Absence of superconductivity in bulk Nd1−xSrxNiO2

Superconductivity at 9–15 K was recently discovered in Nd0.8Sr0.2NiO2 films. Since the Ni1+ ionic state in NdNiO2 may have the same 3d9 outer-shell electronic orbital as in cuprate superconductors, it is interesting to know whether superconductivity has a similar mechanism in these two systems. Here we synthesize bulk samples of Nd1−xSrxNiO2 (x = 0, 0.2, 0.4) with inhomogeneous Sr distribution and Ni deficiency. Resistivity measurements show insulating behavior without the presence of superconductivity, different to the previously reported films. Although applying pressure up to about 50.2 GPa significantly suppresses the insulating behavior, superconductivity remains absent. The magnetization behavior exhibits a Curie–Weiss law with a paramagnetic moment of about 2 μB/f.u. Since the lattice constants derived from our diffraction data are very close to the previously reported superconducting Nd0.8Sr0.2NiO2 films, we suggest that superconductivity in that system may have arisen from interface or stress-related effects, or nickel deficiency in our bulk samples that might prevent the emergence of superconductivity. Superconductivity was recently observed in Nd0.8Sr0.2NiO2 films. Here, superconductivity is found to be absent in bulk polycrystalline samples of Sr-doped NdNiO2, raising questions regarding the origin of superconductivity in this material.

S ince the discovery of high critical temperature superconductivity (HTS) in cuprates in 1986 1 , there are plenty of experimental and theoretical studies to explore the intrinsic mechanism for superconductivity [2][3][4][5] . There is a general agreement that the parent compound of cuprates like La 2 CuO 4 is a Mott insulator with a charge transfer gap and long-range antiferromagnetic (AF) order 6 . With chemical doping, the long-range AF order will be suppressed at a hole doping level (p ≈ 0.02) and d-wave superconductivity emerges at a higher doping level (p ≥ 0.05) [7][8][9] . After the efforts more than three decades, some common features have been observed, but the intrinsic pairing mechanism of HTS remains unresolved yet. These include twodimensional electronic structure and coexistence with an AF order or spin fluctuations, all these also occur in most ironbased 10 and heavy fermion superconductors 11 . Moreover, in cuprates, it is also important that the spin S = 1/2 magnetic moment from 3d 9 electrons forms the basic structure of the AF order. One intuitive way to explore the pairing mechanism of cuprates is to find additional high-T C superconductors with different transition metals but similar crystal and electronic structure 12,13 . The infinite-layer materials RNiO 2 (R = La, Nd) are one of the ideal systems to simulate cuprates. First, the RNiO 2 compounds have the same crystal structure (P4/mmm) as CaCuO 2 , which is a parent compound of high-T C cuprates and can reach a high-T C of about 110 K by hole doping 14 . Second, the Ni 1+ (3d 9 ) oxidation state in RNiO 2 is very similar to 3d 9 configuration of Cu 2+ in cuprates. Thus, many theoretical and experimental efforts have been put forward to investigate the RNiO 2 as a promising candidate of cuprate-like Ni-based superconductor 12,[15][16][17] .
