Studies on effects of impurity doping and NMR measurements of La 1111 and/or Nd 1111 Fe-Pnictide superconductors

Article abstract of DOI:10.1143/JPSJ.79.014710

Measurements of the electrical resistivity ρ, Hall coefficient R _H, thermoelectric power S, and the electronic specific heat coefficient γ have been carried out for samples of LnFe _1-yM_yAsO_1-xF_x (Ln = La, Nd; M = Co, Mn; x = 0:11) obtained by doping M atoms into the superconducting LnFeAsO _1-xF_x (Ln 1111) system. The NMR longitudinal relaxation rate 1/T₁ has also been measured for samples of LnFe _1-yM_yAsO_1-xF_x with various x values. Co atoms doped into the superconducting LnFeAsO_1-xF_x are nonmagnetic, and the rate of T_c-suppression |dT_c/dx| by Co atoms has been found to be too small to be explained by the pair-breaking effect expected for the S± superconducting symmetry proposed as the most probable symmetry for the system. This result throws a serious doubt on whether the symmetry is realized in the system. Instead of the pair breaking, two mechanisms of T_c suppression by the doped impurities have been found: One is the electron localization, which appears when the sheet resistance R_□ exceeds h/4e² = 6:45 kΩ, and the other is the disappearance (or reduction in the area) of the hole Fermi surfaces around the Γ point in the reciprocal space. The latter mechanism has been observed when the number of electrons increases with increasing Co doping level and the system changes from an anomalous metal to an ordinary one. Regarding the two distinct T dependences of the NMR longitudinal relaxation rate 1/T ₁ of LaFeAsO_1-xF_x, (1=T₁ ∝ T⁶ reported by our group in the T region from T_c to ～0:4 T_c for samples with the highest Tc values with varying x, and 1/T₁ ∝ T^2:5-3:0 observed by many groups in almost the entire T region studied below T_c), we discuss the origin of such a difference, and show that, at least, the T^2:5-3:0-like dependence of 1/T₁ cannot be considered as the experimental evidence for the S± symmetry of δ.

Full text of DOI:10.1143/JPSJ.79.014710

Journal of the Physical Society of Japan
Vol. 79, No. 1, January, 2010, 014710
#2010 The Physical Society of Japan
Studies on Effects of Impurity Doping and NMR Measurements
of La 1111 and/or Nd 1111 Fe-Pnictide Superconductors
1
Masatoshi SATO1;2, Yoshiaki KOBAYASHI1;2, Sang Chul LEE ,
1
1
1;2
Hidefumi TAKAHASHI , Erika SATOMI , and Yoko MIURA
1Department of Physics, Division of Material Science, Nagoya University,
Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
2JST, TRIP, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
(Received August 10, 2009; accepted October 28, 2009; published December 25, 2009)
Measurements of the electrical resistivity ꢀ, Hall coefficient RH, thermoelectric power S, and the
electronic specific heat coefficient ꢁ have been carried out for samples of LnFe1ꢀyMyAsO1ꢀxFx
(Ln ¼ La, Nd; M ¼ Co, Mn; x ¼ 0:11) obtained by doping M atoms into the superconducting
LnFeAsO1ꢀxFx (Ln 1111) system. The NMR longitudinal relaxation rate 1=T1 has also been measured
for samples of LaFe1ꢀyCoyAsO1ꢀxFx with various x values. Co atoms doped into the superconducting
LnFeAsO1ꢀxFx are nonmagnetic, and the rate of Tc-suppression jdTc=dxj by Co atoms has been found to
be too small to be explained by the pair-breaking effect expected for the S superconducting symmetry
ꢁ
proposed as the most probable symmetry for the system. This result throws a serious doubt on whether
the symmetry is realized in the system. Instead of the pair breaking, two mechanisms of Tc suppression
by the doped impurities have been found: One is the electron localization, which appears when the sheet
resistance R exceeds h=4e2 ¼ 6:45 kꢀ, and the other is the disappearance (or reduction in the area) of
Ã
the hole Fermi surfaces around the ꢁ point in the reciprocal space. The latter mechanism has been
observed when the number of electrons increases with increasing Co doping level and the system
changes from an ‘‘anomalous metal’’ to an ordinary one. Regarding the two distinct T dependences of the
NMR longitudinal relaxation rate 1=T1 of LaFeAsO1ꢀxFx, (1=T1 / T6 reported by our group in the T
region from Tc to ꢂ0:4 Tc for samples with the highest Tc values with varying x, and 1=T1 / T2:5{3:0
observed by many groups in almost the entire T region studied below Tc), we discuss the origin of such a
difference, and show that, at least, the T2:5{3:0-like dependence of 1=T1 cannot be considered as the
experimental evidence for the S symmetry of ꢂ.
ꢁ
KEYWORDS: LnFe1ꢀy My AsO1ꢀx Fx (Ln ¼ La, Nd; M ¼ Co, Mn), NMR relaxation rate, 1=T1, transport properties,
specific heats
DOI: 10.1143/JPSJ.79.014710
surface but having opposite signs of the order parameters on
1. Introduction
disconnected Fermi surfaces.8–11) Thus, it is important to
In the study of the origin of the high superconducting clarify whether the small Tc suppression rate indicates that
transition temperature Tc of the newly discovered Fe- the superconducting symmetry of the system is different
pnictide systems,1) it is essential to identify the symmetry from the S symmetry. Another result of the studies is that
ꢁ
of their superconducting order parameter ꢂ. At the very the temperature (T) dependence of the NMR longitudinal
early stage of the study, the S -symmetry was proposed for relaxation rate 1=T1 observed by our group for La 1111
ꢁ
the LaFeAsO1ꢀxFx (La 1111) system as the most probable samples with x ¼ 0:1112) can be approximately described by
symmetry2,3) by considering that the superconductivity is the relation 1=T1 / T6 in the T region between ꢂ0:4Tc and
realized by spin fluctuations in the FeAs layers of edge- Tc, which is markedly different from the relation 1=T1 /
sharing FeAs4 tetrahedra. It is characterized by the nodeless T2:5{3:0 observed by many groups13–17) in the wide T region
ꢂ on each Fermi surface but opposite signs of ꢂ values on of ð0:1{0:2ÞTc < T < Tc for samples including one with
the disconnected Fermi surfaces around ꢁ and M points in a similar Tc value to ours. Although the relation 1=T1 /
the reciprocal space.
T2:5{3:0 has been explained by considering the S -symmetry
ꢁ
Various experiments have also been carried out to extract of the order parameter,18–20) it is difficult, as we have pointed
information on the symmetry of ꢂ, and many groups have out,12) to understand the observations of these two distinct T
reported that ꢂ of La 1111 is nodeless on each Fermi dependences simultaneously.
surface,4–7) consistent with the S -symmetry. However,
In this paper, we present detailed results on the small Tc
ꢁ
there is another important point, that is, we have to clarify suppression rate obtained for samples of M-atom-doped Ln
whether the signs of the order parameters are opposite on 1111 systems of the form LnFe1ꢀyMyAsO1ꢀxFx (Ln ¼ La,
two disconnected Fermi surfaces around the ꢁ and M points. Nd; M ¼ Co, Mn; x ¼ 0:11). We also present additional
We have published several reports and argued this point results of the studies on the two distinct T dependences of
based on our experimental studies carried out by trans- 1=T1, and clarify whether the S -symmetry is realized in the
ꢁ
port8–11) and NMR measurements of LaFe1ꢀyCoyAsO1ꢀxFx present system.
