been reinvigorated³⁰ by the discovery of superconducting behavior in hole-doped rare-earth nickelates with an infinite-layer crystal structure.^31–36 This structure can be achieved through the topotactic oxygen deintercalation of the perovskite phase.^37–39 These infinite-layer nickelates with Ni¹⁺ are nominally isoelectronic and isostructural to cuprate high-temperature superconductors with Cu²⁺ ions.⁴⁰ Additionally, superconductivity has been observed in the undoped nickelate Nd₆Ni₅O₁₂,⁴¹ which, however, can be considered a self-doped cuprate analog.⁴² Yet, superconductivity in the material family of nickelates has only been observed in thin film samples,^29,43 even though the latest studies have indicated that it could be an intrinsic property of the bulk phase of doped infinite-layer nickelates.⁴⁴ Furthermore, theoretical studies propose that superconductivity may also arise in electron-doped nickelates, such as La_2.4Zr_0.6Ni₂O₆, where La³⁺ is partially substituted by tetravalent Zr⁴⁺ ions.²⁰ 

Currently, a direct synthesis of the infinite-layer phase of nickelates is unfeasible due to the highly metastable Ni¹⁺ state in square-planar NiO₂ units. Similarly, the direct synthesis of other Ruddlesden–Popper derived nickelates with NiO₂ planes, such as Nd₆Ni₅O₁₂, has yet to be achieved. However, well-established routes exist for the topochemical removal of the apical oxygen from the parent nickelate phases, such as using H₂/Ar gas or CaH₂ powder as a reducing agent.^37,41,45 In particular, the CaH₂-assisted reduction has been successfully demonstrated not only on perovskite thin films^31–36 and polycrystalline powders^43,46,47 but also on single-crystals^48,49 with volumes up to 1 mm³.⁵⁰ 

A technical breakthrough enabling the growth of large R_n+1Ni_nO_3n+1 single-crystals was the advent of the high-oxygen pressure high-temperature optical floating zone (OFZ) technique, yielding bulk single-crystals of LaNiO₃,^{15,16,50–53} PrNiO₃,⁵⁴ La₃Ni₂O₇,⁵⁵ and (La,Pr)₄Ni₃O₁₀.^56,57 However, a problem with oxygen transport toward the center of the boule was observed in this synthesis method.¹⁶ As a result, oxygen deficient phases may form, but they can be alleviated by post-annealing under high gas pressure in autoclaves.

Overall, the technical advances in perovskite single-crystal growth, as well as the demonstrated topotactic reduction of LaNiO₃ single-crystals to infinite-layer LaNiO₂,⁵⁰ call for the previously unexplored synthesis of doped perovskite single-crystals that provide the starting material for the reduction to the infinite-layer phase. In this work, we present the optical floating zone growth of single-crystals of doped perovskite and Ruddlesden–Popper phase nickelates under 300 bars of oxygen partial pressure and discuss the opportunities and limitations of this method. We begin with an overview of the synthesis of the undoped compounds LaNiO₃ and PrNiO₃, as well as an attempt at the growth of the n = 5 Ruddlesden–Popper nickelate Pr₆Ni₅O₁₆. As a key result of the study, we report the phase formations in Ce- and Zr-doped (La,Pr)NiO₃, which are nominally electron-doped. Furthermore, we discuss the first OFZ growth of Sr-doped LaNiO₃, which is nominally hole-doped.

Precursor powders were prepared by mixing the corresponding stoichiometries of La₂O₃ (99.99% Alfa Aesar), Pr₆O₁₁ (Alfa Aesar, 99.99%), and NiO (99.998% Alfa Aesar), as well as CeO₂ (99.99% Alfa Aesar), CaCO₃ (99.999% Alfa Aesar), SrCO₃ (99.998% Roth), ZrO₂ (99.978% Alfa Aesar), and Eu₂O₃ (99.995% Roth). Subsequently, the powders were ball-milled for 20 min, and the mixtures were transferred in alumina crucibles to box furnaces, followed by heating to 1100 °C. Cylindrically shaped feed and seed rods were prepared by ball-milling the sintered materials, which were filled into rubber forms with a 6 mm diameter. The rubber was evacuated and pressed in a stainless steel form filled with water using a Riken type S1-120 70 kN press. All rods were heat treated at 900 °C to avoid cracking or breaking due to the oxidization process when the density of the rod becomes too high.

