⇦Chinese Physics Letters, 2020, Vol. 37, No. 12, Article code 127401 Gap Structure of 12442-Type KCa$_2$(Fe$_{1-x}$Co$_{x}$)$_4$As$_{4}$F$_2$ ($x$ = 0, 0.1) Revealed by Temperature Dependence of Lower Critical Field Jianan Chu (楚佳楠)1,2,3, Teng Wang (王腾)1,2,4, Han Zhang (张瀚)1,2,3, Yixin Liu (刘以鑫)1,2,3, Jiaxin Feng (冯嘉鑫)1,2,3, Zhuojun Li (李卓君)1,2, Da Jiang (姜达)1,2,3, Gang Mu (牟刚)1,2,3*, Zengfeng Di (狄增峰)1,3, and Xiaoming Xie (谢晓明)1,2,3 Affiliations 1State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China 2CAS Center for Excellence in Superconducting Electronics (CENSE), Shanghai 200050, China 3University of Chinese Academy of Sciences, Beijing 100049, China 4School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China Received 9 September 2020; accepted 15 October 2020; published online 8 December 2020 Supported by the Youth Innovation Promotion Association of the Chinese Academy of Sciences (Grant No. 2015187), the “Strategic Priority Research Program (B)” of the Chinese Academy of Sciences (Grant No. XDB30000000), and the National Natural Science Foundation of China (Grant Nos. 11704395 and 11204338).
*Corresponding author. Email: mugang@mail.sim.ac.cn Citation Text: Chu J N, Wang T, Zhang H, Liu Y X, and Feng J X et al. 2020 Chin. Phys. Lett. 37 127401    Abstract We report an in-depth investigation on the out-of-plane lower critical field $H_{\rm c1}$ of the KCa$_2$(Fe$_{1-x}$Co$_{x}$)$_4$As$_{4}$F$_2$ (12442-type, $x$ = 0, 0.1). The multi-gap feature is revealed by the kink in the temperature-dependent $H_{\rm c1}(T)$ curve for the two samples with different doping levels. Based on a simplified two-gap model, the magnitudes of the two gaps are determined to be $\varDelta_1$ = 1.2 meV and $\varDelta_2$ = 5.0 meV for the sample with $x$ = 0, $\varDelta_1$ =  0.86 meV and $\varDelta_2$ = 2.8 meV for that with $x$ = 0.1. With the cobalt doping, the ratio of energy gap to critical transition temperature ($\varDelta/k_{\rm B}T_{\rm c}$) remains almost unchanged for the smaller gap and is suppressed by 20% for the larger gap. For the undoped KCa$_2$Fe$_4$As$_{4}$F$_2$, the obtained gap sizes are generally consistent with the results of angle-resolved photoemission spectroscopy experiments. DOI:10.1088/0256-307X/37/12/127401 PACS:74.20.Rp, 74.25.Ha, 74.70.Dd, 74.25.Op © 2020 Chinese Physics Society Article Text Superconducting (SC) mechanism is the central issue in research of unconventional superconducting materials represented by cuprates[1] and Fe-based superconductors (FeSCs).[2] The symmetry and structure of the energy gap(s) can supply essential information for the boundary condition of the SC mechanism.[3–8] Recently, the 12442 system AB$_2$Fe$_4$As$_4$ C$_2$ (A = K, Rb, and Cs; B = Ca, Nd, Sm, Gd, Tb, Dy, and Ho; C = F and O)[9–13] attracted wide attention due to the unique double-FeAs-layered structure,[9] strong Pauli-paramagnetic effect,[14] rather large critical current density,[15] easy-to-exfoliate features,[16] and so on.[17–19] Gap structure of this system has been investigated by the muon spin relaxation ($\mu$SR),[20–22] heat transport,[23] lower critical field,[24] optical spectroscopy,[25] specific heat,[26] and angle-resolved photoemission spectroscopy (ARPES) measurements.