(x ¼ 0:11).12) One of important results obtained in our
2. Experiments
studies of the symmetry of ꢂ is that the rate of Tc
suppression by the Co doping is much lower than we
Polycrystalline samples of LnFe1ꢀyMyAsO1ꢀxFx (Ln ¼
expected for superconductors with node(s) of ꢂ. It is also La and Nd; M ¼ Co and Mn; x is nominal and fixed at 0.11
true even for superconductors without nodes on each Fermi except for samples used in the NMR studies.) were prepared
014710-1

J. Phys. Soc. Jpn., Vol. 79, No. 1
M. SATO et al.
4.4
8.64
NdFe1-yMnyAsO0.89F0.11
LaFe1-yMnyAsO0.89F0.11
4.08 (a)
9
(a)
4.2
4
8.8
8.6
8.4
4
8.56
8.48
30
20
10
0
(b)
3.92
LaFe1-yCoyAsO0.89F0.11
NdFe1-yCoyAsO0.89F0.11
-1
-0.5
0
0.5
1
-0.3 -0.2 -0.1
0
y
0.1 0.2 0.3
–y(Mn), y(Co)
4
NdFe1-yMnyAsO1-xFx
10
8
0.20
0.005
0.03
0.20
(b)
(c)
(x=0.11)
LaFe1-yMnyAsO0.89F0.11
0.0025
0.0125
LaFe1-yCoyAsO0.89F0.11
0.03
0.02
0.01
3
2
1
0
0.10
0.10
0.05
6
0.005
0
0.05
0.04
0.0075
0.04
0.05
0.075
0
4
0.1
0.25
0.005
0.2
0
100
200
300
2
0.0025
y=0
T (K)
0.4
0.3
0.5
0
2.5
2
0
100
200
300
0
100
200
300
T (K)
T (K)
(c)
NdFe1-yCoyAsO0.89F0.11
Fig. 1. (Color online) (a) Lattice parameters a and c of LaFe1ꢀyMy-
AsO1ꢀxFx (x ¼ 0:11) system plotted against y and ꢀy values for M ¼ Co
and M ¼ Mn, respectively. (b, c) Electrical resistivities ꢀ of the Mn- and
Co-doped samples, respectively, shown against T, where the y value of
each sample is attached to the corresponding data curve.
1.5
1
0.03
0.05
0.005
0.02
0.15
0.2
0.1
0.01
0.5
0
0.0075
0
0
from initial mixtures of Ln, Ln2O3, LnF3, FeAs, and MAs at
nominal molar ratios.9–11) MAs powders were obtained by
annealing mixtures of M and As in an evacuated quartz
ampoule at 850 ꢃC. (Hereafter, we use the nominal values of
x and y.) Details of the preparations and characterizations are
given in our previous papers.9,10) The X-ray powder patterns
were taken with Cu Kꢂ radiation for 7 s at each scattering
0
100
200
300
T (K)
Fig. 2. (Color online) Similar to Figs. 1(a)–1(c) for NdFe1ꢀyMyAsO1ꢀxFx
(M ¼ Co and/or Mn and x ¼ 0:11).
angle 2ꢃ at a step of 0.01ꢃ, where we found that the M atom specific heat jump ꢂC at Tc and simply assuming the
doping had been successfully carried out [see the y relation ꢂC ¼ 1:43ꢁ. For other detailed data of the samples,
dependence of the lattice parameters shown in Figs. 1(a) see our previous papers.9–11)
and 2(a)]. The superconducting diamagnetic moments were
The 75As-NMR measurements were carried out for
measured using a Quantum Design SQUID magnetometer samples of La 1111 with various F concentrations x by the
with the magnetic field H of 10 G under both zero-field- standard coherent pulse method,12) where the spectra were
cooling (ZFC) and field-cooling (FC) conditions. From the measured by recording the integrated spin–echo intensity I
data of the electrical resistivities ꢀ and diamagnetic mo- with a stepwise change in the NMR frequency f or the
ments, the Tc values were determined as described previ- applied magnetic field H. The spectra can be understood
ously.9–11) The Tc values from the two kinds of data agree using the quadrupole frequency ꢄQ ¼ 10:16 MHz for y ¼ 0.
reasonably well for almost all the samples with the nominal In the study of the 75As-NMR 1=T1, the recovery curves
x of 0.11, but for the series of samples used in the studies were obtained by plotting the integrated intensity at the peak
ꢂ
of the NMR 1=T1 in the x region 0:11 ꢄ x ꢄ 0:2, we have position of the I–f curves ( f 51:04 MHz and H ¼ 6:94 T
¼
ꢂ
found that the Tc values determined by the resistivity or f 44:26 MHz and H ¼ 6:005 T) against the time t
¼
measurements are slightly higher than those determined by elapsed after the saturation pulse. The peak corresponds to
the measurements of the diamagnetic moments. This differ- the condition of H in the ab plane. (The typical spectral
ence between these two kinds of Tc’s seems to become more shape taken for the sample used here can be found in Fig. 5
significant with increasing x.
of ref. 9, where the peak is indicated by an arrow.)
The Hall coefficients RH of the polycrystalline samples
were measured with a stepwise increase in T under a
magnetic field H of 7 T, where the sample plates were 3.1 Superconducting transition temperatures and
3. Results
rotated around the axis perpendicular to the field, and the
thermoelectric powers S were measured by the methods
electrical resistivities
In Fig. 1(a), the lattice parameters a and c are plotted for
described in refs. 21 and 22. Measurements of the specific the M-atom-doped La 1111 system (LaFe1ꢀyMyAsO1ꢀxFx)
heat of the samples were carried out using a Quantum against y (ꢀy) for M ¼ Co (Mn), and the T dependences
Design PPMS in the T region between 2 and 60 K with a of the electrical resistivities ꢀ of the Mn- and Co-doped
stepwise increase in T. The electronic specific heat coef- samples are shown in Figs. 1(b) and 1(c), respectively,
ficients ꢁ of the samples which exhibit the superconducting where the numerical number attached to each curve indicates
transition were obtained by estimating the magnitudes of the the corresponding y value. Similar figures are shown in
014710-2

J. Phys. Soc. Jpn., Vol. 79, No. 1
M. SATO et al.
0
-50
40
0.5
LaFe1-yMyAsO1-xFx (x=0.11)
0.4
0.3
(a)
M=Mn
M=Co
30
20
10
0
0.2
0.1
0.05
0.0125
-100
(a)
0
-0.05
0
0.05
0.1
LaFe1-yCoyAsO0.89F0.11
–y(Mn), y(Co)
-150
0
0
100
200 300
T (K)
NdFe1-yMyAsO1-xFx
50
40
30
20
10
0
(b)
(x=0.11)
0.7
M=Co
M=Mn
0.2
0.1
0.05
-50
-100
-150
0
-200
-400
0.04
0.7
0.8
0.5
0.005
0
(c)
0.8
0.9
0.0025
(b)
1
LaFe1-yMnyAsO0.89F0.11
0.9
1
LaFe1-yMnyAsO0.89F0.11
0
0
100
200
300
-0.05
0
0.05
0.1
0.15
0
100
200
300
T (K)
–y(Mn), y(Co)
T (K)
Fig. 3. (Color online) Summary of Tc values for RFe1ꢀyMyAsO0:89F0:11
(R ¼ La and Nd; M ¼ Co and Mn) plotted against y and ꢀy for M ¼ Co
and M ¼ Mn, respectively.
