Impact of Cation Stoichiometry on the Crystalline Structure and Superconductivity in Nickelates

The recent discovery of superconductivity in infinite-layer nickelate films has aroused great interest since it provides a new platform to explore the mechanism of high-temperature superconductivity. However, superconductivity only appears in the thin film form and synthesizing superconducting nickelate films is extremely challenging, limiting the in-depth studies on this compound. Here, we explore the critical parameters in the growth of high quality nickelate films using molecular beam epitaxy (MBE). We found that stoichiometry is crucial in optimizing the crystalline structure and realizing superconductivity in nickelate films. In precursor NdNiO3 films, optimal stoichiometry of cations yields the most compact lattice while off-stoichiometry of cations causes obvious lattice expansion, influencing the subsequent topotactic reduction and the emergence of superconductivity in infinite-layer nickelates. Surprisingly, in-situ reflection high energy electron diffraction (RHEED) indicates that some impurity phases always appear once Sr ions are doped into NdNiO3 although the X-ray diffraction (XRD) data are of high quality. While these impurity phases do not seem to suppress the superconductivity, their impacts on the electronic and magnetic structure deserve further studies. Our work demonstrates and highlights the significance of cation stoichiometry in superconducting nickelate family.

However, the difficulty to reproduce the superconductivity in infinite-layer nickelates is obvious in light of only a few precedents for successful synthesis of superconducting nickelate [9,12,29,30]. Recent reports of the observation on the superconductivity in hole-doped LaNiO2, which was not superconducting previously, also emphasize the importance of the film quality [31,32]. Some influential factors are reported, for instance, the increasing target ablation, different laser fluences in the pulsed laser deposition (PLD) and (002) peak positions in XRD scans, offering meaningful guidance for the Nd1-xSrxNiO3 growth [33]. Some indirect evidence hints their relevance to the stoichiometry [34,35], which deserves, but still lacks, a thorough investigation.
In this work, we employed MBE to grow perovskite neodymium nickelate films with different cation stoichiometries which are of significance in optimization and reproduction of superconductivity in nickelate films. We found that off-stoichiometry in both nickel-rich and nickel-poor leads to obvious lattice expansion, which is shown to hinder the subsequent topotactic reduction and the emergence of superconductivity in infinite-layer nickelates. Additionally, based on the stoichiometry effect, out-of-plane (OOP) lattice constant is found to be helpful in the MBE growth calibration. Finally, an impurity phase in the Sr-doped samples was always shown in RHEED patterns, which can coexist with superconductivity.

METHODS
The NdNiO3 and Nd1-xSrxNiO3 films were epitaxially grown on TiO2-terminated (001)oriented SrTiO3 single-crystalline substrates using a DCA R450 MBE system. Before the growth, we used the quartz crystal microbalance (QCM) to measure a rough beam flux. The value of flux is for reference only, for it depends strongly on the background pressure, installation angle of the crucibles of sources and the shape of the source materials. During the growth, RHEED was employed to monitor the growth process and surface quality. The films were grown at 550 -650 °C (measured by thermocouple thermometer) and under an oxidant (distilled ozone) background pressure of ~ 4.0  10 -6 Torr. Residual gas analyzer (RGA) was utilized to real-time monitor the ozone partial pressure which is essential for the stabilization of the oxidation state of Ni 3+x . SrTiO3 substrates were etched in buffered HF acid for about 70 s and annealed in flowing pure oxygen at 1000 °C for 80 min before growth to obtain TiO2-terminated step-and-terrace surface [36]. The film crystalline structure was examined by XRD using a Bruker D8 Discover diffractometer. The terraced micromorphology of films was revealed by Asylum Research MFP-3D atomic force microscopy (AFM). Specimens for the crosssectional scanning transmission electron microscopy (STEM) were prepared by focused ion beam (FIB) techniques. Atomic-resolution annular dark-field (ADF) images were acquired on the JEOL JEM ARM 200F outfitted with an ASCOR fifthorder probe corrector. In order to attain infinite-layer phase, the Nd0.8Sr0.2NiO3 was sealed in a vacuum chamber together with ~0.1 g CaH2 powder, and then heated to 280 °C for 4h, with warming (cooling) rate of 10-15 °C /min [9]. Temperaturedependent resistivity was measured via the standard Van der Pauw geometry in a homemade transport properties measurement system. Effect of cation stoichiometry on NdNiO3 films Taking the advantage of MBE technique, a series of NdNiO3 films with different Nd:Ni flux ratio were grown. For many perovskite oxides ABO3, the deposition time for each source can be extracted precisely using a shuttered mode [37,38], because the alternative growth of AO and BO2 monolayers leads to RHEED intensity oscillations with intensity saturating at the end of depositing one full atomic monolayer. However, the intensity doesn't saturate at the end of growing an atomic monolayer for NdNiO3. Hence, the co-deposition method where AO and BO2 layers are deposited simultaneously is adopted. The period of RHEED oscillations in the co-deposition corresponds to the growth of one unit cell [39,40]. We adjust the Nd:Ni flux ratio precisely by successively changing the deposition time for Ni, which effectively alters the cation stoichiometry.

