Long-Range Structural Order in a Hidden Phase of Ruddlesden–Popper Bilayer Nickelate La3Ni2O7

The recent discovery of superconductivity in the Ruddlesden–Popper bilayer nickelate, specifically La3Ni2O7, has generated significant interest in the exploration of high-temperature superconductivity within this material family. In this study, we present the crystallographic and electrical resistivity properties of two distinct Ruddlesden–Popper nickelates: the bilayer La3Ni2O7 (referred to as 2222-phase) and a previously uncharacterized phase, La3Ni2O7 (1313-phase). The 2222-phase is characterized by a pseudo F-centered orthorhombic lattice, featuring bilayer perovskite [LaNiO3] layers interspaced by rock salt [LaO] layers, forming a repeated ...2222... sequence. Intriguingly, the 1313-phase, which displays semiconducting properties, crystallizes in the Cmmm space group and exhibits a pronounced predilection for a C-centered orthorhombic lattice. Within this structure, the perovskite [LaNiO3] layers exhibit a distinctive long-range ordered arrangement, alternating between single- and trilayer configurations, resulting in a ...1313... sequence. This report contributes to novel insights into the crystallography and the structure–property relationship of Ruddlesden–Popper nickelates, paving the way for further investigations into their unique physical properties.

Recently, a groundbreaking discovery reported superconductivity in the Ruddlesden-Popper bilayer nickelate La3Ni2O7-δ, achieving a TC up to 80 K in the pressure range of 14 GPa to 43.5 GPa, 17 sparking significant interest in Ruddlesden-Popper phases (n = 2 and n = 3).In the ambient pressure structure of Ruddlesden-Popper bilayer La3Ni2O7-δ, the NiO6 octahedra display rotation/tilt alignment along the c-axis, deviating from the regular square net observed in high TC cuprates.It has been proposed that a structural transition from ambient pressure Amam to the highpressure Fmmm phase occurs at approximately 14 GPa, coinciding with the onset of superconductivity.However, the high pressure phase remains unclear due to the resolution limitations of the reported powder X-ray diffraction (XRD) data.8][19][20][21] The structural ambiguity and the crucial role of the structure-property relationship in comprehending the origins of high TC superconductivity necessitate more focused attention and efforts in the study of the crystal structure in this system.Herein, we present the crystal structure and electrical resistivity of two Ruddlesden-Popper nickelates: bilayer La3Ni2O7-2222, and a hidden phase, La3Ni2O7-1313.Single crystal XRD is employed to determine their crystal structures.Our measurements confirm the pseudo F-centered orthorhombic lattice and its Ruddlesden-Popper bilayer stacking in La3Ni2O7-2222.Remarkably, La3Ni2O7-1313 adopts a strongly preferred C-centered orthorhombic lattice with the space group Cmmm.In this structure, perovskite [LaNiO3] layers exhibit a systematic long-range order, alternating between single-and trilayer configurations (…1313…).This report introduces new possibilities for exploring the crystal structure and the structure-property relationship in Ruddlesden-Popper nickelate superconductors.

Experimental
Materials growth: Crystals of La3Ni2O7-2222 and La3Ni2O7-1313 were grown by a floating zone method at University of Tennessee in a vertical optical-image furnace.Stoichiometric mixtures of La2O3 (pretreated at 1000 °C) and NiO were ground and fired at 1050 °C for 1 day.These precursor powders were hydrostatically pressed into a rod and sintered at 1400 °C for 12-24 hours.Crystals of La3Ni2O7-2222 and La3Ni2O7-1313 were grown directly from the sintered rods in 100% O2 at a pressure of around 14-15 bars.During the crystal growth, the traveling rate was 3-4 mm/hour, and the feed rod and seed were counter-rotated at a rate in the range of 15-20 rpm.La3Ni2O7-2222 and La3Ni2O7-1313 crystals were obtained from some sections of the grown boules.The two kinds of crystals were identified by single crystal X-ray diffraction.No uncommon hazards are noted in this experimental procedure.

Single crystal X-ray diffraction measurement:
The single crystal of La3Ni2O7 was picked up, mounted on a nylon loop with paratone oil, and measured using a XtalLAB Synergy, Dualflex, Hypix single crystal X-ray diffractometer with an Oxford Cryosystems low-temperature device, operating at T = 300(1) K and T = 100(1) K. Data were measured using ω scans using Mo Kα radiation (λ = 0.71073 Å, micro-focus sealed X-ray tube, 50 kV, 1 mA).The total number of runs and images was based on the strategy calculation from the program CrysAlisPro 1.171.43.92a (Rigaku OD, 2023).Data reduction was performed with correction for Lorentz polarization.
Numerical absorption correction based on gaussian integration over a multifaceted crystal model.Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.The structure was solved and refined using the Bruker SHELXTL Software Package. 22,23ectrical resistivity measurement: Temperature-dependent electrical resistivity measurement was performed with a Quantum Design DynaCool physical property measurement system (PPMS) in the temperature range of 1.8-300 K at zero field with a four-probe method using platinum wires on a single crystal sample of La3Ni2O7-1313 in the dimensions of 3.5 mm × 2.8 mm × 1.2 mm.