[27] However, the conclusions concerning the existence or absence of nodal lines and the size of gap(s) are still controversial. Especially, the influence of chemical doping on the gap structure is almost unknown. Consequently, more systematical experimental investigations are urgently required at present. In this Letter, we present a detailed investigation on the temperature dependence of the lower critical field $H_{\rm c1} (T)$, which reflects the superfluid density, of the high-quality KCa$_2$(Fe$_{1-x}$Co$_{x}$)$_4$As$_{4}$F$_2$ ($x\,=\,0$, 0.1) single crystals. The evolution tendency of the experimental data could not been described by a single-gap picture and a two-component-superfluid model with two SC gaps was employed. A careful analysis to the gap magnitudes shows that the cobalt doping has different influences on the smaller and larger gaps. Moreover, the gap sizes of the undoped sample are compared with the results of ARPES experiments. High quality KCa$_2$(Fe$_{1-x}$Co$_{x}$)$_4$As$_{4}$F$_2$ ($x\,=\,0$, 0.1) single crystals were grown using KAs as the self-flux. The detailed growth conditions and the characterizations of the samples can be seen in our previous reports.[28] The crystal structure and lattice constants of the samples were examined by a DX-2700 type powder x-ray diffractometer using Cu $K_{\alpha}$ radiation. The x-ray was incident on the $ab$-plane of the sample. The magnetization measurements were carried out on the magnetic property measurement system (Quantum Design, MPMS 3). The magnetic fields were applied along the $c$ axis of the single crystal in all the measurements. Thus the out-of-plane lower critical field $H_{\rm c1}^c$ is detected in the present study, which will be abbreviated as $H_{\rm c1}$ thereinafter. In Fig. 1(a), the x-ray diffraction spectrum for the co-doped crystal KCa$_2$(Fe$_{1-x}$Co$_{x}$)$_4$As$_{4}$F$_2$ ($x\,=\,0.1$) is displayed together with the undpoed sample for a comparison. Only sharp peaks with the index (00 $2l$) could be observed, suggesting a high $c$-axis orientation of the crystals. It is clear that the diffraction peaks for the Co-doped sample shift to the right sides compared with the undoped one, suggesting the shrinkage of the crystal along the $c$-axis. Quantitatively, the $c$-axis lattice constant is suppressed from 30.991 Å to 30.856 Å by the cobalt doping $x\,=\,0.1$. The extent of suppression is about 0.44%, which is comparable to that observed in the 1111-type CaFe$_{1-x}$Co$_x$AsF system.[29,30] The dc magnetic susceptibility $\chi$ for the KCa$_2$(Fe$_{1-x}$Co$_{x}$)$_4$As$_{4}$F$_2$ ($x\,=\,0$, 0.1) samples was measured under a magnetic field of 2 Oe in the zero-field-cooling mode, which is presented in Fig. 1(b). The $\chi$–$T$ curves show very sharp SC transitions, reflecting the good homogeneity and high quality of our samples. The absolute value of magnetic susceptibility $\chi$ is around 100% after considering the demagnetization effect, which indicates a high superconducting volume fraction. The full isothermal $M$–$T$ curves for the two samples are shown in Fig. 1(c). The shape of these curves is rather symmetric, illustrating the dominance of bulk pinning and a very low surface barrier for the flux lines when entering the samples.
cpl-37-12-127401-fig1.png
Fig. 1. (a) X-ray diffraction pattern of the KCa$_2$(Fe$_{1-x}$Co$_{x}$)$_4$As$_{4}$F$_2$ ($x\,=\,0$, 0.1) crystals. (b) Temperature dependence of magnetic susceptibility for the two samples measured in zero-field-cooled (ZFC) mode. (c) The magnetization hysteresis loops for the two samples measured at 10 K.
cpl-37-12-127401-fig2.png
Fig. 2. (a) and (b) Isothermal $M$–$H$ curves for the two samples with $x\,=\,0$ and 0.1 in the field range of 0–500 Oe. The black dashed line shows the linear fit in the low-field region, which is called the Meissner line. (c) and (d) Deviation of magnetization data from the Meissner line. The two dashed lines in (c) are two different criteria for determining $H_{\rm c1}$. The dashed line in (d) shows the criterion for determining $H_{\rm c1}$. The temperature intervals for (c) and (d) are the same as those in (a) and (b), respectively.
