Evolution of Superconductivity with Sr-Deficiency in Antiperovskite Oxide Sr_3−xSnO

Abstract

Bulk superconductivity was recently reported in the antiperovskite oxide Sr_3−xSnO, with a possibility of hosting topological superconductivity. We investigated the evolution of superconducting properties such as the transition temperature T_c and the size of the diamagnetic signal, as well as normal-state electronic and crystalline properties, with varying the nominal Sr deficiency x₀. Polycrystalline Sr_3−xSnO was obtained up to x₀ = 0:6 with a small amount of SrO impurities. The amount of impurities increases for x₀ > 0.6, suggesting phase instability for high deficiency. Mössbauer spectroscopy reveals an unusual Sn⁴⁻ ionic state in both stoichiometric and deficient samples. By objectively analyzing superconducting diamagnetism data obtained from a large number of samples, we conclude that the optimal x₀ lies in the range 0.5 < x₀ < 0.6. In all superconducting samples, two superconducting phases appear concurrently that originate from Sr_3−xSnO but with varying intensities. These results clarify the Sr deficiency dependence of the normal and superconducting properties of the antiperovskite oxide Sr_3−xSnO will ignite future work on this class of materials.

Introduction

Discoveries of superconductivity with high critical temperatures (T_c’s) in the layered copper oxides¹ and iron pnictides² have opened new research fields not only on their superconductivity but also on neighboring and even wider topics such as strong correlation and multi-orbital effects in d-electron systems. Clarification of the composition dependence of various ordered phases and corresponding electronic properties serves as an important basis towards pioneering such novel fields. Indeed, in both copper oxides and iron pnictides, the establishment of the composition phase diagrams has been playing significant roles^3,4,5. Very recently, some of the present authors reported superconductivity in the antiperovskite oxide Sr_3−xSnO⁶, a new class of oxide superconductors. The superconductivity of this oxide emerges by hole doping to the parent compound Sr₃SnO, which is unique in hosting a negative metal ion Sn⁴⁻ and as a consequence in exhibiting three-dimensional (3D) bulk Dirac dispersion in its electronic state^7,8. However, it was not clear how the superconductivity emerges from the parent 3D Dirac compound as the Sr deficiency x is tuned and whether the negative ionic state is actually realized. In this article, we report the dependence of superconductivity on the nominal Sr deficiency x₀ and reveal that the optimal x₀ is located around x₀ ~ 0.55–0.60. Furthermore, we provide microscopic evidence for the Sn⁴⁻ state in both stoichiometric and deficient Sr_3−xSnO.

Antiperosvskite oxides A₃BO (A = Mg, Ca, Sr, Ba, Eu, Yb and B = Si, Ge, Sn, Pb) have the perovskite crystal structure but with O²⁻ ions occupying the center of the octahedron formed by A²⁺ ions. To satisfy the charge-neutrality relation, the B ions take an unusual 4− oxidation state and as a consequence their p orbitals are almost filled^9,10. This unusual electronic configuration can lead to interesting properties. Indeed, theoretical works on Ca₃PbO predicted a 3D Dirac dispersion in the electronic band^7,8, similar to recently-studied Dirac-material candidates Au2Pb¹¹, Cd3As2^12,13 and Na₃Bi¹⁴. This Dirac dispersion originates from the band inversion of the nearly empty Ca-3d and nearly filled Pb-6p bands near the Γ point, as well as from the avoided hybridization between these bands due to crystal symmetry. The Dirac point is expected to have a small gap of the order of ~10 meV⁷, due to higher-order interactions originating from the spin-orbit coupling. This gapped state was later predicted to be a topological cyrstalline insulator state¹⁵. By changing the A and B ions, one can control the strength of the spin-orbit coupling and band mixing, and eventually tune the system from the topologically trivial insulator to the topological crystalline insulator¹⁶. The parent compound of this study, Sr₃SnO, is located in the vicinity of the topological transition but still in the non-trivial regime¹⁵. Theoretically, it has been proposed that Sr_3−xSnO can host topological superconductivity, reflecting its unusual normal-state electronic states^6,17. More recent theoretical calculations predict various properties and deficiency effects in antiperovskite oxides, including those of Sr₃SnO^18,19,20. Furthermore, it was shown that, in Sr_2.5SnO in different deficiency arrangements, the Fermi level still lies in bands with strong mixing between the Sr-4d and Sn-5p orbitals²¹.