RESULTS AND DISCUSSION
XRD patterns shown in FIGURE 1A demonstrate clear (00l) reflections, indicating the reasonable crystalline quality in these samples. FIGURE 1B shows a plot of the OOP lattice constants calculated from (002) peak position as a function of nominal Nd:Ni flux ratio (represented by the blue triangles), as well as the corresponding Gaussian fit (yellow dashed line). An increment of OOP lattice constant is observed in the both sides of flux ratio deviated from the optimal value. Given that the in-plane lattice is fully strained to the substrates as revealed by the reciprocal space mapping (RSM) shown in FIGURE 1C, it is clear that off-stoichiometry gives rise to a lattice expansion, similar with the situation in SrTiO3 [41]. Since the (002) peak position over 48° was deemed to be indispensable for superconductivity [33], we note the sensitivity of the OOP lattice constant to cation stoichiometry should attract more attention.
Based on this finding, the OOP lattice constant can be employed in turn as a unique indicator of stoichiometry and aided in the calibration of beam flux ratio which is essential in MBE growth. As mentioned above, the precise deposition time of each source is not available using shuttered mode. In the co-deposition, although the oscillations are observed, the overall intensity shows little dependence on the variation of Nd:Ni flux ratio, which is commonly employed in the growth of other systems [42,43]. Hence, another specific way is demanded to conduct the calibration. Using OOP lattice constant as an indicator is proved to be feasible and reliable. As shown in FIGURE 1B, the c-lattice constants as a function of stoichiometry can be nicely fitted with the Gaussian function shown below: The deviation of flux ratio from optimum can be estimated from the fitted parabolic function. A real practice of the calibration process is specifically shown in It should be noted that other factors such as anion concentration also affects the lattice [44], which could explains the slight changes of exact OOP lattice constants of our films. Then, a series of NdNiO3 films were grown using the calibration process mentioned above. The persistent RHEED oscillations confirm the layer-by-layer growth mode, the period of which marked in FIGURE 2A is exactly the time required to deposit a layer of one unit cell NdNiO3. The thickness obtained from RHEED oscillation curve is 27 u.c., in good agreement with the fit of Kiessig fringes [45] shown in FIGURE 2B. The rocking curve measurement (FIGURE 2C) shows a full width at half-maximum (FWHM) value of 0.017°, indicating a high degree of crystalline perfection. The RHEED patterns taken along [110] and [100] direction are shown as insets of FIGURE 2A. The half-order diffractions can be observed, manifesting the existence of NiO6 octahedral rotation [46]. In the atomic-resolution ADF-STEM images shown in FIGURE 2D and E, the abrupt and straight interface between the SrTiO3 substrates and the NdNiO3 film is observed. The film shows high crystalline quality with well-ordered Nd and Ni atoms (denoted by orange and green circle respectively) forming the perovskite lattice, and no defects such as atomic intermixing and stacking faults are observed. The smooth surface with terraced morphology is achieved and revealed by AFM imaging (FIGURE 2F).

