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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 2019 Oct 22;116(45):22458–22463. doi: 10.1073/pnas.1912610116

Evolution of superconductivity in K2−xFe4+ySe5: Spectroscopic studies of X-ray absorption and emission

H T Wang a,1, Anirudha Ghosh b,1, C H Wang c,d, S H Hsieh b,e, Y C Shao b,f, J W Chiou g, C L Chen e, C W Pao e, J F Lee e, Y S Liu f, Y D Chuang f, J H Guo f, M K Wu a,c,2, W F Pong b,2
PMCID: PMC6842620  PMID: 31641068

Significance

We report the study using X-ray absorption and resonant inelastic X-ray scattering techniques to investigate the evolution of superconductivity in K1.9Fe4.2Se5, which was synthesized from its nonsuperconducting parent compound, K2Fe4Se5, by increasing the Fe concentration. The results provide a deeper insight into the magnetic and local electronic properties of K1.9Fe4.2Se5, such as a decrease in antiferromagnetic spin magnetic moment of Fe, charge transfer, and hybridization between Fe 3d–Se 4p orbitals, and increase in the local static structural disorder, to gain an understanding of the evolution of superconductivity in the compound.

Keywords: superconductivity, Fe vacancy disorder, X-ray absorption spectroscopy, resonant inelastic X-ray scattering

Abstract

This study investigates the evolution of superconductivity in K2−xFe4+ySe5 using temperature-dependent X-ray absorption and resonant inelastic X-ray scattering techniques. Magnetization measurements show that polycrystalline superconducting (SC) K1.9Fe4.2Se5 has a critical temperature (Tc) of ∼31 K with a varying superconducting volume fraction, which strongly depends on its synthesis temperature. An increase in Fe-structural/vacancy disorder in SC samples with more Fe atoms occupying vacant 4d sites is found to be closely related to the decrease in the spin magnetic moment of Fe. Moreover, the nearest-neighbor Fe–Se bond length in SC samples exceeds that in the non-SC (NS) sample, K2Fe4Se5, which indicates a weaker hybridization between the Fe 3d and Se 4p states in SC samples. These results clearly demonstrate the correlations among the local electronic and atomic structures and the magnetic properties of K2−xFe4+ySe5 superconductors, providing deeper insight into the electron pairing mechanisms of superconductivity.

Since the discovery of Fe-based superconductors (Fe-SCs) in 2008 (1), significant efforts have been made to better understand these materials. In particular, Fe-chalcogenide SCs have attracted significant attention owing to a variety of characteristics, including a wide range of critical temperatures (Tc), competition among various orders, and potential for the realization of Majorana bound state (2–10). The discovery of the alkali-intercalated iron selenide SC A2−xFe4+ySe5, where A = K, Rb, and Cs, with a Tc of ∼31 K (3, 11, 12) provided an opportunity for better understanding the origin of superconductivity in the Fe-chalcogenide family.

Several studies (12–17) have exploited various experimental techniques to explore the properties of K2−xFe4+ySe5, where x = 0 to 0.3 and y = 0.15 to 0.5. The parent compound, K2Fe4Se5, forms a relatively complex antiferromagnetic (AFM, TN ∼560 K) phase, where all Fe spin moments are oriented along the c axis at 16i sites. The crystal structure of K2Fe4Se5 typically contains 2 Fe sites, 16i and 4d. Fe atoms occupy the 16i sites, whereas the 4d sites remain vacant, as shown in Fig. 1A (18). With an increase in the concentration of Fe atoms at the vacant 4d sites, a structural/vacancy-disordered superconducting material, K2−xFe4+ySe5, is formed with Tc ∼31 K. The most recent high-resolution temperature-dependent X-ray diffraction (XRD) analysis performed by Wang et al. (19), confirmed that the crystal lattice of superconducting K2−xFe4+ySe5 material exhibits the I4/m structural symmetry even at temperatures below the above-mentioned Tc.