The single-crystal growth was carried out in a high pressure, high-temperature optical floating zone furnace (model HKZ, SciDre GmbH, Dresden, Germany) that allows for gas pressures in the growth chamber up to 300 bars. The growth chamber has a length of 72 mm and a 20 mm wall thickness. A xenon arc lamp operating at 5 kW was used as a heating source with the rare vertical mirror alignment of the HKZ. The rods were then aligned in the HKZ on steel holders, followed by the installation of the high pressure chamber. Subsequently, the chamber was filled up to 14/30/85/200/300 bars of oxygen pressure and held at a flow rate of 0.1 l/min. The crucial part in the nickelate growth is the initial melt connection, which is complicated as we typically start with a mixture of the Ruddlesden–Popper phase (La,Pr)₂NiO₄ and NiO, which both have lower melting points than the desired perovskite phase. However, preannealing at high pressures leads to cracking and even breaking of the rods. Therefore, we either increased the power until a homogeneous zone melt was achieved or premelted the rods at the given pressure to perform the final phase. In the former case, achieving a homogeneous zone melt is necessary before connecting the two rods, but the starting process of the growth was often very challenging. Both procedures have been employed for the materials synthesized in this work and have proven to be equally successful. Notably, a premelting of the rods does not increase the oxygen content in the obtained boule, as the given oxygen pressure and oxygen transport in the melt stabilize this, and the subsequent growth is easier.

All growths were conducted under an oxidizing atmosphere, with the partial oxygen pressure tailored to yield the best outcome for each composition (see Tables I and II). Common to all compounds investigated here is the increase in melting temperature when the phase containing Ni³⁺ is formed. This effect is amplified by the endothermal oxidation process, which we counteract with a continuous increase in lamp power, particularly during the early stage of the growth. This means that newly introduced material will be largely overheated and become very fluid. Therefore, without premelting, the diameter of the grown boule is dictated by the flow of the low-viscosity melt, which requires constant feeding. For all growths, we found that a growth rate of 2 mm/h with an additional feed rate of 2 mm/h results in stable conditions.

Powder x-ray diffraction (PXRD) was performed at room temperature using a Rigaku MiniFlex diffractometer with Bragg Brentano geometry, Cu K_α radiation, and a Ni filter. Rietveld refinements were conducted with the FullProf software suite.⁵⁸ The x-ray Laue diffraction images were collected with a Photonic Science CCD detector using a standard W broad x-ray source operated at 35 kV and 40 mA. For indexing the Laue patterns, the software OrientExpress was used.

Electron microscopy images with both secondary electrons (SE) and backscattering electrons (BSE) were taken with a Zeiss Merlin electron microscope operated at 12 kV, 600 mA, at a sample distance of 5 mm. Energy-dispersive x-ray spectra (EDS) were recorded with a NORAN System 7 (NSS212E) detector in a Tescan Vega (TS-5130MM) SEM.

Magnetic susceptibility measurements were performed using a vibrating sample magnetometer [MPMS VSM superconducting quantum interference device (SQUID), Quantum Design] and electrical transport measurements with a Physical Property Measurement System (PPMS, Quantum Design).

X-ray photoelectron spectroscopy (XPS) data were collected using a commercial Kratos AXIS Ultra spectrometer and a monochromatized Al K_α source (photon energy, 1486.6 eV). The base pressure during XPS was in the low 10⁻¹⁰ mbar range. The spectra were collected using an analyzer with a pass energy of 20 eV. XPS spectra were analyzed using the CASAXPS software.⁵⁹ All samples were cleaved in a glove box, mounted on carbon tape or In foil, and transported under an inert atmosphere to the XPS chamber.

Figure 1(a) shows the as-grown LaNiO₃ boule together with the characterization by PXRD and a Laue diffraction image [Fig. 1(e)]. The OFZ synthesis with an HKZ-type furnace of LaNiO₃ as well as PrNiO₃, La₃Ni₂O₇, and (La,Pr)₄Ni₃O₁₀ has been reported previously,^{15,16,50–57} although only a few details were given about the growth, phase diagram, and formation of secondary phases. As can be seen in Fig. 1(a), 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 accordance with previous studies on LaNiO₃, we refine the PXRD data in the rhombohedral space group $R3̄c$⁠, which also describes the structure of the doped La-based perovskites in our study (see Tables I and II). As apparent from Laue diffraction [Fig. 1(e)], 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 [Figs. 1(c) and 1(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. 1(d), where the $(11̄0)$ 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. 1(b)].

