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

P. Puphal<EMAIL_ADDRESS>V. Sundaramurthy  V. Zimmermann  K. Küster  U.
Starke  M. Isobe  B. Keimer  M. Hepting  Max Planck Institute for Solid State
Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany

###### Abstract

The recent discovery of superconductivity in hole-doped infinite-layer
nickelates has triggered a great interest in the synthesis of novel nickelate
phases, which have primarily been examined in thin film samples. Here, we
report the high-pressure optical floating zone (OFZ) growth of various
perovskite and perovskite-derived rare-earth nickelate single-crystals, and
investigate the effects of hole-, electron-, and self-doping. For hole-doping
with Ca and Sr, we observe phase separations during the growth process when a
substitution level of 8% is exceeded. A similar trend emerges for electron-
doping with Ce and Zr. Employing lower doping levels allows us to grow
sizeable crystals in the perovskite phase, which exhibit significantly
different electronic and magnetic properties than the undoped parent
compounds, such as a decreased resistivity and a suppressed magnetic response.
Our insights into the doping-dependent phase formation and the resulting
properties of the synthesized crystals reveal limitations and opportunities
for the exploration and manipulation of electronic states in rare-earth
nickelates.

††preprint: AIP/123-QED

> ##  I Introduction

The Ruddlesden-Popper nickelates $R_{n+1}$NinO3n+1 ($R$ = rare-earth ion) with
the perovskite ($n=\infty$) or perovskite-derived crystal structures
($n\neq\infty$) are prototypical quantum materials Greenblatt (1997), showing
a plethora of electronic, orbital, and magnetic phases already without charge
carrier doping Sugai  _et al._ (1990); Kobayashi  _et al._ (1996); Mazin  _et
al._ (2007); Li  _et al._ (2020a); Catalano  _et al._ (2018). The perovskite-
derived phases with $n=1-3$ have been actively studied since the 1980s Petrov
_et al._ (1988). To synthesize the perovskite phase $R$NiO3, 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 Wold, Post, and Banks (1957), whereas nickelates with $R$ other than
La were realized in 1991 Lacorre  _et al._ (1991). The $R$NiO3 compounds have
been of long-standing interest due to their sharp metal-to-insulator
transition Torrance  _et al._ (1992); Medarde  _et al._ (1992); Catalan (2008)
and a magnetic ground state with an unconventional spin spiral Scagnoli  _et
al._ (2006); Hepting  _et al._ (2018). Additionally, the metal-to-insulator
transition is accompanied by an orthorhombic to monoclinic structural phase
transition Catalan (2008). 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 Wang  _et al._ (2018a); Zheng  _et
al._ (2020).

Upon hole- or electron-doping of the Ruddlesden-Popper nickelate, new
electronic phases can emerge Iglesias, Bibes, and Varignon (2021); Botana,
Pardo, and Norman (2017); Kotiuga and Rabe (2019); Worm  _et al._ (2022);
Chen, Jiang, and Zhong (2023); Patel  _et al._ (2022), along with potential
functional properties Li, Ramanathan, and Comin (2022); Song  _et al._ (2023).
In $R$NiO3 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 Cheong  _et al._ (1994); Alonso, Martínez-Lope, and
Hidalgo (1995); García-Muñoz  _et al._ (1995); Ramadoss  _et al._ (2016).
Typically, the powder synthesis is carried out under high external oxygen gas
pressures Lacorre  _et al._ (1991). Recent studies have reported substitutions
in powders as high as 40% Li  _et al._ (2020b). However, further
investigations are needed to determine if such high substitution
concentrations are homogeneously incorporated into the microstructure of the
$R$NiO3 powder grains.

