The effect of pressure on superconductivity of “122” type Ca1-xNaxFe2As2 (x=0.66) single crystal is investigated through the temperature dependence of resistance measurement. Optimal Na doped (Ca0.34Na0.66)Fe2As2 shows a superconducting transition with Tc ∼ 33 K at ambient pressure. With application of pressure, Tc decreases nearly linearly with dTc/dP ∼ − 1.7K/GPa at pressures lower than 2 GPa, and disappears gradually at higher pressure. The disappearance of superconductivity is also companied with the recovery of standard Fermi liquid behaviors of the normal-state transport properties. Moreover, (Ca0.34Na0.66)Fe2As2 exhibits a tetragonal (T) to collapsed-tetragonal (cT) transition at about 3 GPa. The evolution of non-Fermi liquid behaviors and superconductivity under pressure are both related to the interband fluctuations.

The superconductivity of LaO1−xFxFeAs1 with Tc ∼ 26K has attracted much attention in high temperature superconductor research field as the transition temperature (Tc) is only second to the high Tc cuprates, and many pnictide superconductors were investigated from then on.2–9 Similar to “1111” parent compounds, CaFe2As2 with tetragonal ThCr2Si2-type structure exhibits a spin-density wave (SDW) transition at about 165K, accompanied with a structural phase transition from high temperature tetragonal phase to low temperature orthorhombic phase.10,11 Similar anomalies were observed in BaFe2As212 and SrFe2As213 as well.

Chemical substitution and pressure can both initiate or increase Tc for pnictide parent compounds. For instance, substituting Ba or Sr by K in BaFe2As2 or SrFe2As2 induces superconductivity at 38 K6 and 35 K,14 respectively. A superconductivity transition with Tc of ∼26 K15 for (Ca0.6Na0.4)Fe2As2 or 20 K11 for (Ca0.5Na0.5)Fe2As2 has been reported by the chemical substitution at the Ca site subsequently. A higher Tc ∼ 33 K in (Ca0.34Na0.66)Fe2As216,17 or Tc ∼ 34 K in Ca0.32Na0.68Fe2As2 has also been reported,18 with the two-thirds Na doping at the Ca site, so-called optimal doping. Furthermore, the pressure-tuned superconductivity has been reported in some “1111-”, “122-”, “111-”, or “11”-type pnictide compounds as well.19–27 For some compounds, the superconductivity can be initiated by pressure and the Tc can be pushed to a maximum with initial compression, whereas for some other compounds the Tc is suppressed by application of pressure monotonously. It has been explained that the Tc of pnictide superconductors is closely related to the geometric change of the FeAs4 tetrahedron as well as the anion height from Fe layer,28,29 which is also experimentally confirmed.30,31

CaFe2As2 is somehow different from BaFe2As2 or SrFe2As2 as due to its reduced unit cell volume and c lattice parameter, which is very close to collapsed tetragonal (cT) phase. So it is very sensitive to external pressure and chemical pressure (doping). A pressure-induced tetragonal-to-collapsed tetragonal structure phase transition was observed in CaFe2As2 above 0.35 GPa at 50 K.32 We focus on (Ca0.34Na0.66)Fe2As2 in this work since it shows the highest Tc of ∼ 33 K for (Ca1−xNax)Fe2As2. The high-pressure resistance measurements and the high-pressure X-ray diffraction experiments for optimal doped (Ca0.34Na0.66)Fe2As2 are performed. We mainly discussed the influence of T to cT phase transition on the superconductivity. The resistance changes its low-energy behavior from ρ ∝ T1.3 in the T phase to ρ ∝ T2 in the cT phase, with the disappearance of superconductivity. The interplay of superconductivity and collapsed tetragonal phase suggests the essential role of magnetic fluctuations in the emergence of superconductivity.

The (Ca0.34Na0.66)Fe2As2 single crystals were synthesized using the solid-state reaction method. The detailed conditions and process of synthesis were described in Refs. 16 and 33.

FIG. 1.

The X-ray diffraction of (Ca0.34Na0.66)Fe2As2 single crystal. Inset: Temperature dependent magnetization of (Ca0.34Na0.66)Fe2As2 superconductors at ZFC conditions with H=30Oe.