Figures 2(a) and 2(b) depict 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. 2(a)], a continuous pressure of 300 bars was held for several days. The results of our PXRD analysis of PrNiO₃ and our other growths are summarized in Table I, which displays 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. 2(c), we present the first phase diagram of NiO–PrO₂, which at the given pressure of 300 bars of oxygen only contains four phases: NiO, PrNiO₃, Pr₄Ni₃O₁₀, and PrO₂.

Similarly to LaNiO₃ [Fig. 1(b)], we detect a minor amount of NiO in the stoichiometrically grown PrNiO₃ [Fig. 2(b)]. 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.⁴⁷ In cases of very small NiO admixtures, their presence can be below the detection limit of standard laboratory PXRD. A method that allows us to detect even subtle amounts of NiO inclusions is BSE imaging. In particular, unlike SE images, which reflect the sample topography, BSE images reveal the spatial distribution of the elements. Figure 2(d) 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 in the dark contrast.

In principle, the emergence of NiO rich regions should be alleviated by growth from a precursor with a Pr excess. However, we find that when varying the stoichiometry to a subtle Pr rich content, Pr₄Ni₃O₁₀ forms an intergrown phase, especially in regions in proximity to the surface of the boule [see light contrast in the right panel of Fig. 2(e)]. 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 bars of oxygen partial pressure. If successful, the compound could provide a perspective for topotactic reductions to the Pr₆Ni₅O₁₂ phase, in analogy to superconducting Nd₆Ni₅O₁₂ films,⁴¹ 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. 2(b)], 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 the n = 5 variant La₃Eu₃Ni₅O₁₆ cannot be stabilized under 300 bars of oxygen (see Table I), despite 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 the large Ba facilitates the stabilization of complex layered structures. Here, we find that instead of n = 5, the n = 1 and 3 Ruddlesden–Popper phases form. Hence, we conclude that at a given pressure of 300 bars, 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 the substitution of the trivalent Pr ions by nominally tetravalent Ce ions. Here we carry out the OFZ growth at 280 and 300 bars of oxygen partial pressure, respectively, aiming for 5% Ce doping of the perovskite phase. The upper panel in Fig. 3(a) shows the as-grown boules for 280 (top) and 300 bars (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 bars 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. 3(a)], 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. 3(b) giving a wide-scale overview of the cross section of the boule along the growth direction.

In OFZ growth, we are constantly feeding the weighed-in stoichiometry; therefore, 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. 3(c)] 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. 3(b), which shows a large cross section of the boule via BSE with elemental resolution. Here, black lines are visible, revealing these eutectic rings. Figure 3(d) 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 homogeneous parts exist as well, similar to what is visible in Fig. 3(b) 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. 3(b) and 3(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. 2(e). Instead, we already observe the formation of (Pr,Ce)O₂, which is an end member of the growth phase diagram. Hence, we propose the modified growth phase diagram shown in Fig. 3(c) 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. 4(a). Large crystals could not be extracted from the growth, and we find a low wt. % of the perovskite phase (see Table II). Therefore, we go for lower substitutions and obtain large single-crystals with millimeter dimensions [as shown in Fig. 4(a)] 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. 4(b) and 4(c)] and the BSE image [Fig. 4(e)], revealing that La₂Ce₂O₇ is embedded in the single crystalline perovskite matrix as eutectic rings together with NiO. Hence, the 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 is the substitution of tetravalent Zr ions. Such doping was recently proposed theoretically for the topotactically reduced n = 2 compound La_2.4Zr_0.6Ni₂O₆,²⁰ 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 bars of oxygen. While such pressure was sufficient to synthesize the non-substituted n = 2 compound La₃Ni₂O₇,⁵⁵ we find for the Zr-doped variant that a phase mixture between the perovskite and the double-perovskite phase La₂NiZrO₆ forms (see Table II). As the n = ∞ phase is typically stable starting with 30 bars,⁵² we reduce the pressure and attempt a synthesis at 2.5–4.5 bars (see Table II). In this case, however, we obtain a mixture of the n = 0 and n = ∞ 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 maximum 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. 5(a)]. During the growth, we observe that all substitutions help 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 by the decrease of a single contrast matrix [see Figs. 5(f) and 5(g)]. A rudimentary proposal for the pseudo-binary phase diagram is shown in Fig. 5(h), which notably only provides points in the center, where our PXRD characterization [exemplary PXRD patterns in Figs. 5(b) and 5(c)] reveals 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 bars (not shown here). We find that for stable growth of the perovskite phase, at least 35 bars of pressure are required. Above this pressure, however, we do not detect significant changes in the phase formation or 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 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 for 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 ∼8% for substitutions with elements other than Zr (see below).