Fig. 1.

Fig. 1.

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(A) Unit cell of crystal structure of K2Fe4Se5 with I4/m space group. The crystal structure comprises alternating layers of alkali, K, atoms, and interconnected FeSe4 tetrahedra. The Se–Fe–Se layer contains 2 sets of Fe sites: Fe(16i) are 16i sites that are occupied by Fe atoms (Bottom Right), whereas Fe(4d) are vacant 4d sites (Bottom Left). (B) Room-temperature XRD patterns of all samples, revealing similar majority I4/m phase. (C) Temperature-dependent magnetic susceptibility reveals a superconducting transition temperature of Tc∼31 K in SC samples. The inset magnifies the temperature-dependent magnetic susceptibility plot of SC-750.

Detailed structural studies conducted by Wang et al. (19), verified that the emergence of superconductivity in K2−xFe4+ySe5 is not due to the impurity phase (K0.5Fe2Se2), but due to the random occupation of Fe atoms in the lattice. However, several questions remain to be answered regarding the exact origin of the superconductivity. To gain deeper insight into the origin of superconductivity in this intriguing material, additional information is needed about its local electronic and atomic structure and magnetic properties (20–22). This study presents detailed experimental results of the temperature-dependent resonant inelastic X-ray scattering (RIXS), X-ray absorption near-edge structure (XANES), and extended X-ray absorption fine structure (EXAFS) of powdered (SC) K1.9Fe4.2Se5 and (NS) K2Fe4Se5 samples. The obtained results elucidate the evolution of superconductivity and its association with the Fe-vacancy order–disorder, magnetic spin moments, and Fe 3d-Se 4p hybridization in the K2−xFe4+ySe5 SC.

Results and Discussion

Polycrystalline SC K1.9Fe4.2Se5 and NS K2Fe4Se5 samples were synthesized by quenching at 820 °C (SC-820 and NS-820) and 750 °C (SC-750 and NS-750). Details regarding the sample preparation processes have been provided in 2 previous studies (16, 19). The crystal structure of the parent compound, K2Fe4Se5 (phase group I4/m), comprised a layer of K atoms sandwiched between 2 Se–Fe–Se triple-layer composites. The atoms comprising the triple layer are interconnected by FeSe4 tetrahedra, as shown in Fig. 1A. Fe vacancies were identified at the Fe(4d) sites (12, 23). As the concentration of Fe in K1.9Fe4.2Se5 is increased, the added Fe atoms primarily occupy the vacant 4d sites of the parent K2Fe4Se5 compound. Fig. 1B shows the room-temperature XRD patterns of all SC and NS samples. The overall I4/m crystal symmetry is conserved in both SC and NS samples with only a slight difference in their lattice parameters (19). Consequently, the XRD features are similar across the samples with an exception of the (002) peak intensity, which increases with respect to the intensity of the (123) peak in the SC samples. The XRD patterns (Fig. 1B) of all SC and NS samples reveal no additional second phase, detectable within the instrument resolution, in agreement with the report by Wang et al. (19). Fig. 1C displays the temperature-dependent magnetic susceptibility of all SC and NS samples in the temperature range 2 to 300 K, with the inset showing the susceptibility curve of the SC-750 sample near transition Tc = ∼31 K. Although both SC-820 and SC-750 samples exhibit the same Tc, the diamagnetic signal of SC-820 is much larger than that of SC-750 (16).