Fig. 4. (Color online) T dependences of the thermoelectric powers S
of the samples of LaFe1ꢀyMyAsO1ꢀxFx (x ¼ 0:11) shown for M ¼ Co
(a) and Mn (b). In (c), the selected data in (b) are shown with a different
vertical scale. The y value of each sample is attached to the corresponding
data curve.
Figs. 2(a)–2(c) for the M-atom-doped Nd 1111 system
NdFe1ꢀyMyAsO1ꢀxFx (M ¼ Co and Mn and x ¼ 0:11).
From the data of the lattice parameters, we can find that
the M-atom doping was successful. It can be also found that
y does not deviate significantly from its nominal value,
because the parameter c is linear in the entire y range of 0.0–
1.0, at least for LaFe1ꢀyMnyAsO1ꢀxFx [see Fig. 1(a)].
The resistivity data show that a small amount of the
Mn impurity doped into the host system LnFeAsO1ꢀxFx
(Ln ¼ La and Nd; x ¼ 0:11) induces a significant increase
in low-T resistivity. The result is in contrast to the y
dependence of low-T resistivity (T > Tc) observed for
M ¼ Co: For the Co doping, it first increases with increasing
y, but the rate of increase is much smaller than that for
M ¼ Mn. With further increasing Co concentration y
through ꢂ0:05, low-T resistivity decreases and the system
enter the non-superconducting metallic phase at y ꢂ 0:08 for
Ln ¼ La and at a y value slightly larger than 0.10 for
Ln ¼ Nd. For M ¼ Mn, low-T resistivity monotonically
increases with y, indicating the significant effect of the
electron localization. These behaviors of the resistivities are
discussed in §4.1 to study the impurity effects on Tc in
relation to the symmetry of the order parameter.
0.5
0.4
0
0.1
0.0025
0.03
0
-0.01
0.01
(a)
0
0.005
-0.02
H=7 T
LaFe1-yCoyAsO0.89F0.11
0
100
200
0
300
T (K)
0
-0.01
-0.02
0.2
0.2
0.02
0.1
0.1
0
0.05
H=7 T
0.005
0
0.02
-0.01
0.03
(b)
(c)
-0.02
H=7 T
NdFe1-yMnyAsO0.89F0.11
NdFe1-yCoyAsO0.89F0.11
0.04
0
100
200
300
0
100
200
300
T (K)
T (K)
Fig. 5. (Color online) Hall coefficients RH of LaFe1ꢀyCoyAsO1ꢀxFx (a),
and NdFe1ꢀyMyAsO1ꢀxFx with M ¼ Co (b) and Mn (c) shown against T.
The y value of each sample is attached to the corresponding data curve.
The Tc values are summarized in Figs. 3(a) and 3(b).
From these figures, the values of the initial suppression rate
jdTc=dyj for LaFe1ꢀyMyAsO1ꢀxFx (x ¼ 0:11) are estimated
to be ꢂ2:5 and 55 K/% for M ¼ Co and Mn, respectively. the samples of LaFe1ꢀyMyAsO1ꢀxFx (x ¼ 0:11) are shown
Those for NdFe1ꢀyMyAsO1ꢀxFx are ꢂ2:9 and 9 K/% for in Fig. 4(a) for M ¼ Co and in Figs. 4(b) and 4(c) for
M ¼ Co and Mn, respectively. It is remarkable that the Tc- M ¼ Mn. Similar data of the Hall coefficient RH of
suppression rates of Co and Mn impurities are very different. LaFe1ꢀyCoyAsO1ꢀxFx (x ¼ 0:11) are shown in Fig. 5(a),
and those of NdFe1ꢀyMyAsO1ꢀxFx are shown in Figs. 5(b)
3.2 Thermoelectric powers and Hall coefficients of
LnFe1ꢀyMyAsO1ꢀxFx (Ln ¼ La, Nd; M ¼ Co, Mn;
x ¼ 0:11)
and 5(c) for M ¼ Co and Mn, respectively. From the figures,
we can see that both S and RH exhibit anomalous T
dependences, particularly in the superconducting y region,
The T dependences of the thermoelectric powers S of similar to those observed in high-Tc Cu oxides,21,22) although
014710-3

J. Phys. Soc. Jpn., Vol. 79, No. 1
M. SATO et al.
500
400
300
200
100
0
0
LaFe1-yCoyAsO0.89F0.11
[+100]
(a)
(a)
y=0.005
[+150]
y=0.03
-50
[+200]
y=0.05
La 1111 Co-doped
-100
[+50]
y=0.0025
La 1111 Mn-doped
La 1111 Non doped
Nd 1111 Co-doped
Nd 1111 Mn-doped
Nd 1111 Non doped
y=0
0
10
20
30
40
-150
T (K)
-0.6 -0.4 -0.2
0
0.2 0.4 0.6
150
100
50
150
x–y(Mn), x+y(Co)
LaFe1-yCoyAsO0.89F0.11
LaFe1-yMnyAsO0.89F0.11
(b)
(c)
0.04
0.05
0
-0.004
-0.008
-0.012
-0.016
100
50
0.8
0.2
1.0
0.7
0.5
0.02
(b)
0.3
0.1
0.0025
0
0
0
0
100
200
300
400
100
200
300
400
T
2 (K2)
T
2 (K2)
La 1111 Co-doped
La 1111 Mn-doped
La 1111 Non doped
Nd 1111 Co-doped
Nd 1111 Mn-doped
Nd 1111 Non doped
Fig. 7. (Color online) (a) Specific heat divided by T plotted against T for
various superconducting samples of LaFe1ꢀyCoyAsO1ꢀxFx (x ¼ 0:11).
Anomalies can be observed at Tc. (b) Data of C=T plotted against T2 for
selected values of y of the non-superconducting metallic samples of
LaFe1ꢀyCoyAsO1ꢀxFx (x ¼ 0:11). (c) C=T plotted against T2 for the
samples of LaFe1ꢀyMnyAsO1ꢀxFx (x ¼ 0:11). In all the figures (a)–(c),
the y value of each sample is attached to the corresponding data curve.
-0.6 -0.4 -0.2
0
0.2 0.4 0.6
x-y(Mn), x+y(Co)
Fig. 6. (Color online) Thermoelectric powers S (a) and the Hall coef-
ficients RH (b) of LnFe1ꢀyMyAsO1ꢀxFx (Ln ¼ La and Nd; M ¼ Co and
Mn; x ¼ 0:11) shown against x þ y and x ꢀ y at 100 K for M ¼ Co and
Mn, respectively. The dip structures are evident in both panels, showing
the anomalous nature of the transport properties of the system in the
narrow range of carrier concentrations.
relation ꢂC=Tc ¼ 1:43ꢁ. For the non-superconducting sam-
ples, the ꢁ values were roughly determined as the value at
T ! 0 from the data shown in Figs. 7(b) and 7(c), because
the linear relationship between C=T and T2 is not apparent
the anomalous behaviors of RH of NdFe1ꢀyMyAsO1ꢀxFx owing to the magnetically active nature of the systems.
