# Synthesis and physical properties of LaNiO2 crystals

P. Puphal<EMAIL_ADDRESS>Max-Planck-Institute for Solid State Research,
Heisenbergstraße 1, D-70569 Stuttgart, Germany  B. Wehinger  European
Synchrotron Radiation Facility, 71 Avenue des Martyrs, F-38043 Grenoble,
France  J. Nuss  Max-Planck-Institute for Solid State Research,
Heisenbergstraße 1, D-70569 Stuttgart, Germany  K. Küster  Max-Planck-
Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart,
Germany  U. Starke  Max-Planck-Institute for Solid State Research,
Heisenbergstraße 1, D-70569 Stuttgart, Germany  G. Garbarino  European
Synchrotron Radiation Facility, 71 Avenue des Martyrs, F-38043 Grenoble,
France  B. Keimer  Max-Planck-Institute for Solid State Research,
Heisenbergstraße 1, D-70569 Stuttgart, Germany  M. Isobe  Max-Planck-Institute
for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany  M.
Hepting<EMAIL_ADDRESS>Max-Planck-Institute for Solid State Research,
Heisenbergstraße 1, D-70569 Stuttgart, Germany

###### Abstract

Infinite-layer (IL) nickelates are an emerging family of superconductors whose
similarities and differences to cuprate superconductors are under intense
debate. To date, the IL phase of nickelates can only be reached via topotactic
oxygen reduction of the perovskite phase, using H2 gas or reducing agents such
as CaH2. While the topotactic reduction method has been widely employed on
thin film and polycrystalline powder samples, the reduction of La1-xCaxNiO3
single-crystals with lateral dimensions up to 150 $\mu$m was achieved only
recently, using an indirect contact method with CaH2. Here we report the
topotactic transformation of much larger LaNiO3 crystals with lateral
dimensions of more than one millimeter, via direct contact with CaH2. We
characterize the crystalline, magnetic, and electronic properties of the
obtained IL LaNiO2 crystals by powder and single-crystal x-ray diffraction
(XRD), magnetometry, electrical transport, and x-ray photoelectron
spectroscopy (XPS) measurements. The amount of incorporated topotactic
hydrogen due to the reduction process is determined by a gas extraction
method. In addition, we investigate the evolution of the lattice parameters
under hydrostatic pressure up to 12 GPa, using high-resolution synchrotron
XRD. Furthermore, we provide a direct comparison of several physical
properties of the LaNiO2 crystals to their powder and thin film counterparts.

##  I Introduction

Superconductivity in the material class of nickelates was first discovered in
Nd0.8Sr0.2NiO2 thin films that were epitaxially grown on SrTiO3 substrates Li
_et al._ (2019a). In the meantime, the superconducting transition in
Nd0.8Sr0.2NiO2 films has been confirmed by other groups Zeng  _et al._ (2020);
Li  _et al._ (2021); Gao  _et al._ (2021), and was similarly observed for
various choices of rare-earth ions ($R$ = La, Pr, Nd) Li  _et al._ (2020a);
Osada  _et al._ (2020, 2021); Wang  _et al._ (2022a), divalent dopant ions
($A$ = Sr, Ca) Zeng  _et al._ (2022a), and substrates Ren  _et al._ (2021);
Lee  _et al._ (2022). The reported transition temperatures $T_{c}$ are
situated between 9-15 K, although it was found that hydrostatic pressure can
enhance the $T_{c}$ of Pr0.82Sr0.18NiO2 films to more than 30 K Wang  _et al._
(2022b). Moreover, while superconductivity in the infinite-layer compounds
$R_{1-x}A_{x}$NiO2 occurs only for substitution levels between $x\approx 0.1$
and 0.3 Lee  _et al._ (2022), it was recently reported that the quintuple-
layer nickelate Nd6Ni5O12 shows superconductivity already without rare-earth
substitution Pan  _et al._ (2022). Taken together, these findings suggest that
low-valence nickelates are a novel class of superconductors.

Nickelate superconductors exhibit several similarities but also differences to
the cuprate superconductors. For instance, IL nickelates and cuprates share
the same nominal $3d^{9}$ electronic configuration of the Ni (Cu) ion and are
isostructural, with Ni (Cu) and O ions arranged in square planar coordination
within NiO2 (CuO2) planes. On the other hand, the parent IL nickelates $R$NiO2
lack long-range antiferromagnetic (AFM) order Hayward  _et al._ (1999);
Hayward and Rosseinsky (2003); Lin  _et al._ (2022); Fowlie  _et al._ (2022);
Ortiz  _et al._ (2022), which is a hallmark of parent cuprates Scalapino
(2012), and show a distinct multiorbital electronic structure Hepting  _et
al._ (2020); Goodge  _et al._ (2021). Another notable distinction of
nickelates is that to date only thin film samples were found to superconduct
Bernardini  _et al._ (2022a); Li  _et al._ (2020b); Wang  _et al._ (2020); He
_et al._ (2021), whereas various types of cuprate samples, including single-
crystals, polycrystalline powders, and films, can realize superconductivity.
In fact, bulk single-crystalline cuprate samples often show superior
properties over their thin film and polycrystalline counterparts, such as a
higher crystalline quality and an elevated $T_{c}$ Rao  _et al._ (1993).
Hence, the question arises whether epitaxy to the substrate and/or interface
effects are critical for the emergence of superconductivity in nickelates
Geisler and Pentcheva (2020); He  _et al._ (2020); Bernardini  _et al._
(2022a), or the previously available nickelate bulk samples exhibited quality
issues that prevented the emergence of superconductivity. For instance, in the
case of powder samples, possible impediments for superconductivity include
enhanced disorder, inclusions of secondary phases, and diminishing sizes of
infinite-layer single domains in powder grains Hayward  _et al._ (1999);
Crespin  _et al._ (2005); Li  _et al._ (2020b); Wang  _et al._ (2020); He  _et
al._ (2021); Puphal  _et al._ (2022).

To shed new light on possible differences between bulk and thin film IL
nickelates, some of us have recently synthesized high-quality perovskite
La1-xCaxNiO3 single-crystals, which were subsequently reduced to the IL phase
Puphal  _et al._ (2021). The samples in the perovskite phase were obtained via
a perchlorate-chlorate flux mixture in an external temperature gradient growth
under high pressure in a 1000-metric ton press, yielding crystals with typical
lateral dimensions of 150 $\mu$m. For the topotactic reduction, which lasted
2-4 weeks, CaH2 was used as a reducing agent in spatial separation from the
crystals. The resulting La1-xCaxNiO2 crystals showed metallic behavior at high
temperatures and a weakly insulating upturn at low temperatures, which is
closely analogous to undoped and lightly-doped $R_{1-x}A_{x}$NiO2 films Li
_et al._ (2019a); Zeng  _et al._ (2020); Li  _et al._ (2021); Gao  _et al._
(2021); Li  _et al._ (2020a); Osada  _et al._ (2020, 2021); Wang  _et al._
(2022a); Zeng  _et al._ (2022a); Ren  _et al._ (2021); Lee  _et al._ (2022),
but in stark contrast to powder samples, which in turn show insulating
behavior at all temperatures Li  _et al._ (2020b); Wang  _et al._ (2020); He
_et al._ (2021). Yet, a superconducting transition was not observed in Ref.
Puphal  _et al._ , 2021, which is possibly due to the fact that electrical
transport measurements were only realized on crystals with Ca-substitutions up
to $x\approx 0.08$, i.e., at a hole-doping level below the onset of the
superconducting dome of corresponding thin films Zeng  _et al._ (2022a).
Single-crystals with higher substitution levels might thus allow to finally
clarify whether superconductivity is an exclusive thin film property. The
obtained sizes of high-pressure grown perovskite crystals Puphal  _et al._
(2021) tend to decrease with increasing Ca-substitution level, which poses a
challenge for electrical transport measurements and the characterization of
other physical properties.