Fig. 2A displays the Fe Lα,β RIXS spectra of all SC and NS samples at 300 K. These were obtained at various excitation energies, labeled as a–j (green bars). The Fe L3,2-edge XANES of the SC-820 sample at 300 K is shown in the inset of Fig. 2A. The RIXS spectrum denoted by j, with an excitation energy of 736.4 eV, shows 2 main emission features around 704.3 (Lα) and 717.4 eV (Lβ), which occur due to the transition of electrons from the occupied Fe 3d states to the 2p3/2 and 2p1/2 core-hole states (21, 24), respectively. The emission intensity of the 2p1/2 feature is weaker than the Fe L2-edge XANES partially because of the Coster–Kronig decay of electrons from the Fe 2p3/2 to the 2p1/2 energy level (24). At all excitation energies from 707.0 to 736.4 eV, the RIXS spectra reveal a main feature around 704.3 eV (blue dashed line), resulting from the fluorescent feature whose position is independent of the excitation energy (20, 24). The low-energy tail region of Lα is lower for SC samples in comparison with NS samples. This could imply a lower charge transfer (CT) in SC samples than that in NS samples. In addition, an apparent shoulder-like feature (near 705.9 eV) is observed in the spectra b–e (close to the Fe L3-edge excitation energy), which is a unique feature present only in K2−xFe4+ySe5 systems, whereas it is absent in other Fe-related superconductors (20, 24). For a better view of this shoulder-like feature, the energy-loss RIXS spectra, d, of all samples are plotted in Fig. 2B. An Fe metal sample is used as a reference.

Fig. 2.

Fig. 2.

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(A) Fe Lα,β RIXS spectra of SC and NS samples obtained at various excitation energies (a–j), which are indicated by Fe L3,2-edge XANES (Upper Inset). Two main features, Lα (∼704.3 eV) and Lβ (∼717.4 eV), arise from transitions from 3d to 2p3/2 and 2p1/2 states, respectively. Small bump-like features originating from the d–d excitation are indicated by the downward arrows. (B) Energy-loss feature of Fe Lα,β RIXS with resonant excitation energy of 707.8 eV in SC and NS samples. The black solid line at 0 eV represents the elastic peak of reference Fe metal, while the red (blue) dashed line at an energy loss of approximately −1.9 eV (−3.5 eV) corresponds to Fe d–d excitation (fluorescence) feature). (C) Fe Lα,β RIXS spectra of SC and NS samples at an excitation energy of 720.4 eV (corresponding to L2 edge) at 300 and 20 K. (Inset) Plot of the variation of RRs (Iβ/Iα) of SC and NS samples at 300 and 20 K.

The spectral feature at the zero energy loss of the Fe metal in Fig. 2B arises from elastic scattering. Since all RIXS spectra for Fe metal, SC, and NS samples were collected at the same scattering angle, the absence of the elastic feature in SC and NS samples may be due to their higher surface roughness and density of defects compared to those of the Fe metal. The fluorescent feature near ∼−3.5 eV (blue dashed line) is observed in all samples and Fe metal, which is due to the emission from Fe 3d to 2p3/2 (Lα). The shoulder-like feature near −1.9 eV in Fig. 2B arises from the intraelectronic transition from Fe t2g to eg states and is referred to as the d–d excitation (21, 25, 26). The d–d excitation feature is prominent in the b–e spectra, whereas it is embedded in the high-energy tail of the f spectra and appears as humps (black arrows) in g and h. In the spectra of a and i, it possibly lies hidden within the Lα and Lβ peaks. The emergence of this d–d excitation feature (−1.9 eV, Fig. 2B), in both SC and NS samples suggests considerable crystal field splitting of Fe ions in the FeSe4 tetrahedra.