Since 2019, the field has been reinvigorated Mitchell (2021) by the discovery
of superconducting behavior in hole-doped rare-earth nickelates with the
infinite-layer crystal structure Li  _et al._ (2019); Zeng  _et al._ (2020);
Lee  _et al._ (2020); Osada  _et al._ (2021); Gao  _et al._ (2021); Zeng  _et
al._ (2022). This structure can be achieved through the topotactic oxygen
deintercalation of the perovskite phase Crespin, Levitz, and Gatineau (1983);
Hayward  _et al._ (1999); Hayward and Rosseinsky (2003). These infinite-layer
nickelates with Ni1+ are nominally isoelectronic and isostructural to cuprate
high-temperature superconductors with Cu2+ ions Hepting, Dean, and Lee (2021).
Additionally, superconductivity has been observed in the undoped nickelate
Nd6Ni5O12 Pan  _et al._ (2021), which, however, can be considered a self-doped
cuprate analogue Botana  _et al._ (2022). Yet, superconductivity in the
material family of nickelates has only been observed in thin film samples Wang
_et al._ (2020); Li  _et al._ (2020b), even though the latest studies have
indicated that it could be an intrinsic property of the bulk phase of doped
infinite-layer nickelates Goodge  _et al._ (2023). Furthermore, theoretical
studies propose that superconductivity may also arise in electron-doped
nickelates, such as La2.4Zr0.6Ni2O6 where La3+ is partially substituted by
tetravalent Zr4+ ions Worm  _et al._ (2022).

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 Crespin, Levitz, and Gatineau (1983); Zhang
_et al._ (2017a); Pan  _et al._ (2021). In particular, the CaH2-assisted
reduction has been successfully demonstrated not only on perovskite thin films
Li  _et al._ (2019); Zeng  _et al._ (2020); Lee  _et al._ (2020); Osada  _et
al._ (2021); Gao  _et al._ (2021); Zeng  _et al._ (2022) and polycrystalline
powders Wang  _et al._ (2020); Puphal  _et al._ (2022); Ortiz  _et al._
(2022), but also on single-crystals Puphal  _et al._ (2021); Wu  _et al._
(2023) with volumes up to 1 mm3 Puphal  _et al._ (2023).