FIG. 1.

The X-ray diffraction of (Ca0.34Na0.66)Fe2As2 single crystal. Inset: Temperature dependent magnetization of (Ca0.34Na0.66)Fe2As2 superconductors at ZFC conditions with H=30Oe.

Close modal
FIG. 2.

(a) The temperature dependence of in-plane resistance Rab for (Ca0.34Na0.66)Fe2As2 single crystals at variant pressures up to 2.4 GPa using piston-cylinder-type pressure cell; (b) The definition of Tc: two extrapolated lines are drawn through the resistance curve before and after superconducting transition. The Tc is determined from the intersection of two lines.

FIG. 2.

(a) The temperature dependence of in-plane resistance Rab for (Ca0.34Na0.66)Fe2As2 single crystals at variant pressures up to 2.4 GPa using piston-cylinder-type pressure cell; (b) The definition of Tc: two extrapolated lines are drawn through the resistance curve before and after superconducting transition. The Tc is determined from the intersection of two lines.

Close modal
FIG. 3.

(a) The temperature dependence of in-plane resistance Rab for (Ca0.34Na0.66)Fe2As2 single crystals at variant pressures up to 3.7 GPa using DAC cell; (b) The second experiment using DAC cell at variant pressures up to 6.9 GPa.

FIG. 3.

(a) The temperature dependence of in-plane resistance Rab for (Ca0.34Na0.66)Fe2As2 single crystals at variant pressures up to 3.7 GPa using DAC cell; (b) The second experiment using DAC cell at variant pressures up to 6.9 GPa.

Close modal
FIG. 4.

The TcP phase diagram of (Ca0.34Na0.66)Fe2As2 obtained from resistance measurements. Experimental data are the points with error bar. The pattern of As-Fe-As bond angles and anion height from Fe layer is also given, the blue spheres are As atoms (all around), and the yellow sphere is Fe atom (middle).

FIG. 4.

The TcP phase diagram of (Ca0.34Na0.66)Fe2As2 obtained from resistance measurements. Experimental data are the points with error bar. The pattern of As-Fe-As bond angles and anion height from Fe layer is also given, the blue spheres are As atoms (all around), and the yellow sphere is Fe atom (middle).

Close modal
FIG. 5.

The low-temperature part of R-T curves (Tc < T < 130 K) can be fitted by the formula as shown in the figure, which exhibits a change from approximately T-linear to T-square dependence of resistance.

FIG. 5.

The low-temperature part of R-T curves (Tc < T < 130 K) can be fitted by the formula as shown in the figure, which exhibits a change from approximately T-linear to T-square dependence of resistance.

Close modal
FIG. 6.

(a) The synchrotron X-ray diffraction pattern for a wide angle range from ambient pressure up to 5.1GPa at room temperature. Each peak is labeled with the corresponding (hkl) at 0 GPa and 3.1 GPa respectively; (b) Pressure dependence of crystal parameters a, c and volume, which shows a T to cT phase transition.

FIG. 6.

(a) The synchrotron X-ray diffraction pattern for a wide angle range from ambient pressure up to 5.1GPa at room temperature. Each peak is labeled with the corresponding (hkl) at 0 GPa and 3.1 GPa respectively; (b) Pressure dependence of crystal parameters a, c and volume, which shows a T to cT phase transition.

Close modal
FIG. 7.

The pressure-temperature phase diagram of (Ca0.34Na0.66)Fe2As2.

FIG. 7.

The pressure-temperature phase diagram of (Ca0.34Na0.66)Fe2As2.

