⇦Chinese Physics Letters, 2023, Vol. 40, No. 10, Article code 107403Express Letter Superconductivity above 30 K Achieved in Dense Scandium Xin He (何鑫)1,2,3†, Changling Zhang (张昌玲)1,2†, Zhiwen Li (李芷文)1,2, Sijia Zhang (张思佳)1, Shaomin Feng (冯少敏)1, Jianfa Zhao (赵建发)1,2, Ke Lu (卢可)1,2, Baosen Min (闵保森)1,2, Yi Peng (彭毅)1,2, Xiancheng Wang (望贤成)1,2*, Jin Song (宋静)1, Luhong Wang (王鲁红)4, Saori I. Kawaguchi5, Cheng Ji (吉诚)6, Bing Li (李冰)6, Haozhe Liu (刘浩哲)6, J. S. Tse7, and Changqing Jin (靳常青)1,2,3* Affiliations 1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China 3Songshan Lake Materials Laboratory, Dongguan 523808, China 4Shanghai Advanced Research in Physical Sciences, Shanghai 201203, China 5Japan Synchrotron Radiation Research Institute, SPring-8, Sayo-gun Hyogo 679-5198, Japan 6Center for High Pressure Science & Technology Advanced Research, Beijing 100094, China 7Department of Physics, University of Saskatchewan, Canada Received 26 August 2023; accepted manuscript online 13 September 2023; published online 20 September 2023 †These authors contributed equally to this work.
*Corresponding authors. Email: wangxiancheng@iphy.ac.cn; Jin@iphy.ac.cn Citation Text: He X, Zhang C L, Li Z W et al. 2023 Chin. Phys. Lett. 40 107403    Abstract Superconductivity is one of most intriguing quantum phenomena, and the quest for elemental superconductors with high critical temperature ($T_{\rm c}$) is of great scientific significance due to their relatively simple material composition and the underlying mechanism. Here we report the experimental discovery of densely compressed scandium (Sc) becoming the first elemental superconductor with $T_{\rm c}$ breaking into 30 K range, which is comparable to the $T_{\rm c}$ values of the classic La–Ba–Cu–O or LaFeAsO superconductors. Our results show that $T_{\rm c}^{\rm onset}$ of Sc increases from $\sim$ $3$ K at around 43 GPa to $\sim$ $32$ K at about 283 GPa ($T_{\rm c}^{\rm zero} \sim 31$ K), which is well above liquid neon temperature. Interestingly, measured $T_{\rm c}$ shows no sign of saturation up to the maximum pressure achieved in our experiments, indicating that $T_{\rm c}$ may be even higher upon further compression.
cpl-40-10-107403-fig1.png
cpl-40-10-107403-fig2.png
cpl-40-10-107403-fig3.png
cpl-40-10-107403-fig4.png
 DOI:10.1088/0256-307X/40/10/107403 © 2023 Chinese Physics Society Article Text Searching for high $T_{\rm c}$ superconductors is one of most important research topics in physical sciences. Elemental superconductors attract special and growing attention due to the simplicity of their singular composition.[1,2] About 20 elemental solids are known to show superconductivity at ambient pressure, of which niobium has the highest superconducting transition temperature $T_{\rm c} \sim 9.2$ K[1] and its alloy NbTi has been widely used for its excellent superconducting performance.[3] High pressure is a powerful tool and has been playing an important role in exploring new elemental superconductors and tuning superconducting properties.[2] For simple elemental metals, high pressure usually suppresses $T_{\rm c}$ because of the electronic band broadening and resulting reduction of the density of states near the Fermi energy. Lattice stiffness is another important factor that $T_{\rm c}$ goes down under pressure. However, these pressure effects on superconductivity may be altered by subtle structural and electronic changes associated with bonding or phase transitions. Pressure may also enable non-superconducting metals or even insulating solids at ambient pressure to host superconductivity at high pressure. For example, calcium is non-superconducting at ambient pressure, but exhibits a high $T_{\rm c}$ of 25 K at 161 GPa,[4] and insulating sulfur shows superconductivity with $T_{\rm c} \sim 17$ K at 200 GPa.[5] All known elemental superconductors with $T_{\rm c}$ near or above 20 K are realized under pressure, such as Li with $T_{\rm c} \sim 16$–20 K at 43–48 GPa[6,7] and yttrium with $T_{\rm c} \sim 17$ K at 89 GPa.[8] Our recent study showed that elemental titanium can reach $T_{\rm c}$ of 26.2 K at pressure of 248 GPa.[9] It is indicated that both Ca and Ti show very high $T_{\rm c}$ among elemental solids because of the pressure induced $s$–$d$ electron transition, which also drives a sequence of phase transitions.[4,9-14] The structure instability associated with the pressure induced tendency and occurrence of phase transitions favors superconductivity because of the lattice softening enhanced electron-phonon coupling strength.