Experimental works on antiperovskite oxides in the last several years were triggered by theoretical predictions^7,8,15, and now there are reports on antiperovskite oxides in various forms, including single crystals^10,22, polycrystals^6,23, and thin films^24,25,26,27. Recently, the predicted Dirac dispersion has been experimentally observed by angle-resolved photoemission spectroscopy (ARPES) using Ca₃PbO single crystals²², supporting the claim from theoretical calculations. Recent ¹¹⁹Sn-NMR of nearly stoiciometric Sr_3−xSnO suggests the presence of Dirac electrons in the normal state²⁸.

In the initial report of superconductivity in bulk Sr_3−xSnO⁶, it was proposed that hole doping due to Sr deficiency was necessary for the appearance of superconductivity. Nevertheless, quantitative analysis of the deficiency was difficult due to the uncontrolled evaporation of Sr during the synthesis. We more recently found a way to suppress the Sr evaporation²⁹. In this work, we produced a large number of Sr_3−xSnO samples using this method with varying the nominal deficiency x₀ and examined their superconducting and normal-state properties.

Results and Discussion

Phase Characterization

In Fig. 1(a), we present the magnetization for a superconducting sample with nominal x₀ = 0.5 (chunk of 30 mg) showing M nearly equal to the ideal Meissner value ${M}_{{\rm{Meissner}}}=$ $-\,(1/4\pi )HV=-\,64.2\,{\rm{emu}}/{\rm{mol}}$ without the demagnetization correction, where H = 10 Oe is the external magnetic field and V = 81.0 cm³/mol is the molar volume. In order to allow subsequent XRD measurement, we placed the sample piece in a plastic capsule sealed with Kapton tape, all within an argon glovebox, to protect it from decomposing in air. The sample was later taken out from the capsule, and crushed into powder for XRD measurement. The measured XRD pattern for this entire piece is presented in Fig. 1(b), together with the expected diffraction patterns of Sr₃SnO, insulating SrO, and other superconducting materials reported in the Sr-Sn-O systems^30,31,32,33: β-Sn, SrSn₄, and SrSn₃. The XRD pattern we measured matches well with that expected for Sr₃SnO and small shoulder peaks characteristic of SrO (cubic, a = 5.16 Å)³⁴ can also be seen. Notice that the peak at 24.48° corresponds to the (011) peak of Sr₃SnO^9,10, and is not expected for SrO. This peak signifies that Sr_3−xSnO is the dominant phase. The simulated XRD patterns of the other compounds do not match the measured pattern, either. From this comparison, the superconductivity with M close to M_Meissner certainly originates from Sr_3−xSnO, providing strong confirmation for its bulk superconductivity.

Figure 1

(a) DC magnetization measured with an applied field of 10 Oe as a function of temperature of a sample with x₀ = 0.5 (Batch No. AP164). Degaussing was performed between the two measurements, both reproducibly showing strong superconducting 5-K phase, close to 100% volume fraction. Demagnetization correction was not done. After these measurements, the remnant field was checked using a reference superconductor (Pb, 99.9999% purity) and found to be below 1 Oe. (b) XRD pattern of the same superconductive x₀ = 0.5 sample, taken after the magnetization measurements shown in (a), compared with expected diffraction patterns of Sr₃SnO, SrO, β-Sn, SrSn₃, and SrSn₄⁴⁰. β-Sn, SrSn₃, and SrSn₄ are also superconducting with T_c ’s indicated in the figure^30,31,32,33. The vertical axis is in a linear scale. The peak marked with asterisk cannot be assigned to these impurity phases, but does not decrease in intensity even after this sample decomposes in air.