Close modal

The pressure-induced evolution of Tc in (Ca0.34Na0.66)Fe2As2 single crystal was investigated by four-probe electrical resistance measurement methods at variant pressures. The experiments were performed using both piston-cylinder-type pressure cell with liquid transmitting medium silicone oil and diamond anvil cell (DAC) with solid transmitting medium hexagonal boron nitride (h-BN). In piston-cylinder-type pressure cell, the silicone oil was used as pressure-transmitting medium to measure the temperature dependence of resistance under different hydrostatic pressures. The size of the sample was about 1.5 x 0.9 x 0.05 mm3. All the pressure values quoted in this paper were measured at room temperature. For DAC experiment, pressure was generated by a pair of diamonds with 500-μm-diameter culet. The stainless steel gasket was pre indented from 250 μm to ∼40 μm thickness with a 250-μm hole in the center that serves as the sample chamber. The sample size was about 100 μm × 100 μm × 30 μm. The pressure was determined by ruby fluorescence method at room temperature before and after each cooling down. The DAC experiments were performed twice with two different samples.

The X-ray diffraction experiments at high pressure with synchrotron radiation were done at the National Light Synchrotron Source (NSLS) of the Brookhaven National Laboratory with a wavelength 0.407 Å using a symmetric Mao Bell diamond anvil cell at room temperature. The crystal structures were refined using GSAS package.34 

The (Ca0.34Na0.66)Fe2As2 single crystals used in the high pressure experiments has a single-phase nature.16 Fig. 1 shows the X-ray diffraction pattern of (Ca0.34Na0.66)Fe2As2 single crystal with (00l) peaks. The magnetization curve shows sharp superconducting transition around 33K with full shielding fraction, which indicates the good quality of the sample. Fig. 2(a) shows the in-plane resistance Rab of (Ca0.34Na0.66)Fe2As2 as a function of temperature at different pressures up to 2.4 GPa using piston-cylinder-type pressure cell. Above 2 GPa, the width of superconducting transition increases apparently, from 0.5 K at pressures lower than 2 GPa to 3 K at 2.4 GPa. Because of the limitation of pressure in piston-cylinder-type pressure cell, we also perform the high-pressure resistance experiments using DAC cell, the results of two times are shown in Fig. 3. The width of superconducting transition increases rapidly with increasing pressure so that the zero-resistance disappears above 2 GPa, and the superconducting transition disappears completely at higher pressures. The values of Tc at variant pressures are determined from the intersection of two extrapolated lines, which extract from the experimental curve before and after transition as shown in Fig. 2(b). The Tc–pressure phase diagram of (Ca0.34Na0.66)Fe2As2 from piston-cylinder-type pressure cell is shown in Fig. 4. It is noteworthy that Tc decreases linearly as the pressure increases with a slope dTc/dP = − 1.7 K/GPa. The Tc evolution behavior with pressure is closely related to the change of strong Fermi surface nesting between hole and electron sheets through tuning the As-Fe-As bond angles and the anion height from Fe layer directly by pressure.28,29 So pressure probably makes the structure distort away from optimal position so that Tc decreases with increasing pressure in (Ca0.34Na0.66)Fe2As2.

To investigate the normal-state transport properties of (Ca0.34Na0.66)Fe2As2, the formula R(T) = R0 + ATα is used for fitting the low-temperature part of R-T curve beyond transition temperature, the result is shown in Fig. 5. It exhibits an approximate T-linear dependence in a wide temperature range (Tc < T < 130 K) at 0.2 GPa, which suggests a strong similarity to the non-Fermi-liquid (non-FL) behaviors governed by quantum fluctuations in strongly correlated electron systems. Similar anomalous T-linear behaviors that deviate from the standard Fermi-liquid (FL) properties have been reported in several Fe-pnictides.35–41 With increasing pressure, α increases and the FL behavior recovers gradually. The width of superconducting transition of (Ca0.34Na0.66)Fe2As2 also increases rapidly with the recovery of FL behavior. The Fermi surface structure with interband nesting plays an important role for superconductivity in Fe-pnictides. Thus there must be a large change of Fermi surface nesting between the hole and electron sheets induced by pressure, which resulting the non-FL to FL transition.39 