[9] The crystal structure and physical properties of Sc metal under pressure were examined in previous studies,[15-24] which showed that Sc has the hcp structure (Sc I) under ambient conditions, and pressure generates four structural transitions at about 23, 104, 140, and 240 GPa, respectively, producing high-pressure phases of Sc II, Sc III, Sc IV, and Sc V, respectively.[17-19] Sc II phase crystallizes in an incommensurate composite structure comprising a body centered host structure and a $C$ face centered guest structure,[18] and Sc V phase has a hexagonal lattice consisting of six screw helical chains,[17] while Sc III and Sc IV phases are not fully determined.[19] Previous work reported that Sc starts to show superconductivity at 21 GPa with $T_{\rm c} \sim 0.35$ K.[21] With further compression, $T_{\rm c}$ reaches as high as 19.6 K at 107 GPa, which occurs just at the phase boundary of Sc II and Sc III. However, $T_{\rm c}$ was reported to drop to $\sim$ $10$ K when pressure is further increased and Sc III phase appears.[20] Here, we report high-pressure measurements up to 283 GPa to explore superconductivity in Sc. A maximal $T_{\rm c}$ above 30 K was observed at the highest experimental pressure, which sets a new record among elemental superconductors. To date, Sc is the only known elemental superconductor with $T_{\rm c}$ breaking into 30 K temperature range. Experimental. The electrical resistance measurements were performed by using the four probe van der Pauw method for tiny specimen as described in the literature.[25,26] The pressure was calibrated via the shift of the first order Raman edge frequency from the diamond cutlet as shown in the previous reports.[9,27,28] The applied current is 100 µA. Diamond anvil cells were used to produce high pressures. A variant of anvils with double beveled culet size of 20/140/300 µm, 30/140/300 µm, or 50/140/300 µm were adopted in the experiments. A plate of T301 stainless steel covered with mixture of c-BN powder and epoxy as insulating layer was used as the gasket. A hole of approximately $15 \sim 30$ µm in diameter depending on top culet size was drilled in the center of the gasket to serve as high pressure chamber. Also, h-BN powder was used as pressure transmitting medium that filled the high pressure chamber. We used the ATHENA procedure to produce the specimen assembly.[26] Four Pt foils with thickness of approximately 0.5 µm as the inner electrode were deposited on the culet surface, after which cross shaped Sc specimens with side lengths $\sim$ $10$ µm $\times 10$ µm and thickness of 1 µm were adhered on the electrodes and culet surface. Tens of specimens are prepared for the experiments. Diamond anvil cells were put into a MagLab system that provides synergetic extreme environments with temperatures from 300 to 1.5 K and magnetic fields up to 9 T for the transport measurements. Results and Discussion. Figure 1(a) shows the temperature dependence of electrical resistance at high pressure up to 215 GPa measured during the warming process for Sc sample 1. The Sc metal starts to show superconductivity with $T_{\rm c}$ above 3.3 K at 43 GPa. The $T_{\rm c}$ monotonously rises to $\sim$ $26.2$ K at 215 GPa, which is much higher than the 8.2 K at 74 GPa reported by Hamlin et al.[22] and 19.6 K at 107 GPa reported by Debessai et al.[20] Considering that $T_{\rm c}$ shows an increasing tendency with further compression, we extended to higher pressures up to 283 GPa for sample 2 and observed enhancement of $T_{\rm c}$ in dense Sc metal. Temperature dependence of the electrical resistance for sample 2 under various pressures are shown in Fig. 1(b). With further increasing pressure, $T_{\rm c}$ reaches 32 K at the maximum experimental pressure of 283 GPa as shown in Fig. 2, where both cooling and warming curves are presented. It is evidenced in the experiments that cooling process usually gave rather higher transition temperature since it is not easy to reach thermal equilibrium with helium cooling rate. Alternatively the warming process can be subtly tuned to reach thermal equilibrium that approaches the intrinsic properties of the measured samples. We hence chose the $T_{\rm c}$ measured from warming process. For the warming process the onset critical temperature ($T_{\rm c}^{\rm onset}$) and the zero resistance critical temperature ($T_{\rm c}^{\rm zero}$) of superconducting transition at 283 GPa can be determined by the derivative of resistance with respect to temperature, i.e., $dR/dT$, to be 32 K and 31 K, respectively, demonstrating a very narrow superconducting transition. The data for samples 3 and 4 shown by Figs. S1(a) and S1(b) in the Supplementary Materials further confirm the superconductivity of Sc under high pressure with $T_{\rm c}$ above 30 K.