In Fig. 2, we present the XRD patterns of samples prepared with x₀ = 0.0–0.7. For $0.0\le {x}_{0}\le 0.6$, the dominant phase is Sr_3−xSnO, as confirmed by the presence of the (011) peak. Shoulder peaks characteristic of SrO are seen on the left side of some of the main peaks, but this phase remains a minor one for ${x}_{0}\le 0.6$. For x₀ = 0.7, however, the peaks of SrO become rather substantial. In addition, some peaks of additional unidentified impurity phases were observed as marked with asterisks in Fig. 2, likely originate from Sr-Sn alloys. From the XRD patterns, we evaluate the lattice constant a for each sample. Interestingly, a is found to be almost x₀ independent, with a = 5.139 ± 0.002 Å for all x₀. This fact indicates that the cubic Sr₃SnO phase survives even with high Sr deficiency without changing the lattice constant. Such unchanging lattice parameter is similar to reports on titanium and vanadium compounds with perovskite-type structure^35,36. The cubic phase for the perovskite titanate is preserved for the deficiency of 0.5 on the O site^35,36, while the antiperovskite structure Sr_3−xSnO survives up to the deficiency of 0.6 on the Sr site. The existence of two Sr_3−xSnO phases with different deficiencies would overlap in the XRD pattern, which would explain the superconducting transitions and the Mössbauer spectra. We should comment here that other antiperovskite oxides may have various deficiency limits as observed for different perovskite oxides with different constituent elements³⁵. We also comment that the deficiency in the Sr site may be accompanied by deficiency on the O site, but we expect greater deficiencies in the Sr by considering the existence of the satellite peak in Mössbauer spectra, as we will discuss in the next subsection.

Figure 2

Powder XRD pattern of Sr_3−xSnO samples prepared with various x₀, plotted on a linear (a) and semi-log (b) scale. Each curve is shifted vertically for clarity. Minor impurity peaks from the SrO phase can be seen as the left shoulders of some peaks (such as (111), (002), (022)) of the main phase, but the shoulder was absent in the (011) peak, as expected from the crystalline symmetry of Sr₃SnO and SrO. Additional weak peaks due to impurities (marked with asterisks) can be seen between the (011) and (002) peaks. Expected peak positions for Sr₃SnO, SrO, β-Sn, SrSn₄, and SrSn₃ are indicated with the short vertical lines at the bottom.

Representative energy dispersive x-ray spectroscopy (EDX) results for samples with x₀ = 0.5 are shown in Fig. 3. We should comment that the surface of these samples was likely oxidized and decomposed during a short transfer (~1 min) from our glovebox to the EDX measurement chamber. This surface oxidization results in the high percentage of oxygen in EDX results, as seen in the panels (a), (f), and (k) of Fig. 3. However, we expect that the Sr/Sn ratio should not be drastically affected by this short exposure to air. This ratio is mapped in the panels (d), (i), and (n) of Fig. 3, where the white regions correspond to Sr/Sn = 2.5, expected from the nominal value x₀ = 0.5. In these panels, we can also see some Sr-rich regions, likely originating from SrO phase in the sample. In the panel (n) of Fig. 3, we can see Sn-rich regions reflecting either an impurity formed during synthesis or decomposition on the surface during transfer to the chamber. The bottom panels show histograms of the distribution of the Sr/Sn ratio. In Fig. 3(e) and (j), the Sr/Sn ratio distribution in the investigated regions is centered around 2.5, in agreement with the Sr_2.5SnO phase in these samples. In Fig. 3(o) the distribution is broader, but regions with the ratio close to 2.5 are still visible.

Figure 3

EDX results of various Sr_3−xSnO samples with x₀ = 0.5. The panels (a–c) respectively show mappings of the contents of O, Sr, and Sn atoms in at% value of a typical sample surface (Batch No. AP165). The ratio between Sr and Sn contents is mapped in the panel (d), and the distribution of this ratio is shown in the histogram in the panel (e). In (d) and (e), the white color corresponds to the ratio Sr/Sn = 2.5, expected for the nominal x₀ value, while the green and blue colors correspond to more Sr-rich and Sn-rich ratios, respectively. The panels (f–j) present similar information but for a different region of the same sample (Batch No. AP165), and the panels (k–o) for another sample (Batch No. AP210). The sizes of the views are 41.6 × 32.5 μm² for (a–d), 55.4 × 43.3 μm² for (f–i), and 61.3 × 47.9 μm² for (k–n).

Mössbauer Spectroscopy

In order to investigate the valence of Sn ions in our samples, we performed ¹¹⁹Sn Mössbauer spectroscopy at room temperature. In Fig. 4, we present ¹¹⁹Sn- Mössbauer spectra for samples with x₀ = 0.0, 0.4, and 0.5. The isomer shift, the peak position of the absorption spectra, represents the difference in the energies of the ground and excited states of the Sn nucleus of the sample, with respect to those of a reference material (with the same ionic state of Sn as the source). The source we used was CaSnO₃ and we took the isomer shift of BaSnO₃ as the origin, as explained in Methods.