In order to have a clear impression for the data in low-field region, we show the enlarged view of the isothermal $M$–$H$ curves in Figs. 2(a) and 2(b). One can see the evolution from the low-field linear tendency to the crooked behavior with the increase of field. The former represents the Meissner state and the latter reflects the penetration of field into the interior of the sample. The black dashed lines represent the linear $M$–$H$ relation in the very low-field region due to the Meissner effect, which are called the Meissner lines. In order to have a solid determination for the onset point of the field penetration, i.e., $H_{\rm c1}$, the deviations of the magnetization data from the Meissner line are checked carefully. Field dependence of such a deviation $\Delta M$ is displayed in Figs. 2(c) and 2(d) for the two samples, respectively. For the sample with $x\,=\,0$, two criteria, $\Delta M\,=\,6.3$ and 12.6 emu/cm$^3$ (equivalent to 2 and 4 Oe respectively), are adopted for the determination of $H_{\rm c1}$. As revealed by the two dashed lines in Fig. 2(c), although the variation of criterion will affect the obtained $H_{\rm c1}$ values, the evolution behavior of the normalized $H_{\rm c1}(T)/H_{\rm c1}(0)$ with temperature is not affected by the selection of criterion [see Fig. 3(a)]. Thus we will focus on the analysis of the normalized values $H_{\rm c1}(T)/H_{\rm c1}(0)$, which are more solid and reliable. For the sample with $x\,=\,0.1$, a similar criterion $\Delta M\,=\,10.2$ emu/cm$^3$ (equivalent to 4 Oe) is applied.
cpl-37-12-127401-fig3.png
Fig. 3. (a) and (b) The extracted $H_{\rm c1}(T)$ [normalized by the zero-temperature value $H_{\rm c1}(0)$] as a function of temperature for the two samples with $x\,=\,0$ and 0.1. The data from two criteria are displayed in (a). The solid lines are the fitting curves using the two-gap model. The contributions of the two components with different gap magnitudes are also shown by the dashed and dotted lines.
Table 1. Information about the energy gaps derived from the two-gap model.
$x$ $T_{\rm c}$ (K) $\varDelta_1$ (meV) $\varDelta_2$ (meV) $w_1$ $\varDelta_1/k_{\rm B}T_{\rm c}$ $\varDelta_2/k_{\rm B}T_{\rm c}$
0 34 1.2 5.0 0.49 0.41 1.71
0.1 24 0.86 2.8 0.55 0.42 1.33
Temperature dependence of the normalized lower critical field $H_{\rm c1}(T)/H_{\rm c1}(0)$ for the two samples with $x\,=\,0$ and 0.1 is shown in Figs. 3(a) and 3(b), respectively. It is known that typically the FeSCs are in the local limit.[31] Thus the local London model is applicable. According to this model, the value of $H_{\rm c1}(T)/H_{\rm c1}(0)$ in the out-of-plane orientation has a close relation with the normalized superfluid density $\widetilde{\rho}_{\rm s}^{\rm ab}$ within the $ab$ plane (abbreviated as $\widetilde{\rho}_{\rm s}$ thereinafter):[24,31,32] $$ \frac{H_{\rm c1}(T)}{H_{\rm c1}(0)}\,=\,\widetilde{\rho}_{\rm s}(T) \equiv \frac{\lambda_{ab}^{2}(0)}{\lambda_{ab}^{2}(T)},~~ \tag {1} $$ where $\lambda_{ab}$ is the penetration depth within the $ab$ plane. The band-structure calculations and angle-resolved photoemission spectroscopy measurements have revealed the nearly-ideal-cylinder shaped Fermi surfaces in the present system.[27,33] In this case, $\widetilde{\rho}_{\rm s}$ of the $i$th Fermi surface can be given by[34] $$ \widetilde{\rho}_{\rm si}(T)\,=\,1+2\int_{\varDelta_i}^{\infty}dE\frac{\partial f(E)}{\partial E}\frac{E}{\sqrt{E^2-\varDelta_i^2}},~~ \tag {2} $$ where $f(E)$ and $\varDelta_i$ are the Fermi function and the value of the energy gap on the $i$th Fermi surface respectively. We first attempt to simulate the experimental data using an isotropic single-gap model, which could not follow the evolution tendencies of $H_{\rm c1}(T)/H_{\rm c1}(0)$ for both the samples with different doping levels. Considering the multiple Fermi surface sheets in the present system,[27,33] the multi-gap picture is rather natural and reasonable to be adopted in understanding our observations. In order to simplify the discussion, here we adopt a two-gap model, in which the total normalized superfluid density can be expressed as $$ \widetilde{\rho}_{s}(T)\,=\,w_1\widetilde{\rho}_{s1}(T)+w_2\widetilde{\rho}_{s2}(T),~~ \tag {3} $$ where $w_{i}$ is the weighting factor for the component $\widetilde{\rho}_{\rm si}(T)$. The value of $w_{i}$ is determined by the integral of the Fermi velocity over the $i$th Fermi surface sheet.