cpl-40-10-107403-fig1.png
Fig. 1. Temperature dependence of the electrical resistance of elemental Sc metal measured at high pressures for (a) sample 1 and (b) sample 2.
cpl-40-10-107403-fig2.png
Fig. 2. The resistance curves measured at 283 GPa in both cooling and warming processes, where the derivative of the resistance with respect to temperature, $dR$/$dT$, for the warming process is plotted to clearly show the $T_{\rm c}^{\rm onset}$ and $T_{\rm c}^{\rm zero}$.
Among elemental superconductors, niobium has the highest $T_{\rm c}$ of 9.2 K at ambient pressure, while under high pressure several elements exhibit high $T_{\rm c}$ near or above 20 K, such as Li ($T_{\rm c} \sim 15$–20 K at 48 GPa[6,7]), Ca ($T_{\rm c} \sim 25$ K at 220 GPa[4]), Y ($T_{\rm c} \sim 20$ K near 100 GPa[8]), V ($T_{\rm c} \sim 17$ K at 120 GPa[29]), S ($T_{\rm c} \sim 17$ K at 220 GPa[5]), and Ti ($T_{\rm c} \sim 26.2$ K near 248 GPa[9]). Superconductivity above 30 K in elemental solids has never been reported before, and Sc is the first and so far only known elemental superconductor with $T_{\rm c}$ breaking into the record-setting 30 K range, which is comparable to the $T_{\rm c}$ of the classic LaBaCuO[30] and LaFeAsO superconductors.[31]
cpl-40-10-107403-fig3.png
Fig. 3. (a) Temperature dependence of the electrical resistance of Sc metal measured at different magnetic fields under fixed pressure of 283 GPa. The dashed line marks the 90% of the normal state resistance. (b) Upper critical field $\mu_{0}H_{\rm c2}$ versus temperature at 283 GPa. The Ginzburg–Landau (GL) fit for the $H_{\rm c2}$ (T) is shown by the solid lines. The star symbol represents the $H_{\rm c2}$ (0) values calculated via the Werthamer–Helfand–Hohenberg (WHH) model.
To further probe superconductivity of dense Sc metal under high pressure, we measured transport properties under different magnetic fields for sample 2. Figure 3(a) presents the electrical resistance measured at 283 GPa with applying magnetic fields. It is seen that the superconducting transitions are gradually suppressed by the magnetic field. Here, the temperature at 90% of normal state resistance was used to plot the data of $T_{\rm c}^{90\%}$ versus magnetic field measured at 283 GPa as shown in Fig. 3(b), from which the upper critical field at zero temperature $\mu_{0}H_{\rm c2}(0)$ can be estimated. A linear fitting of $H_{\rm c2}(T)$ leads to the slope of $dH _{\rm c2}/dT$|$_{T_{\rm c}}$ of $-$2.65 T/K. Using the Werthamer–Helfand–Hohenberg (WHH) formula of $\mu_{0}H_{\rm c2}(T) =-0.69 \times [dH _{\rm c2}/dT$|$_{T_{\rm c}}]\times T_{\rm c}$, the $\mu_{0}H_{\rm c2}(0)$ value controlled by orbital depairing mechanism in a dirty limit [$\mu_{0}H_{\rm c2}^{\rm orb}(0)$] was calculated to be 58 T. The Ginzburg–Landau (GL) formula of $\mu_{0}H_{\rm c2}(T) = \mu_{0}H_{\rm c2}(0) \times [1-(T/T_{\rm c})^{2}]$ is also used to estimate the upper critical field at zero temperature. As shown in Fig. 3(b), the fitting of $\mu_{0}H_{\rm c2}(T)$ by the GL formula gives a value of $H_{\rm c2}(0) = 43.7$ T, which is slightly smaller than $\mu_{0}H_{\rm c2}^{\rm orb}(0)$. Using the obtained value of $H_{\rm c2}(0)$, the GL coherence length was calculated to be $\xi = 27.4$ Å via $\mu_{0}H_{\rm c2}(0) = \varPhi_{0}/2\pi \xi^{2}$, where $\varPhi_{0} = 2.067 \times 10^{-15}$ Web is the magnetic flux quantum.