Recently, superconductivity was observed at 9-15 K in the strontium doped infinite-layer nickelate thin films of Nd 0.8 Sr 0.2 NiO 2 deposited on the SrTiO 3 substrate 18 . This work has stimulated enormous interests, and plenty of theoretical works have been carried out [19][20][21][22][23][24][25][26][27][28][29][30][31] . Among them, Zhang et al. propose the parent compound of Nd 0.8 Sr 0.2 NiO 2 as a self-doped Mott insulator 26 . This work suggests that the low-density Nd-5d conduction electrons couple with the localized Ni-3d electrons, which suppresses the long-range AF order and forms Kondo spin singlets at low temperatures. While, Botana and Norman argue that a large ratio of longer-range hopping to near-neighbor hopping is conducive for superconductivity both in cuprates and nickelates 20 . And Ryee et al. demonstrate that magnetic two-dimensionality induced by hole doping is the key factor for superconducting Nd 1−x Sr x NiO 2 25 . Bernardini et al. 31 propose a possible difference between cuprates and nickelates based on the computed London penetration depth, and suggest that the latter does not follow the Uemura plot which holds well in underdoped cuprates. Hirayama et al. 30 compare the electronic structure of cuprates and NdNiO 2 , and conclude that the Nd layer also forms Fermi pockets. And they also propose some other promising compounds analogues to high-T C cuprates. Several other groups also studied the dominant pairing instability in the framework of t-J model 23,27 . They proposed that superconductivity in nickelates has a d-wave symmetry, which is analogous to cuprates. However, since the report of discovering superconductivity in Nd 0.8 Sr 0.2 NiO 2 18 thin films, no other experimental works have been reported up to now.
In this paper, we report the successful synthesis and physical properties of bulk Nd 1−x Sr x NiO 2 (x = 0, 0.2, 0.4) samples. By using a three-step method, we prepare bulk Sr-doped NdNiO 2 polycrystalline samples successfully with the similar doped composition of Sr as in the reported films. The structural and composition analyses reveal the formation of bulk Nd 1−x Sr x NiO 2 phase which at this moment has low crystallinity, nickel deficiency, and inhomogeneous strontium distribution. The low crystallinity may be a common feature for the low-temperature topotactic reduction method, which can also be seen in the bulk form NdNiO 2 samples 32 and the superconducting Nd 0.8 Sr 0.2 NiO 2 18 thin film. Magnetization measurements of the sample show a Curie-Weiss (C-W) like feature at high fields (1 and 3 T). The resistivity measurements at ambient and high pressures exhibit insulating behavior without the presence of superconductivity. We think the contradictory results compared with that of the reported films 18 may be attributed to the interface or stress effect in films. Furthermore, in our samples, we find appreciable deficiency (5-9%) of Ni in the NiO 2 planes. It would be interesting to know whether this feature occurs also in the reported films, which may lead to the absence of superconductivity in our bulk samples.

Results
Sample characterization. Figure 1a shows the schematic crystal structures and the transformation from the 113 to 112 phase through the low-temperature topotactic reduction method. Here Nd/Sr, Ni and oxygen atoms are represented by the orange/ purple, green and red spheres, respectively. To verify the formation of bulk Nd 1−x Sr x NiO 2 phase, we conduct the room temperature XRD measurements with 2θ from 10°to 90°and the Rietveld refinements 33 of Nd 1−x Sr x NiO 2 (x = 0.2, 0.4) bulk samples. The results are shown in Fig. 1b  contain mainly the infinite-layer 112 phase and some amount of extra Ni appears as disconnected segregations. Some peaks of Nd 1−x Sr x NiO 2 seem to be broader than others or have unexpected strong intensities, which may be induced by the disorder in these reflection planes and anisotropic particle size in layered materials. And the low crystallinity is a common feature for the