Table 1: Summary of the materials without doping grown with the HKZ. The columns indicate the desired nominal composition of the material, $n$ labels the formed Ruddlesden-Popper (RP) phase, wt% is the weight percentage of the RP phase, and $a,b,c$ are the lattice constants determined from Rietveld refinements of PXRD data. Furthermore, the space group (structure) and the oxygen partial pressure of the growth are indicated. If only one wt% value is given, the remaining phase is NiO. Nominal comp. |  $n$ in RP | wt% | a (Å) | b (Å) | c (Å) | structure | p(O2) (bar)
---|---|---|---|---|---|---|---
LaNiO3 | $\infty$ | 97.9(7) | 5.45408(7) | - | 13.1255(2) | $R\bar{3}c$ | 85
PrNiO3 | $\infty$ | 97.3(6) | 5.4095(1) | 5.3703(1) | 7.6147(2) | $Pbnm$ | 300
Pr6Ni5O16 | 3 | 72.5(6) | 5.3717(2) | 5.4565(1) | 27.534(1) | $P2_{1}/a$ | 300
“ | 2 | 27.5(3) | 5.4406(3) | 5.3763(3) | 7.6166(4) | $Pbnm$ | 300
La3Eu3Ni5O16 | 3 | 74.9(7) | 5.3657(2) | 5.4599(2) | 27.4703(9) | $P2_{1}/a$ | 300
“ | 1 | 11.1(3) | 3.808(2) | - | 12.515(1) | $I4/mmm$ | 300
Table 2: Summary of the materials with doping grown with the HKZ. The columns indicate the desired nominal composition of the material, $n$ labels the formed Ruddlesden-Popper (RP) phase (where DP stands for double perovskite), wt% is the weight percentage of the RP phase, $x$ is the substitution content determined by EDS, and $a,b,c$ are the lattice constants determined from Rietveld refinements of PXRD data. Furthermore, the space group (structure) and the oxygen partial pressure of the growth are indicated. If only one wt% value is given, the remaining phase is NiO. The labels (in), (mid), and (out) indicate whether the powder for the PXRD analysis was extracted from the inner, middle, or outer part of the boule, as depicted in Fig. 7. Nominal comp. |  $n$ in RP | wt% |  $x$ from EDS | a (Å) | b (Å) | c (Å) | structure | p(O2) (bar)
---|---|---|---|---|---|---|---|---
Pr0.95Ce0.05NiO3 | $\infty$ | 41.3(3) | 0.02(1) | 5.4097(1) | 5.3748(2) | 7.6201(3) | $Pbnm$ | 300
La0.95Ce0.05NiO3 | $\infty$ | 77.5(4) | 0.046(3) | 5.45350(8) | - | 13.1235(2) | $R\bar{3}c$ | 85
La0.91Ce0.09NiO3 | $\infty$ | 85.81(5) | 0.057(7) | 5.4530(1) | - | 13.1201(3) | $R\bar{3}c$ | 85
La0.8Ce0.2NiO3 | $\infty$ | 69.2(4) | 0.07(1) | 5.4532(1) | - | 13.1193(3) | $R\bar{3}c$ | 200
La2.4Zr0.6Ni2O7 | $\infty$ | 46.14(4) | 0.12(1) | 5.5019(2) |  | 13.2531(5) | $R\bar{3}c$ | 14
“ | DP | 52.6(5) | - | 5.6231(2) | 5.7053(3) | 7.9891(4) | $P2_{1}/n$ | 14
La2.4Zr0.6Ni2O7 | DP | 60.5(7) | - | 5.6404(2) | 5.7442(3) | 8.0209(4) | $P2_{1}/n$ | 4.5
“ | 1 | 19.3(2) | - | 3.8637(1) | - | 12.6857(7) | $I4/mmm$ | 4.5
La0.98Zr0.02NiO3 | $\infty$ | 99.5(2) | 0.026(6) | 5.48144(2) | - | 13,18948(7) | $R\bar{3}c$ | 85
La0.95Zr0.05NiO3 | $\infty$ | 99.5(2) | 0.071(4) | 5.48144(2) | - | 13,18948(7) | $R\bar{3}c$ | 85
La0.8Zr0.2NiO3 | $\infty$ | 57.8(5) | 0.12(1) | 5.5027(1) | - | 13.2596(4) | $R\bar{3}c$ | 30
“ | DP | 39.39(4) | - | 5.6223(2) | 5.6987(3) | 7.9781(4) | $P2_{1}/n$ | 30
La0.92Sr0.08NiO3 | $\infty$ | 65.2(6) | 0.12(5) | 5.4471(2) | - | 13.1691(1) | $R\bar{3}c$ | 200
La0.84Sr0.16NiO3 (in) | $\infty$ | 27.5(2) | 0.13(1) | 5.44551(7) | - | 13.1395(3) | $R\bar{3}c$ | 300
“ | 1 | 67.1(4) | - | 3.82578(4) | - | 12.7002(1) | $I4/mmm$ | 300
La0.84Sr0.16NiO3 (mid) | $\infty$ | 54.9(3) | - | 5.44372(6) | - | 13.1341(2) | $R\bar{3}c$ | 300
“ | 1 | 31.7(2) | - | 3.81085(6) | - | 12.7141(9) | $I4/mmm$ | 300
La0.84Sr0.16NiO3 (out) | $\infty$ | 72.1(4) | - | 5.44539(4) | - | 13.1382(1) | $R\bar{3}c$ | 300
“ | 1 | 29.4(2) | - | 3.81860(5) | - | 12.7172(3) | $I4/mmm$ | 300

A technical breakthrough enabling the growth of large $R_{n+1}$NinO3n+1
single-crystals was the advent of the high-oxygen pressure high-temperature
optical floating zone technique, yielding bulk single-crystals of LaNiO3 Guo
_et al._ (2018); Wang  _et al._ (2018a); Zhang  _et al._ (2017b); Zheng  _et
al._ (2020); Dey  _et al._ (2019); Puphal  _et al._ (2023), PrNiO3 Zheng  _et
al._ (2019), La3Ni2O7 Liu  _et al._ (2022), and (La,Pr)4Ni3O10 Zhang  _et al._
(2020); Huangfu  _et al._ (2020). However, a problem with the oxygen transport
towards the center of the boule was observed in this synthesis method Zheng
_et al._ (2020). As a result, oxygen deficient phases may form, but can be
alleviated by post annealing under high gas pressure in autoclaves.

