{'fraction_non_alphanumeric': 0.0392508691263878, 'fraction_numerical': 0.01805539979813839, 'mean_word_length': 4.673027989821883, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Stoichiometry, Spin Fluctuations, and Superconductivity in LaNiPO

Superconductivity in LaNiPO is disrupted by small (~5%) amounts of non-stoichiometry on the lanthanum site, even though the electronic contribution to the heat capacity increases with increasing non-stoichiometry. All samples also exhibit specific heat anomalies consistent with the presence of ferromagnetic spin fluctuations (Tsf ~ 14 K). Comparison of layered nickel phosphide and nickel borocarbide superconductors reveals different structure-property correlations in the two families.


Results and Discussion
Despite being prepared in nominally the same way, each of the three samples of LaNiPO exhibit different superconducting properties. Fig. 1 shows zero field cooled DC susceptibility data for each sample. Samples "A" and "B" both display bulk superconductivity, with transition temperatures of 4.2 K and 3.2 K respectively. The bulk nature of the superconductivity in samples "A" and "B" is confirmed by the presence of anomalies in the specific heat at T c (inset).
In contrast, sample "C" displays only a trace of superconductivity.
Rietveld refinement of NPD data was used to understand the differences between the three samples. The structure of LaNiPO consists of Ni 2 P 2 layers of edge-sharing Ni-P tetrahedra, separated by La-O 2 -La units ( Fig. 2(a) inset). In the unit cell, only the positions along the c axis of the lanthanum and phosphorus are not fixed by symmetry. Structural parameters were freely refined in the fits, including isotropic thermal parameters for all atoms, one positional parameter for La and P, and the occupancies of the La and O sites. The occupancies of the Ni and P sites were found not to deviate significantly from full occupancy and were therefore fixed at one for the final refinements. The refinements indicate that none of the samples are stoichiometric: the refined values in Table I are consistent with a slight (3-4%) oxygen deficiency, statistically significant at the 3.5-4σ level. While it is possible that in some circumstances reduced site occupation in structure refinements may be due to correlation of the occupancy with the thermal parameter, refinements that minimize this correlation indicate that it is real (see below). The relatively small oxygen thermal parameters, compared to phosphorus, then reflect the ionic nature of the La-O 2 -La sandwich layer compared to the more covalent Ni 2 P 2 layers. A typical fit is shown in Fig. 2(a), and final refinement atomic parameters and agreement values are shown in Table I. The lanthanum and phosphorus positional parameters and the oxygen site occupancies are the same for all samples within the standard deviations. However, the refined occupancy of the lanthanum site in non-superconducting sample "C" (0.951 (13)) is less than that in the best superconductor, "A" (0.995 (9)). This is statistically significant at the 4σ level. This slight difference in stoichiometry is not reflected in the lattice parameters due to its small amount and the competing effects of the presence of vacancies, which would tend to contract the lattice, and increased electostatics when La 3+ ions are missing, which would tend to expand the lattice. As a further confirmation that sample "C" is lanthanum deficient, and that all are oxygen deficient, a second series of refinements was performed in which occupancies were fixed at a systematic series of values near the optimal, and all other parameters were allowed to refine freely. This approach minimizes correlations between occupancy and thermal parameters. Contour plots of the fit quality factor versus La and O occupancy from such refinements in shown in Fig. 2(b) for samples "A" and "C". In both cases, the best fits are obtained with a 3-4% deficiency on the oxygen sites. While the La content of "A" is nearly stoichiometric, the best fit for "C" clearly occurs at a lower La occupancy. In addition, there is a small amount of La 2 O 3 impurity phase (3%) in sample "C" that is not present in "A". These two observations both indicate a lower La content of the main phase in "C". Thus the structure refinements and property characterizations show that lanthanum deficiency destroys superconductivity in LaNiPO.
The normal state electronic contributions to the specific heat are also consistent with the differences in stoichiometry. The region above T c is not linear on a C/T vs. T 2 plot for any of the samples, even when the superconductivity has been suppressed by application of a 9 T magnetic field ( Fig. 3(a) inset). Instead, there is an upturn at low temperatures, suggestive of spin fluctuations. The low temperature specific heat for a spin fluctuation system is 23 , which includes contributions from the electrons, the lattice, and spin fluctuations respectively. Using the rules of logarithms, and dividing both sides by T, this can be rewritten in a form suitable for data fitting, . This expression fits the observed data very well ( Fig. 3(a)). To fit the upturns below 1 K seen for two of the high field measurements, a representing the high temperature part of a nuclear Schottky anomaly, was also included. A similar anomaly was observed in LaFePO 24 and LaNiAsO 25 , and is ascribed to the freezing out of 139 La(S=7/2) nuclear spins. The fitted values are tabulated in Table II ). This increase in the electronic contribution to the specific heat is consistent with greater chemical doping in "B" and "C", which apparently arises as a result of the lanthanum deficiency found in the NPD refinements ( Fig. 3(b) (Table II, all three samples), where the field tends to suppress the mass enhancement due to the spin fluctuations 23 .
Quantitative analysis of the dependence of γ on applied field was not performed due to the large uncertainties in the values.