[34] By tuning the values of $\varDelta_i$ and $w_i$, the simulating curves well describing the experimental data can be obtained, which are shown by the yellow and blue solid curves in Figs. 3(a) and 3(b) for the two samples ($x\,=\,0$ and 0.1), respectively. This consistency between the experimental data and the fitting curves suggests that the two-gap model has grasped key features of this system. The dashed and dotted lines reveal the contributions from the two components with different gaps. The detailed parameters for the gaps and corresponding weighting factors are summarized in Table 1. The $T_{\rm c}$ values listed in Table 1 are derived from the $\chi$–$T$ data. The temperature points, where the values of $H_{\rm c1}(T)/H_{\rm c1}(0)$ vanish, display a deviation of $\pm 1$ K compared with $T_{\rm c}$ determined from the $\chi$–$T$ data [see Fig. 1(c)]. From the data of $w_{i}$, we can see that the contributions from the two superfluid components are roughly half and half for both the samples. Such a behavior is similar to that reported for the CsCa$_2$Fe$_4$As$_{4}$F$_2$ system.[24] As for the sizes of the gaps, the ratio to $T_{\rm c}$ ($\varDelta/k_{\rm B}T_{\rm c}$, $k_{\rm B}$ is the Boltzmann constant) is almost unchanged by doping for the smaller gap. Meanwhile, the doping of 10% suppresses this ratio by about 20% (from 1.71 to 1.33) for the larger gap. The parameters obtained here supply important information about gap structure. The limitations of the results are mainly manifested in the following two aspects. Firstly, the present data cannot discriminate the presence of nodes or not. More experiments under lower temperature are needed to clarify this issue. Currently the energy gaps are set to be isotropic within the $k_x$–$k_y$ plane for each Fermi surface sheet. Secondly, the simplification of the two-gap model typically only grasps the contributions from the particular two gaps with the highest weighting factors of the superfluid. Under the circumstances that there are more than two Fermi surface sheets and gap values, which is exactly the case for the present system, some details about other gaps with relatively smaller contributions will be missing. Nevertheless, our results can supply an effective comparison with the gap values obtained from other measurements,[20,21,24,25,27] see Table 2. Among these experiments, the ARPES measurements were performed on the single-crystalline samples of the same K-based 12442 system, which can supply band-dependence information about the gap values. Thus here we make a detailed comparison with the results of ARPES, which reveal six Fermi surface sheets and the same number of gaps in the undoped KCa$_2$Fe$_4$As$_{4}$F$_2$. These gaps can be divided into three groups according to their sizes: two gaps with the size around 2 meV, three around 5 meV, and one around 8 meV. It is highly likely that our experiments have detected the first two groups and the one with the size of 8 meV is missing due the small contribution to the overall superfluid. The deviation between 1.2 meV (our result) and 2 meV (ARPES result) may be interpreted by the relatively large error bars in the ARPES experiments due to the limited energy resolution.
Table 2. Comparison of the gap sizes obtained with different experimental methods in the 12442 system.