cpl-40-10-107403-fig4.png
Fig. 4. Phase diagram of superconducting transition temperature $T_{\rm c}$ and crystal structure versus pressure for Sc. The measured results on all the five samples show consistent trends.
Combining our high-pressure x-ray experiments (Fig. S2) and the phase transition behaviors reported previously,[17-19] we plot the pressure-driven structure-superconductivity phase diagram as shown in Fig. 4. Five different crystal structures of Sc are identified when pressure varies from ambient pressure to 297 GPa. No superconductivity above 2 K was observed in Sc I within the pressure range 0–23 GPa. With increasing pressure, $T_{\rm c}$ monotonously rises from 3.1 K at 43 GPa to 32 K at 283 GPa as shown by the data of thin foil samples 1–4. One remarkable interesting feature is the pressure dependence of $T_{\rm c}$, showing non-saturating behavior, which suggests that $T_{\rm c}$ could be further enhanced by further compression under higher-pressure conditions. We note that the monotonous rise of $T_{\rm c}$ is different from the previous work reported by Debessai et al.,[20] where an abrupt $T_{\rm c}$ drop is found at 111 GPa that is near the boundary between the Sc II and Sc III phases. To double check this discrepancy, one additional high-pressure transport measurement was performed on powder Sc sample instead of thin film. As shown in Figs. S1(c) and S1(d), at 102 GPa there exist two superconducting transitions at 17.5 K and 14 K, respectively. With further increasing pressure, the low-$T_{\rm c}$ transition gradually shifts toward high temperature while the high $T_{\rm c}$ transition disappears, which implies that there does exist a phase transition near 102 GPa. The low-$T_{\rm c}$ superconductivity should arise from the Sc III phase, which is consistent with the $T_{\rm c}$ drop near the phase transition reported in the previous work.[20] Except for the data in the Sc II phase in the range 82–102 GPa, the pressure dependences of $T_{\rm c}$ for the thin film and powder samples are well matched. Sc II phase adopts an incommensurate modulated host-guest structure with space group $I4/mcm$ ($\gamma$).[18] This incommensurate structure consists of two interpenetrating sublattices, a body-centered host structure and a $C$ face centered guest structure, along the crystallographic $c$ axis. For powder Sc sample, the incommensurability increases with pressure[18] and $T_{\rm c}$ increases accordingly.[20] It is speculated that the strain in the thin film samples should suppress the increase of incommensurability under high pressure relative to the powder sample and lead to the $T_{\rm c}$ discrepancy. In the phases from Sc III to Sc V, $T_{\rm c}$ rises consistently at rising pressure. Sc III and Sc IV phases are not fully resolved, although a recent theoretical study suggested that the Ccca20 phase and Cmca32 phase are likely candidates for the observed Sc III and Sc IV, respectively.[19] Sc V phase occurs when pressure exceeds 240 GPa, which adopts a hexagonal lattice (space group $P6_{1}22$) consisting of six screw helical chains.[17] These results suggest that pressure-induced structure instability plays a key role in driving rising $T_{\rm c}$ in dense Sc, possibly driven by rising contribution of $d$ orbital electronic states near the Fermi energy and the lattice softening associated with the phase transitions, both of which strengthen the electron phonon coupling. We also have performed electron phonon coupling density functional calculations to confirm the experimentally observed superconductivity as seen in Fig. S3. Details of the calculations are given in the Supplementary Materials. The predicted $T_{\rm c}$ at 240 GPa varies from 30 K to 33 K with empirical Coulomb repulsion parameter from 0.13 to 0.1. The results are similar to those reported in Ref. [32]. A valence electronic configuration Sc of 3$s^{1.56}3p^{5.25}3d^{2.42}4s^{0.25}$ was obtained from the Mulliken population analysis of the crystal orbitals calculated using an atom-centered localized basis set.