In consequence, new strategies and synthesis methods for single-crystalline IL
nickelates with enhanced sample sizes are highly desirable. Moreover, a
considerable increase of the bulk sample sizes will facilitate the application
of advanced spectroscopy techniques, including angle resolved photoemission,
optical, x-ray and electron spectroscopy, tunneling microscopy, as well as
inelastic x-ray and neutron scattering. These techniques have provided
invaluable insights into the charge, spin, lattice, and orbital degrees of
freedom of strongly correlated quantum materials such as cuprate
superconductors Damascelli  _et al._ (2003); Fink  _et al._ (2001); Fischer
_et al._ (2007); Basov and Timusk (2005); Devereaux and Hackl (2007); Ament
_et al._ (2011); Fujita  _et al._ (2012), but were only occasionally applied
to IL nickelates yet Hepting  _et al._ (2021); Rossi  _et al._ (2021); Gu  _et
al._ (2020); Ortiz  _et al._ (2021); Rossi  _et al._ (2022); Lu  _et al._
(2021); Zeng  _et al._ (2022b); Cervasio  _et al._ (2022); Shen  _et al._
(2022); Fürsich  _et al._ (2022); Krieger  _et al._ (2022); Tam  _et al._
(2022), mostly because the sample mass of thin films is insufficient for
techniques with a small scattering cross section and the highly invasive
topotactic reduction deteriorates the film surface, which is problematic for
surface sensitive techniques.

In the context of large single-crystalline samples, recent technical advances
in the high-pressure floating zone growth have enabled the synthesis of
centimeter-sized LaNiO3 single-crystals under 30-130 bar oxygen partial
pressure, using either a laser diode floating zone furnace Tomioka  _et al._
(2021), or a vertical optical-image floating-zone (OFZ) furnace that was
designed for operation at elevated gas pressures Phelan  _et al._ (2019);
Zhang  _et al._ (2017); Guo  _et al._ (2018); Wang  _et al._ (2018); Dey  _et
al._ (2019); Zheng  _et al._ (2020). Moreover, in a variant of the latter
furnace, oxygen gas pressures of up to 300 bar can be achieved, providing the
required oxidizing conditions to stabilize the Ni3+ valence state not only in
perovskite LaNiO3, but even in PrNiO3 Zheng  _et al._ (2019).

In this work, we utilize the OFZ method to synthesize LaNiO3 single-crystals,
from which we obatin millimeter-sized LaNiO2 crystals via topotactic reduction
using CaH2 in direct contact with the crystals. For insufficiently reduced
crystals, powder x-ray diffraction (PXRD) measurements reveal the presence of
residual contributions of the LaNiO2.5 phase, whereas excessively reduced
crystals decompose into elemental Ni, La2O3, and LaOH, with the latter
compound emerging due to a topotactic reaction with the reducing agent, as
evidenced by hydrogen gas extraction analysis. For selected LaNiO2 crystals,
we carry out single-crystal x-ray diffraction (XRD) under hydrostatic pressure
to determine the lattice constants and the bulk modulus. Furthermore, we
compare the magnetic susceptibility and electrical resistivity of reduced
crystals with corresponding polycrystalline powder and thin film samples,
suggesting that our crystals are closely analogous to thin films. Finally, we
perform x-ray photoelectron spectroscopy (XPS) measurements, which show a
satellite peak around the Ni 3$p$ core level peak, which we interpret as a
signature of the $3d^{9}$ electronic configuration of LaNiO2.

##  II Methods

### High gas pressure optical floating zone growth

For the high gas pressure OFZ growth, La2O3 powder was dried at 1000∘C for one
day. Subsequently, we mixed and ground the dried La2O3 powder (10.284 g, 31.6
mmol, Alfa Aesar 99.99%) in a 0.5:1 molar ratio with NiO (4,7155 g, 31.6 mmol,
Alfa Aesar 99.998%) to obtain by oxidization in a high O2 partial pressure
stoichiometric LaNiO3 single crystals. The powder mixture was transferred to
an alumina crucible and sintered for 2 days at 900∘C in air followed by
subsequent grinding and repeated sintering. The powder was then transferred to
rubber forms, evacuated, and pressed at 700 bar in a Riken CD-10 press and
subsequently sintered at 1000∘C in air. The rods were centered and installed
in a high-pressure high-temperature optical floating zone furnace (Model HKZ,
SciDre GmbH, Dresden), followed by a growth at 150 bar oxygen pressure with a
flow of 0.1 l/min. The floating zone was moved with 4 mm/h, where due to the
low viscosity of the melt at these conditions a constant feeding of 2 mm/h was
necessary since a wider diameter of the seed developed. The obtained boule was
analyzed with x-ray Laue diffraction, and crystals with lateral dimensions of
several millimeters were extracted for subsequent reduction treatment.

### Topotactic reduction via direct and indirect contact

For the topotactic reduction with direct contact between the LaNiO3 single-
crystals and the reducing agent CaH2, a number of as-grown single-crystals
with lateral dimensions between $\sim$1 mm and $\sim$500 $\mu$m were selected,
such that a total mass of $\sim$100 mg was reached. Subsequently, $\sim$250 mg
CaH2 powder (Sigma Aldrich 97%) was loaded in a glass crucible and put into a
DURAN glass tube, together with the LaNiO3 crystals. The glass tube was then
evacuated ($\sim 10^{-7}$ mbar) and sealed to ampules with dimensions of
$\phi_{\text{out}}=1.7$ mm, $\phi_{\text{in}}=1.5$ mm, and $h=10$ cm. The
reduction was carried out by heating slowly to 300∘C in an optimized low
temperature furnace and held for 2-3 weeks before slowly cooling down to room
temperature. Subsequently, the ampules were opened and the obtained crystals
were handled in air.

In addition, several OFZ grown LaNiO3 crystals were reduced in spatial
separation to the reducing agent CaH2. This indirect contact method and the
used parameters are closely similar to the conditions in previous reports for
the reduction of LaNiO3 powder samples Ortiz  _et al._ (2022) and small
La1-xCaxNiO3 crystals Puphal  _et al._ (2021). Here, several OFZ grown
crystals with lateral dimensions of a few hundred micrometers and a total mass
of $\sim$100 mg were wrapped in aluminum foil and transferred to a glove box.
A glass crucible was loaded with 400-600 mg CaH2 powder and put into a DURAN
glass tube. The wrapped crystals were inserted into the glass tube and placed
above the crucible with CaH2. Subsequently, the glass tube was evacuated and
sealed to ampules. The reduction was carried out by heating the specimen
slowly to 300∘C and holding it for 8 weeks before slowly cooling down to room
temperature.

### Hydrogen gas extraction

The hydrogen content of the samples was determined with an Eltra ONH-2000
analyzer, for which pulverized crystals were placed in a Ni crucible, clipped
and heated. A carrier gas takes the hydrogen out of the sample and the
hydrogen is detected by a thermal-conductivity-cell. Each measurement is
repeated three times and compared to a standard. The quoted error bars give
the statistical error. We remark that the investigated LaNiO2.5 sample was
obtained from an indirect contact reduction after 8 weeks. The LaNiO2 sample
and the sample containing $\alpha$-La2O3 and elemental Ni were obtained from a
direct contact reduction after 2 weeks.