Motivated by these insights, we next carried out the growth of crystals with a 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. 6(a) and 6(b)] and BSE imaging [Fig. 6(d)] as well as EDS analysis (see  Appendix B).

Hole-doping of perovskite nickelates can be achieved through 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,⁴⁸ 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 to 300 bars, we perform growths with nominal compositions of 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 at such high substitution levels (not shown here). Since our floating zone growth with Zr revealed a solubility limit around 8% [Fig. 5(e)], we next attempt the growth of La_0.92Sr_0.08NiO₃. However, we find that connecting the corresponding feed and seed rods at 300 bars of pressure is unfeasible due to 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 bars, stable growth is achieved. The results of the growth are presented in Table II.

To confirm the anticipated solubility limit of Sr of 8%, we subsequently attempted the growth of La_0.84Sr_0.16NiO₃. Unlike in the 8% case, a direct connection at 300 bars of 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 7(a) 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 toward the center of the boule [see inset in Fig. 7(a)]. In particular, we find that the fraction of the desired perovskite phase decreases toward the center of the boule, which is in accord with an increasing oxygen deficiency reported in previous floating zone growths of LaNiO₃.¹⁶ The wt. % and lattice constants from three different regions of the boule are summarized in Table II.

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. 7(b) and 7(c)]. As can be seen especially in Figs. 7(b) and 7(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. 7(b)], whereas the situation is reversed in the outer regions, where the Ruddlesden–Popper phase and NiO form small inclusions in the perovskite phase [Fig. 7(c)]. Such intergrowth behavior appears to be a general characteristic for all investigated substitutions above 8% and points toward 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,³³ 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 Table II), which is comparable to the highest value detected by EDS in high-pressure flux grown Ca-substituted LaNiO₃ single-crystals.⁴⁸ 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 (Table II), which is compatible with a solubility limit of 8%. In conclusion, complementary studies with analysis 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.^22,24 In electron-doped Nd_1−xCe_xNiO₃ films, a suppression of the metal-to-insulator transition of NdNiO₃ was reported, favoring a shift toward a metal-to-metal transition for Ce doping levels as subtle as 2.5%.²⁴ 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 bars for 5 days, followed by a rapid cooling down to room temperature. This methodical approach ensures the exclusion of the influence of oxygen deficiency on the measured properties. Figure 8(a) 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.⁵⁴ 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. 8(b). This change from a metal-to-insulator to a metal-to-metal transition is qualitatively similar to that in Nd_1−xCe_xNiO₃ films.²⁴ 

In the magnetic susceptibility, anomalies with hysteretic behavior occur at similar temperatures as the metal-to-insulator and metal-to-metal transitions in PrNiO₃ and (Pr,Ce)NiO₃, respectively [Figs. 8(c) and 8(d)]. These anomalies indicate the presence of an antiferromagnetic transition.⁵⁴ Above the transition, the susceptibility can be well described by a Curie-Weiß law χ = $CT−θW$⁠, which yields the Curie constant C = 2.20(6) emu K/mol, Oe⁻¹ = 27.6(7) · 10⁻⁶ m³ K/mol, and θ_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) · 10⁻⁶ m³ K/mol, and θ_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. 8(b) and 8(d)].