(M ¼ Co and Mn) are less significant than that of (Only for the Co-doped sample with y ¼ 0:7 and the Mn-
LaFe1ꢀyCoyAsO1ꢀxFx. The results indicate that the system doped sample with y ¼ 0:05, we estimated the ꢁ values by
is magnetically active, similarly to the superconducting Cu neglecting the low-T upturn of the specific heat observed as
oxides.23) In Figs. 6(a) and 6(b), the thermoelectric powers S T decreases.) The ꢁ values thus obtained are plotted in
and Hall coefficients RH of LnFe1ꢀyMyAsO1ꢀxFx (Ln ¼ La Fig. 8(b) against y (ꢀy) for the Co (Mn) impurities. (Again,
and Nd) at 100 K are plotted against (x þ y) for M ¼ Co the values of 0:11 þ y and 0:11 ꢀ y correspond to the
and against (x ꢀ y) for M ¼ Mn, where the values on the numbers of electrons in the Co- and Mn-doped systems,
horizontal axes correspond to the numbers of electrons of respectively. In Fig. 8(c), the calculated data of the
24)
the systems from the value of the nondoped system of electronic density of states NðEÞ are shown, for compar-
LnFeAsO. (We will show later that, at least for the Co-doped ison, against the electron energy E, where the Fermi energy
system, the rigid band picture can be applied reasonably (EF) of LaFeAsO is located at E ¼ 0 and EF of LaCoAsO is
well.) Anomalous dips appear in the range of the number of at the position indicated by the arrow. By comparing the
electrons between ꢂ0:05 and ꢂ0:2. This range essentially characteristic structures of the calculated NðEÞ and the
corresponds to the superconducting x region1) of LnFe- observed ꢁ, we find that the rigid band picture is essentially
AsO1ꢀxFx.
applicable to the system, as noted above.
3.3 Specific heat of LaFe1ꢀyMyAsO1ꢀxFx (M ¼ Co, Mn;
x ¼ 0:11)
3.4 T dependence of 75As-NMR 1=T1 for
LaFe1ꢀyCoyAsO1ꢀxFx (x ¼ 0:11)
Figures 7(a) and 7(b) show several examples of the
Figure 9 shows the T dependence of the 75As-NMR
specific heat (C) data obtained for LaFe1ꢀyCoyAsO1ꢀxFx longitudinal relaxation rates obtained here for several
(x ¼ 0:11). Similar plots are also shown for the samples samples of LaFe1ꢀyCoyAsO1ꢀxFx (x ¼ 0:11) with Tc ꢅ
of LaFe1ꢀyMnyAsO1ꢀxFx (x ¼ 0:11) in Fig. 7(c). In these 26 K. As we reported previously,12) the relation 1=T1 / T6
figures, the numerical number attached to each curve can be observed in the T range between ꢂ0:4Tc and Tc,
indicates the corresponding y value. In Fig. 7(a), we can which is in contrast to the relation 1=T1 / T2:5{3:0 reported
see anomalies at Tc. From the anomalies, we roughly by many groups.13–17) We note here that the former relation
estimated the jump magnitudes ꢂC of the specific heat at Tc, is observed for the samples irrespective of whether the rather
as shown in Fig. 8(a). Then, the electronic specific heat rapid decrease slightly above Tc (from ꢂ40 K) is observed
coefficients ꢁ were calculated by simply assuming the with decreasing T.12) T6-like behavior has also been
014710-4

J. Phys. Soc. Jpn., Vol. 79, No. 1
M. SATO et al.
LaFe1-yMyAsO0.89F0.11 (M=Co, Mn)
LaFeAsO0.89F0.11(28K)
LaFeAsO0.89F0.11(26K)
LaFe0.925Co0.0075AsO0.89F0.11
(22.6K)
350
300
250
200
150
10
10
1
LaFeAsO0.89F0.11
Singh et al.
(c)
(a)
8
Tc
6
0.3
0.1
Δ
C/Tc
4
0.2
0.1
0
T 3
0.01
0.001
0.0001
2
0
20
24
28
32
36
-2
-1
0
1
2
T 6
T (K)
E (eV)
0
100
T(K)
200
30
25
20
15
10
5
0.1
1
10
(b)
T/Tc
Tc=27 K
super
Fig. 9. (Color online) T dependence of the 75As-NMR longitudinal
relaxation rates of several samples of LaFe1ꢀyCoyAsO1ꢀxFx (x ¼ 0:11).
As we reported previously,12) the relation 1=T1 / T6 can be observed in
the T region between ꢂ0:4Tc and Tc. The inset shows the data plotted
with linear scales.
25.5 K
25 K
Non-super metal
21.5 K
16 K
Mn-
doped
Co-doped
our measurements. We propose, in the next section, that the
smaller exponent n of the relation 1=T1 / Tn is caused by
the spatial inhomogeneity of Tc or superconducting gap, by
presenting additional data of n obtained for various samples
of LaFeAsO1ꢀxFx with different x values or electron
concentrations.
0
-0.2
0
0.2
0.4
0.6
0.8
1
–y(Mn), y(Co)
Fig. 8. (Color online) (a) Jump magnitudes of the electronic specific heat
divided by T, ꢂC=T, of LaFe1ꢀyCoyAsO1ꢀxFx at Tc estimated for the
superconducting samples. (b) Electronic specific heat coefficients ꢁ of
LaFe1ꢀyMyAsO1ꢀxFx shown against y and ꢀy for M ¼ Co and Mn,
respectively. The ꢁ values were roughly estimated for the superconduct-
ing samples by simply assuming the BCS relation ꢂC=Tc ¼ 1:43ꢁ. Those
of the non-superconducting metallic samples were determined as the
values at T ! 0. For M ¼ Co and y ¼ 0:7, and for M ¼ Mn and
y ¼ 0:05, the extrapolated values from the T region above 50 K are used.
(c) Electronic density of states calculated for LaFeAsO23) shown as a
function of electron energy. The arrow indicates the Fermi level of
LaCoAsO. From these figures, we can see that the rigid band picture
works reasonably well.
4. Discussion
4.1 Effects of Impurities on Tc and characteristics of the
transport properties
In §3.1–§3.3, effects of Co and Mn doping into
LnFeAsO1ꢀxFx (x ¼ 0:11) on various quantities were pre-
sented for Ln ¼ La and Nd, where we found an anomalous T
dependence of the transport quantities. We also found that
the rigid band picture can be applied to the doped systems
reasonably well. Regarding the anomalous nature of the
observed in refs. 20 and 25 for Ba1ꢀxKxFe2As2 samples. transport quantities, we have already pointed out11) for
We also note that the 1=T1 observed in our study for LaFe1ꢀyCoyAsO1ꢀxFx (x ¼ 0:11) that a clear change exists
BaFe1:8Co0:2As2 (not shown) has an almost identical T
dependence to that reported by Ning et al.26) It exhibits T3{4
like behavior slightly below Tc.