### Single-crystal x-ray diffraction

The single-crystal XRD data at ambient pressure were collected at room
temperature with a SMART APEXI CCD X-ray diffractometer (Bruker AXS,
Karlsruhe, Germany), using graphite-monochromated Mo-Kα radiation
($\lambda=0.71073\,$Å). Since very small crystal pieces are generally more
suitable for single-crystal XRD, all crystals investigated in this study are
fragments from larger crystals that were broken off in high viscosity oil. A
piece with lateral dimensions of approximately 50 $\mu$m was broken off from a
larger LaNiO2.5 crystal that was obtained from an indirect contact reduction
after 8 weeks. A similar piece was broken off from a LaNiO2 crystal that was
obtained from a direct contact reduction after 2 weeks. The pieces were
mounted with some grease on a loop made of Kapton foil (MicromountsTM,
MiTeGen, Ithaca, NY). The reflection intensities were integrated with the
SAINT subprogram in the Bruker Suite software package. The investigated
crystals with tetragonal symmetry showed systematic twinning by reticular
merohedry. The threefold axes of the (pseudo)cubic perovskite structure become
twinning elements, and the three twin domains are related by transformation
matrices: (1 0 0) (0 1 0) (0 0 1); (0 1 0) (0 0 1) (1 0 0); (0 0 1) (1 0 0) (0
1 0). To handle this, the reflection intensities were integrated with the help
of the orientation matrices of all three twin-domains, and a multi-scan
absorption correction was applied using TWINABS. The structure was solved by
direct methods and refined by full-matrix least-square fitting with the
SHELXTL software package.

The single-crystal XRD data at high pressure were collected at the beamline
ID27 at the European Synchrotron Radiation Facility (ESRF). We used membrane
driven diamond anvil cells with an angular opening of 70 degrees. These were
equipped with single crystalline diamonds with culet sizes of 500 $\mu$m.
Helium was used as pressure transmitting medium and the applied pressure was
determined by ruby fluorescence. Monochromatic x-rays with a wavelength of
0.3738 Å and a spot size of 1.5 $\times$ 1.8 $\mu$m2 were scattered from the
LaNiO2 crystal. Scattering intensities were collected in continuous rotation
and shutterless mode using an Eiger9M detector (Dectris, Switzerland) equipped
with 750 $\mu$m thick CdTe sensors with a pixel size of 75 $\times$ 75
$\mu$m2. The angular steps were 0.25 degrees, spanning 64 degrees in total.
The scattering geometry was calibrated using a CeO2 powder standard (NIST,
USA) and a vanadinite single-crystal. The detector distance was 216.445 mm.
For the measurement of the XRD at ambient pressure, a piece with a size of
approximately 40 $\times$ 40 $\times$ 30 $\mu$m3 was broken off from a larger
LaNiO2 crystal that was obtained from a direct contact reduction after 2
weeks. For the high-pressure XRD another piece was broken off from the same
crystal, with a size of approximately 50 $\times$ 50 $\times$ 30 $\mu$m3.

### X-ray photoelectron spectroscopy

Prior to the XPS measurements, a centimeter-sized LaNiO3 single crystals was
cleaved and mounted on carbon tape. LaNiO2 crystals with sizes between 1 mm
and 500 $\mu$m were transferred into the glove box rapidly after the reduction
process was finished. In the glove box, they were broken into slightly smaller
pieces to expose freshly cleaved surfaces and distributed on an indium foil.
All samples were transferred under inert gas into the XPS chamber. The XPS
data were collected using a commercial Kratos AXIS Ultra spectrometer and a
monochromatized Al $K_{\alpha}$ source (1486.6 eV). The base pressure during
XPS was below $10^{-9}$ mbar. Survey spectra were acquired with a pass energy
of 80 eV and detailed spectra with a pass energy of 20 eV. Since the LaNiO2
spectra showed some charging the binding energy was calibrated to the La
3$d_{5/2}$ peak at the lowest binding energy of LaNiO3. The intensity of the
spectra was normalized to the most intense La 3$d$ peak.

### Physical properties measurements

Magnetic susceptibility measurements were carried out in a range of 1.8 - 350
K and 0 - 7 T using a Quantum Design Magnetic Property Measurements System
(MPMS). The resistivity measurements were carried out using the standard
option of a Physical Property Measurements System (PPMS).

Figure 1: a) The top panel shows a PXRD pattern of a pulverized LaNiO2 crystal
taken with Cu Kα radiation. The solid red line in the top panel is the fit
from a Rietveld refinement, which includes the LaNiO2 phase (upper green
symbols) and a minority LaNiO2.5 phase (lower green symbols). The most
prominent Bragg peaks of the latter phase are indicated by asterisks. The
inset shows the IL nickelate structure with the green, grey, and red spheres
corresponding to La, Ni, and O respectively. The bottom panel shows a XRD
pattern from an out-of-plane scan of a crystal prior to pulverization. The
peaks of the (0 0 $L$), ($H$ 0 0), and ($H$ 0 $L$) families of the LaNiO2
phase with the tetragonal $P4/mmm$ unit cell are indicated. The inset displays
a rocking curve of the (0 0 2) peak. b) Photograph of four representative
reduced crystals on millimeter paper, where one crystal was used for the
diffraction measurements in panel a. c) EDX spectra from cleaved surfaces of
an as-grown LaNiO3 (black) and a reduced (red) crystal. Note the reduced
intensity of the O $K_{\alpha_{1}}$ peak after reduction, whereas the La and
Ni lines remain essentially unchanged, as expected. d) SEM image of a crystal
surface after reduction (not cleaved). Note that the cracks and furrows
visible on the surface are mostly arranged in rectangular patterns and likely
correspond to domain boundaries between tetragonal LaNiO2 twin domains. A few
cracks are arranged in angles of $\sim 120^{\circ}$, which is possibly a
consequence of the presence of rhombohedral domain boundaries in the pristine
LaNiO3 phase prior to the reduction. The same crystal was used for the
resistivity measurements in Fig. 5.

##  III Results

###  III.1 Crystal growth and topotactic reduction

For the synthesis of sizable perovskite LaNiO3 crystals, we employ a high gas
pressure OFZ furnace with 150 bar oxygen pressure. In the obtained boule with
a diameter of 6-8 mm and a length of 8 cm, a single grain develops during the
growth after a few mm. For the subsequent topotoactic reduction, crystals from
the boule are broken into smaller fragments, from which we select pieces with
lateral dimensions between 1.5 mm and 500 $\mu$m.

In a previous reduction study, an indirect contact method with up to 4 weeks
reduction time was applied to La1-xCaxNiO3 crystals with typical dimensions of
150 $\times$ 150 $\times$ 150 $\mu$m3 Puphal  _et al._ (2021). Notably, we
find for millimeter sized LaNiO3 crystals that even 8 weeks of indirect
contact reduction only lead to the intermediate LaNiO2.5 phase, suggesting
that for sizable crystals the reduction beyond the intermediate phase
progresses exponentially slow Puphal  _et al._ (2022) and a tremendous
reduction time would be required to reach the IL phase via the indirect
contact method. In the present study, we thus apply direct contact between the
millimeter-sized LaNiO3 crystals and the reducing agent CaH2 for 2-3 weeks.
This yields a transformation of the majority of our crystals to the IL phase
(Fig. 1a)), although a minority phase of incompletely reduced LaNiO2.5 can
still be detected in PXRD (top panel in Fig. 1a)).