2
Effect of cation stoichiometry on the emergence of superconductivity The growth of Sr-doped NdNiO3 is conducted using a similar co-deposition method based on both optimal and off-stoichiometric NdNiO3. Shutter times (deposition time per unit cell) for Nd and Ni are corresponding to single period of RHEED intensity oscillations during NdNiO3 co-deposition growth. The period of SrTiO3 film is also calibrated in advance to obtain precise shutter time of Sr. Take Nd0.8Sr0.2NiO3 for instance, in the one-unit-cell growth, the shutters of Sr, Nd and Ni are opened together and Sr is closed at 20% shutter time, Nd at 80% and Ni at 100%.
The RHEED intensity oscillations of 18 u.c. thick Nd0.8Sr0.2NiO3 under the optimal flux ratio is shown in FIGURE 3A. The oscillations are not perfectly smooth but still sustained for a long time. The disparity in crystalline quality originating from stoichiometry is obvious from the comparison of 2θ-ω diffraction patterns of Nd0.8Sr0.2NiO3 films under different flux ratio (FIGURE 3B and D). The (002) diffraction peak of off-stoichiometric Nd0.8Sr0.2NiO3 film is obviously weaker and broader and the peak position is below 48 o marked by the yellow dashed line, let alone its (001) peak nearly indistinguishable. No infinite-layer phase is detectable after the reduction though under the same annealing condition, and the insulating behavior shown in FIGURE 3C is also as expected. As such, our results demonstrate the significance of stoichiometry, which will help to optimize the synthesis of nickelate.
Furthermore, for the optimal Nd0.8Sr0.2NiO3 (inset of FIGURE 3A), though the diffraction pattern of Nd0.8Sr0.2NiO3 is clear and sharp as shown by the green arrows, there exists impurity phases as indicated by the red dashed open circles, so do most of our Sr-doped samples. It should be noted that no corresponding diffraction peak was detected in XRD scan, suggesting possible short-range order of the impurity phases, but its chemical composition is not clear up to now. Even so, these impurity phases do not seem to suppress the superconductivity in Nd1-xSrxNiO2 (FIGURE 3C). As shown in FIGURE 3B, after topotactic reduction, the OOP lattice constant shrinks to ~3.38 Å (calculated from (001) peak position). According to the documented doping level dependence of OOP lattice constant [12,15], the actual Sr concentration in our film is consistent with the nominal value determined in the growth process. We also employed the Scherrer equation (2.1) to estimate the thickness of nickelate film in infinite-layer phase [33,47] where dScherrer is the Scherrer thickness, K is the Scherrer constant, 1.091 in our case [33], λ is the wavelength of X-ray which is 1.5418 Å, θ and b are the bragg angle and the full width at half maximum intensity of the corresponding diffraction peak, respectively. The calculated Scherrer thickness (58.07 Å) basically matches with the situation where the precursor perovskite has been fully converted into the infinite-layer structure (60.84 Å). Moreover, XRD patterns of the Nd1-xSrxNiO3 film usually show a double-peak-like feature after capping with SrTiO3 layers, which is reminiscent of the stacking faults in previous reports [33,48]. However, we measured the same sample before and after capping and found the peak only appearing in the latter (FIGURE 3B), implying that the peak at ~48 o is more corresponding to the first-order thickness fringe of SrTiO3 capping layer, the intensity of which is enhanced by both the film and substrate.

CONCLUSION
In summary, optimizing of the quality of nickelate films was investigated in this work using MBE. The crystalline lattice and topotactic reduction of nickelates are both susceptible to off-stoichiometry. Obvious lattice expansion was observed caused by offstoichiometry in NdNiO3 films, and the crystalline structure as well as transport properties are both influenced after the subsequent topotactic reduction. Our finding is consistent with a previous report, where the (002) peak position over 48 o in precursor phase nickelate is deemed as the requisite for superconductivity [33]. In addition, we introduced a new practical method using OOP lattice constant to calibrate the Nd:Ni flux ratio in NdNiO3 growth. Moreover, we found the repetitive appearance of some impurity phases in RHEED patterns for most of our Sr-doped samples, which appear to be unavoidable but do not seem to suppress the superconductivity. Given the sensitivity of the structure of nickelate films to the variation of cation stoichiometry, any growth parameters that may affect the final stoichiometry in the films should be controlled carefully. For MBE, PLD and many other growth techniques, lots of parameters have impact on the stoichiometry, including beam flux ratio, chemical composition of targets, growth temperature, background pressure, laser plume, laser fluence and target ablation, etc. [34,35,[49][50][51][52][53]. These growth parameters can be adjusted referring to our findings about the stoichiometry dependence on the OOP lattice constant. Finally, although the superconductivity is not obviously affected by the impurity phases in Sr-doped nickelates, further investigation on their potential impacts on the electronic and magnetic structure is demanded.

DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.

AUTHOR CONTRIBUTIONS
YN conceived the project. YL, WS and WG grew the nickelate films. YL, WS, WG and JY conducted the materials and structural characterization. XC and YZ conducted the STEM measurements. JY, YL and WS conducted the reduction experiments. YL and WS performed the transport measurements. YL and YN prepared the manuscript with contribution from all authors. YL acknowledges discussions with JW and HS.

FIGURE 3|
Effect of cation stoichiometry on the reduction of Nd1-xSrxNiO3. A RHEED intensity oscillations and pattern (inset) of an 18 u.c. thick optimal Nd0.8Sr0.2NiO3 film grown on SrTiO3 substrate. The red open dashed circles and green arrows indicate the diffractions of the impurity phases and the perovskite phase of the film, respectively. B High-resolution XRD 2θ-ω scans of the nickelate films grown under optimal flux ratio. The Nd0.8Sr0.2NiO3 film before and after capping SrTiO3 layer is called bare and capped Nd0.8Sr0.2NiO3, respectively. The dashed line represents the critical two theta value of 48°. C Temperature dependent resistivity for Nd0.8Sr0.2NiO2 films grown under optimal and off-stoichiometric flux ratios. The resistivity of reduced Nd0.8Sr0.2NiO2 was divided by ten times for clarity. Inset shows the zoom-in view at low temperature from 3 K to 30 K. The onset transition temperature is about 14.7 K, and zero resistivity is achieved at about 4.7 K. D High-resolution XRD 2θ-ω scans of the nickelate films grown under off-stoichiometric flux ratio. The film after reduction shows no diffraction peaks, thus is called by reduced Nd0.8Sr0.2NiO3.