Overall, the technical advances in the perovskite single-crystal growth as
well as the demonstrated topotactic reduction of LaNiO3 single-crystals to
infinite-layer LaNiO2 Puphal  _et al._ (2023), call for the synthesis of doped
perovskite single-crystals that can possibly be reduced 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
bar of oxygen partial pressure, and discuss the opportunities and limitations
of this method. We begin with an overview on the synthesis of the undoped
compounds LaNiO3 and PrNiO3, as well as an attempt of the growth of the $n=5$
Ruddlesden-Popper nickelate Pr6Ni5O16. As a second type of samples, we
investigate Ce- and Zr-doped (La,Pr)NiO3, which are nominally electron-doped.
We also report on Sr-doped LaNiO3, which is nominally hole-doped.

##  II Methods

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 minutes 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 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 bar.
The growth chamber has a length of 72 mm and 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 bar 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, a preannealing at high pressures leads to cracking and even breaking
of the rods. Thus, we either increased the power until a homogeneous zone melt
was achieved, or premelted the rods at the given pressure to preform the final
phase. In the former case, achieving a homogenous 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
stabilizes this, and the subsequent growth is easier.

All growths were conducted under oxidizing atmosphere, with the partial oxygen
pressure tailored to yield the best outcome for each composition (see Tab. 1,
2). 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 counteracted by a continuous
increase of the lamp power, particularly during the early stage of the growth.
This means that newly introduced material will be largely overheated and
becomes very fluid. Thus, without premelting, the diameter of the grown boule
is dictated by the flow of the low-viscosity melt that 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 Kα radiation
and a Ni filter. Rietveld refinements were conducted with the FullProf
software suite Rodríguez-Carvajal (1993). 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 of 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 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 $K_{\alpha}$ 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 pass
energy of 20 eV. XPS spectra were analyzed using the CASAXPS software Fairley
_et al._ (2021). All samples were cleaved in a glove box, mounted on carbon
tape or In foil, and transported under inert atmosphere to the XPS chamber.

##  III Results

###  III.1 Undoped nickelates

Figure 1: (a) Image of the grown LaNiO3 boule and the PXRD pattern. The solid
black line corresponds to the calculated intensity from the Rietveld
refinement. The calculated Bragg peak positions of the LaNiO3 majority
(97.9(7) wt%) and NiO minority phase (2.1(2) wt%) are indicated as green and
red vertical bars, respectively. The blue line corresponds to the difference
between the experimental and calculated intensity. (b) Schematic of the
rhombohedral unit cell (hexagonal axes) of perovskite LaNiO3, viewed along the
same direction as the cleave shown in panel (d). (c) Picture of the cross
section of the boule obtained after cleaving a single crystal. (d) Picture of
a cleave along growth direction of a single crystalline piece with indexed
orientations determined from the Laue diffraction pattern in panel (e).
Figure 2: (a) Image of the grown PrNiO3 boule and the PXRD pattern. The
calculated Bragg peak positions of the PrNiO3 majority (97.3(7) wt%) and NiO
minority phase (2.7(2) wt%) are indicated as green and purple vertical bars,
respectively. (b) Image of the boule of the attempted Pr6Ni5O16 growth and the
PXRD pattern, which indicates only the Pr4Ni3O10 (72.5(6) wt%) and the PrNiO3
phase (27.5(3) wt%). (c) Sketch of the growth phase diagram for the phase
formations of the OFZ melt under 300 bar oxygen partial pressure for NiO and
PrO2. (d,e) Simultaneously acquired SE (left) and BSE (right) images of broken
surfaces from the boules grown from a precursor corresponding to nominally
stoichiometric PrNiO3 (d) and a Pr-excess precursor nominally corresponding to
Pr1.05NiO3 (e). The inclusions with a dark contrast in (d) correspond to NiO,
while regions with a light contrast in (e) correspond to intergrown Pr4Ni3O10.

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.