Figure 1b) shows four representative crystals with lateral dimensions of
approximately 1 $\times$ 1 mm2, which were obtained after two weeks of direct
contact reduction. The weight of each crystal is about 2 mg. Indications for
the reduced oxygen content in the crystals after the topotactic treatment can
be recognized from scanning electron microscopy (SEM) with energy-dispersive
x-ray spectroscopy (EDX) analysis (Fig. 1c)), albeit a quantitative
determination of the LaNiO2 and LaNiO2.5 fractions is challenging due to the
low sensitivity of the technique to light elements such as oxygen. On the
other hand, a Rietveld refinement of PXRD data can allow for a more robust
analysis, in particular due to the distinct lattice constants of the different
phases. In more detail, as the entire crystal is pulverized for the PXRD, all
constituent phases of the crystal can be exposed (top panel in Fig. 1a)). The
PXRD data can be refined reasonably well when assuming that the crystal
consists of LaNiO2 in space group $P4/mmm$ Hayward  _et al._ (1999); Lin  _et
al._ (2022); Puphal  _et al._ (2021) and the intermediate LaNiO2.5 phase, with
the former contributing 83.7 wt% and the latter 16.3 wt%. The lattice
parameters obtained from the refinement are presented in Tab. 1. While the
fraction of the incompletely reduced minority phase is considerable in the
PXRD of the crystal of Fig. 1a), a XRD out-of-plane scan ($\omega-2\Theta$
scan) taken on a crystal prior to pulverization shows virtually no traces of
the LaNiO2.5 phase (bottom panel in Fig. 1a)). Instead, only specific LaNiO2
Bragg reflections are present, which are associated with the (0 0 $L$), ($H$ 0
0), and ($H$ 0 $L$) peak families of the IL structure in space group $P4/mmm$.
Note that in the XRD pattern the relative intensities between the peak
families differ from the PXRD pattern, which is due to a dominance of the (0 0
$L$) and ($H$ 0 0) oriented domains in the measured crystal in the bottom
panel of Fig. 1a). The inset in Fig. 1a) shows a rocking curve of the (0 0 2)
peak of the LaNiO2 crystal, which exhibits a relatively broad width. This
indicates that the mosaic spread of the crystallographic planes is large when
averaging over the entire crystal. Nonetheless, it is likely that on a local
scale the mosaic spread is substantially smaller and the planes of the IL
crystal lattice are highly aligned, similarly to the local crystal structure
that was revealed by scanning transmission electron microscopy (STEM) within
the domains of La1-xCaxNiO2 crystals Puphal  _et al._ (2021).

Notably, it was found previously that La1-xCaxNiO2 crystals tend to break
along the boundaries between the three orthogonal domains of the tetragonal
space group $P4/mmm$ Puphal  _et al._ (2021). This separation of
crystallographic domains occurs especially upon excessive reduction, but
precursors of the separation can be observed already earlier in the form of
cracks and furrows on the crystal surface. A representative SEM image of a
LaNiO2 crystal surface is shown in Fig. 1d), where several adjacent cracks are
oriented either in a parallel or orthogonal fashion. The average distance
between these cracks is much larger than the typical domain size of 10
$\times$ 10 $\times$ 10 $\mu$m3 in La1-xCaxNiO2 crystals Puphal  _et al._
(2021), suggesting an increased domain size for the OFZ grown and directly
reduced crystals in the present study. This notion is supported by the fact
that the 50 $\times$ 50 $\times$ 30 $\mu$m3 crystal used in the high-pressure
measurements (see below) shows an XRD signal that originates almost
exclusively from one domain. The occurrence of numerous cracks on larger
lengths scales is likely responsible for the broad width of the rocking curve
in the inset in Fig. 1a), as the spatial separation of the domains can lead to
a misalignment of the crystallographic planes in the macroscopic average.
Nevertheless, we note that in spite of the onset of domain separation, the
crystals in Fig. 1b) were robust and not brittle when they were handled during
our study.

Figure 2: a) PXRD pattern of a pulverized crystal that experienced excessive
reduction (decomposition). The Rietveld refinement includes various phases, as
indicated in the legend. b) SEM image of the decomposed crystal. The image
shows a cleaved surface of the crystal, which was exposed after the topotactic
reduction. c) Hydrogen content determined by gas extraction from a pristine
sample (LaNiO3), indirect contact reduced sample (LaNiO2.5), direct contact
reduced sample (LaNiO2), as well as the decomposed direct contact sample. The
hydrogen is given in weight-% (left axis) and for the assumption of a
hypothetical LaNiO3-xHy composition of each sample, where $x$ is 0, 0.5, and
1, respectively (right axis). Figure 3: Maps of XRD intensities in the ($H$
$K$ 0) planes of the reduced crystals. a), b) Maps acquired at ambient
conditions with Mo Kα radiation ($\lambda=0.71073\,$Å) from a LaNiO2.5 and
LaNiO2 crystal, respectively. The LaNiO2.5 map shows superstructure
reflections between the main Bragg reflections, which are not present in the
LaNiO2 map. The inset in each panel magnifies the region around a three-fold
split Bragg reflection (see dashed white box), with the out-of-plane dimension
corresponding to the XRD intensity. In the inset in panel a) the main
reflection can be indexed as (1 1 0), while the two weaker reflections
originate from the (1 0 1) and (0 1 1) twin domain, respectively. Very weak
superstructure reflections can also be seen in the inset. In the inset in
panel b), the three reflections of the twin domains exhibit similar
intensities, indicating an equal population of the domains in the investigated
crystal. c), d) High-resolution XRD maps of a different LaNiO2 crystal
acquired with synchrotron radiation ($\lambda=0.3738\,$Å) for applied
pressures of 0.3 and 12 GPa, respectively. The insets highlights the dominant
intensity of the of the (1 1 0) domain in the investigated crystal. e)
Evolution of the lattice constants as a function of reduced oxygen content.
For LaNiO3, the lattice constants $a=c$ refer to the pseudocubic unit cell
(Ni-Ni bond distance, see text). For LaNiO2.5 and LaNiO2, $a$ and $c$ are
derived from their tetragonal $P4/mmm$ unit cells (see text). f) Lattice
constants of LaNiO2 as a function of hydrostatic pressure.

###  III.2 Excessive reduction and hydrogen incorporation

Besides the presence of the insufficiently reduced LaNiO2.5 phase, also an
excessive reduction is detrimental for the realization of high-quality LaNiO2
crystals. Fig. 2a) shows the PXRD pattern of a crystal that was reduced far
beyond the ideal IL LaNiO2 composition, revealing that the sample contains
elemental Ni, crystalline $\alpha$-La2O3 and LaOH, as well as remnants of
LaNiO2. In more detail, the composition in weight-% obtained from Rietveld
refinement is 62.3 wt% La2O3, 15.15 wt% Ni, 13.22 wt% LaOH, and 9.33 wt%
LaNiO2. Note that LaOH is a relatively uncommon compound, but it is typically
obtained as a byproduct when treating La2O3 with hydrogen Malaman and Brice
(1984). In the following, we will refer to excessively reduced samples as
decomposed crystals, although we note that the sample retains some crystalline
integrity, while exhibiting an increased number of cracks and furrows (Fig.
2b)). In other words, the LaNiO2 phase in the sample is mostly decomposed,
whereas a crystalline structure of other phases is still present to a certain
degree.

Remarkably, the decomposed crystals (Figs. 2a,b)) and the LaNiO2 crystals in
Fig. 1 were obtained from the same reduction batch, i.e., the crystals were
exposed to closely similar reduction conditions. However, one notable
difference between the crystals are the dimensions, with the decomposed
crystal exhibiting a much larger size of approximately 2 $\times$ 1.5 $\times$
1.5 mm3. Moreover, we find that crystals with somewhat smaller dimensions than
the crystals from Fig. 1 show a trend of enhanced LaNiO2.5 contributions,
i.e., the reduction appears to have not progressed as much. We attribute these
observations to an exothermal nature of the topotactic reduction process,
where additional heat generated within large crystals expedites the reduction,
which is very sensitive to temperature Hayward and Rosseinsky (2003). Hence,
we conclude that the reduction parameters of the present study (see Methods)
are best suited for the reduction of LaNiO3 crystals with dimensions of
approximately 1 mm3, whereas modifications would be required for an optimal
reduction of larger or smaller crystals.

One vividly debated aspect of the topotactic reduction of nickelates is the
possible incorporation of hydrogen in the crystal lattice Onozuka  _et al._
(2016); Si  _et al._ (2020); Malyi  _et al._ (2022); Carrasco Álvarez  _et
al._ (2022); Bernardini  _et al._ (2022b); Si  _et al._ (2022), which could
lead to the formation of oxyhydride nickelates, in analogy to topotactically
reduced vanadates of composition SrVO2H Denis Romero  _et al._ (2014). In
fact, some of us recently reported the presence of a significant amount of
hydrogen that accumulates in powder samples during the reduction from LaNiO3
to LaNiO2 when using CaH2 in indirect contact Puphal  _et al._ (2022).
However, as the key result, the analysis of neutron diffraction data revealed
that hydrogen or OH molecules were likely not incorporated at proper lattice
positions in the LaNiO2 unit cell. Instead, we proposed that the hydrogen,
which was detected by a gas extraction method, is trapped at Ni impurities
and/or at grain surfaces and boundaries Puphal  _et al._ (2022).