Fig. 2C shows the Fe Lα,β RIXS spectra of i (720.4 eV) of SC and NS samples at 300 and 20 K. Two prominent emission features, Lα and Lβ, are observed for all samples. We calculate the resonant ratio (RR) of the integrated intensities, Iβ/Iα (Iβ: 695.0 to 710.0 eV and Iα: 710.0 to 725.0 eV in the emission spectrum), to provide insight into the local spin states of Fe ions in SC and NS samples at both 300 and 20 K. The RRs of all samples, as shown in the Fig. 2C (Inset) are closely related to the variation of the samples’ magnetic spin state (22, 27). A higher value of RR typically reflects a higher magnetic moment of magnetic ions. As shown in Fig. 2C (Inset) the RRs of SC and NS samples at both temperatures lie between the corresponding values for FeO (1.38) and Fe metal (0.40), implying an intermediate spin magnetic moment of Fe ions. A comparison of the RRs of the SC samples with those of the NS samples reveals that not only they decrease with higher Fe concentration but also decrease with the higher quenching temperature. This decrease in the magnetic moment of Fe ions in the SC samples may arise from the magnetic frustration of Fe spins in the material which is caused by the occupation of additional Fe ions at the vacant 4d sites (28). This significant decrease in the AFM moment in SC samples is in agreement with another report (29) and may not responsible for the electron pairing mechanism in the evolution of superconductivity (30, 31).

To obtain a deeper insight into the evolution of superconductivity, we investigated the CT/hybridization property of both SC and NS samples (32, 33). Accordingly, we acquired the Fe L3,2-edge and Se K-edge XANES spectra of the samples, which provide valuable information to investigate the electronic structures at/near the Fermi level (34–36). Fig. 3A presents the Fe L3,2-edge XANES of SC and NS samples measured at 300 and 20 K. The L3- (∼707.8 eV) and L2- (∼720.8 eV) edge features of the Fe L3,2-edge XANES are dominated by electron transitions from the Fe 2p3/2 and 2p1/2 to unoccupied 3d states above the Fermi level, respectively. All spectra are normalized at the pre-L3 and post-L2 edges region. The general line shape of the spectra of SC and NS samples in Fig. 3A is consistent with that of other Fe-chalcogenide SCs (20, 22). The insets (top and bottom at 300 and 20 K, respectively) in Fig. 3A indicate that the intensity of the white-line feature at the Fe L3-edge XANES of SC samples is lower than that of the NS samples at both temperatures. The intensity of the white line of the SC-820 (NS-750) sample is the lowest (highest) at both temperatures. These results indicate that the Fe 3d energy levels in SC samples have fewer unoccupied (hole) states compared to NS samples.

Fig. 3.

Fig. 3.

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(A) Fe L3,2-edge XANES of SC and NS samples at 300 and 20 K. The insets magnify the L3-edge feature. Black dashed lines depict the best-fitted arctangent function, which are representative of the background intensity that arises from the transition to the continuum band above the Fermi level. (B) Se K-edge XANES spectra of SC and NS samples at 300 K. The upper inset magnifies the feature “A.” The lower inset plots variation of integrated intensities of the white-line feature at the Fe L3 edge and feature “A” at the Se K edge of SC and NS samples. The tail of the B Gaussian feature is considered as the background and depicted by a black dashed line.