Results and Discussion
Crystal structure determination: The crystal structures of Ruddlesden-Popper bilayer La3Ni2O7-δ (δ = 0.00 and 0.08) were initially determined as F-centered orthorhombic Fmmm through powder X-ray diffraction (XRD) and Rietveld refinement. 24Recognizing the significant uncertainty in determining oxygen coordinates via XRD analysis, neutron powder diffraction (NPD) was subsequently employed. 25,26The results obtained indicated that the Fmmm space group was inappropriate, as it failed to account for extra weak peaks, hinting at a lower symmetry.This led to the proposal that the most suitable structure model involves a C-centered orthorhombic lattice of the space group Cmcm. 26The challenges inherent in the pseudo F-centered orthorhombic lattice, the influence of oxygen vacancies on the structure, and the coexistence of Ruddlesden-Popper bilayer and trilayer phases underscore the complexities in structure determination, necessitating the growth of pure La3Ni2O7 single crystals.In a recent development, the highpressure floating zone method, enabling 100% O2 atmosphere with controllable gas pressure, has successfully facilitated the single crystal growth of Ruddlesden-Popper nickelates with high purity. 27This advancement opens possibilities for studying crystal structures using X-rays, which is more cost-effective and accessible than neutrons and provides precise enough structure determination results.
Here, utilizing this high-pressure floating zone method, high-purity single crystals of Ruddlesden-Popper bilayer nickelate La3Ni2O7 (termed La3Ni2O7-2222) have been obtained.Our single crystal XRD investigations confirm the presence of a pseudo F-centered orthorhombic lattice and the characteristic Ruddlesden-Popper bilayer stacking, as shown in Figure 1.The single crystal XRD refinement details are summarized in Table 1 and 2 Furthermore, our observations reveal the existence of a hidden phase in this system, termed La3Ni2O7-1313, which adopts a strongly preferred C-centered orthorhombic lattice with space group Cmmm.In its structural arrangement, the perovskite [LaNiO3] layers exhibit a systematic long-range order, alternating between single-and trilayer configurations (…1313…), as elucidated in Figure 1, represented by the identical chemical formula La3Ni2O7 to bilayer La3Ni2O7-2222.
The single crystal XRD refinement details of La3Ni2O7-1313 at 300 K and 100 K are summarized in Table 1 and 3    Goodness-of-fit on F 2 1.130 1.304   Remarkably, the bond valence sums of the inner and outer Ni in the trilayer of La3Ni2O7-1313 exhibit no significant difference from those reported in La4Ni3O10, 27 suggesting a connection between trilayer building blocks.
Our experimental reciprocal lattice planes are presented in Figure 3.To enable a clearer visual comparison between La3Ni2O7-1313 and La3Ni2O7-2222, the Cmcm unit cell (details in Table 1) of La3Ni2O7-2222 was transformed to a symmetry-equivalent Amam setting (c axis perpendicular to perovskite layers).Begin with La3Ni2O7-1313, given its space group Cmmm, reflections at h + k = 2n would be expected due to C-centering, a condition met by all involved reflections.In contrast, for La3Ni2O7-2222, besides A-centering (k + l = 2n), the presence of the a glide plane perpendicular to b axis results in absences in the (h0l) reciprocal plane when h = 2n + 1.Thus, the overall reflection conditions in the (h0l) plane are defined by h = 2n and l = 2n.
Consequently, when examining the (h0l) plane, we expect to see twice as many reflections along c* when h = 2n in La3Ni2O7-1313 compared to La3Ni2O7-2222.