Figure 4

Sn Mössbauer spectra of Sr_3−xSnO samples prepared with different values of x₀. The origin of the isomer shift is defined as of BaSnO₃, and isomer shifts of some reference materials³⁸ with different Sn valencies are indicated with the vertical lines at the top. The dotted curves indicate Lorentzian fits for the main (green) and satellite (red) peaks. Each curve is offset vertically by 0.05 for clarity.

In stoiciometric samples, the isomer shift of the main peak is about +1.8 mm/s. This shift does not match those expected for ordinary valences Sn⁴⁺, Sn²⁺, and Sn⁰; but is equal to that reported for Mg₂Sn³⁷, where the Sn⁴⁻ valence is expected based on the charge balance consideration (Mg²⁺)₂Sn⁴⁻. Thus, our result provides the first microscopic support for the presence of the unusual Sn⁴⁻ ions with almost fully occupied Sn-5p orbitals. In deficient samples, we also observed the main peak at +1.80 mm/s, revealing the presence of negative Sn ions even for x₀ > 0. In addition, a shoulder-like structure can be seen in the high-shift side. By fitting the overall spectrum with two Lorentzian peaks, a satellite peak centered at +2.59 mm/s is found. This peak is barely seen in the x₀ = 0 samples, but we, nevertheless, fitted the x₀ = 0 sample data with two Lorentzian peaks with one peak position fixed at +2.59 mm/s. The integrated peak intensity ratio of the main and satellite peaks are 100:4 for both x₀ = 0 samples, 100:19 and 100:9 for the two x₀ = 0.4 samples, and 100:19 for the x₀ = 0.5 sample. This isomer shift of the satellite peak is close to that of β-Sn (+2.55 mm/s)³⁸. Thus, one possible origin of this satellite peak is β-Sn impurity phase contained in the sample. However, this scenario is less likely considering the fact that β-Sn peaks in the XRD pattern is absent or quite weak in our samples (see Figs 1 and 2). Thus, presumably the satellite originates from Sn sites in Sr_3−xSnO neighboring to Sr deficiency. Naively, Sn sites next to a Sr deficiency are expected to have less p electrons and thus to exhibit higher isomer shift due to weaker screening effect, agreeing with the experimental fact. This scenario also explains the observation that the satellite peak intensity becomes stronger for higher x₀. Moreover, the existence of the satellite peak indicate that the Sn valence is clearly changed by the Sr deficiency. Thus, oxygen deficiency, which would push the Sn valency back to −4 and thus tend to avoid the Mössbauer peak change, is not significant in our samples. Notice that, even for Sr-deficient samples, a large fraction of the Sn sites is still surrounded fully by Sr without deficiencies and should exhibit Mössbauer peak at the original position. If two Sr_3−xSnO phases with distinct deficiencies are in our samples, then the shoulder peak at +2.59 mm/s may originate from one of these phases.

We should comment here on the possible phase separation in the samples as indicated by the magnetization analysis (see the next subsection). Within the deficiency scenario for the origin of the satellite peak, if the sample consists of non-superconducting region with negligible deficiency and superconducting region with large deficiency of around 0.5, the former is expected to have the main peak only and the latter could show both the main and satellite peaks, with comparable intensities. Thus, the small intensity of the satellite even for the x₀ = 0.5 sample agrees with the phase separation discussed later. The emergence of the satellite peak in deficient samples may be related to the observed superconductivity in Sr_3−xSnO. Future investigation of the Mössbauer at low temperature in deficient superconducting samples may provide crucial information about the superconductivity in Sr_3−xSnO.

Dependence of Superconducting Properties on x ₀

Figure 5(a) represents the temperature dependence of DC magnetization down to 1.8 K of representative Sr_3−xSnO samples prepared with various values of x₀. Superconductivity appears for some samples with 0.35 < x₀ < 0.70. The onset T_c is observed to be commonly 5 K for such superconductive samples, but the ratio M/M_Meissner at 2 K varies a lot. These facts suggest some inhomogeneity in the samples: our samples consist of regions with different deficiency, non-superconducting region with small x and superconductive region with large x. We emphasize again that M/M_Meissner close to 1 in zero-field-cooling (ZFC) measurements observed in some samples provides strong evidence for the bulk superconductivity of Sr_3−xSnO, considering the sample purity demonstrated by XRD.