To better understand the difference in the CT between Fe 3d and Se 4p states, Se K-edge XANES measurements of SC and NS samples were conducted at 300 K; the results are shown in Fig. 3B. The general line shape of the XANES spectra clearly exhibits 3 prominent features depicted by A–C. Feature A designates the electron excitation from Se 1s to the unoccupied Se 4p states above the Fermi level, whereas the other 2 features B and C arise from the scattering of emitted photoelectrons by the nearest-neighbor (NN) and next-NN of Fe and Se atoms (37). Here we refer to CT as this variation in the electron occupancies in Fe 3d and Se 4p orbitals which primarily occur due to change in Fe 3d-Se 4p covalent mixing in SC and NS samples. Fig. 3B (Top Inset) illustrates the magnified details of feature A. The intensity of feature A increases from NS (NS-750→NS-820) to SC (SC-750→SC-820) samples, on the contrary to the trend exhibited by the white-line intensity at the Fe L3-edge absorption for NS and SC samples, as shown in Fig. 3A (Insets). For a better analysis of the CT phenomenon between Fe 3d and Se 4p states, the corresponding background is subtracted from their respective spectra. The integrated intensities of the white line in the Fe L3-edge absorption spectra (between 704.0 and 717.6 eV) at 300 and 20 K and the feature A in the Se K-edge XANES spectra (between 12,654.4 and 12,660.4 eV) at 300 K are obtained, as shown in Fig. 3B (Lower Inset). These results clearly indicate a lower CT between Fe 3d and Se 4p states in SC samples than in NS samples, which is in agreement with our RIXS analysis (Fig. 2A). The CT-type Mott insulating property of the NS sample has been proposed in a previous study (32), which suggests a strong CT in the material. The decrease in CT/hybridization between Fe 3d-Se 4p states in SC samples leads to the reduction of Fe 3d unoccupancy (hole), and therefore explains the orbital-selective disappearance of spectral weight in one of the Fe 3d orbitals. This observation is in agreement with the orbital-selective Mott phase (30, 31), which suggests that the pairing mechanism in superconductivity may arise from local electron exchange interactions. Therefore, the present results implying the electron–electron correlation is mediated by the local electron exchange interactions, without the involvement of Fe spins, in the evolution to superconductivity in SC samples. However, we cannot rule out that the Fe spin fluctuations, associated with the decrease in Fe magnetic moment in SC samples based on the RIXS results, can be the source to mediate the electron–electron pairing mechanism in the evolution to superconductivity.

In our earlier discussion on the Fe Lα,β RIXS spectra, we showed that the variations in the magnetic moment of SC and NS samples are closely associated with the occupation of Fe-vacant sites, which is consistent with the results of detailed structural studies provided by Wang et al. (19). To further understand this observation, we have conducted element-specific EXAFS measurements at the Fe K edge. Fig. 4A displays the Fe K-edge Fourier transform (FT) spectra of SC and NS samples at 300 and 20 K, and the inset shows the corresponding EXAFS oscillations. The FT spectra exhibit only 1 feature because of experimental uncertainty and the small difference in bond lengths of NN Fe–Se and Fe–Fe bond (∼2.4 and 2.7 Å, respectively) (37). The quantitative details of the short-range local environment of Fe atoms in SC and NS samples, such as the coordination number (CN), bond length (R), and Debye–Waller factor [DWF, σ2(T)], are obtained from the Fe K-edge EXAFS spectra at both 300 and 20 K using the Arthemis fitting program (38, 39), and the results are shown in Fig. 4 B–D, respectively. As shown in Fig. 4B, the CNFe–Fe, which is related to the Fe concentration, is substantially higher for SC samples than for NS samples at both temperatures (SC-820 has the highest CNFe–Fe). Earlier studies (16, 18, 19) have shown that the Fe(4d) sites in the parent compound, K2Fe4Se5, are vacant, such that additional Fe ions preferentially occupy the vacant 4d sites. Therefore, an increase in the Fe concentration at the vacant 4d sites in SC samples (particularly in the SC-820 sample) will increase the overall CNFe–Fe around the Fe sites. Furthermore, the CN Fe–Fe of SC-820 sample is higher than that of the SC-750 sample at both 300 and 20 K, which is consistent with the result of higher occupation of Fe(4d) sites reported (19). On the contrary, the NS (NS-820 and NS-750) samples exhibit no significant change in CNFe−Fe, which is expected, as no additional Fe atoms are presented to occupy the vacant 4d sites. This result demonstrates that the SC-820 sample comprises more Fe atoms that occupy the vacant 4d sites, which can contribute to structural/vacancy disorder in the material (16, 19). The data exhibit no significant difference in CNFe−Se values between SC and NS samples, which reveals an unaltered FeSe4 tetrahedral network in both samples, consistently with the discussion in Fig. 2B. Fig. 4C shows a significant increase in both the Fe–Se and Fe–Fe bond lengths of SC samples compared to the NS samples. This finding is consistent with the increase in occupation of vacant Fe(4d) sites in SC samples (19). The larger bond length is likewise consistent with the decrease in Fe 3d-Se 4p hybridization and CT between Fe 3d and Se 4p states in the SC samples as that in the NS samples.