Compound$^{\rm a}$ Type$^{\rm b}$ Method $\varDelta_1$ (meV) $\varDelta_2$ (meV) $\varDelta_3$ (meV) References
K-12442 Poly- $\mu$SR 1.84$^{\rm c}$ 10.13 [21]
K-12442 Single- ARPES$^{\rm d}$ $\sim $2.0 $\sim $5.0 $\sim $8.0 [27]
K-12442 Single- $H_{\rm c1}$ 1.2 5.0 This work
Cs-12442 Poly- $\mu$SR 1.5$^{\rm c}$ 7.5 [20]
Cs-12442 Single- Optical 7.0$^{\rm e}$ [25]
Cs-12442 Single- $H_{\rm c1}$ 2.32 6.75 [24]
Rb-12442 Single- $\mu$SR 0.88 8.15 [22]
$^{\rm a}$K-12442, Cs-12442 and Rb-12442 are the abbreviations for KCa$_2$Fe$_4$As$_{4}$F$_2$, CsCa$_2$Fe$_4$As$_{4}$F$_2$ and RbCa$_2$Fe$_4$As$_{4}$F$_2$, respectively. $^{\rm b}$Poly- and Single- are the abbreviations for Polycrystalline and single-crystalline, respectively. $^{\rm c}$The symmetry of this gap is d wave. $^{\rm d}$Actually the ARPES measurement revealed six gaps. Based on their sizes, we divides them into three groups. $^{\rm e}$This value is obtained at 7 K.
In summary, we have conducted magnetization measurements on KCa$_2$(Fe$_{1-x}$Co$_{x}$)$_4$As$_{4}$F$_2$ ($x\,=\,0$, 0.1) single crystals, from which the lower critical field $H_{\rm c1}$ is extracted. It is found that the temperature-dependent $H_{\rm c1}$ cannot be described by a simple single-gap model. Instead, the tendency of the $H_{\rm c1}(T)/H_{\rm c1}(0)-T$ curves are simulated commendably based on a two-gap picture. The ratio of the smaller gap $\varDelta_1$ to $T_{\rm c}$ ($\varDelta_1/k_{\rm B}T_{\rm c}$) is not affected by cobalt doping, while the larger one $\varDelta_2/k_{\rm B}T_{\rm c}$ is suppressed significantly. For the undoped KCa$_2$Fe$_4$As$_{4}$F$_2$, the gap sizes obtained in this study show a good correspondence with the ARPES results. References Possible highT c superconductivity in the Ba?La?Cu?O systemIron-Based Layered Superconductor La[O 1- x F x ]FeAs ( x = 0.05−0.12) with T c = 26 KGap symmetry and structure of Fe-based superconductorsUnconventional Superconductivity with a Sign Reversal in the Order Parameter of LaFeAsO 1 − x F x Minimal two-band model of the superconducting iron oxypnictidesArsenic-bridged antiferromagnetic superexchange interactions in LaFeAsOOrigin of the 150-K Anomaly in LaFeAsO: Competing Antiferromagnetic Interactions, Frustration, and a Structural Phase TransitionStrong Correlations and Magnetic Frustration in the High T c Iron PnictidesSuperconductivity in KCa 2 Fe 4 As 4 F 2 with Separate Double Fe 2 As 2 LayersCrystal structure and superconductivity at about 30 K in ACa2Fe4As4F2 (A = Rb, Cs)Superconductivity at 35 K by self doping in RbGd 2 Fe 4 As 4 O 2Synthesis, Crystal Structure and Superconductivity in RbLn 2 Fe 4 As 4 O 2 (Ln = Sm, Tb, Dy, and Ho)Superconductivity at 33–37 K in A L n 2 Fe 4 As 4 O 2 ( A = K and Cs ; L n = lanthanides ) Strong Pauli