Figure 5

(a) DC magnetization as a function of temperature of Sr_3−xSnO samples prepared with various values of x₀. Superconductivity appears for x₀ > 0.35 and becomes much weaker for x₀ ≥ 0.7. (b) Real and (c) imaginary parts of AC susceptibility, χ_AC, normalized by the sample mass, plotted as functions of temperature. Two superconducting transitions at 5 K and 1 K appear for superconducting samples.

In Fig. 5(b) and (c), the real and imaginary parts of the χ_AC signal normalized by the sample mass are shown for representative samples. Interestingly, another superconducting transition appears at ~1 K for all superconducting samples. The magnitude of the superconducting signals of these two superconducting phases varies depending on the sample. In the examples shown in Fig. 5(b) and (c), the x₀ = 0.52 sample exhibits a stronger transition at 5 K, while in the x₀ = 0.43 sample the 5-K and 1-K transitions have similar magnitudes. This fact indicates that two transitions originate from different parts of a sample, presumably with slightly different Sr contents. The magnetic field effect on the 1-K phase was investigated as plotted in Fig. 6, where χ_AC(T) curves under different magnetic fields are shown. The 1-K superconducting phase completely disappears at 200 Oe, indicating that the upper critical field of the 1-K phase is less than this value.

Figure 6

Temperature dependence of (a) real and (b) imaginary parts of AC susceptibility, χ_AC, normalized by the sample mass, measured under various magnetic fields to emphasize the effect of magnetic field on the 1 K superconducting phase. The measurements were performed for a sample with x₀ = 0.3. The magnetic field values indicated in the figure is evaluated considering the estimated remnant field of 125 Oe after the adiabatic demagnetization refrigeration process. Because this sample was made with a different Sr (Furuuchi, 99.9%), results of this sample are not included in other figures.

The x₀ dependence of superconducting properties, namely T_c and the size of the diamagnetic signal, evaluated based on the DC magnetization and χ_AC measurements are summarized in Fig. 7. Superconductivity with T_c of about 5 K and 1 K appears in the range 0.35 ≤ x₀ ≤ 0.65, with almost no change of T_c, as shown in Fig. 7(a). Figure 7(c) shows the ratio M/M_Meissner of 45 samples, corresponding to the volume fraction without demagnetization correction, of the 5-K phase superconductivity calculated using the DC magnetization of the ZFC process at 1 Oe and 1.8 K. The ratio is strongly sample-dependent even among samples with similar x₀ values. Nevertheless, there is a tendency that strongly superconducting samples are more likely to be found around x₀ ~ 0.5. To clarify this tendency more objectively and more quantitatively, we evaluate the mass-weighted average of the M/M_Meissner ratio, ${\bar{v}}_{{\bar{x}}_{0}}$, of the range ${\bar{x}}_{0}-\,0.025 < {x}_{0} < {\bar{x}}_{0}+0.025$ as

$${\bar{v}}_{{\bar{x}}_{0}}=\frac{\sum _{i}{m}_{i}{v}_{i}}{\sum _{i}{m}_{i}}$$

(1)

where m_i and v_i are the mass and M/M_Meissner of the i-th sample and summation over i is taken for samples whose x₀ value is in the range mentioned above. The results are presented in Fig. 7(d). Here, a dome-like-shaped peak appears centered at ${\bar{x}}_{0}=0.55\,\sim \,0.60$; hinting at a specific phase favorable for superconductivity.

Figure 7

(a) T_c as a function of x₀ based on the DC magnetization (down to 1.8 K) and the AC susceptibility (down to 0.1 K). (b) Mass-normalized diamagnetic signal χ_AC of the 5-K and 1-K phases. (c) M/M_Meissner evaluated using DC magnetization data at 1.8 K, without demagnetization correction. (d) Mass-weighted average of M/M_Meissner, $\bar{v}$, taken over 0.05 intervals of x₀ indicated by horizontal bars. The vertical error bars indicate the weighted standard errors.

The normalized χ_AC diamagnetic signal of the 5-K and 1-K phases are summarized in Fig. 7(b). Here, the changes in the signal from 6 K to 2 K and from 2 K to 0.1 K are chosen to represent the diamagnetic signal of the 5-K and 1-K phases, respectively. Some samples are dominated by the 1-K phase, while others have a stronger contribution from the 5-K phase. Nevertheless, we again observe a tendency that high signals are found for samples with x₀ ~ 0.5. We comment here that the M/M_Meissner presented in Fig. 7(c) may be an underestimate due to dominance of the 1-K phase in some of these samples, such as the x₀ = 0.45 sample presented in Fig. 5(b).