[33] It is obvious that the substantial charge migration from the Sc 4$s$ to the 3$d$ orbital is responsible for the strong electron phonon coupling. In summary, we have investigated transport properties of Sc under high pressure up to 283 GPa, and found that $T_{\rm c}$ is monotonously enhanced by pressure from 3.1 K at around 43 GPa to 32 K at around 283 GPa, following a sequence of high-pressure phase transitions from Sc II to Sc V. The increase of $T_{\rm c}$ shows no sign of saturation up to the highest experimental pressure of 283 GPa, which indicates that $T_{\rm c}$ of superconducting Sc still has room to go higher upon further compression. Scandium is the only currently known elemental superconductors with the $T_{\rm c}^{\rm onset}$ breaking through 30 K at high pressure. The present results offer fresh insights for exploring high-$T_{\rm c}$ superconductivity at ultrahigh pressures in diverse element solids. During preparing the paper (arXiv:2303.01062) we became aware that an independent similar work (arXiv:2302.14378) has been carried out by J. J. Ying et al.[32] Acknowledgments. This work was supported by the National Key R&D Program of China (Grant No. 2021YFA1401800, 2022YFA1403800, and 2022YFA1403900), the National Natural Science Foundation of China (Grant Nos. 11921004 and U2032220), and Chinese Academy of Sciences (Grant No. XDB33010200). J. S. Tse wishes to thank NSERC Canada for a Discovery Grant. We thank C. F. Chen for helpful discussion. References Assembling the puzzle of superconducting elements: a reviewSuperconductivity in the metallic elements at high pressuresSuperconducting materials for large scale applicationsSuperconductivity of Ca Exceeding 25 K at Megabar PressuresSuperconductivity in the chalcogens up to multimegabar pressuresSuperconductivity in compressed lithium at 20 KSuperconductivity in Dense LithiumSuperconductivity at 20K in yttrium metal at pressures exceeding 1MbarRecord high Tc element superconductivity achieved in titaniumPhase transitions in alkaline earth metals under pressureA new distorted body-centred cubic phase of titanium ( -Ti) at pressures up to 220 GPaTitanium metal at high pressure: Synchrotron experiments and ab initio calculationsExotic behavior and crystal structures of calcium under pressure T c up to 23.6 K and robust superconductivity in the transition metal δ − Ti phase at megabar pressureHigh-pressure phase transformation in scandiumEvidence for the occurrence of a prototype structure in Sc under pressureNew Helical Chain Structure for Scandium at 240 GPaIncommensurate composite crystal structure of scandium-IIFirst-principles investigation of Sc-III/IV under high pressureComparison of the pressure dependences of T c in the trivalent d -electron superconductors Sc, Y, La, and Lu up to megabar pressuresSuperconductivity in a New High-Pressure Phase of ScandiumPressure-induced superconductivity in Sc to 74 GPa Determination of the Structural Parameters of an Incommensurate Phase from First Principles: The Case of Sc-IIThe ideal commensurate value of Sc and the superconducting phase under high pressureSuperconductivity above 200 K discovered in superhydrides of calciumA Combinatory Package for Diamond Anvil Cell ExperimentsSuperconductivity in zirconium polyhydrides with Tc above 70 KSuperconductivity above 80 K in polyhydrides of hafniumPressure effect on superconductivity of vanadium at megabar pressuresEvidence for superconductivity above 40 K in the La-Ba-Cu-O compound systemIron-Based Layered Superconductor La[O1- x F x ]FeAs ( x = 0.05−0.12) with Tc = 26 KRecord High 36 K Transition Temperature to the Superconducting State of Elemental Scandium at a Pressure of 260 GPaPrecise density-functional method for periodic structures