Here, we also use gas extraction to investigate the occurrence of possible
hydrogen incorporation during the reduction of our OFZ grown LaNiO3 single-
crystals. Figure 2c) shows the extracted hydrogen content in weight-% for
LaNiO3, LaNiO2.5, LaNiO2, as well as the decomposed crystal from Figs. 2a,b).
For the former three cases, we find a steady increase of the detected amount
of hydrogen with increasing reduction progress, quantitatively similar to the
powder reduction in Ref. Puphal  _et al._ , 2022. In the case of the
decomposed crystal, however, the amount of hydrogen is strongly increased by
more than a factor of five, although this crystal was exposed to the reduction
process for the same duration as the LaNiO2 crystal. This observation supports
the notion that LaNiO2 is not prone to topotactic hydrogen incorporation
Puphal  _et al._ (2022), but instead that hydrogen in topotactic nickelate
samples is closely associated with impurities and/or decomposed phases. In
particular, while the decomposition into La2O3 and Ni as a source for hydrogen
trapping was already suggested in Ref. Puphal  _et al._ , 2022, the Rietveld
refinement of the significantly decomposed crystal in Fig. 2a) can only be
performed when also including LaOH. Thus, while we do not find indications for
the formation of any oxyhydride nickelate, the observed La-based hydroxide
likely explains the steep increase of detected hydrogen gas for the decomposed
sample (Fig. 2c)). The small amount of hydrogen gas detected for the LaNiO2.5
and LaNiO2 samples can be due to subtle NiO impurities that are readily
incorporated in as-grown LaNiO3 crystals and gradually reduce to elemental Ni,
acting as a hydrogen trap. Alternatively, local parts of the LaNiO2.5 and
LaNiO2 crystals might have overheated in the exothermal reaction, readily
yielding minor amounts of LaOH, although we note that this phase was not
identified in the corresponding PXRD patterns (see for instance Fig. 1a)).

In conclusion, the reducing agent CaH2 provides not only the hydrogen
atmosphere facilitating the topotactic reduction, but can also lead to a
solid-solid (oxide-hydride) reaction and the formation of LaOH. Future studies
are required to clarify the onset of the reaction and its influence on the
progression of the topotactic reduction, similarly to previous thin film
studies comparing the application of reducing agents in direct contact and the
reduction in a hydrogen gas atmosphere Ikeda  _et al._ (2014).

###  III.3 Crystal structure at ambient and high pressures

Detailed information on the structure of the reduced crystals can be obtained
from reconstructed intensity maps of single-crystal XRD data (Fig. 3). As a
first step, we analyze the XRD data of a crystal that was reduced until the
intermediate LaNiO2.5 phase. In the reconstructed map of the ($H$ $K$ 0)
planes (Fig. 3a)), sharp superstructure reflections with minor intensity
appear in addition to the main Bragg reflections. These superstructure
reflections cannot be captured by a simple tetragonal unit cell. Nonetheless,
for better comparability with the fully reduced samples, we perform the
Rietveld refinement in the tetragonal space group $P4/mmm$, i.e., the same
space group that is commonly employed for the IL nickelates Hayward  _et al._
(1999); Hayward and Rosseinsky (2003); Puphal  _et al._ (2022); Ortiz  _et
al._ (2022). However, in contrast to the IL crystal structure, we allow for
the occupation of apical oxygen sites in the unit cell, reflecting the oxygen
stoichiometry of the LaNiO2.5 phase. Note that the refinement of LaNiO2.5 in
$P4/mmm$ is different from previous powder studies on the material, which
employed the larger monoclinic $P2_{1}/n$ unit cell Alonso  _et al._ (1997).
The refined lattice parameters are presented in Tab. 1.

Next, we acquire single-crystal XRD maps from a crystal after completed
reduction. This crystal is a fragment with approximate dimensions of 50
$\times$ 50 $\times$ 50 $\mu$m3, which was broken off from a much larger
reduced crystal. The obtained reconstructed maps are similar to those of
La1-xCaxNiO2 crystals Puphal  _et al._ (2021). In particular, a three-fold
splitting of the XRD reflexes is present (see Fig. 3b)), which is indicative
of the domain formation upon reduction that was already recognized in the SEM
image (Fig. 1d)). The onset of a three-fold splitting is also observable in
the XRD map of the intermediate LaNiO2.5 phase (see Fig. 3a). The refinement
of the LaNiO2 crystal is carried out taking into account a statistical
distribution of three orthogonally oriented twin domains of the tetragonal
$P4/mmm$ unit cell, with the lattice constants $a,b=3.9901(11)$ Å and
$c=3.3918(14)$ Å. These lattice constants are slightly larger than the values
reported for LaNiO2 powder and La1-xCaxNiO2 crystals Hayward  _et al._ (1999);
Puphal  _et al._ (2022); Ortiz  _et al._ (2022); Puphal  _et al._ (2021),
which might point to a small amount of remaining apical oxygen ions or
residual domains of the LaNiO2.5 phase in the investigated crystal fragment.

Figure 3e) focuses on the evolution of the lattice parameters as a function of
reduced oxygen content. For better comparability, we convert the rhombohedral
lattice constants of LaNiO3 into a pseudocubic setting, where the pseudocubic
lattice constants $a=b=c$ are equivalent to the Ni-Ni bond distance. The
rhombohedral lattice constants (see Tab. 1) were obtained from Rietveld
refinement of a pulverized LaNiO3 single-crystal. As a key result we find that
the topotactic reduction from LaNiO3 to the intermediate LaNiO2.5 phase leaves
the Ni-Ni bond distance almost unchanged, whereas a clear variation occurs for
the transition from LaNiO2.5 to LaNiO2, with a moderate increase of the in-
plane lattice constant and a dramatic collapse of the $c$-axis lattice
constant. This behavior can be rationalized when considering that the partial
occupation of the apical oxygen sites in LaNiO2.5 can still stabilize the
original unit cell volume, whereas the complete lack of apical oxygen in the
IL structure leads to the $c$-axis collapse.

Table 1: Refined lattice constants of unreduced and reduced nickelate crystals. The powder samples were a pulverized pristine LaNiO3 crystal that was refined in the rhombohedral space group $R\bar{3}c$ (hexagonal axes) and a pulverized reduced crystal that was refined with a LaNiO2.5 minority phase in the monoclinic space group $P2_{1}/c$ and LaNiO2 majority phase in the tetragonal space group $P4/mmm$. The crystalline samples were a LaNiO2.5 and a LaNiO2 crystal. Unlike the LaNiO2.5 powder with space group $P2_{1}/c$, the LaNiO2.5 crystal was considered in a simplified approach and refined in $P4/mmm$ (see text). For crystalline LaNiO2, high-resolution synchrotron XRD data was refined in $P4/mmm$ for the cases of p = 0, 0.3, 6, and 12 GPa pressure. | type | symmetry | p [GPa] |  $a$ [ Å ] |  $c$ [ Å ]
---|---|---|---|---|---
LaNiO3 | powder | $R\bar{3}c$ | - | 5.45409(7) | 13.12546(19)
LaNi2.5 | powder | $P2_{1}/c$ | - | 7.914(2) | 7.443(2)
| crystal | $P4/mmm$ | - | 3.8664(17) | 3.812(2)
LaNiO2 | powder | $P4/mmm$ | - | 3.9540(3) | 3.3744(3)
| crystal | $P4/mmm$ | - | 3.9901(11) | 3.3918(14)
| crystal | $P4/mmm$ | 0.3 | 3.9619(3) | 3.360(3)
| crystal | $P4/mmm$ | 6.0 | 3.9082(7) | 3.318(7)
| crystal | $P4/mmm$ | 12 | 3.8953(8) | 3.28(10)