samples fabricated by the low-temperature topotactic reduction method 32 . From the indices of those peaks as shown in Fig. 1c, it is obvious that the diffraction peaks of the class <hk0> are sharper. And the broader peaks are from the class where l has a nonzero value. It means that the NiO 2 plane may be disordered, which is corresponding to the result of the nickel deficiency in present samples as inferred from the EDS measurement. The crystallographic data obtained from the Rietveld refinement profiles are shown in Table 1 and Supplementary Table 1. The lattice constant of c-axis increases with increasing doping contents. The lattice parameters of our bulk sample (x = 0.2) are a = 3.91 Å, c = 3.33 Å, which are in good agreement with the previous reports on the reported Nd 0.8 Sr 0.2 NiO 2 thin film 18 . Figure 2a, b display the scanning electron microscope (SEM) images of Nd 1−x Sr x NiO 2 (x = 0.2, 0.4) samples. As we can see, the grains could be clearly separated into two major morphologies, which are characterized by the argenteous crystals (dominant phase) and dark gray areas. The argenteous grains are interconnected, while the dark gray ones are well separated with each other. In order to have a deeper insight of the difference between the two different grains, energy dispersive X-ray spectroscopy (EDS) is used to analyze the element concentration of all three samples. In each sample, we measure more than 20 spots randomly (marked by the red crosses in images of Fig. 2a, b and Supplementary Fig. 1). The results are shown in Fig. 2c-f. As there is uncertainty for the composition of carbon and oxygen, here we only study the contents of Nd, Sr, and Ni. Noting that the starting ratio of Nd/Sr/Ni in Nd 1−x Sr x NiO 2 is stoichiometric when we fabricate the sample. The typical EDS patterns of different samples are given in Fig. 2c, d, we find that the argenteous grains have a composition of Nd 1−x Sr x Ni y O 2 , while the dark gray grains show a composition of Ni (see Supplementary Fig. 2 and Supplementary Note 1). Two typical features can be identified for the Nd 1−x Sr x Ni y O 2 : (1) The ratio of Ni: (Nd+Sr) is close to 1, although an appreciable deficiency of Ni can be seen from the EDS data. Figure 2e shows the mean value of Ni occupancy normalized by the summed concentration of Nd and Sr. The deficiency of Ni should be in the scale of 5-9% in all three samples (x = 0, 0.2, 0.4). The vacancies in nickel sites may cause the distortion of NiO 2 plane and hence result in the shrinkage of the lattice constants of a and b. And the disorder in those reflection planes may induce the peak broadening of XRD. As shown in Supplementary Table 1, the concentration of nickel metal extracted from our XRD data is about 15 wt% for x = 0.2 sample and 17wt% for x = 0.4 sample, which is larger than the observed nickel deficiency in EDS measurement (about 5-9%). Table 1 Lattice parameters obtained from the Rietveld refinements. (2) 3.239 (6) Supplementary  Fig. 3). As we know, the defects and inhomogeneity in transition metal oxides should play an important role in the electronic transport, which have been widely observed in cuprates. For example, by using an X-ray microdiffraction apparatus, scientists found that the superconducting transition temperature and charge-density-wave domain are highly affected by the inhomogeneous oxygen defect order [34][35][36] . And also in nickelates, by using the similar apparatus on a NdNiO 3 film, the paradigm of nanoscale phase inhomogeneity has been extended to the correlated electron system with an AFM ground state 37 . Thus, we believe the electronic transport in Nd 1−x Sr x NiO 2 system may also be affected by the inhomogeneous distributions of Sr and Ni concentrations. Anyway, we believe our samples contain the right phase of Nd 1−x Sr x Ni y O 2 (x = 0.2, 0.4, y ranges from 0.91 to 0.95). The sensitivity of the SQUID instrument should be sufficient to detect the superconducting signal if partial of these grains are superconductive.