The results presented in Fig. 7 indicate that the samples contain three different regions with different deficiencies: non-superconducting parts and two parts exhibiting superconductivity at 5 K and 1 K. Thus, the change in the nominal deficiency x₀ results in changes in the relative volume fractions of these phases, but not in the change of the actual deficiency in each of these phases. Let us define here the actual x values for the non-superconducting part as x_n, that for the 5-K superconducting region as x_5K and that for the 1-K superconducting region as x_1K. Because samples with x₀ < 0.35 do not exhibit superconductivity, x_n is probably close to 0. From the analysis in Fig. 7(d), x_5K probably lies in the range 0.55–0.60. Since all superconducting sample exhibit both the 5-K and 1-K superconductivity, x_1K must be close to x_5K. Comparing Fig. 7(b) and (d), the peak in the 1-K superconductivity volume is located at the lower deficiency side. Thus, x_1K is expected to be slightly smaller than x_5K. It is also possible that these two superconductive phases differ in the oxygen stoichiometry. Concurrency of the two superconducting phases with x_5K and x_1K may result from phase stability feature near the reaction temperature: there may be two thermodynamically stable phases with x_5K and x_1K and actual samples exhibit phase separation to these two phases during the growth. Control of such phase separation is not yet achieved but should be tried in future. In addition, carrier doping by methods other than deficiency, such as substitution of Sr with K or Na, will provide hints toward clarifying this issue.

Conclusion

In summary, we have reported comprehensive bulk and microscopic investigation of Sr_3−xSnO samples with the nominal Sr deficiency x₀ varying from 0.0 to 0.7. We provided evidence for the unusual Sn⁴⁻ state with the filled 5p orbital in both stoichiometric and deficient samples. We have demonstrated that superconductivity appears for samples with 0.35 < x₀ < 0.70. All superconducting samples exhibit two superconducting transitions, at about 5 K and 1 K. The present findings, clarifying the composition necessary for the appearance of superconductivity in Sr_3−xSnO, serve as important bases toward investigation of the proposed topological superconductivity in this system^6,17. Producing superconducting Sr_3−xSnO single crystals or thin-films can be a next important step to the goal.

Methods

Bulk polycrystalline Sr_3−xSnO samples were prepared by heating mixtures of the starting materials Sr (Aldrich, 99.99%) and SnO (Furuuchi, 99.9%) in varying ratios Sr:SnO = (3−x₀):1 to control the amount of Sr deficiency. Reaction was carried out at 825 °C in an alumina crucible inside a quartz tube sealed with 0.3 atm (at room temperature) of argon. Sr (Furuuchi, 99.9%) was used only for the sample shown in Fig. 6. Details of the synthesis are described in ref.²⁹. Throughout this article, x₀ refers to the nominal value. Powder X-ray diffraction (XRD) patterns were collected for various samples using a commercial diffractometer (Bruker AXS, D8 Advance) utilizing the CuK_α radiation. The samples were placed on a glass stage inside a glovebox and covered with a 12-μm-thick polyimide film (DuPont, Kapton), which was attached to the sample stage with vacuum grease (Dow Corning Toray). With this setup, we minimized contact of the samples with air, and we confirmed that the sample degradation is negligible within typical measurement time of 200 min. The lattice constant was estimated using WPPD method using the software TOPAS. The chemical composition at the sample surface was characterized using an energy dispersive X-ray spectroscopy (EDX) system, a scanning electron microscope (Keyence, VE-9800) equipped with an X-ray detector (AMETEK, Element K). Mössbauer spectra were collected using Ca^119mSnO₃ γ-ray source and the origin of the isomer shift was chosen to be that of BaSnO₃. The isomer shift is closely related to the local electronic density at the nucleus position. Thus, the isomer shift is most sensitive to the number of s electrons, which has a large wavefunction weight at the nuclear position, whereas p and d electrons lead to opposite weaker shift compared to s electrons via the screening effect. DC magnetization was measured using a commercial superconducting quantum interference device (SQUID) magnetometer (Quantum Design, MPMS), while χ_AC was measured using a miniature susceptometer³⁹, which was installed in a commercial cryostat (Quantum Design, PPMS) with an adiabatic demagnetization refrigerator (ADR) option.