###  III.2 Electron-doping of PrNiO3

Figure 3: (a) Images of the boules grown at 280 and 300 bar, and the PXRD
pattern from a growth of the nominal composition Pr0.95Ce0.05NiO3. The
calculated Bragg peak positions of the Pr1-xCexNiO3 majority (41.3(3) wt%) and
NiO (27.7(4) wt%) and (Pr,Ce)O2 (31.0(2) wt%) minority phases are indicated as
orange, purple, and green vertical bars, respectively. (b) BSE image of a
broken surface from the grown boule, with the growth direction running from
bottom left to top right. The blue arrow indicates lines of eutectic freezing,
which form when the solubility limit is reached. The regions with darker and
lighter contrast correspond to NiO and (Pr,Ce)O2, respectively. (c) Phase
diagram for the phase formations of the OFZ melt under 300 bar of oxygen
partial pressure for (Pr,Ce)O2 and NiO. (d) Magnified BSE image of the same
broken surface as in (b), but zoomed into an eutectic separation region.

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.

###  III.3 Electron-doping of LaNiO3

Figure 4: Images of the boules and the PXRD patterns from growths of the
nominal compositions (a) La0.8Ce0.2NiO3, (b) La0.95Ce0.05NiO3, and (c)
La0.91Ce0.09NiO3. The calculated Bragg peak positions of the La1-xCexNiO3
majority (85.8(5) wt%) and NiO (6.2(2) wt%) and La2Ce2NiO7 (8.00(7) wt%)
minority phases are indicated as green, red, and blue vertical bars,
respectively. (d) Image of a cleaved single crystal of La0.95Ce0.05NiO3, which
was utilized in the XPS study. The growth direction runs from the bottom to
the top. (e) BSE image of a surface of the La0.91Ce0.09NiO3 boule cleaved
perpendicular to the growth direction. Regions with darker and lighter
contrast correspond to NiO and La2Ce2NiO7, respectively.  Figure 5: (a) Image
of the boule with a nominal La1-xZrxNiO3 composition, where the white lines
separate sections with nominal Zr-substitutions of 5%, 8.75%, 12.5%, 16.75%,
and 20% (from bottom to top), respectively. (b,c) PXRD patterns of pulverized
pieces from the sections with the nominal La0.95Zr0.05NiO3 (b) and
La0.8Zr0.2NiO3 (c) compositions. The calculated Bragg positions of the
La1-xZrxNiO3 majority and NiO minority phase are indicated by purple and green
vertical bars, respectively. In (b) and (c), the majority phase contributes
99.5(2) wt% and 57.8(5) wt%, respectively, while the NiO minority phase
corresponds to 0.5(2) wt% and 2.8(2) wt%, respectively. In addition, the
La2ZrNiO6 double-perovskite phase is present (39.4(4) wt%) in the PXRD in (c),
as indicated by purple vertical bars. (d-g) SE (left) and BSE (right) images
of broken surfaces from the sections with nominal Zr-substitutions of 5% (d),
8.75% (e) 12.5% (f), and 16.75% (g). The inclusions with a dark contrast in
the BSE images correspond to NiO or dirt on the surface, while a lighter
contrast (indicated by the arrows) in (f) and (g) corresponds to La2ZrNiO6
(highlighted by blue arrows). (h) Pseudo binary phase diagram of (Zr,La)Ox and
NiO at 85 bar oxygen partial pressure.

Next, we focus on the electron-doping of LaNiO3. As a first attempt we
attempted to synthesize crystals of composition La0.8Ce0.2NiO3, 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 La0.95Ce0.05NiO3 and La0.91Ce0.09NiO3. 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-xCexNiO3 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 La2.4Zr0.6Ni2O6 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 La0.8Zr0.2NiO3
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).

Figure 6: (a,b) Images of the boules and the PXRD patterns from the growths of
the nominal compositions La0.98Zr0.02NiO3 (a) and La0.95Zr0.05NiO3 (b). The
calculated Bragg peak positions of the majority La1-xZrxNiO3 (97.5(4) wt% and
99.5(6) wt%, respectively) and minority NiO phases (3.5(5) wt% and 0.5(2) wt%,
respectively) are indicated by green and brown vertical bars, respectively.
(c) Image of a cleaved single crystal from the La0.95Zr0.05NiO3 boule. (d) SE
(left) and BSE (right) images of the polished surface of the La0.95Zr0.05NiO3
crystal analyzed in Fig. 9. The dark spots correspond to NiO.