Magnetic and Electrical transport properties. magnetization of all three samples shows a drop of magnetization at about 5 K, together with an obvious irreversibility between the ZFC and FC curves (see Supplementary Fig. 4). Such abnormal behavior at low field magnetization curve may indicate the presence of spin glassy state, probably due to magnetic impurities in compounds. To obtain a deeper understanding of magnetization behavior, we measure the magnetization hysteresis (M-H) curves of the Nd 0.8 Sr 0.2 NiO 2 sample at different temperatures and show the data in Fig. 3d. We can safely exclude the possibility that the anomalous drop of magnetization at about 5 K is caused by superconductivity, because no superconducting like M-H curve is observed at 3 K (inset of Fig. 3d). The M-H curves show the presence of paramagnetic background with a ferromagnetic component, and the paramagnetic component decreases as the temperature increases. We think the ferromagnetic component is originated from the segregated phase of Ni. And the paramagnetic behavior is attributed to the Nd 1−x Sr x NiO 2 phase. We have tried to fit the high field M-T curves in low-temperature region by the C-W law The fitting results are given in Fig. 3e, as shown by the red solid line, indicating a good quality of C-W fitting. Through the C-W fitting, we derive the effective magnetic moments μ eff of Nd 0.8 Sr 0.2 NiO 2 and Nd 0.6 Sr 0.4 NiO 2 , which are about 2.32 μ B /f.u. and 2.03 μ B /f.u., respectively. It should be noted that, before doing the C-W fitting, we need to remove the ferromagnetic background of nickel from the M-T curves by subtracting the curves of 1 T from those of 3 T. This is valid since the magnetization of Ni gets already saturated at the magnetic fields of 1 T and 3 T, as shown in Supplementary Fig. 5. The subtracted paramagnetic magnetic Electrical transport measurements are carried out at ambient pressure in the temperature range from 2 to 300 K. Figure 4a shows the comparison of the temperature dependence of resistivity for Nd 1−x Sr x NiO 2 (x = 0, 0.2, 0.4) samples. It can be clearly seen that the resistivity of the three samples all show insulating behaviors. The inhomogeneous distributions of Sr and Ni concentrations we discussed above may play an important role in electrical transport behavior, but it cannot affect the conclusion that superconductivity is absent in our samples. Assuming partial grains or some fraction of the grains show superconductivity below a certain temperature, the resistivity and magnetization should present a drop. To understand the underlying physics of the electrical transport behavior in present materials, in Fig. 4b we present the ρ (T) curve within the frame of variable range hopping (VRH) model 38 described as ρ ¼ ρ 0 expðT 0 =TÞ À1=4 , we can see that in a short period of temperature, it gives a linear relationship as highlighted by the red line, while the global fitting is not good. Also the band-gap model (ln ρ ∝ 1/T, shown in the bottom-right inset) and resistivity versus log1/T (shown in the top-left inset) are plotted, but all failed to fit the data at ambient pressure, suggesting that the insulating is not originated from the band gap and should possess by itself some exotic scattering reasons. Figure 4c, d shows the magnetic field dependent resistivity measured at different temperatures (T = 2, 5, 10, 20, 50 K). A sizable negative magnetoresistance (MR) Δρ=ρ 0 ¼ ðρ H À ρ 0 Þ=ρ 0 (about −10% at 5 T) is observed at 2 K. The negative MR at low temperature decreases with the increase of temperature, then the MR shows the crossover from a negative to a small positive MR behavior above 20 K. The negative MR in correlated oxides may be attributed to various mechanisms such as hopping conduction, magnetic scattering, or de-localization effect. As for the positive MR, researchers have proposed that the exchange correlation in different hopping sites (VRH type conduction) could give rise to positive MR 39,40 . Owing to the nickel segregations in our samples, the origin of negative and positive MR observed in the present compounds is not clear and more works deserve to be done.