To explain the T2:5{3:0 dependence of 1=T1 by the S
in the transport behaviors with increasing y or number of
electrons ðx þ yÞ ¼ ð0:11 þ yÞ doped into LaFeAsO from the
superconducting region to the nonsuperconducting metallic
region, and that the anomalous T dependences of the
-
ꢁ
symmetry, Parker et al.18) introduced the effects of the thermoelectric powers S and Hall coefficients RH, reminis-
intermediate scattering centers, which induce the energy cent of those of high-Tc Cu oxides,21,22) are significant in the
levels within the superconducting gap. Yashima et al.20) also superconducting region of (x þ y) (we call this phase the
considered the S symmetry of the superconducting order ‘‘anomalous metal’’ phase). In the present work, we found
ꢁ
parameter with the gap anisotropy or the existence of two that there exist similar anomalous T dependences in all
different gaps on two disconnected Fermi surfaces around the systems shown in §3.1 and §3.2. They are particularly
the ꢁ and M points as an intrinsic feature of the system. significant for the number of electrons, corresponding to the
However, as we pointed out in our previous paper,12) the superconducting region (ꢂ0:05 ꢄ x ꢄ ꢂ0:2) of LaFeAs-
former consideration cannot explain why the two distinct T
O1ꢀxFx. This feature can be clearly seen as anomalous dip
dependences have been observed even for a sample with structures in the S–y and RH–y curves respectively shown
almost equal Tc values,15) because the Tc values of samples in Figs. 6(a) and 6(b) at 100 K for LaFe1ꢀyMyAsO1ꢀxFx
with intermediate scatterers should be significantly lower (M ¼ Co and Mn; x ¼ 0:11). They indicate that the
for the S symmetry than those of samples without such electronic state in the dip region [0:11 ꢄ ðx þ yÞ ꢄ ꢂ0:2
ꢁ
scattering centers. The latter idea cannot explain the for M ¼ Co, and ꢂ0:05 ꢄ ðx ꢀ yÞ for M ¼ Mn] is different
existence of the two distinct T dependences itself, because from those in the other regions of y. This point will be
the anisotropy or the existence of two distinct gaps is the clarified after the discussion presented below.
intrinsic feature of the system, the T2:5{3:0 dependences
The anomalous transport behaviors described above and a
should be observed for all samples including those used in possible origin of the anomalous dips observed in Figs. 6(a)
014710-5

J. Phys. Soc. Jpn., Vol. 79, No. 1
M. SATO et al.
and 6(b) can be understood as described below. Here, we
adopt the rigid band picture, which has been found, as
already shown above, to be applicable to the present system.
First, we consider the Co doping, that is, ðx þ yÞ ꢅ 0:11. In
this case, the number of electrons donated by F and Co
atoms into LnFeAsO is (x þ y), and these electrons bury the
hole pockets around the ꢁ point in the reciprocal space,
causing the disappearance (or reduction) of the hole-Fermi-
surfaces around ꢁ. Owing to this disappearance of the hole
Fermi surfaces with a heavy effective mass,24) the strong
magnetic fluctuations of this Fermi surface disappear,
allowing the electrons around the M point to move without
being subjected to the scattering by such magnetic fluctua-
tions. Judging from the data in Figs. 6(a) and 6(b), this
change takes place at ðx þ yÞ ꢂ 0:2, and the transport
properties become ordinary ones as in the case of high-Tc
Cu oxides. (In high-Tc Cu oxides, the anomalous transport
behavior diminishes as the number of hole carriers doped
into the Mott insulating state increases and the magnetic
fluctuation is weakened by the holes.23)) This consideration
is supported by the specific heat data shown in Fig. 8(b),
where the minimum ꢁ or NðEÞ appears at y ꢂ 0:1 or ðx þ
yÞ ꢂ 0:2 with increasing y or E, indicating that the hole
Fermi surfaces disappear at this concentration. The coinci-
dence of this concentration with that of the upper edge of the
dips of the curves in Figs. 6(a) and 6(b) suggests that for the
dip structure, the existence of the hole Fermi surfaces is
important. Because the superconductivity seems to occur
within the region of the anomalous dips, we think that the
existence of the hole Fermi surfaces is also important for the
occurrence of the superconductivity.
60
40
20
0
NdFe1-yCoyAsO0.89F0.11, ρ(51K)
(a)
(b)
NdFe1-yMnyAsO0.89F0.11, ρ(51K)
LaFe1-yCoyAsO0.89F0.11 ρ(30K)
LaFe1-yMnyAsO0.89F0.11, ρ(30K)
LaFeAsO0.9F0.1
neutron irradiation
ρ(40K)
Karkin et al.
0
1
2
3
4
5
6
ρ (mΩ·cm)
60
40
20
NdFe1-yCoyAsO0.89F0.11, ρ(51K)
0.01
0
0.05
LaFe1-yCoyAsO0.89F0.11 ρ(50K)
0.03
0.05
0.1
0.1
0.2
0.3-0.5
0.15
0.075
0
0
1
2
3
4
5
6
ρ (mΩ·cm)
Fig. 10. (Color online) (a) Tc values plotted against the electrical resis-
tivities ꢀ for LaFe1ꢀyMyAsO1ꢀxFx and NdFe1ꢀyMyAsO1ꢀxFx (M ¼ Co
and Mn) at the temperatures indicated in the figure. Data for samples
of LaFe1ꢀyCoyAsO1ꢀxFx with the F concentration x smaller than the
nominal value (¼ 0:11) are included. The data of Karkin et al.27) are also
shown. (b) Tc values plotted against the resistivities obtained at the
To consider the case of Mn doping, that is, for
ðx ꢀ yÞ ꢄ 0:11, we briefly discuss the data of the electrical
resistivities ꢀ shown in Figs. 10(a) and 10(b) obtained for
LnFe1ꢀyMyAsO1ꢀxFx (Ln ¼ La and Nd; M ¼ Co and Mn)
at the temperatures indicated in the figures. In Fig. 10(a),
data are intentionally included for samples of LaFe1ꢀyCoy-
temperatures indicated in the figure for the samples of LaFe1ꢀy
-
CoyAsO1ꢀxFx and NdFe1ꢀyCoyAsO1ꢀxFx in the region near the boundary
between the superconducting (y < yc) and the non-superconducting
metallic (y > yc) phases. The y values are attached to the data points.