For (Ca0.34Na0.66)Fe2As2, the width of superconducting transition of R-T curve increases and zero-resistance disappears above 2 GPa. The phenomena indicate that the sample is no longer a single phase. To further investigate the evolution of structure of (Ca0.34Na0.66)Fe2As2 under high pressure, we perform the high pressure X-ray diffraction experiments. Fig. 6(a) shows the synchrotron X-ray diffraction pattern for a wide angle range from ambient pressure up to 5.1GPa at room temperature. Each peak is labeled with the corresponding (hkl). The GSAS program software package is used to obtain the lattice parameters at each pressure, which is listed in Fig. 6(b). With increasing pressure, the c axis shrinks and a axis slightly expands, between 2.3GPa and 3.1 GPa, there is a rapid reduction as large as ∼6% of the c axis whereas the a axis expands by ∼1%, indicating the T to cT phase transition, which has been reported in the parent CaFe2As2 under pressure.32,42,43 With further increasing pressure, both a axis and c axis smoothly decrease. Because of the destruction of interband nesting in cT phase, the lack of magnetic fluctuations could be responsible for the recovery of FL behaviors and the absence of superconductivity. Similar with (Ca0.34Na0.66)Fe2As2 in cT phase, both the absence of superconductivity and the recovery of FL behaviors have also been observed in cT phase of CaFe2As2 or doped Ca122 Fe pnictides.39,44–47

In summary, we have shown that the Tc of (Ca0.34Na0.66)Fe2As2 decreases nearly linearly with a slope dTc/dP ∼ − 1.7 K/GPa with increasing pressure. Anomalous non-FL behaviors of R-T curves are also observed at lower pressures in (Ca0.34Na0.66)Fe2As2, whereas the recovery of FL transport properties corresponds to the disappearance of superconductivity. Meanwhile, (Ca0.34Na0.66)Fe2As2 exhibits a tetragonal (T) to collapsed-tetragonal (cT) transition at about 3GPa according to high pressure synchrotron X-ray diffraction experiments. The pressure–temperature phase diagram is shown in Fig. 7. The results strongly suggest that the superconductivity and the observed non-FL transport properties are both closely related to the interband-associated strong spin and orbital fluctuations in Fe pnictides.

This work is supported by NSF and MOST of China through research projects.