Resistivity under high pressure. As shown above, an obvious conclusion drawn from the ρ (T) curves at ambient pressure is the insulating behavior. One can see that not only the magnitude of resistivity, but also the insulating features are strongly suppressed by doping more Sr. In order to induce a metallic or even a superconducting state, we also conduct high pressure electrical resistance measurement. The temperature dependence of resistivity at various pressures in Nd 0.8 Sr 0.2 NiO 2 and Nd 0.6 Sr 0.4 NiO 2 samples are shown in Fig. 5a and Supplementary Fig. 6. As discussed above, ρ (T) curves of Nd 1−x Sr x NiO 2 exhibit an insulating behavior at ambient pressure. With application of pressure, the overall magnitude of the resistivity is continuously reduced. The insulating behavior is significantly weakened. The ratio ρ 2K /ρ 300K of Nd 0.8 Sr 0.2 NiO 2 sample is about 350 with the external pressure of 3.2 GPa. With increasing pressure, the magnitude of ρ 2K /ρ 300K decreases progressively as shown in Fig. 5b. The improvement of conductivity under high pressures may be related to the redistribution of the Sr concentrations and modification of the nickel deficiency within grains. However, to prove this, one may need some microscopic analysis tools, such as synchrotron hard X-ray nanoimaging or small-angle scattering under high pressures, which have been used to reveal a novel micron-scaled ribbon phase in optimally doped Bi 2 Sr 2 CaCu 2 O 8+δ 41 . At the highest pressure of 50.2 GPa, the value of ρ 2K /ρ 300K has dropped to 6; however the ρ (T) curve still exhibits a semiconducting-like feature in whole temperature region. Then we try to fit the electrical transport behavior of Nd 0.8 Sr 0.2 NiO 2 sample at the highest pressure and show the fitting in Fig. 5c. The fitting curves of band gap model (the top-left inset) and VRH model (the bottom-right inset) are given. The results show that both the band gap model and the VRH model fail to fit the data. Surprisingly, the ρ versus log(1/T) curve at the highest pressure (P = 50.2 GPa) becomes roughly linear, as highlighted by the red linear line in a temperature range between 3.5 and 23 K. This strange ρ ∝ log(1/T) behavior has been reported in some correlated oxides such as underdoped and overdoped cuprates or vanadium oxide V 2 Se 2 O, which may result from the electron correlation effect in correlated oxides with 3d transition metals [42][43][44] . Meanwhile, the high pressure may change the distribution of Sr element and Ni deficiency within the grains, but due to the high diffusing barrier between different grains, we would not believe the high pressure will change the composition distribution of Sr and Ni among different grains. Thus the improvement of conductivity under pressure may be attributed to two factors. (1) The pressure can improve the electric conduction through optimizing the grain boundaries among different grains; (2) The pressure can modify the electronic band structure by making the redistribution of Sr and Ni deficiency within each grain, as well as the bandwidth through compressing the atomic lattice. These possibilities can be better resolved in future work.

Discussions
After a systematic analysis of the data, a main experimental finding in bulk infinite-layer nickelates Nd 1−x Sr x NiO 2 (x = 0, 0.2, 0.4) is the insulating behavior, which is in contrast to the metallic state and the superconductivity below 9-15 K in Nd 0.8 Sr 0.2 NiO 2 thin film 18 . It is certainly very important to know whether the insulating behavior in the bulk Nd 1−x Sr x NiO 2 is intrinsic. Based on the nice fitting to the XRD data and composition analysis on the grains of the samples, we can safely conclude that the main phase in the samples is definitely the Nd 1−x Sr x NiO 2 (x = 0.2, 0.4) with only some disconnected segregation clusters of Ni. From previous literatures, we find that nickel is a metal with the resistivity of about 7.2 mΩ cm at room temperature 45 , so it would be a metallic behavior if the segregated grains of nickel form a conductive network. However, from our SEM image, the segregated nickel grains are well separated with each other. The behavior of resistance both in ambient and high pressure indicates that the insulating behavior is robust in our samples. Thus, the existence of disconnected nickel regions in samples may only affect the absolute value of resistivity, but not gives rise to the intrinsic insulating behavior. In principle, high pressure can compress the cell volume and reduce the lattice parameters of compound, resulting in insulator-metal transitions and even superconductivity 46,47 . The clear suppression of insulating behavior in our high-pressure study may be induced by the improving of the grain boundaries, modification of the bands, or the weakening of the correlation effect, which leads to an enhanced effective density of states at the Fermi energy.
Since we do not find superconductivity in our bulk samples with the same structure and close lattice constants as the reported films 18 , we would like to suggest several reasons to interpret this discrepancy. Firstly, the superconductivity in Nd 0.8 Sr 0.2 NiO 2 films may arise from the interface or the stress effect given by the substrates. In the interface region, both the electron band and the doping level would be strongly modified, which could lead to superconductivity. The second reason may be the appreciable Ni deficiency (5-9%) in grains of Nd 1−x Sr x NiO 2 of our samples, which may cause stronger buckling of the NiO 2 planes and lead to a strong localization or scattering of charges. If this is the case, we need to make samples without Ni deficiency. It would be interesting to know whether the reported films also have Ni deficiency.