paramagnetic effect in the upper critical field of KCa2Fe4As4F2Anisotropic physical properties and large critical current density in K Ca 2 Fe 4 As 4 F 2 single crystalObservation of Two-dimensional Superconductivity in an Ultrathin Iron-Arsenic SuperconductorProbing superconducting anisotropy of single crystal KCa 2 Fe 4 As 4 F 2 by magnetic torque measurementsElastoresistance measurements on CaKFe 4 As 4 and KCa 2 Fe 4 As 4 F 2 with the Fe site of C 2 v symmetryNeutron Spin Resonance in a Quasi-Two-Dimensional Iron-Based SuperconductorTwo-gap superconductivity with line nodes in CsCa 2 Fe 4 As 4 F 2 Nodal multigap superconductivity in KCa 2 Fe 4 As 4 F 2 Multigap Superconductivity in RbCa 2 Fe 4 As 4 F 2 Investigated Using μSR MeasurementsMultigap nodeless superconductivity in CsCa 2 Fe 4 As 4 F 2 probed by heat transportGiant anisotropy in superconducting single crystals of CsCa 2 Fe 4 As 4 F 2 Band-selective clean-limit and dirty-limit superconductivity with nodeless gaps in the bilayer iron-based superconductor CsCa 2 Fe 4 As 4 F 2 Low temperature specific heat of 12442-type KCa2Fe4As4F2 single crystalsSpectroscopic evidence of bilayer splitting and strong interlayer pairing in the superconductor KCa 2 Fe 4 As 4 F 2 Single-Crystal Growth and Extremely High H c2 of 12442-Type Fe-Based Superconductor KCa 2 Fe 4 As 4 F 2Growth and characterization of millimeter-sized single crystals of CaFeAsFGrowth and characterization of CaFe1-Co AsF single crystals by CaAs flux methodEvidence for Two Energy Gaps in Superconducting Ba 0.6 K 0.4 Fe 2 As 2 Single Crystals and the Breakdown of the Uemura PlotTwo-gap superconductivity in CaFe0.88Co0.12AsF revealed by temperature dependence of the lower critical field Hc1c (T)Self-hole-doping–induced superconductivity in KCa 2 Fe 4 As 4 F 2Magnetic penetration depth of MgB2
[1] Bednorz J G and Müller K A 1986 Z. Phys. B 64 189
[2] Kamihara Y, Watanabe T, Hirano M and Hosono H 2008 J. Am. Chem. Soc. 130 3296
[3] Hirschfeld P J, Korshunov M M and Mazin I I 2011 Rep. Prog. Phys. 74 124508
[4] Mazin I I, Singh D J, Johannes M D and Du M H 2008 Phys. Rev. Lett. 101 057003
[5] Raghu S, Qi X L, Liu C X, Scalapino D J and Zhang S C 2008 Phys. Rev. B 77 220503
[6] Ma F, Lu Z Y and Xiang T 2008 Phys. Rev. B 78 224517
[7] Yildirim T 2008 Phys. Rev. Lett. 101 057010
[8] Si Q and Abrahams E 2008 Phys. Rev. Lett. 101 076401
[9] Wang Z C, He C Y, Wu S Q, Tang Z T, Liu Y, Ablimit A, Feng C M and Cao G H 2016 J. Am. Chem. Soc. 138 7856
[10] Wang Z, He C, Tang Z, Wu S and Cao G 2017 Sci. Chin. Mater. 60 83
[11] Wang Z C, He C Y, Wu S Q, Tang Z T, Liu Y, Ablimit A, Tao Q, Feng C M, Xu Z A and Cao G H 2017 J. Phys.: Condens. Matter 29 11LT01
[12] Wang Z C, He C Y, Wu S Q, Tang Z T, Liu Y and Cao G H 2017 Chem. Mater. 29 1805