1.
Y.
Kamihara
,
T.
Watanabe
,
M.
Hirano
, and
H.
Hosono
,
J. Am. Chem. Soc.
130
,
3296
(
2008
).
2.
Z. A.
Ren
,
J.
Yang
,
W.
Lu
,
W.
Yi
,
X. L.
Shen
,
Z. G.
Li
,
G. C.
Che
,
X. L.
Dong
,
L. L.
Sun
,
F.
Zhou
, and
Z. X.
Zhao
,
Europhys. Lett.
82
,
57002
(
2008
).
3.
X. H.
Chen
,
T.
Wu
,
G.
Wu
,
R. H.
Liu
,
H.
Chen
, and
D. F.
Fang
,
Nature
453
,
761
(
2008
).
4.
H. H.
Wen
,
G.
Mu
,
L.
Fang
,
H.
Yang
, and
X. Y.
Zhu
,
Europhys. Lett.
82
,
17009
(
2008
).
5.
G. F.
Chen
,
Z.
Li
,
D.
Wu
,
G.
Li
,
W. Z.
Hu
,
J.
Dong
,
P.
Zheng
,
J. L.
Luo
, and
N. L.
Wang
,
Phys. Rev. Lett.
100
,
247002
(
2008
).
6.
C.
Wang
,
L. J.
Li
,
S.
Chi
,
Z. W.
Zhu
,
Z.
Ren
,
Y. K.
Li
,
Y. T.
Wang
,
X.
Lin
,
Y. K.
Luo
,
S.
Jiang
,
X. F.
Xu
,
G. H.
Cao
, and
Z. A.
Xu
,
Europhys. Lett.
83
,
67006
(
2008
).
7.
M.
Rotter
,
M.
Tegel
, and
D.
Johrendt
,
Phys. Rev. Lett.
101
,
107006
(
2008
).
8.
X. C.
Wang
,
Q. Q.
Liu
,
Y. X.
Lv
,
W. B.
Gao
,
L. X.
Yang
,
R. C.
Yu
,
F. Y.
Li
, and
C. Q.
Jin
,
Solid State Commun.
148
,
538
(
2008
).
9.
F. C.
Hsu
,
J. Y.
Luo
,
K. W.
Yeh
,
T. K.
Chen
,
T. W.
Huang
,
P. M.
Wu
,
Y. C.
Lee
,
Y. L.
Huang
,
Y. Y.
Chu
,
D. C.
Yan
, and
M. K.
Wu
,
Proc. Natl. Acad. Sci. USA
105
,
14262
(
2008
).
10.
N.
Ni
,
S.
Nandi
,
A.
Kreyssig
,
A. I.
Goldman
,
E. D.
Mun
,
S. L.
Bud’ko
, and
P. C.
Canfield
,
Phys. Rev. B
78
,
014523
(
2008
).
11.
G.
Wu
,
H.
Chen
,
T.
Wu
,
Y. L.
Xie
,
Y. J.
Yan
,
R. H.
Liu
,
X. F.
Wang
,
J. J.
Ying
, and
X. H.
Chen
,
J. Phys. Condens. Matter
20
,
422201
(
2008
).
12.
M.
Rotter
,
M.
Tegel
,
D.
Johrendt
,
I.
Schellenberg
,
W.
Hermes
, and
R.
Pöttgen
,
Phys. Rev. B
78
,
020503
(
2008
).
13.
J.-Q.
Yan
,
A.
Kreyssig
,
S.
Nandi
,
N.
Ni
,
S. L.
Bud’ko
,
A.
Kracher
,
R. J.
McQueeney
,
R.W.
McCallum
,
T. A.
Lograsso
,
A. I.
Goldman
, and
P. C.
Canfield
,
Phys. Rev. B
78
,
024516
(
2008
).
14.
G. F.
Chen
,
Z.
Li
,
G.
Li
,
W. Z.
Hu
,
J.
Dong
,
X. D.
Zhang
,
P.
Zheng
,
N. L.
Wang
, and
J. L.
Luo
,
Chin. Phys. Lett.
25
,
3403
(
2008
).
15.
P. M.
Shirage
,
K.
Miyazawa
,
H.
Kito
,
H.
Eisaki
, and
A.
Iyo
,
Appl. Phys. Express
1
,
081702
(
2008
).
16.
K.
Zhao
,
Q. Q.
Liu
,
X. C.
Wang
,
Z.
Deng
,
Y. X.
Lv
,
J. L.
Zhu
,
F.Y.
Li
, and
C. Q.
Jin
,
J. Phys. Condens. Matter
22
,
222203
(
2010
).
17.
K.
Zhao
,
Q. Q.
Liu
,
X. C.
Wang
,
Z.
Deng
,
Y. X.
Lv
,
J. L.
Zhu
,
F.Y.
Li
, and
C. Q.
Jin
,
Phys. Rev. B
84
,
184534
(
2011
).
18.
S.
Johnston
,
M.
Abdel-Hafiez