Conclusion
All samples show the presence of 4-5% oxygen vacancies, but whether this nonstoichiometry is necessary for superconductivity was not addressed in the current study. It is found that 5% La vacancies are sufficient to suppress superconductivity, despite a 25% increase in the Sommerfeld coefficient. We speculate that prolonged heating in silica tubes with trace amounts of oxygen is what results in the lanthanum deficiency. The low temperature specific heat data on all three samples are consistent with the presence of spin fluctuations. Whether these spin fluctuations are related to the superconductivity cannot be determined from the present data.
If these fluctuations are related to T c , then some difference in T sf would have been expected between the superconducting ("A" and "B") and non-superconducting ("C") specimens, but no such difference was observed. However, our observation that T c is highest in the samples with the smallest γ is unexpected in a typical BCS picture.
The empirical structure-property relationship in the Ni 2 P 2 -and Ni 2 As 2 -based materials is different than that in another structurally related family of superconductors, the nickel borocarbides, which contain isostructural Ni 2 B 2 layers. Fig. 4 shows the observed superconducting transition temperatures of all three sets of materials as a function of the shape of the NiX 4 tetrahedron [14][15][16][26][27][28][29] . In the Ni 2 P 2 and Ni 2 As 2 materials, as the across-plane X-Ni-X bond angle decreases away from 109.45° (i.e. as the tetrahedron becomes less ideal), T c increases. This is even as the nickel atoms in the square planes get further apart. This is in contrast to the nickel borocarbide superconductors [30][31][32][33][34] , where T c goes up at the nickel-nickel distances decrease and the tetrahedra become more ideal (Fig. 4). Further study is warranted to understand this difference in relationship between structure and superconductivity in nickelbased materials. Additionally, the results in Fig. 4 suggest that stretching the Ni 2 P 2 layers could result in a higher T c in this class of compounds. LaNiPO "A" "B" "C" a 4.04669(6) 4.04768 (7) 4.04766(9) c 8.1089 (2) 8.1104 (2) contribution to T C / , representing the high temperature part of a nuclear Schottky anomaly, was also included for the 9 T fits. The data ranges used were 0.4 to 10 K for 3+ T fields, and 5.5 to 10 K for fields < 3 T (to avoid the superconducting transition contribution).
Field γ (mJ/mol*K 2 ) β (mJ/mol*K 4 ) A (mJ/mol*K 4 ) B (mJ*K/mol) "A" 0 T 5.  Contour plots of the refinement agreement statistic χ 2 as a function of lanthanum and oxygen occupations, with the thermal parameters allowed to refine freely. The results indicate that superconducting sample "A" is stoichiometric in La, whereas sample "C", which shows little superconductivity, is La-deficient. These plots also show that both samples have a slight oxygen deficiency (3-4%).
The stars show the minima in the agreement indices, indicating the best structural models, which correspond to the final refinements in Table I.