To gain insights into the stability and elasticity of the IL structure
obtained after the $c$-axis collapse, we carry out high-resolution synchrotron
XRD measurements under high pressure in a diamond anvil cell. Figure 3f)
displays the dependence of the lattice parameters on the applied pressure,
which was measured on a piece broken off from the same LaNiO2 crystal that was
measured in ambient conditions. We find that under the application of 12 GPa,
the lattice parameters compress to $a=3.8953(8)$ Å and $c=3.284(10)$ Å. The
calculated bulk modulus via the unit cell volume $V$ extracted from refinement
yields a large value of $K=-V\cdot dp/dV=155.39$ GPa, similar to what is
reported for cuprates ranging from 60-180 GPa Qin  _et al._ (2005); Hyatt  _et
al._ (2001), highest for the related IL cuprates. In this context, we note
that the application of pressure is a powerful knob to tune the properties of
cuprate superconductors Mark  _et al._ (2022), yielding the record transition
temperature $T_{c}$ of more than 150 K in mercury-based cuprates at 30 GPa Chu
_et al._ (1993). Similarly, a recent pressure study on IL nickelates
demonstrated that the $T_{c}$ of Pr0.82Sr0.18NiO2 thin films can be increased
from 17 K to $\sim 31$ K under 12.1 GPa of hydrostatic pressure, suggesting a
$T_{c}$ vs. pressure enhancement law with a slope of 0.96 K/GPa Wang  _et al._
(2022b). Along these lines, our analysis reveals that 12 GPa pressure shrinks
the $c$-axis lattice constant of LaNiO2 by 0.11 Å, which presumably increases
the hybridization between the Ni $3d$ and rare-earth $5d$ orbitals
considerably. The presence of this hybridization is a hallmark of IL
nickelates Hepting  _et al._ (2021), whereas it is absent in the IL cuprate
CaCuO2 Botana and Norman (2020). On the other hand, the decrease of the in-
plane lattice constant under pressure leads to a decrease of the Ni-O-Ni bond
angle in the NiO2 plane and therewith a decrease of the hybridization between
the planar Ni $3d_{x^{2}-y^{2}}$ and O $2p$ orbitals can be expected Wang  _et
al._ (2022b); Kang  _et al._ (2022). While this hybridization is already small
in unstrained IL nickelates Lee and Pickett (2004), the application of
hydrostatic pressure apparently provides a tool to impede it further.

###  III.4 Magnetic susceptibility

Figure 4a) shows the susceptibility of a LaNiO2 crystal measured in a small
external field. The observed evolution of the susceptibility as a function of
temperature is reminiscent of polycrystalline LaNiO2, which was reported in
detail in Ref. Ortiz  _et al._ , 2022 together with a theoretical modeling of
the associated magnetic correlations. Along the lines of previous works on
polycrystalline nickelates Huangfu  _et al._ (2020); Ortiz  _et al._ (2022);
Lin  _et al._ (2022); Wissel  _et al._ (2022), we interpret the splitting of
the curves measured upon zero field cooling (ZFC) and field cooling (FC), as
well as the cusp of the ZFC curve around $\sim$30 K, as the signature of a
spin-glass state. The glassy dynamics in infinite-layer nickelates are
possibly related to subtle local oxygen disorder in the form of remaining
apical oxygen that can yield clusters with enhanced moments from Ni2+, which
dominate the low field susceptibility signal of topotactic bulk LaNiO2 samples
Ortiz  _et al._ (2022). As expected, we observe that for stronger applied
fields the bifurcation between the ZFC and FC curve decreases gradually Ortiz
_et al._ (2022), and for a field of 7 T we find the gap to be completely
closed and both curves merged (Fig. 4b)). The apparent Pauli paramagnetic
behavior in Fig. 4b) can be fitted by a Curie-type law
$\chi(T)=\chi_{0}(1-aT^{2})+C/T$ Zhou  _et al._ (2014), with $a=1.81(3)\cdot
10^{-6}$ K2, $C=0.072(5)\cdot 10^{-6}$ m3/mol K-1 and $\chi_{0}=0.1100(2)\cdot
10^{-6}$ m3/mol, where $\chi_{0}$ is a temperature-independent constant and
$C$ the Curie constant. The obtained fit parameters are comparable to the
results from a Curie-type fit of La1-xCaxNiO2 crystals Puphal  _et al._
(2021).

Figure 4: a) Susceptibility of a LaNiO2 crystal, measured upon zero field
cooling (ZFC) and field cooling (FC) in a small external field of 0.1 T. b)
Susceptibility of the same crystal measured in a strong field of 7 T. c)
Comparison of the corrected magnetic susceptibilities of the LaNiO2 crystal
(green symbols), LaNiO2 powder (red symbols), and a La0.93Ca0.07NiO2 crystal
(blue symbols). The LaNiO2 powder was obtained from an indirect contact
reduction of LaNiO3 powder synthesized via the citrate-nitrate method Ortiz
_et al._ (2022). The La0.93Ca0.07NiO2 crystal was obtained from an indirect
contact reduction of a La0.93Ca0.07NiO3 crystal synthesized via salt flux
growth with oxidizer in a multi-anvil press Puphal  _et al._ (2021). The
corrected susceptibilities were extracted via the Honda-Owen method (see text)
from magnetization versus field curves.

While the glassy dynamics are suppressed in strong fields, Ref. Ortiz  _et
al._ , 2022 pointed out that the high-field susceptibility signal can be
influenced by elemental Ni impurities. Thus, in order to discern between the
ferromagnetic Ni background and intrinsic paramagnetic behavior of the
majority phase, we apply the Honda-Owen method Honda (1910); Owen (1912) to
isotherms measured between $4$ and $7$ T. This method extrapolates the
measured susceptibility $M/H=M_{\text{c}orr}/H+C_{\text{sat}}M_{\text{sat}}/H$
for $1/H\rightarrow 0$, where $M/H$ is the measured susceptibility,
$M_{\text{c}orr}/H$ the corrected (intrinsic) susceptibility, $C_{\text{sat}}$
the presumed ferromagnetic impurity content and $M_{\text{sat}}$ its
saturation magnetization. The resulting corrected susceptibility of a LaNiO2
crystal is presented in Fig. 4c) (green symbols). In addition, the corrected
susceptibility from a powder sample of LaNiO2 Ortiz  _et al._ (2022) (red
symbols) and a batch of several La1-xCaxNiO2 crystals (blue symbols) Puphal
_et al._ (2021) are shown. Whereas the corrected susceptibilities of the
former two samples exhibit a subtle minimum around $\sim$65 K and increase
almost linearly towards room temperature, the susceptibility of the Ca-
substituted sample decreases in this temperature range. The increase of the
susceptibility of LaNiO2 indicates non-Curie-Weiss behavior and can be
ascribed to enhanced AFM fluctuations Ortiz  _et al._ (2022). We note that the
corrected susceptibilities of the LaNiO2 crystal and the LaNiO2 powder are
almost identical across the entire measured temperature range, in spite of the
fact that the LaNiO3 precursor phases were synthesized by different methods
and presumably contained a different amount of NiO and other secondary phases.
Hence, the closely similar susceptibility values extracted by the Honda-Owen
method, corroborate that the method is viable to determine the intrinsic
susceptibility of the majority IL phase in the samples. Notably, the non-
Curie-Weiss behavior of LaNiO2 resembles the susceptibility of lightly doped
cuprates, such as La2-xSrxCuO4 with $x\geq 0.04$ Nakano  _et al._ (1994),
hinting towards an analogy between magnetic correlations in parent IL
nickelates and doped cuprates Ortiz  _et al._ (2022). In this context, the
effects of self-doping due to rare-earth electron pockets on the magnetic
response are an interesting topic for future studies on parent IL nickelates.