AsO1ꢀxFx in which the actual F concentrations are appreci- prepared under high-pressure syntheses often have smaller
ably smaller than the nominal value (¼ 0:11), and therefore resistivities than those synthesized by ordinary preparation
their resistivities are larger than those of the samples without processes.28) possibly because of the difference between the
the reduction in x from its nominal value. It is interesting grain boundary effects.) Here, in the analyses of the data
that the Tc values of each series of samples in the figure are plotted in Fig. 10(a), we estimate the in-plane resistivity
almost on a single line. [We here note the following. The expected for single crystals by multiplying the observed
deviation of x from its nominal value to the lower value-side values of ꢀ by a factor of ꢂ1=4 to roughly remove grain
can be distinguished as deviations of the resistivities and boundary and anisotropy effects, obtaining a critical in-plane
lattice parameters c towards the larger-value side and the Tc resistivity of 0.75 mꢀꢆcm, which corresponds to a sheet
value towards the lower-value side. These types of deviation resistance R ¼ 8:6 kꢀ (close to the value of 6:45 kꢀ ¼
Ã
cannot be explained by the change in y, because with h=4e2, the inverse of the minimum metallic conductivity).
increasing (decreasing) y in the region y < 0:05, resistivity The existence of the common critical resistivity ꢀ roughly
increases (decreases), and Tc and c decrease (increase). The equal to the minimum metallic conductivity 4e2=h suggests
effects of the deviation of x are not so significant for that the loss of the metallic nature (or the electron
NdFe1ꢀyMyAsO1ꢀxFx (M ¼ Co or Mn and x ¼ 0:11).] We localization) is the origin of the disappearance of Tc,
also included the data reported by Karkin et al.27) for a as has also been known for the Cu-oxide system: For
sample whose lattice defect density was controlled by Bi2Sr2YxCa1ꢀxCu2O8, Tc disappears when R exceeds 8 kꢀ
Ã
successive heat treatments after neutron irradiation without (ꢂh=4e2), even though the resistivity upturn is not so
changing the carrier number density. From the figure, we significant with decreasing T.29) This idea is supported by
find that the superconductivity disappears approximately the the observation that Tc vanishes at ꢀ ꢂ 0:5 mꢀꢆcm30) (or
common value of the critical resistivity of ꢂ3 mꢀꢆcm. (The
R
ꢂ 7:7 kꢀ) for single crystals of Ba(Fe1ꢀxCox)2As2.
Ã
absolute values of the resistivity of polycrystalline samples
may not have a very strict significance, because they depend cause the doping induces a significant increase of the resistiv-
For LnFe1ꢀyMnyAsO1ꢀxFx (x ¼ 0:11; x ꢀ y < 0:11), be-
on the preparation conditions. For example, samples ity, the zero Tc is realized, as will be shown later, with the
014710-6

J. Phys. Soc. Jpn., Vol. 79, No. 1
M. SATO et al.
3
2
1
0
loss of the metallic nature. The anomalous transport behav-
iors also disappear along with the loss of the itinerant nature.
Now, two mechanisms have been found to be relevant
to the disappearance of Tc in the Co- and Mn-doped
LnFeAsO1ꢀxFx (x ¼ 0:11) system: One is the electron
LaFe1-yMnyAsO1-xFx
(x =0.11)
LaFe1-yCoyAsO1-xFx
4
3
2
1
0
(a)
(c)
(x =0.11)
localization, which appears when the sheet resistance R
Ã
0
0.02
0.04
0.06
0
0.05
0.15 0.2 0.25
0.1y
exceeds h=4e2 ¼ 6:45 kꢀ, and the other is the disappearance
(or reduction in area) of the hole Fermi surfaces around the ꢁ
point, which have strong magnetic fluctuations and essential
for the appearance of the anomalous metallic phase. [In
Fig. 10(b), it is clearly observed that with increasing Co
concentration y, the low temperature resistivity becomes very
small, indicating that the system goes out of the anomalous
metallic phase and enter the nonsuperconducting metallic
phase, due to the disappearance of the hole Fermi surface
around the ꢁ point.] There is no experimental evidence for
the existence of pair breaking or strong Tc suppression of Co
y
NdFe1-yCoyAsO1-xFx
4
3
2
1
0
NdFe1-yMnyAsO1-xFx
1.5
1
(b)
(d)
(x =0.11)
(x =0.11)
0.5
0
0
0.05 0.1 0.15 0.2 0.25
0
0.02
0.04
0.06
y
y
ρ ∝(1/n)× (1/τm + 1/τCo)
3
2
1
0
1/τm: magnetic fluctuation
(e)
ordinary metal
impurities expected for S symmetry superconductors.
ꢁ
1/τCo: scatt. by Co
Here, assuming that pair breaking by impurity scattering
exists in the present system, we estimate the pair-breaking
parameter ꢂ. First, we show in Figs. 11(a)–11(d) the y
dependences of the residual resistivities of LnFe1ꢀyMy-
AsO1ꢀxFx (Ln ¼ La or Nd; M ¼ Co or Mn; x ¼ 0:11), which
were obtained by the extrapolation of the ꢀ–T curve to T ¼ 0
from the T region where the electron localization or
resistivity upturn with decreasing T is not appreciable. From
the figure, we find that the initial rate of resistivity increase
with y is at least ꢂ0:3 mꢀꢆcm/% for polycrystal samples of
LaFe1ꢀyCoyAsO1ꢀxFx (x ¼ 0:11). To estimate the impurity
scattering rate 1=ꢅ of the electrons, we consider that the
resistivities of single-crystal samples are, as stated above,
smaller than those of polycrystals by a factor of ꢂ4, and other
parameters are estimated as follows. For the estimation of the
carrier number n at y ¼ 0, we have adopted an RH value of
7 ꢇ 10ꢀ3 cm3/C at a rather high temperature of 200 K to
avoid the effect of the anomalous increase in RH with
decreasing T induced by the magnetically active nature of
the system (regarding this point, see the discussion in ref. 24
electron
localization
0
0.1
0.2
0.3
0.4
x + y (%)
y (%)
Fig. 11. (Color online) (a)–(d) Residual resistivities ꢀ of LnFe1ꢀyMy-
AsO1ꢀxFx (Ln ¼ La and Nd; M ¼ Co and Mn; x ¼ 0:11) plotted against
y. They are obtained by extrapolating the ꢀ–T curve to T ¼ 0 from the T
region where the resistivity upturn with decreasing T is not appreciable.
The initial rate of increase in ꢀ with y can be estimated using the broken
lines for the Co doping. (e) Schematic behavior of residual resistivity
shown for LaFe1ꢀyCoyAsO1ꢀxFx against (x þ y). In the figure, the (x þ y)
dependence of the rates of scattering by the doped Co atoms, 1=ꢅCo
,
and magnetic fluctuations, 1=ꢅm, are shown schematically, where their
relative magnitudes have no significance. The superconducting region of
LaFe1ꢀyCoyAsO1ꢀxFx is shaded. The region x < 0:11 corresponds to a F
concentration smaller than the nominal value, or to (x ꢀ y) used for Mn
doping.