,
L.
Harnagea
,
V.
Grinenko
,
D.
Bombor
,
Y.
Krupskaya
,
C.
Hess
,
S.
Wurmehl
,
A. U. B.
Wolter
,
B.
B¨uchner
,
H.
Rosner
, and
S.-L.
Drechsler
,
Phys. Rev. B
89
,
134507
(
2014
).
19.
H.
Takahashi
,
K.
Igawa
,
K.
Arii
,
Y.
Kamihara
,
M.
Hirano
, and
H.
Hosono
,
Nature
453
,
376
(
2008
).
20.
N.
Takeshita
,
A.
Iyo
,
H.
Eisaki
,
H.
Kito
, and
T.
Ito
,
J. Phys. Soc. Jap
77
,
075003
(
2008
).
21.
W.
Yi
,
L. L.
Sun
,
Z.
Ren
,
W.
Lu
,
X. L.
Dong
,
H. J.
Zhang
,
X.
Dai
,
Z.
Fang
,
Z. C.
Li
,
G. G.
Che
,
J.
Yang
,
X. L.
Shen
,
F.
Zhou
, and
Z. X.
Zhao
,
EPL
83
,
57002
(
2008
).
22.
M. S.
Torikachvili
,
S. L.
Bud’ko
,
N.
Ni
, and
P. C.
Canfield
,
Phys. Rev. Lett.
101
,
057006
(
2008
).
23.
A.
Mani
,
N.
Ghosh
,
S.
Paulraj
,
A.
Bharathi
, and
C. S.
Sundar
,
EPL
87
,
17004
(
2009
).
24.
K.
Igawa
,
H.
Okada
,
H.
Takahashi
,
S.
Matsuishi
,
Y.
Kamihara
,
M.
Hirano
,
H.
Hosono
,
K.
Matsubayashi
, and
Y.
Uwatoko
,
J. Phys. Soc. Jpn.
78
,
025001
(
2009
).
25.
S. J.
Zhang
,
X. C.
Wang
,
R.
Sammynaiken
,
J. S.
Tse
,
L. X.
Yang
,
Z.
Li
,
Q. Q.
Liu
,
S.
Desgreniers
,
Y.
Yao
,
H. Z.
Liu
, and
C. Q.
Jin
,
Phys. Rev. B.
80
,
014506
(
2009
).
26.
S. J.
Zhang
,
X. C.
Wang
,
Q. Q.
Liu
,
Y. X.
Lv
,
X. H.
Yu
,
Z. J.
Lin
,
Y. S.
Zhao
,
L.
Wang
,
Y.
Ding
,
H. K.
Mao
, and
C. Q.
Jin
,
EPL
88
,
47008
(
2009
).
27.
Y.
Mizuguchi
,
F.
Tomioka
,
S.
Tsuda
,
T.
Yamaguchi
, and
Y.
Takano
,
Appl. Phys. Lett.
93
,
152505
(
2008
).
28.
C. H.
Lee
,
A.
Iyo
,
H.
Eisaki
,
H.
Kito
,
M. T.
Fernandez-Diaz
,
T.
Ito
,
K.
Kihou
,
H.
Matsuhata
,
M.
Braden
, and
K.
Yamada
,
J. Phys. Soc. Jpn.
77
,
083704
(
2008
).
29.
Y.
Mizuguchi
,
Y.
Hara
,
K.
Deguchi
,
S.
Tsuda
,
T.
Yamaguchi
,
K.
Takeda
,
H.
Kotegawa
,
H.
Tou
, and
Y.
Takano
,
Supercond. Sci. Technol.
23
,
054013
(
2010
).
30.
J. G.
Zhao
,
L. H.
Wang
,
D. W.
Dong
,
Z. G.
Liu
,
H. Z.
Liu
,
G. F.
Chen
,
D.
Wu
,
J. L.
Luo
,
N. L.
Wang
,
Y.
Yu
,
C. Q.
Jin
, and
Q. Z.
Guo
,
JACS
130
,
13828
(
2008
).
31.
Q. Q.
Liu
,
X. H.
Yu
,
X. C.
Wang
,
Z.
Deng
,
Y. X.
Lv
,
J. L.
Zhu
,
S. J.
Zhang
,
H. Z.
Liu
,
W. G.
Yang
,
L.
Wang
,
H. K.
Mao
,
G. Y.
Shen
,
Z. Y.
Lu
,
Y.
Ren
,
Z. Q.
Chen
,
Z. J.
Lin
,
Y. S.
Zha
, and
C. Q.
Jin
,
J. Am. Chem. Soc.
133
,
7892
(
2011
).
32.
A.
Kreyssig
,
M. A.
Green
,
Y.
Lee
,
G. D.
Samolyuk
,
P.
Zajdel
,
J. W.
Lynn
,
S. L.
Bud’ko
,
M. S.
Torikachvili
,
N.
Ni
,
S.
Nandi
,
J. B.
Leão
,
S. J.
Poulton
,
D. N.
Argyriou
,
B. N.
Harmon