Electrical resistivity measurement:
The temperature dependence of electrical resistivity and its temperature derivative of La3Ni2O7-1313 in the range of 2-300 K was presented in Figure 4.The resistivity at 300 K measures approximately 0.035 Ω cm, a value small enough to preclude the presence of significant contact resistance.Our measurements indicate that the sample exhibit a semiconductor-like behavior, a departure from the characteristics reported for La3Ni2O7-2222. 17A kink at about 50 K was observed in our resistivity curve, which was attributed to unstable contacts.
It is essential to emphasize that this kink should not be accounted for the intrinsic properties of La3Ni2O7-1313 but rather considered a result of contact instability.Two very recent reports on La3Ni2O7-1313 notes metallic behavior at ambient pressure, 33,34

Conclusion
In conclusion, we present the crystal structure and electrical resistivity of two Ruddlesden-
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For Table of Contents Only
This study delves into the crystallographic and electrical properties of two polymorphs of
, and TableS1and S2, respectively.Negligible vacancy has been observed regarding oxygen stoichiometry.Figure1also presents the characteristic stacking of single-, bilayer, and trilayer structures in Ruddlesden-Popper nickelates.26,29A clear difference arises between La3Ni2O7-1313 and La3Ni2O7-2222 when considering perovskite layers and rock salt layers as the structure building blocks.The La3Ni2O7-1313 structure is constructed through a long range order of single-and trilayer perovskite building blocks in La2NiO4 and La4Ni3O10, respectively, without the bilayer counterparts present in La3Ni2O7-2222.Recent research on the design and synthesis of a hybrid layered Ruddlesden-Popper nickelate by a flux method, featuring a …1212… sequence,30 could provide a potential avenue for experimental validation.

Figure 2
Figure 2 View of the characteristic out-of-plane Ni-O-Ni bond angle in (a) bilayer La3Ni2O7-2222 (Cmcm and Fmmm settings) and (b) the hidden phase La3Ni2O7-1313.Green, grey, and red represent La, Ni, and O atoms.The corresponding oxygen atoms and bond angles are labeled as presented.

Figure 1 )
in comparison to the inner Ni of the trilayer (Ni3) and Ni in the single layer (Ni2).This aligns with reports in other multilayer Ruddlesden-Popper phases.31Meanwhile, the Ni-O bond lengths within the perovskite layers on the outer side (Ni1-O3 and Ni2-O1) are approximately 10% greater than Ni-O inside (Ni1-O5 and Ni3-O5) in La3Ni2O7-1313.To evaluate the valence states of three crystallographically unique Ni in the structure, bond valence sums were calculated ( 0 = 1.689,  = 0.347)32 .The obtained values for Ni in the single layer, and inner and outer Ni in the trilayer reveal differences, indicating charge differentiation among them and providing evidence for potential charge transfer in the system.
suggesting sample-dependent electrical resistivity.Considering the structure building blocks derived from Ruddlesden-Popper single layer La2NiO4 and trilayer La4Ni3O10 in La3Ni2O7-1313, we propose that the efficiency of charge-transfer between Ni in these single-and trilayer perovskite layers may dictate the bulk electrical resistivity behaviors of this system.

Figure 4
Figure 4 Temperature-dependent electrical resistivity and its temperature derivative of La3Ni2O7-1313.The kink at ~50 K comes from unstable contacts.
Popper nickelates: bilayer La3Ni2O7-2222, and the hidden phase, La3Ni2O7-1313.Our single crystal XRD measurements confirm that La3Ni2O7-2222 features the pseudo F-centered orthorhombic lattice with bilayer perovskite [LaNiO3] layers separated by rock salt [LaO] layers (…2222…).Remarkably, the semiconductor-like La3Ni2O7-1313 adopts a strongly preferred Ccentered orthorhombic lattice with the space group Cmmm.In the structure, perovskite [LaNiO3] layers exhibit a systematic long-range order, alternating between single-and trilayer configurations (…1313…).This report introduces new possibilities for exploring the crystal structure and the structure-property relationship in Ruddlesden-Popper nickelates.

Ruddlesden-
Popper nickelates La3Ni2O7: bilayer 2222-phase, and a hidden 1313-phase.The 1313phase demonstrates a C-centered orthorhombic lattice (Cmmm, #65) with long-range ordering alternating between single layer and trilayer (…1313… sequence).This unique layer stacking shed light on the structure-property relationship in La3Ni2O7, opening avenues for further exploration of their physical properties.

Table 1
The crystal structure and refinement of La3Ni2O7-2222 and La3Ni2O7-1313 at 300 K.

Table 2
Atomic coordinates and equivalent isotropic atomic displacement parameters (Å 2 ) of La3Ni2O7-2222 at 300 K.  eq is defined as one third of the trace of the orthogonalized  ij tensor.

Table 3
Atomic coordinates and equivalent isotropic atomic displacement parameters (Å 2 ) of La3Ni2O7-1313 at 300 K.  eq is defined as one third of the trace of the orthogonalized  ij tensor.

Table 4
provides a summary of Ni-O bond lengths and Ni-O-Ni bond angles in the structure of La3Ni2O7-1313.A noteworthy observation is the larger distortion of [NiO6] octahedra in the outer Ni of the trilayer (Ni1 in