For NdFe1ꢀyCoyAsO1ꢀxFx, the initial rate of resistivity
for Cu-oxide systems). Then, on the assumption that RH is increase with y is at least ꢂ0:18 mꢀꢆcm/% for polycrystal
determined at this temperature by electron carriers with a samples. Using an n value of 1:2 ꢇ 1021/cm3, similarly
lighter mass than that in the hole bands, n ꢂ 0:9 ꢇ 1021/cm3 obtained to the case of LaFe1ꢀyCoyAsO1ꢀxFx, we can
has been obtained, consistent with the result of the band estimate the pair-breaking parameter ꢂ [¼ h=ð2ꢆk T ꢅÞ;
ꢃ
B
c0
calculation.24) The ab plane effective mass mꢈ is considered Tc0 ¼ 50 K in this case], as for the LaFe1ꢀyCoyAsO1ꢀxFx
to be equal to the free electron mass m, which can also be samples, to be 0.39 at y ¼ 0:01. This result indicates that
deduced approximately by the band calculation.24) Then, a very small amount of Co (less than 1%) completely
using the relation 1=ꢀ ¼ mꢈ=ðne2ꢅÞ, we simply estimate the suppresses the superconductivity, if the pair-breaking effect
electron scattering time ꢅ, and the pair breaking-parameter by nonmagnetic scattering exists. We presume that detailed
ꢂ ¼ h=ð2ꢆk T ꢅÞ, which appears in the following well- considerations of the coexistence of the hole and electron
ꢃ
known equation for determining the Tc value for the S
symmetry in the presence of nonmagnetic impurities:
B
c0
Fermi surfaces may change the magnitude of the pair
breaking by a certain factor. We may also have to consider
other ambiguities introduced in the estimation of the
parameters used in the above analyses. However, it is not
easy to explain the observed small effect of Co doping on
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ ꢁ
Tc0
Tc
1
2
ꢂ
1
ln
¼
þ
ꢀ
;
2t
2
where ðzÞ is the digamma function defined as ðzÞ ꢉ Tc. Therefore, we think the pair-breaking effect of the
ln½dꢁðzÞ=dz=ꢁðzÞꢊ, Tc0 is the superconducting Tc of the nonmagnetic impurities does not have a primary role in
nondoped system (ꢂ28 K for LaFeAsO1ꢀxFx) and t ¼ Tc=Tc0. Tc suppression. This conclusion can also be obtained
Numerically, ꢂ is estimated from the residual resistivity from the data reported by Karkin et al.27) for a neutron-
shown above to be 0.84 at y ¼ 0:01. (Note that Tc becomes irradiated sample, where no change in the number of
ꢂ
zero at ꢂ 0:28). The initial slope dT =dy is about ꢀ60 electrons takes place. (In their case, the 0.9 mꢀꢆcm change
¼
c
K/%, much steeper than the observed slope of about ꢀ2:5 of the residual resistivity induces the Tc change of only less
K/%.
than 2 K.)
014710-7

J. Phys. Soc. Jpn., Vol. 79, No. 1
M. SATO et al.
Upon doping with Mn, the electron localization becomes
significant at low temperatures at the very small doping
level, and the superconductivity disappears owing to the loss
of the itinerant nature. Figure 11(e) shows the schematic
60
50
40
30
20
10
0
Sm
Nd
Pr
Ce
behavior of residual resistivity against (x þ y) for LaFe1ꢀy
-
CoyAsO1ꢀxFx. In the figure, the qualitative (x þ y) depend-
ences of the rates of scattering by the doped Co atoms,
1=ꢅCo, and magnetic fluctuations, 1=ꢅm, are also shown
(1=ꢅm approaches zero as T approaches zero. Although the
absolute value of 1=ꢅm has no significance, the (x þ y) or
(x ꢀ y) dependence can be presumed from the NMR 1=T1
data12,31)). Even when y is increased, resistivity does not
reach the critical value of ꢀc ꢂ 3 mꢀꢆcm (or the critical
La
60
60
40
20
0
NdFeAsO0.89F0.11
Nd
Pr
40
20
0
LaFeAsO0.89F0.11
La
8.72c (Å)8.74
8.52
8.58 8.7
8.76
8.54c (Å)8.56
sheet resistances R ¼ 6:45 kꢀ) for LaFe1ꢀyCoyAsO1ꢀxFx
8.4
8.5
8.6
8.7
8.8
Ã
c-axis length (Å)
(x ¼ 0:11) and superconductivity remains until the hole
Fermi surface around the ꢁ point in the reciprocal space
exhibits a significant reduction.
Fig. 12. (Color online) Maximum Tc values of LnFeAsO1ꢀꢇ obtained by
changing ꢇ32) are shown by open circles for various rare-earth elements
Ln. The Tc values of LaFeAsO1ꢀxFx and NdFeAsO1ꢀxFx obtained for the
samples prepared here starting from the nominal x value of 0.11 are also
shown by solid circles for many samples from different batches. They are
very sensitive, particularly LaFeAsO1ꢀxFx, to the lattice parameter c.
Insets show the data with enlarged horizontal axes.
Onari and Kontani32) have pointed out, using a five-band
model, that the Tc suppression by nonmagnetic impurities is
expected to be significant. Recent experimental findings,
showing that various species of impurity atoms such as Rh,
Ni, Ru, and Ir33–37) also induce superconductivity, suggest
that the suppression of the superconductivity by these
impurities is not large. Considering these results, the
insensitivity of the Tc of the present Co-doped system
should be considered seriously in arguing the superconduct-
ing symmetry, although the above arguments seem to
conflict with the data of neutron scattering, which suggest
the existence of the so-called resonance peak expected for
100
10-1
10-2
10-3
10-4
100
10-1
10-2
10-3
10-4
(b)
(a)
~T3
~T3
our data
our data
the S symmetry.38,39) We also note here that, quite recently,
ꢁ
it has been reported40) that ꢂ1:5% Zn doping into the
LaFeAsO0:85 system prepared by the high pressure syntheses
completely suppresses Tc, where the increase of the residual
resistivity by ꢂ0:9 mꢀꢆcm was observed with a slight
resistivity upturn with decreasing T at low T. (The absolute
value is ꢂ1:2 mꢀꢆcm.) Detailed studies are necessary on that
system, too, to clarify which of the localization- or pair-
breaking mechanism can explain the results.
0.1
1
0.1
1
T/Tc
T/Tc
Fig. 13. 1=T1–T curves obtained by fitting calculated results to the
data for our sample of LaFeAsO0:89F0:11 is shown by the thick solid lines.
The thin solid lines were obtained by fitting to the relation 1=T1 / T3.
The calculations have been carried out under the assumption that the
distribution of the order parameter exists (thin solid line) and does not
exist (thick solid line). In (a), the coherence factor for an isotropic order
parameter is considered, and in (b), it is not considered. The BCS type T
dependence is used for the superconducting order parameter. Detailed
parameters are shown in the text.
4.2 On the two distinct 75As-NMR 1=T1 of
LaFe1ꢀyCoyAsO1ꢀxFx (x ¼ 0:11)
As stated in §3.2, the two distinct T dependences have
been observed for the 75As-NMR 1=T1 of LaFeAsO1ꢀxFx
(x ¼ 0:11). Although explanations of the relation 1=T1 /
T2:5{3:0 have been proposed by considering the S -symme- LaFe1ꢀyCoyAsO1ꢀxFx (x ¼ 0:11).10,11) This type of irregular
ꢁ
try,18,20) there exist difficulties in understanding these data y dependence is not so significant for NdFe1ꢀyCoyAsO1ꢀxFx
consistently. To solve these difficulties, we first show (x ¼ 0:11) as compared with that for LaFe1ꢀyCoyAsO1ꢀxFx.
Fig. 12, where the maximum Tc values of LnFeAsO1ꢀꢇ
The above considerations present a clue to answering
reported previously41) are shown against the lattice param- the puzzle of 1=T1, that is, the spatial inhomogeneity or
eter c by open circles for various rare-earth elements Ln. The irregularity of the superconducting Tc or the order parameter
Tc values of LaFeAsO1ꢀxFx and NdFeAsO1ꢀxFx prepared may affect the T dependence of 1=T1. Because the effect is
here starting from the initial x value of 0.11 are also shown not an intrinsic one, it depends on samples used in the
by solid circles for many samples from different batches. measurements, explaining the T dependences reported.