[1] Buzea C and Robbie K 2005 Supercond. Sci. Technol. 18 R1
[2] Hamlin J J 2015 Physica C 514 59
[3] Scanlan R M, Malozemoff A P, and Larbalestier D C 2004 Proc. IEEE 92 1639
[4] Yabuuchi T, Matsuoka T, Nakamoto Y, and Shimizu K 2006 J. Phys. Soc. Jpn. 75 083703
[5] Gregoryanz E, Struzhkin V V, Hemley R J, Eremets M I, Mao H K, and Timofeev Y A 2002 Phys. Rev. B 65 064504
[6] Shimizu K, Ishikawa H, Takao D, Yagi T, and Amaya K 2002 Nature 419 597
[7] Struzhkin V V, Eremets M I, Gan W, Mao H K, and Hemley R J 2002 Science 298 1213
[8] Hamlin J J, Tissen V G, and Schilling J S 2007 Physica C 451 82
[9] Zhang C L, He X, Liu C, Li Z W, Lu K, Zhang S J, Feng S M, Wang X C, Peng Y, Long Y W, Yu R C, Wang L H, Prakapenka V, Chariton S, Li Q, Liu H Z, Chen C F, and Jin C Q 2022 Nat. Commun. 13 5411
[10] Olijnyk H and Holzapfel W B 1984 Phys. Lett. A 100 191
[11] Akahama Y, Kawamura H, and Le B T 2002 J. Phys.: Condens. Matter 14 10583
[12] Ahuja R, Dubrovinsky L, Dubrovinskaia N, Guillen J M O, Mattesini M, Johansson B, and Le B T 2004 Phys. Rev. B 69 184102
[13] Oganov A R, Ma Y, Xu Y, Errea I, Bergara A, and Lyakhov A O 2010 Proc. Natl. Acad. Sci. USA 107 7646
[14] Liu X Q, Jiang P, Wang Y M, Li M T, Li N N, Zhang Q, Wang Y D, Li Y L, and Yang W G 2022 Phys. Rev. B 105 224511
[15] Vohra Y K, Grosshans W, and Holzapfel W B 1982 Phys. Rev. B 25 6019
[16] Zhao Y C, Porsch F, and Holzapfel W B 1996 Phys. Rev. B 54 9715
[17] Akahama Y, Fujihisa H, and Kawamura H 2005 Phys. Rev. Lett. 94 195503
[18] Fujihisa H, Akahama Y, Kawamura H, Gotoh Y, Yamawaki H, Sakashita M, Takeya S, and Honda K 2005 Phys. Rev. B 72 132103
[19] Zhu S C, Yan X Z, Fredericks S, Li Y L, and Zhu Q 2018 Phys. Rev. B 98 214116
[20] Debessai M, Hamlin J J, and Schilling J S 2008 Phys. Rev. B 78 064519
[21] Wittig J, Probst C, Schmidt F A, and Gschneidner K A 1979 Phys. Rev. Lett. 42 469
[22] Hamlin J J and Schilling J S 2007 Phys. Rev. B 76 012505
[23] Arapan S, Skorodumova N V, and Ahuja R 2009 Phys. Rev. Lett. 102 085701
[24] Tsuppayakorn-aek P, Luo W, Pungtrakoon W, Chuenkingkeaw K, Kaewmaraya T, Ahuja R, and Bovornratanaraks T 2018 J. Appl. Phys. 124 225901
[25] Li Z W, He X, Zhang C L, Wang X C, Zhang S J, Jia Y T, Feng S M, Lu K, Zhao J F, Zhang J, Min B S, Long Y W, Yu R C, Wang L H, Ye M Y, Zhang Z S, Prakapenka V, Chariton S, Ginsberg P A, Bass J, Yuan S H, Liu H Z, and Jin C Q 2022 Nat. Commun. 13 2863
[26] Jia Y T, He X, Feng S M, Zhang S J, Zhang C L, Ren C W, Wang X C, and Jin C Q 2020 Crystals 10 1116
[27] Zhang C L, He X, Li Z W, Zhang S J, Feng S M, Wang X C, Yu R C, and Jin C Q 2022 Sci. Bull. 67 907
[28] Zhang C L, He X, Li Z W, Zhang S J, Min B S, Zhang J, Lu K, Zhao J F, Shi L C, Peng Y, Wang X C, Feng S M, Yu R C, Wang L H, Prakapenka V B, Chariton S, Liu H Z, and Jin C Q 2022 Mater. Today Phys. 27 100826
[29] Ishizuka M, Iketani M, and Endo S 2000 Phys. Rev. B 61 R3823
[30] Chu C W, Hor P H, Meng R L, Gao L, Huang Z J, and Wang Y Q 1987 Phys. Rev. Lett. 58 405
[31] Kamihara Y, Watanabe T, Hirano M, and Hosono H 2008 J. Am. Chem. Soc. 130 3296
[32] Ying J J, Liu S Q, Lu Q, Wen X K, Gui Z G, Zhang Y Q, Wang X M, Sun J, and Chen X H 2023 Phys. Rev. Lett. 130 256002
[33] te Velde G and Baerends E J 1991 Phys. Rev. B 44 7888