[13] Wu S Q, Wang Z C, He C Y, Tang Z T, Liu Y and Cao G H 2017 Phys. Rev. Mater. 1 044804
[14] Wang T, Zhang C, Xu L C, Wang J H, Jiang S, Zhu Z W, Wang Z S, Chu J N, Feng J X, Wang L L, Li W, Hu T, Liu X S and Mu G 2020 Sci. Chin. Phys. Mech. & Astron. 63 227412
[15] Pyon S, Kobayashi Y, Takahashi A, Li W, Wang T, Mu G, Ichinose A, Kambara T, Yoshida A and Tamegai T 2020 Phys. Rev. Mater. 4 104801
[16] Zhang C, Hu T, Wang T, Wu Y, Yu A, Chu J, Zhang H, Xiao H, Peng W, Di Z, Qiao S and Mu G 2020 arXiv:2006.03338 [cond-mat.supr-con]
[17] Yu A B, Wang T, Wu Y F, Huang Z, Xiao H, Mu G and Hu T 2019 Phys. Rev. B 100 144505
[18] Terashima T, Matsushita Y, Yamase H, Kikugawa N, Abe H, Imai M, Uji S, Ishida S, Eisaki H, Iyo A, Kihou K, Lee C H, Wang T and Mu G 2020 Phys. Rev. B 102 054511
[19] Hong W, Song L, Liu B, Li Z, Zeng Z, Li Y, Wu D, Sui Q, Xie T, Danilkin S, Ghosh H, Ghosh A, Hu J, Zhao L, Zhou X, Qiu X, Li S and Luo H 2020 Phys. Rev. Lett. 125 117002
[20] Kirschner F K K, Adroja D T, Wang Z C, Lang F, Smidman M, Baker P J, Cao G H and Blundell S J 2018 Phys. Rev. B 97 060506(R)
[21] Smidman M, Kirschner F K K, Adroja D T, Hillier A D, Lang F, Wang Z C, Cao G H and Blundell S J 2018 Phys. Rev. B 97 060509
[22] Adroja D T, Kirschner F K K, Lang F, Smidman M, Hillier A D, Wang Z C, Cao G H, Stenning G B G and Blundell S J 2018 J. Phys. Soc. Jpn. 87 124705
[23] Huang Y Y, Wang Z C, Yu Y J, Ni J M, Li Q, Cheng E J, Cao G H and Li S Y 2019 Phys. Rev. B 99 020502(R)
[24] Wang Z C, Liu Y, Wu S Q, Shao Y T, Ren Z and Cao G H 2019 Phys. Rev. B 99 144501
[25] Xu B, Wang Z C, Sheveleva E, Lyzwa F, Marsik P, Cao G H and Bernhard C 2019 Phys. Rev. B 99 125119
[26] Wang T, Chu J N, Feng J X, Wang L L, Xu X G, Li W, Wen H H, Liu X S and Mu G 2020 Sci. Chin. Phys. Mech. & Astron. 63 297412
[27] Wu D, Hong W, Dong C, Wu X, Sui Q, Huang J, Gao Q, Li C, Song C, Luo H, Yin C, Xu Y, Luo X, Cai Y, Jia J, Wang Q, Huang Y, Liu G, Zhang S, Zhang F, Yang F, Wang Z, Peng Q, Xu Z, Qiu X, Li S, Luo H, Hu J, Zhao L and Zhou X J 2020 Phys. Rev. B 101 224508
[28] Wang T, Chu J N, Jin H, Feng J X, Wang L L, Song Y K, Zhang C, Li W, Li Z J, Hu T, Jiang D, Peng W, Liu X S and Mu G 2019 J. Phys. Chem. C 123 13925
[29] Ma Y H, Zhang H, Gao B, Hu K K, Ji Q C, Mu G, Huang F Q and Xie X M 2015 Supercond. Sci. Technol. 28 085008
[30] Ma Y H, Hu K K, Ji Q C, Gao B, Zhang H, Mu G, Huang F Q and Xie X M 2016 J. Cryst. Growth 451 161
[31] Ren C, Wang Z S, Luo H Q, Yang H, Shan L and Wen H H 2008 Phys. Rev. Lett. 101 257006
[32] Wang T, Ma Y H, Li W, Chu J N, Wang L L, Feng J X, Xiao H, Li Z J, Hu T, Liu X S and Mu G 2019 npj Quantum Mater. 4 33
[33] Wang G, Wang Z and Shi X 2016 Europhys. Lett. 116 37003
[34] Carrington A and Manzano F 2003 Physica C 385 205