The insets show the data for Ln ¼ La and Nd with the
In Figs. 13(a) and 13(b), results of the trial calculations of
expanded horizontal scales. We can see that Tc depends on 1=T1 with (thin solid line) and without (thick solid line)
the lattice parameter c very sensitively, that is, for a larger c, consideration of the inhomogeneity of the order parameter,
which corresponds to a smaller F concentration, as described are shown. In the former figure, the coherence factor for an
in §4.1,42) Tc is smaller. Detailed structure analyses by the isotropic order parameter is considered, and in the latter, it is
Rietveld method have also given the same results. We think not considered, and can therefore be used for the S
ꢁ
that this change in the F concentration is the origin of symmetry. The BCS-type T dependence is used for the
the irregular y dependence of Tc observed previously for superconducting order parameter ꢂ and its zero T value
014710-8

J. Phys. Soc. Jpn., Vol. 79, No. 1
M. SATO et al.
7
100
10
n
(a)
1/T1 ∝T
our data
ref.31
ref.14
ref.17
ref.15
ref.43
(c) LaFeAsO1-xFx, x=0.15
(Tc(H=0) =20 K)
0.11
0.15
6
5
4
3
2
0.15
20
Tc(H~6T)
0.18
14
1
16
18
22
24
26
28
30
Tc (K)
7
(b)
our data
ref.31
ref.14
ref.17
ref.15
0.1
0.11
6
5
4
3
2
~T 3
0.01
0.001
1/T1 ∝T n
0.15
H ~6 T
0.18
0.1
1
10
100
0
0.2
0.3
0.4
0.5
0.6
0.7
1/T1T(50K) (s-1K-1)
T (K)
Fig. 14. Values of the exponent n obtained from the relation 1=T1 / Tn are plotted against (a) Tc and (b) 1=T1T at 50 K. (c) 1=T1 of the sample of
LaFeAsO1ꢀxFx with x ¼ 0:15 shown against T in the logarithmic scales.
is ꢂ0. In Fig. 13(a), the following parameters are used to
The above arguments are supported by the following data.
obtain the thick solid line: 2ꢂ0=kBTc ¼ 8. The Lorentzian- In Figs. 14(a) and 14(b), the exponent n obtained by fitting
type broadening ꢁ ¼ 0:24ꢂ0 of the quasi-particle energy " is the relation 1=T1 / Tn (ꢂ0:4Tc < T < Tc) to the observed
simply introduced with the cutoff of the quasi-particle data of LaFeAsO1ꢀxFx is plotted against (a) Tc and (b) 1=T1T
density of states Nð"Þ at an energy of 0:9kBTc, below which at 50 K, with x or the number of electrons doped into
Nð"Þ is zero. To obtain the thin solid line of Fig. 13(a), the LaFeAsO being the internal parameter. These data directly
three values of the parameter 2ꢂ0=kBTc ¼ 8, 6.5, and 5 are indicate that the exponent n depends on x. In the figure, our
considered to have equal weights, their broadenings are all own samples are shown by the solid circles and the x values
ꢁ ¼ 0:24ꢂ0, and the cutoff energy is 0:3kBTc. In Fig. 13(b), are attached to the corresponding data points. Other data
the parameters for the thick solid line are as follows: points except the open square correspond to the results
2ꢂ0=kBTc ¼ 6, ꢁ ¼ 0:07ꢂ0, and no cutoff has been intro- reported by other groups14,15,17,31,43) (the open square
duced. To obtain the thin solid line of Fig. 13(b), the three indicates the n of a sample of LaFeAsO1ꢀꢇ
.
15)) The
values of the parameter 2ꢂ0=kBTc ¼ 6, 4, and 2 are assumed 1=T1–T data obtained for x ¼ 0:15 are shown, for example,
to have equal weights, their broadenings are all 0:12ꢂ0, and in Fig. 14(c). Because 1=T1T monotonically depends on the
the cutoff energy is 0:25kBTc. The rather broad distribution number of doped electrons,31) we simply expect that the data
of ꢂ0 or Tc is not unrealistic for the samples, because, as are on a single line in Fig. 14(b). Actually, our data of n are
shown in Fig. 12, Tc very sensitively depends on c or x. on a single line (solid line). However, the data reported by
The inhomogeneity of ꢂ0 or Tc is considered to be more other groups are found to be on a different line (dotted line).
significant for samples with Tc smaller than the maximum As for the plot against Tc, the data points except the open
value, because jdTc=dxj is larger. As we can find from square are on a single line (solid line), even though Tc has a
the Figs. 13(a) and 13(b), the introduction of the simple dome-shaped-dependence on x or the number of electrons
distribution of the order parameter ꢂ can explain the doped into LaFeAsO. The largest n is found to correspond to
difference rather well. The above results are not very the highest Tc or optimal x. This is consistent with the above
different from those expected for anisotropy considerations consideration: At the maximum Tc point, because jdTc=dxj
of the order parameter in the sense that the broadening of ꢂ or jdꢂ0=dxj is smallest, the distribution width of Tc or ꢂ0 is
is introduced. However, our model states that the T6-like also expected to be smallest. We can exclude the difference
behavior of 1=T1 observed in the rather wide T region of the in 2ꢂ0=kBTc among the samples, as the origin of the
superconducting phase from immediately below Tc is the one observed difference of n, because the samples with equal Tc
expected for samples without spatial inhomogeneity. This is values have different n values and because those with equal
in contrast to the models for explaining the relation 1=T1 / 1=T1T (or equal x values) have different n values.
T2:5{3:0 by the effects of intermediate scatterers18) or by the
Finally, we note that our NQR spectra obtained for the
intrinsic distribution of order parameters.20) We add here that sample with the maximum Tc (ꢂ 28 K) show no significant
detailed Rietveld analyses of the samples used in the NMR anomaly that can be considered as the origin of the T6
studies have shown that the structural parameters indicate no dependence of 1=T1, which is different from the T2:5{3:0
deviation from the published data, indicating that there is no dependence reported by other groups. On the basis of the
reason for conceiving the differences between in structural above results, we stress here that the relation 1=T1 / T2:5{3:0
parameters as the origin of the difference in the behaviors cannot be, at least at present, the experimental evidence for
of 1=T1.
the S symmetry of the superconductivity of this system.
ꢁ
014710-9

J. Phys. Soc. Jpn., Vol. 79, No. 1
M. SATO et al.
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5. Summary
Results of the transport studies and data of the specific
heat coefficients ꢁ of LnFe1ꢀyMyAsO1ꢀxFx (Ln ¼ La and
Nd; M ¼ Co and Mn; x ¼ 0:11) have been presented. The
results of the measurements of the 75As-NMR 1=T1 of
LaFe1ꢀyCoyAsO1ꢀxFx have also been presented. The doped
Co atoms are nonmagnetic, and the rate of Tc-suppression
jdTc=dxj by Co atoms has been found to be too small to be
explained by the pair-breaking effect. This result throws
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ꢁ
system. For the present systems, two mechanisms are
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014710-10