In contrast, the corrected susceptibility of La1-xCaxNiO2, which is hole-doped
due to the Ca-substitution, is clearly distinct from LaNiO2. Remarkably,
overdoped cuprates, such as La2-xSrxCuO4 with $x\geq 0.22$ Nakano  _et al._
(1994), show a similar susceptibility with a strong upturn towards lower
temperatures, thus underscoring the analogy between the magnetic correlations
in IL nickelates and cuprates, although with a substantial offset with respect
to the nominal hole-doping levels. For completeness, we note that the
corrected susceptibility of La1-xCaxNiO2 exhibits a sharp drop below $\sim$6
K, which is a similar temperature as the $T_{c}$ of La1-xCaxNiO2 films Zeng
_et al._ (2022a). However, we emphasize that the data in Fig. 4c) were
extracted from isotherms measured in high fields between $4$ and $7$ T where
any superconductivity should be (at least partially) suppressed. Instead, the
sharp downturn—which more subtly occurs also in the LaNiO2 data— is likely
related to the glassy state with spins that are frozen in arbitrary directions
at these low temperatures, although with underlying AFM correlations, which is
an effect that is not properly filtered out by the Honda-Owen method that is
suitable for ferromagnetic impurities.

Figure 5: Electronic transport of reduced samples. a) Resistivity of a LaNiO2
crystal. b) The same resistivity data, but on a linear-log scale. The solid
black line is a guide to the eye, highlighting the temperature range with a
logarithmic dependence. c) Resistivity at 4 K measured as a function of the
applied magnetic field from -9 to 9 T. No magnetoresistance effect is observed
within the experimental error. d) Resistivities of pressed powder pellets. The
green curve corresponds to a pulverized LaNiO2 crystal, the red curve to a
LaNiO2 powder samples that was readily reduced in powder form (see Ref. Ortiz
_et al._ , 2022), and the black curve is from a decomposed crystal.

###  III.5 Electronic transport

Figure 5 displays the resistivity of various reduced samples. As expected, the
measurement of a LaNiO2 crystal reveals metallic behavior at high temperatures
and a weakly insulating upturn at low temperatures (Fig. 5a)). Qualitatively,
this behavior is analogous to the resistivity of small La0.92Ca0.08NiO2
crystals Puphal  _et al._ (2021) and the in-plane resistivity of
$R_{1-x}A_{x}$NiO2 films with low doping Osada  _et al._ (2020); Zeng  _et
al._ (2020); Li  _et al._ (2021); Gao  _et al._ (2021); Li  _et al._ (2020a);
Osada  _et al._ (2021); Wang  _et al._ (2022a); Ren  _et al._ (2021); Lee  _et
al._ (2022). Moreover, metallic behavior with a low-temperature upturn is
reminiscent of underdoped cuprates Takagi  _et al._ (1992). The magnitude of
our resistivity is comparable to previous reports on LaNiO2 thin films Kawai
_et al._ (2009); Kaneko  _et al._ (2009); Zeng  _et al._ (2022a), although we
note that some studies achieved films with much lower residual resistivities
Osada  _et al._ (2021); Ikeda  _et al._ (2016). Since our data were acquired
from a reduced crystal with dimensions as large as 1.4 $\times$ 0.8 $\times$
0.8 mm3, it can be assumed that a large quantity of IL domains contributes to
the resistivity in Fig. 5a), with each domain likely exhibiting an anisotropy
between the in-plane and out-of-plane transport, which, however, is not yet
established quantitatively for IL nickelates. Furthermore, it is possible that
residual domains in the LaNiO2.5 phase and/or the presence of insulating La2O3
influence the transport and lead to an increased value of our measured
resistivity.

Nevertheless, we emphasize that on a linear-log scale, our data closely follow
a logarithmic temperature (ln $T$) dependence below the resistivity minimum at
$\sim$100 K (Fig. 5b)). This temperature dependence has been identified as a
hallmark of the resistivity of the parent compounds of the IL nickelates Hsu
_et al._ (2022) and was discussed in the context of a Mott-Kondo scenario
Zhang  _et al._ (2020); Yang and Zhang (2022), or strong electron correlations
Hsu  _et al._ (2021). Moreover, below 10 K, high-quality LaNiO2 films showed a
deviation from the logarithmic temperature dependence and tend towards a
plateau Hsu  _et al._ (2022); Zhang  _et al._ (2020), while arguably even
further optimized films showed a downturn beyond the plateau at lowest
temperatures, which was interpreted as a possible onset of superconductivity
Osada  _et al._ (2021). In Fig. 5b), the emergence of a plateau-like behavior
is also visible, yet no downturn occurs until the lowest measured temperature
($\sim$4 K).

Insights into the origin of the upturn of the resistivity below $\sim$100 K
can be obtained from magnetoresistance measurements. Figure 5c) presents the
resistivity of the LaNiO2 crystal at 4 K as a function of an applied magnetic
field. Remarkably, the resistivity shows virtually no dependence on the field,
which makes a Mott-Kondo scenario implausible and also suggests that the
upturn is not dominated by disorder and weak localization effects. The absence
of a field dependence was similarly observed in lightly hole-doped nickelate
films Lee  _et al._ (2022) and is compatible with an effective freezing of
mobile charge carriers due to intrinsic strong correlations Hsu  _et al._
(2021). Nonetheless, we remark that the presence of diffuse scattering
intensity around the Bragg peaks in the XRD maps (Fig. 3) and spin glass
behavior (Fig. 4) are clear indications for the presence of disorder, although
it is still possible that the correlation effect is predominant in the low-
temperature transport.

In order to further explore the effects of disorder and an anticipated
transport anisotropy, we probe the resistivity of a pulverized LaNiO2 crystal
that was pressed into a pellet form (Fig. 5d)). The PXRD of the same powder is
given in Fig. 1a). While at high temperatures the magnitude of the resistivity
of the crystal (Fig. 5a)) and the pressed powder are similar, the latter
samples lack a decrease of the resistivity with decreasing temperature between
300 and $\sim$100 K, where the resistivity minimum of the former sample
occurred. The continuous increase of the resistivity of the powder, which
signals semi-conducting behavior, is presumably a consequence of the hampered
transport across boundaries between powder grains. Moreover, since the powder
resistivity measurement corresponds to an average of the different
crystallographic directions of LaNiO2, it reflects the transport anisotropy
and also suggests that the data in Figs. 5a,b) were mostly influenced by the
transport within the more conducting NiO2 planes.

In addition, we compare the resistivity of the pulverized crystal and LaNiO2
powder that was obtained via the topotactic reduction of LaNiO3 powder. This
powder exhibits a very high purity, with secondary phases below 2 wt% (details
of the synthesis and characterization are given in Refs. Ortiz  _et al._ ,
2022; Puphal  _et al._ , 2022). Nevertheless, we find that the resistivity of
the powder obtained readily from powder reduction is strongly enhanced across
the entire temperature range and reaches even the semi-conducting/insulating
regime (Fig. 5d)). We ascribe this behavior to the exposure of an increased
surface area of the powder grains during the topotactic reduction. In
particular, the reduction of powder likely facilitates the formation of local
defects in the surface regions of grains and might also lead to an enhanced
water adsorption Puphal  _et al._ (2022). Regarding a future realization of
superconducting bulk IL nickelates, these findings suggest that for achieving
superconductivity it might be detrimental to reduce powder samples. On the
other hand, if bulk crystals with sufficient hole-doping host
superconductivity, a crystal pulverized after the topotactic reduction might
show superconductivity, provided that the superconducting coherence length in
the $c$-axis direction is sufficiently long.

For comprehensiveness, we also report the resistivity of a decomposed crystal.
As can be seen in Fig. 5d), the resistivity evolves in a strongly insulating
regime at all temperatures, i.e., the presence of metallic elemental Ni in
such a sample is not relevant for the macroscopic transport properties.