To summarize, we have successfully synthesized bulk Nd 1−x Sr x NiO 2 (x = 0, 0.2, 0.4) samples and performed comprehensive studies of the physical properties. From structure and composition analyses by XRD and EDS, the tetragonal Nd 1−x Sr x NiO 2 (x = 0, 0.2, 0.4) phase is established and the strontium content is inhomogeneous and sufficient in most grains, but the Ni is deficient. The electrical transport and magnetization measurements reveal an insulating behavior and a C-W like feature with a ferromagnetic background caused by nickel segregations. Electrical transport measurements under high pressure show that the insulating behavior can be effectively suppressed but superconductivity is still not observed.

Methods
Sample growth. To synthesize polycrystalline samples of Nd 1−x Sr x NiO 2 (x = 0, 0.2, 0.4), we first prepare polycrystalline Nd 2−2x Sr 2x NiO 4 (x = 0, 0.2, 0.4) samples by the solid-state reaction of Nd 2 O 3 , NiO, and SrO at 1200°C for 24 h. And then we use precursor Nd 2−2x Sr 2x NiO 4 , NiO, and KClO 4 to synthesize the Nd 1−x Sr x NiO 3 (x = 0, 0.2, 0.4) with high pressure and high temperature. Here KClO 4 is used as an excess oxygen source. Then the mixture is pressed into a pellet and sealed in a gold capsule. This procedure is done in a glove box with oxygen and water concentrations less than 0.1 ppm. The gold capsule is placed in a BN capsule and heated up to 1000°C and stayed for 2 h at this temperature under a pressure of 2 GPa. The resultant compound is the perovskite Nd 1−x Sr x NiO 3 phase which is verified by powder X-ray diffraction at room temperature (see Supplementary Fig. 7 and Supplementary Note 3). Next, the samples of Nd 1−x Sr x NiO 2 are obtained by reacting Nd 1−x Sr x NiO 3 (x = 0, 0.2, 0.4) with CaH 2 , which is similar to the previous report 48,49 . The obtained Nd 1−x Sr x NiO 3 samples are washed by distilled water and then dried, ground with the CaH 2 in a ratio of 1:3 and then pressed into pellets. The pellets are sealed in a quartz tube, followed by heating treatment at 280°C for 20 h. Then the resultant pellets are crushed and washed with saturated NH 4 Cl in anhydrous ethanol to remove the residual CaH 2 and the reacted byproduct CaO, and then dried in an evacuated oven. The target sample of the 112 phase in powder form is obtained. For measuring resistivity, the powders are pressed into a pellet again, and sealed with untouched CaH 2 powders in a quartz tube, followed by another heating treatment at 180°C for 10 h.
Physical properties measurements. The crystal structures of the prepared samples are determined by powder X-ray diffraction (XRD) (Bruker D8 Advance) using Cu-Kα radiation at room temperature with a scanning step of 0.01°and 2θ from 10°to 90°. The Rietveld refinements are done based on the TOPAS4.2 software 32,50 . The SEM photograph of the polycrystalline and the energy dispersive X-ray microanalysis spectrum are done by Phenom ProX (Phenom). The measurements are performed at an accelerating voltage of 15 kV. The DC magnetization is measured with a SQUID based on the vibrating sample technique (SQUID-VSM 7T, Quantum Design). The electrical resistances at ambient pressure are measured by the standard four-probe method using the physical property measurement system (PPMS 16T, Quantum Design). The high pressure resistivity measurements are performed by using the diamond avail cell (cryoDACPPMS, Almax easyLab) 51 .

Data availability
The data supporting the findings of this study are available from the corresponding author upon reasonable request.