,
R. J.
McQueeney
,
P. C.
Canfield
, and
A. I.
Goldman
,
Phys. Rev. B
78
,
184517
(
2008
).
33.
J. S.
Kim
,
K.
Zhao
,
C. Q.
Jin
, and
G. R.
Stewart
,
Solid State Communications
193
,
34
(
2014
).
34.
A. C.
Larson
and
R. B.
Von Dreele
,
Los Alamos National Laboratory Report LAUR 86-748
(
Los Alamos National Laboratory
, Los Alamos, NM,
1994
).
35.
R. H.
Liu
,
G.
Wu
,
T.
Wu
,
D. F.
Fang
,
H.
Chen
,
S. Y.
Li
,
K.
Liu
,
Y. L.
Xie
,
X. F.
Wang
,
R. L.
Yang
,
L.
Ding
,
C.
He
,
D. L.
Feng
, and
X. H.
Chen
,
Phys. Rev. Lett.
101
,
087001
(
2008
).
36.
M.
Gooch
,
B.
Lv
,
B.
Lorenz
,
A. M.
Guloy
, and
C.-W.
Chu
,
Phys. Rev. B
79
,
104504
(
2009
).
37.
X. F.
Wang
,
T.
Wu
,
G.
Wu
,
R. H.
Liu
,
H.
Chen
,
Y. L.
Xie
, and
X. H.
Chen
,
New J. Phys.
11
,
045003
(
2009
).
38.
S.
Kasahara
,
T.
Shibauchi
,
K.
Hashimoto
,
K.
Ikada
,
S.
Tonegawa
,
R.
Okazaki
,
H.
Shishido
,
H.
Ikeda
,
H.
Takeya
,
K.
Hirata
,
T.
Terashima
, and
Y.
Matsuda
,
Phys. Rev. B
81
,
184519
(
2010
).
39.
S.
Kasahara
,
T.
Shibauchi
,
K.
Hashimoto
,
Y.
Nakai
,
H.
Ikeda
,
T.
Terashima
, and
Y.
Matsuda
,
Phys. Rev. B
83
,
060505(R)
(
2011
).
40.
Y. M.
Dai
,
B.
Xu
,
B.
Shen
,
H.
Xiao
,
H. H.
Wen
,
X. G.
Qiu
,
C. C.
Homes
, and
R. P. S. M.
Lobo
,
Phys. Rev. Lett.
111
,
117001
(
2013
).
41.
Y. M.
Dai
,
H.
Miao
,
L. Y.
Xing
,
X. C.
Wang
,
P. S.
Wang
,
H.
Xiao
,
T.
Qian
,
P.
Richard
,
X. G.
Qiu
,
W.
Yu
,
C. Q.
Jin
,
Z.
Wang
,
P. D.
Johnson
,
C. C.
Homes
, and
H.
Ding
,
Physi. Rev. X
5
,
031035
(
2015
).
42.
W.
Yu
,
A. A.
Aczel
,
T. J.
Williams
,
S. L.
Budko
,
N.
Ni
,
P. C.
Canfield
, and
G. M.
Luke
,
Phys. Rev. B
79
,
020511(R)
(
2009
).
43.
M. S.
Torikachvili
,
S. L.
Budko
,
N.
Ni
,
P. C.
Canfield
, and
S. T.
Hannahs
,
Phys. Rev. B
80
,
014521
(
2009
).
44.
Masataka
Danura
,
Kazutaka
Kudo
,
Yoshihiro
Oshiro
,
Shingo
Araki
,
Tatsuo C.
Kobayashi
, and
Minoru
Nohara
,
J. Phys. Soc. Jpn.
80
,
103701
(
2011
).
45.
R. S.
Dhaka
,
Rui
Jiang
,
S.
Ran
,
S. L.
Bud’ko
,
P. C.
Canfield
,
B. N.
Harmon
,
Adam
Kaminski
,
Milan
Tomić
,
Roser
Valentí
, and
Yongbin
Lee
,
Phys. Rev. B
89
,
020511
(
2014
).
46.
K.
Tsubota
,
T.
Wakita
,
H.
Nagao
,
C.
Hiramatsu
,
T.
Ishiga
,
M.
Sunagawa
,
K.
Ono
,
H.
Kumigashira
,
M.
Danura
,
K.
Kudo
,
M.
Nohara
,
Y.
Muraoka
, and
T.
Yokoya
,
J. Phys. Soc. Jpn.
82
,
073705
(
2013
).
47.
Y.
Furukawa
,
B.
Roy
,
S.
Ran
,
S. L.
Bud’ko
, and
P. C.
Canfield
,
Phys. Rev. B
89
,
121109
(
2014
).