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 La0.98Zr0.02NiO3 and La0.95Zr0.05NiO3 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).

###  III.4 Hole-doping of LaNiO3

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 La0.8Ca0.2NiO3 and Pr0.8Ca0.2NiO3. However, we find that
only the $n=1$ Ruddlesden-Popper phases La1.6Ca0.4NiO4 and Pr1.6Ca0.4NiO4 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 La0.92Sr0.08NiO3. 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.

Figure 7: Image of the cross section of the boule (inset) and PXRD patterns
from a growth of the nominal composition La0.84Sr0.16NiO3. The three PXRD
patterns are taken from pieces from different positions in the boule, as
indicated by the blue arrows. The calculated Bragg peak positions (vertical
bars) and the difference between the experimental and calculated (blue line)
are shown for the bottom PXRD pattern. The corresponding wt% of the phases are
summarized in Tab. 2. (b,c) BSE images from different parts of the cross
section revealing a perovskite matrix with NiO (dark) and (La,Sr)2NiO4 (light)
eutectic inclusions.

To confirm the anticipated the solubility limit of Sr of 8%, we subsequently
attempt the growth of La0.84Sr0.16NiO3. 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 Ni3.16+ oxidation state
compared to Ni3.08+ in La0.92Sr0.08NiO3. 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.

###  III.5 Physical properties

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 Nd1-xCexNiO3, 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
Pr0.95Ce0.05NiO3, 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 Nd1-xCexNiO3 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).

Figure 8: (a,b) Resistivity as a function of temperature for a PrNiO3 (a) and
a Pr0.95Ce0.05NiO3 crystal (b). The current direction coincides with the
$c$-axis direction. The upper inset in (b) shows the cut Pr0.95Ce0.05NiO3
crystal and the lower inset the specific heat measured upon cooling. (c,d)
Magnetization as a function of temperature for the PrNiO3 (c) and
Pr0.95Ce0.05NiO3 crystal (d). The insets display a magnification of the
hysteresis loops observed around the magnetic transitions.

Next, we characterize the physical properties of a selection of La-based
compounds. To this end, we analyze large crystals of LaNiO3, La0.95Zr0.05NiO3,
and La0.91Ce0.09NiO3 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
La0.91Ce0.09NiO3, 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.

Figure 9: (a) Images of the shaped and polished LaNiO3, La0.91Ce0.09NiO3, and
La0.95Zr0.05NiO3 single-crystals (left to right), with horizontal $c$-axis
orientation. (b) Resistivity as a function of temperature for the three
crystals. The current direction coincides with the $c$-axis direction. (c)
Magnetization as a function of temperature for the three crystals. A field of
0.1 T was applied along the $c$-axis direction.  Figure 10: (a) XPS spectra of
LaNiO3 (black) Puphal  _et al._ (2023), La0.92Sr0.08NiO3 (green),
La0.95Zr0.05NiO3 (blue), and La0.91Ce0.09NiO3 (red) across a wide binding
energy range from 100-1200 eV. (b) Zoom into the region between 875 and 825
eV, which includes the La 3$d$ and Ni 2$p$ edges. (c) Zoom into the region
between 916.5 and 881.5 eV, which includes the Ce 3$d$ edge. Data of a CeO2
film from Ref. Pfau, Schierbaum, and Göpel (1996) are shown for comparison.
(d) Zoom into the region between 187 and 176 eV, corresponding to the Zr 3$d$
edge. Data of a ZrO2 film from Ref. Lackner  _et al._ (2019) and a
La2(Zr,Cu)O4 pellet from Ref. Anderson and Fierro (1994) are shown for
comparison. (e) Zoom into the region between 140 and 125 eV, corresponding to
the Sr 3$d$ edge. Data of a (La,Sr)CoO3 from Ref. Wang  _et al._ (2018b) are
shown for comparison.