The susceptibility curves in Figs. 8(c) and 8(d) are expected to be dominated by the paramagnetic signal of the Pr³⁺ cations. Nevertheless, the effective moment is extracted using $μeff=3kC/NμB2=2.828C$⁠. Assuming the effective paramagnetic moment of non-disproportionated Ni³⁺ LS $(μeff=1.73μB=3kC/NμB2)$⁠, $CNi3+$ is estimated to be 0.375 emu K/mol. Subsequently, if we consider C = C_Ni + C_Pr, the μ_eff of Pr is calculated to be 3.82 μ_B, which is only slightly larger than the expected moment of 3.5 μ_B and the reported one for PrNiO₃.⁶⁰ 

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 $(11̄0)$ direction pointing out of the plane, while the c-axis and (110) direction lie in the horizontal plane [Fig. 9(a)]. Subsequently, the surfaces of the shaped and oriented crystals are polished using a 1 μm grain size. The crystals are then annealed in a high gas pressure autoclave at 600 °C under an oxygen partial pressure of 600 bars 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 order.^32, Figure 9(b) 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.^{16,50,52,53,61} 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.^51,52 While the Ce substitution lowers the overall resistivity, as expected for electron doping, the Zr substitution appears to have the opposite effect.

Due to its 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 cannot be described by simple Pauli paramagnetism.¹⁵ A Stoner enhanced maximum (highlighted by an arrow) is observed in LaNiO₃ centered around 220 K [Fig. 9(c)], which cannot be 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) · 10⁻³ emu K/mol, Oe⁻¹ = 1.89(4) · 10⁻⁸ m³ K/mol, and θ_W = −2.2(1) K. As discussed earlier, we take C_Zr to be C − 0.375. This results in μ_eff = 3 μ_B, which is comparable to an expected moment $μZr2+=2.8μB$ 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 to susceptibility. Therefore, 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 investigated the 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 3d and Ni 2p 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. 10(a). In Fig. 10(b), the peaks at 854.8 and 851.2 eV correspond to La 3d_3/2, while the doublet at 837.9 and 834.6 eV can be identified as La 3d_5/2, indicating the La³⁺ oxidation state. The La 3d_3/2 and Ni 2p_1/2 peaks overlap,⁶⁶ and the Ni 2p_3/2 peak is accompanied by a satellite line, which is positioned ∼6–7 eV higher in binding energies. The Ni 2p_1/2 peak follows at 872.3 eV.

Figure 10(c) focuses on the XPS of La_0.91Ce_0.09NiO₃. Ce 3d is known to exhibit 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 CeO₂,⁶² 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 880.9/885.2 and 899.1/903.4 eV,⁶⁷ 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 3d_5/2 binding energy is expected to be around 182 eV.⁶³ However, we observe two Zr 3d_5/2 doublets, corresponding to binding energies of 181.1 and 180 eV, clearly indicating a lower Zr valency and likely even a mixed valence state [see reference data from ZrO₂ in Fig. 10(d)]. 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. 9(b)]. Nevertheless, we cannot rule out that the shape of the spectrum in Fig. 10(d) is strongly influenced by surface effects, as in the case of Sr-doping, which is described below.

Finally, 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,^31–35 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 3d multiplet exhibits several overlapping peaks [Fig. 10(e)], in particular the 3d_5/2 peaks at 131.8 and 133.8 eV, and the 3d_3/2 peaks at 133.6 and 135.6 eV. These peaks differ from the simpler 3d doublet at 134.3 and 132.5 eV of Sr²⁺ in SrTiO₃.⁶⁸ Yet, our observed peak structure is closely similar to that of the Sr ions in La_0.4Sr_0.6CoO₃.⁶⁵ 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.

In summary, we have successfully grown La_0.98Zr_0.02NiO₃, La_0.95Zr_0.05NiO₃, and La_0.92Sr_0.08NiO₃. The realization of these doped perovskite nickelates signifies a prominent advancement compared to earlier works that were focused on undoped LaNiO₃ and PrNiO₃ single-crystals. On the other hand, the (La,Pr,Eu)₆Ni₅O₁₆ and La_2.4Zr_0.6Ni₂O₇ phases did not form under the employed growth conditions. The initial synthesis of Pr_0.95Ce_0.05NiO₃, La_0.95Ce_0.05NiO₃, La_0.91Ce_0.09NiO₃, and La_0.84Sr_0.16NiO₃ was accomplished, albeit with the drawback of substantial amounts of impurity inclusions in the matrix. As a key aspect of our study, we identify that substitutions higher than 8% or any electron doping of the Ruddlesden–Poppers phases (n = 2, 3) lead to phase separation for OFZ growth under 300 bars of oxygen pressure.