Fig. 4.

Fig. 4.

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(A) Magnitude of Fe K-edge FT spectra of SC and NS samples at 300 K and 20 K. (Inset) The corresponding EXAFS data, k2χ, within the range k = 3.0 to 14.1 Å. The solid line depicts the fit obtained using Artemis programs, and open symbols represent results obtained from experimental data. Parameters obtained from fitting the FT spectra of SC and NS samples are (B) coordination numbers CNFe–Se and CNFe–Fe, (C) Fe–Se and Fe–Fe bond lengths, R, and (D) Fe–Se and Fe–Fe DWF, σ2(T), at 300 and 20 K.

Fig. 4D presents the variation in the DWF derived from the NN Fe–Se and Fe–Fe bonds at 300 and 20 K. The DWFs of Fe–Se and Fe–Fe bonds in SC samples are much higher than those in the NS samples. The DWF that derives from the Fe–Fe bonds in SC-820 is higher than that of SC-750 at both temperatures, whereas there is no significant variation in the DWF related to Fe–Se or Fe–Fe bonds in NS-820 and NS-750 samples. This finding strongly indicates that the SC samples, particularly SC-820, which has the highest SC volume fraction, have greater local structural disorder around the Fe atoms than the NS samples at both measured temperatures. Furthermore, a close examination of Fig. 4D reveals no significant variation in the DWF corresponding to Fe–Se bonds between SC-820 and SC-750 samples at either temperature.

To gain a comprehensive understanding of the temperature-dependent local atomic structures that correspond to the NN Fe–Se and Fe–Fe bonds in the SC and NS samples, Fig. 5 A and B plot the temperature-dependent FT of the Fe K-edge EXAFS spectra of SC-750 and NS-750 samples, respectively, from 300 to 20 K. The insets show the corresponding k2χ oscillations. Fig. 5C displays the temperature-dependent NN Fe–Se and Fe–Fe bond lengths that are obtained from the fitted EXAFS spectra. The Fe–Se and Fe–Fe bond lengths in both samples in the range of 20–300 K are fairly temperature-independent, revealing no structural transition in the measured range, which is in agreement with the neutron diffraction investigation (12). Both Fe–Se and Fe–Fe bond lengths are higher in SC samples than in NS samples in the measured temperature range. Fig. 5D shows the plot of the DWF [σ2(T)] for Fe–Se and Fe–Fe bond as a function of temperature. The DWF [σ2(T)] generally comprises 2 components, σ2stat and σ2(T)vib, which are associated with the temperature-independent static atomic disorder and the temperature-dependent thermal vibrations (39), respectively. σ2(T)vib generally become smaller as the temperature decreases. Therefore, with a decrease in the temperature, the σ2(T) of the SC-750 and NS-750 samples also decreases due to σ2(T)vib factor, as shown in Fig. 5D. The SC-750 sample has a higher DWF for both bond correlations in the entire measured temperature range. Notably, in the low-temperature range (below 50 K), there is no significant temperature dependence. Therefore, we extrapolate this linear region to 0 K, where the thermal vibrations are absent and DWF’s primary contribution is due to the σ2stat component. The DWF at 0 K reveals that the σ2stat values of the SC-750 sample are ∼3.0 × 10−3 and ∼1.9 × 10−3 Å2 for Fe–Se and Fe–Fe bond correlations, respectively, which are significantly higher than the corresponding bond correlations (∼1.1 × 10−3 and ∼0.7 × 10−3 Å2) of the NS-750 sample. As discussed above, the static disorder component arises from the local structural disorder; hence, the higher σstat2 components of DWF reveal an increase in the structural/vacancy disorder with higher Fe concentration at the 4d sites in SC-750. In NS-750, however, vacant 4d sites are mostly ordered, and therefore the σstat2 is significantly lower than that of SC-750. Detailed theoretical calculations, based on the variation in the DWF, should certainly provide a perspective in future studies to understand whether any electron–phonon coupling coexists in the present system along with electron–electron correlation.