###  III.6 Valence states

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 La0.91Ce0.09NiO3. Ce 3$d$ is known to exhibit
a very complex multiplet splitting, resulting in several peaks. Notably, the
multiplet structure observed in our La0.91Ce0.09NiO3 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 La1-xZrxNiO3, 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 3d5/2 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 La0.92Sr0.08NiO3. 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 La0.92Sr0.08NiO3 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
La0.4Sr0.6CoO3Wang  _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.

##  IV Summary

In summary, we have successfully grown single-crystals of LaNiO3, PrNiO3,
La0.98Zr0.02NiO3, La0.95Zr0.05NiO3, and La0.92Sr0.08NiO3. On the other hand,
the (La,Pr,Eu)6Ni5O16 and La2.4Zr0.6Ni2O7 phases did not form under the
employed growth conditions. The synthesis of Pr0.95Ce0.05NiO3,
La0.95Ce0.05NiO3, La0.91Ce0.09NiO3, and La0.84Sr0.16NiO3 was accomplished,
albeit with the drawback of substantial amounts of impurity inclusions in the
matrix. In general, we find 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 bar 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. Thus, co-doping with more than one ionic species or
self doping via the oxygen stoichiometry, as previously established in
cupratesFrano  _et al._ (2019), might offer a path to realize
superconductivity in topotactically reduced nickelate crystals.

###### Acknowledgements.

We thank 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.

##  Appendix A Pressure dependence

Before the OFZ growth of La1-xZrxNiO3 substitution series, we performed a
study on the growth pressure during a single growth of La0.8Zr0.2NiO3. Our
initial attempt employed 15 bar oxygen pressure, as used in the nominally
grown La2.4Zr0.6Ni2O7, and we gradually increased the pressure up to 150 bar,
where the growth remained stable. We note that the application of 300 bar
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 bar onwards. Consequently, we
chose an intermediate pressure of 85 bar 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 coexist
alongside of tiny domains of NiO and the $n=1$-Ruddlesden-Popper phase.

Figure 11: (a) Image of the boule of a growth of the nominal composition
La0.8Zr0.2NiO3 using various oxygen pressures, together with the PXRD patterns
from the edge region of the 35 bar part (black), the middle region (red), and
the middle region of the 150 bar part (blue). The green bars indicate the peak
positions of the perovskite phase from the refinement, while the gray bars
indicate the double-perovskite phase. (b) The SE images feature broken pieces
of the two separate phases, primarily consisting of $n=1$ Ruddlesden-Popper
(left) and perovskite phase (right), and an exemplary EDS result (center). The
resulting average stoichiometry is given in the legend, with
La1.1(2)Zr0.5(1)Ni1.1(2)O4.0(3) and La0.81(1)Zr0.15(7)Ni1.4(3)O3.09(3).

##  Appendix B Elemental Dispersive X-ray Spectroscopy

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 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)
Pr0.93(3)Ce0.02(1)NiO3, (b) La0.96(2)Ce0.046(3)NiO3, (c) 5%:
La0.99(9)Zr0.071(4)NiO3, 8.75%: La0.96(5)Zr0.11(1)NiO3, 12.5%:
La0.9(2)Zr0.12(2)NiO3, 16.75%: La0.91(6)Zr0.12(1)NiO3, (d)
La0.9(2)Zr0.07(2)NiO3, (e) La0.8(1)Sr0.12(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. 12f. 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.

Figure 12: EDS scans of crystals, with an exemplary SE image of a broken piece
shown in the inset, for nominally grown (a) Pr0.95Ce0.05NiO3, (b)
La0.91Ce0.09NiO3, (c) (La,Zr)NiO3 (d) La0.95Zr0.05NiO3, (e) La0.92Sr0.08NiO3.
(f) EDS map of La0.84Sr0.16NiO3 of a "cleaved" cross section of the boule,
with all elements overlaid in one picture on the SE picture, using the color
code: La (red), Sr (purple), O (blue), Ni (green).

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