Our physical properties and XPS characterizations reveal that electron-doping is realized for Ce-substituted PrNiO₃ and LaNiO₃, whereas Zr-substitution likely results in mixed-valent states, potentially affecting the metallic ground state and the Stoner enhanced maximum in the magnetic susceptibility.

Our results underscore the pressing need for new, cutting-edge strategies that transcend the conventional single dopant route to realize bulk crystals of nickelate superconductors. Therefore, co-doping with more than one ionic species or self doping via the oxygen stoichiometry, as previously established in cuprates,⁶⁹ might offer a path to realize superconductivity in topotactically reduced nickelate crystals.

We acknowledge F. Predel for acquiring BSE images at an early stage of this project and C. Busch for technical support. We acknowledge helpful discussions with S. Hayashida and are grateful for access to the Merlin SEM at the Scientific Facility Nanostructuring Lab (NSL) at MPI FKF.

The authors have no conflicts to disclose.

P. Puphal: Conceptualization (equal); Formal analysis (lead); Investigation (lead); Writing – original draft (lead); Writing – review & editing (equal). V. Sundaramurthy: Formal analysis (equal); Investigation (equal). V. Zimmermann: Investigation (equal). K. Küster: Investigation (equal). U. Starke: Conceptualization (equal); Writing – review & editing (equal). M. Isobe: Conceptualization (equal); Writing – review & editing (equal). B. Keimer: Conceptualization (equal); Writing – review & editing (equal). M. Hepting: Conceptualization (equal); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Before the OFZ growth of the La_1−xZr_xNiO₃ substitution series, we performed a study on the growth pressure during a single growth of La_0.8Zr_0.2NiO₃. Our initial attempt employed 15 bars of oxygen pressure, as used in the nominally grown La_2.4Zr_0.6Ni₂O₇, and we gradually increased the pressure up to 150 bars, where the growth remained stable. We note that the application of 300 bars of pressure led to growth instabilities.

In Fig. 11, we present a summary of the pressure change effects, revealing that phase formation remains unaffected from 35 bars onwards. Consequently, we chose an intermediate pressure of 85 bars for our final growth. Although the BSE images display a significant phase mixture (Fig. 5), we can still isolate small pieces of major phase accumulations from the n = 1 Ruddlesden–Popper phases and perovskite phases. Interestingly, the perovskite parts appear to contain an increased substitutional content of Zr (Fig. 5), which coexists alongside tiny domains of NiO and the n = 1 Ruddlesden–Popper phase.

In addition to the extensive XRD and BSE analysis, we also performed EDS characterization, with representative results summarized in Fig. 12. We focused the EDS analysis on homogeneous pieces with lower doping levels, confirming the successful substitution through a systematic examination of at least 20 points across various regions of the grown boule on the phase-pure part of the perovskite matrix. An example SEM image is provided in Fig. 12.

By averaging over all measured points and considering the standard deviation as error bars, we obtained the following substitutional contents: (a) Pr_0.93(3)Ce_0.02(1)NiO₃, (b) La_0.96(2)Ce_0.046(3)NiO₃, (c) 5%: La_0.99(9)Zr_0.071(4)NiO₃, 8.75%: La_0.96(5)Zr_0.11(1)NiO₃, 12.5%: La_0.9(2)Zr_0.12(2)NiO₃, and 16.75%: La_0.91(6)Zr_0.12(1)NiO₃, (d) La_0.9(2)Zr_0.07(2)NiO₃, and (e) La_0.8(1)Sr_0.12(5)NiO₃.

The phase separation, evident in both BSE and XRD data for doping levels of 8% and higher, is due to the solubility limit of the substituent. This phenomenon is also reflected in the EDS data, which reveal a limited substitution content in the bulk matrix. It is important to note that, in comparison to the rare-earth elements, the Zr and Sr content is systematically overestimated in our EDS analysis by a few percent. The radial distribution of phases in the boule, resulting from the varying oxygen partial pressure within the melt, is best illustrated in our EDS map displayed in Fig. 12(f). In this figure, all elements are color coded and superimposed onto the same SE image, revealing a red perovskite region at the exterior and a blue n = 1 Ruddlesden–Popper phase region at the interior of the grown boule.