###  III.6 Electronic structure

Figure 6: XPS spectra of LaNiO3 (black) and LaNiO2 crystals (red) for a)
binding energies between 885 and 825 eV and b) energies between 80 and 60 eV.
The spectra are normalized to the maximum intensity and offset in vertical
direction for clarity. The LaNiO2 spectra are shifted horizontally by -2.1 eV
to compensate for a charging effect. The inset in a) zooms into the Ni
$2p_{1/2}$ region, after subtraction of a fitted Shirley background. The red
arrow in b) indicates the satellite peak for LaNiO2.

XPS can provide valuable information on the electronic structure of materials,
but is highly surface sensitive as photoelectrons are emitted only from
regions in close proximity to the surface. As a consequence, previous
photoemission studies on IL nickelates are sparse Chen  _et al._ (2022); Fu
_et al._ (2020); Higashi  _et al._ (2021), because the invasive topochemical
reduction typically deteriorates the surface region of thin film and powder
samples. In principle, a few unit cell thick SrTiO3 capping layer on top of
thin films can prevent an impairment of the topmost nickelate layers, however,
at the same time, the capping shields the nickelate film, which greatly
hampers the realization of photoemission experiments. Along these lines, large
LaNiO2 crystals provide tremendous opportunities, as they can be cleaved.
Thus, fresh surfaces can be obtained that were not directly exposed during the
topotactic reduction process.

For our XPS measurements, we prepared samples in a glove box under Ar
atmosphere, which were subsequently transferred under inert gas into the XPS
chamber. Specifically, we fractured a large as-grown LaNiO3 crystal in the
glove box and unveiled a $\sim$16 mm2 freshly cleaved surface. In the case of
LaNiO2, several $\sim$1 mm2 pieces were transferred to the glove box rapidly
after completion of the topotactic reduction and broken into smaller pieces
that were distributed on an indium foil. Hence, the XPS signal from this
sample stems from a mixture of fresh surfaces and surfaces that were exposed
to the topotactic process. Nonetheless, it can be expected that the hallmarks
of the transformation of Ni3+ (nominal $3d^{7}$ configuration) to Ni1+
(nominal $3d^{9}$ configuration) are discernible in the XPS spectra.

Figure 6a) compares the XPS of our LaNiO3 and LaNiO2 samples across a wide
range of binding energies, including the La $3d$ and Ni $2p$ edges. As
expected, the La $3d_{5/2}$ peaks Mickevičius  _et al._ (2006); Qiao and Bi
(2011), which are separated by the multiplet splitting $\Delta E$, remain
similarly before and after the reduction, which implies that the electronic
configuration of the La3+ ion remains essentially unchanged. Nevertheless, we
note a small reduction of the splitting from $\Delta E=4.1(3)$ eV to $3.60(5)$
eV from LaNiO3 to LaNiO2. We attribute this change to the presence of a subtle
amount of LaOH in the reduced sample Li  _et al._ (2019b), which can be due to
fragments in the broken crystals that were possibly already decomposed (see
also Fig. 2). In this context, we also note that the sample presumably also
contains insufficiently reduced regions with insulating LaNiO2.5 Misra and
Kundu (2016); Shin and Rondinelli (2022), which can explain a slight charging
effect that was observed during the XPS acquisition from the reduced sample
but not for the LaNiO3 sample.

Compared to the La $3d_{5/2}$ peaks, the La $3d_{3/2}$ multiplet experiences a
more distinct change upon reduction. While the shape of these peaks might also
be influenced by the presence of LaOH, the multiplet overlaps with the Ni
$2p_{3/2}$ binding energies. Thus, the changes in the region between 850 and
870 eV are likely mostly due to the transformation of the electronic
configuration of Ni3+ towards a monovalent state, although between 855 and 865
eV additional contributions from the La MNN Auger lines are also present. As a
consequence of the various overlapping spectral contributions in the range
between 850 and 870 eV, disentangling the evolution of the peaks associated
with Ni $2p_{3/2}$ is problematic and we therefore refrain from carrying out
peak profile fits and direct comparisons with the $2p_{3/2}$ lines of cuprates
van der Marel  _et al._ (1988). A fit of the Ni $2p_{1/2}$ region is also
challenging, which is due to the small intensity of these peaks and the
intense background originating from inelastically scattered electrons from the
La 3$d$ orbitals. Nevertheless, it can be recognized that the low binding
energy edge of LaNiO3 is steeper than that of LaNiO2 (see inset in Fig. 6a)),
which is consistent with a reduced oxidation state of Ni in the latter case
that emerges at lower binding energies.

A multiplet of Ni that is free from overlap with other features is the Ni $3p$
region between 60 and 75 eV (Fig. 6b)). The clear shift of the peak maximum
upon reduction can be indicative of the reduced screening of the core hole
potential of monovalent Ni after the reduction. In addition to the shift of
the Ni $3p$ peak of LaNiO2, we find an emerging shoulder at binding energies
above the main peak (red arrow in Fig. 6b)). In a previous study, the Ni $3p$
multiplet of reduced LaNiO3 was fitted with two doublets for the $3p_{3/2}$
and $3p_{1/2}$ lines and the Ni3+/Ni2+ ratio was determined Qiao and Bi
(2011). Recently, however, it was pointed out that the $3p$ peak shape is
convoluted by a more complex multiplet splitting and an accurate modeling
requires cluster-model calculations that take the local crystal field symmetry
into account Baeumer  _et al._ (2021). While such calculations for Ni1+ in
square-planar coordination are an interesting topic for future studies, we
emphasize the qualitative similarity to the $3p$ line of divalent cuprates,
featuring a dominant main peak and one or more high binding energy satellite
peaks that correspond to $3p^{5}3d^{10}\underline{L}$ and $3p^{5}3d^{9}$ final
states, respectively, with $\underline{L}$ denoting a ligand hole van der Laan
_et al._ (1981).

##  IV Conclusion

In summary, we have synthesized millimeter-sized LaNiO2 crystals using a
direct contact CaH2 treatment, whereas in previous studies on thin films and
polycrystalline powders an indirect contact method was sufficient. Our
characterization of the crystals revealed the hallmarks of a self-doped
correlated metal with strong antiferromagnetic fluctuations. The observed non-
Curie Weiss behavior of the intrinsic magnetic susceptibility corroborates the
previously proposed analogy between parent IL nickelates and doped cuprates.
Remarkable similarities to cuprates were also derived from the response of the
lattice to hydrostatic pressure. Specifically, we unveiled a close similarity
between the bulk moduli of IL nickelates and cuprates, and we anticipate that
our report of the lattice parameters at 12 GPa will serve as an important
input for theoretical calculations examining the $T_{c}$ enhancement in
nickelates under hydrostatic pressure. Furthermore, the application of
pressure can provide a platform to tune the hybridization between the orbitals
that contribute to the low-energy electronic structure of IL nickelates,
including the Ni 3$d$, O 2$p$, and rare-earth 5$d$ orbitals. Our comparison of
the electronic transport of a pulverized crystal and topotactically reduced
powder demonstrated the need for single crystals to determine the intrinsic
behavior of IL nickelates and provides an explanation for previously observed
insulating behavior of IL powder, as well as a hint about the origin of the
absence of superconductivity in powder samples. Moreover, we demonstrated that
hydrogen in reduced nickelates is predominantly incorporated in secondary and
decomposed phases, such as LaOH, whereas oxyhydride nickelates were not formed
for our employed experimental conditions. Finally, our XPS measurements
revealed the fingerprints of the highly unusual Ni1+ oxidation state in the
electronic structure of IL nickelates. These results strongly encourage future
investigations of the LaNiO2 crystals with advanced spectroscopic methods,
which might provide additional insights into the magnetic and electronic
properties that remain elusive in thin film studies.

## Acknowledgements

We acknowledge technical support from Jeroen Jacobs and Stany Bauchau for the
high-pressure experiments. We thank Valentin Zimmermann, Vignesh
Sundaramurthy, Hangoo Lee, and Shohei Hayashida for helpful discussions, and
Samir Hammoud for carrying out the hydrogen gas extraction studies.

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