Fig. 5.

Fig. 5.

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Temperature-dependent FT magnitudes of Fe K-edge EXAFS of (A) SC-750, (B) NS-750 samples. (Insets) Corresponding EXAFS data, k2χ, within the range k = 3.0 to 14.1 Å. Parameters obtained from the fitted FT spectra are (C) NN Fe–Se and Fe–Fe bond lengths, R, and (D) DWF, σ2(T), as a function of temperature for SC-750 and NS-750 samples. Green lines represent the extrapolation of the low-temperature range, 75–20 K of DWF data, to 0 K.

Conclusion

In summary, temperature-dependent XANES and EXAFS measurements both provide evidence of the Fe 3d and Se 4p hybridized states and a strong static disorder of Fe atoms, elucidating the evolution of superconductivity of SC (K1.9Fe4.2Se5) samples. The magnetic and EXAFS data analyses reveal that the superconducting volume fraction can be enhanced by quenching at a higher temperature during the sample synthesis procedure, thereby increasing the structural/vacancy disorder around Fe atoms, as depicted in the SC-820 sample. An analysis of the RR based on RIXS spectra reveals a decrease in the magnetic moment of Fe ions resulting from the occupation of Fe at the vacant 4d sites, and thereby reducing the overall magnetic moment in SC samples. Furthermore, an increase in the Fe–Se bond length in SC samples reflects a reduction in hybridization and CT between Fe 3d and Se 4p states. These results support electron–electron pairing mechanism, mediated by local electron exchange interaction, in the evolution of superconductivity in K1.9Fe4.2Se5. Finally, we believe that the results present here provide the detailed element-selective local electronic/atomic information, which certainly is valuable to better understand the origin of superconductivity in Fe-chalcogenide.

Methods

Preparation and Characterization of Samples.

Polycrystalline superconducting K1.9Fe4.2Se5 (SC) and nonsuperconducting K2Fe4Se5 (NS) samples were synthesized by quenching these compounds at 820 °C (SC-820 and NS-820) and 750 °C (SC-750 and NS-750). The detailed procedure is provided in previous studies (16, 19). Room-temperature XRD experiments were conducted with an in-house X-ray diffractometer with Cu Kα1 radiation to characterize the crystalline structures of the SC and NS samples. To investigate the interplay of various parameters that drive the evolution of superconductivity, temperature-dependent magnetic susceptibility, RIXS, XANES, and EXAFS experiments were carried out. Magnetic susceptibility measurements were performed using a superconducting quantum interference device. The Fe L3,2-edge XANES and Fe Lα,β RIXS were measured at the iRIXS-endstation (40), at beamline 8.0.1 of the Advanced Light Source at Lawrence Berkeley National Laboratory, Berkeley, USA. The Se K-edge XANES and Fe K-edge EXAFS spectra were obtained in bulk sensitive total fluorescence yield mode at the SWLS-01C and Wiggler-17C beamlines, respectively, at the Taiwan Light Source of National Synchrotron Radiation Research Center, Taiwan. The energy resolutions of the XANES measurements were set to ∼0.1 eV at the Fe L3,2 edge and ∼0.5/1.0 eV at the Fe/Se K edge, respectively. Fe and Se foils were used to calibrate the photon energy at the corresponding edges.

Acknowledgments

M.K.W. and W.F.P. would like to thank the Ministry of Science and Technology (MoST) of Taiwan for providing financial support under the project numbers MoST-106-2633M-001-001, MoST-105-2112-M-032-001-MY3, and MoST-106-2632-M-032-001-MY3. M.K.W. also thanks Academia Sinica for the support of Thematic Research Grant AS-TP-106-M01.

Footnotes

The authors declare no competing interest.

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