Thermoelectric properties of LaFePO1-xFx and LaFeAs1-xFx possibility of the hidden mass enhancement of LaFeAsO1-xFx

Article abstract of DOI:10.1143/JPSJ.80.044704

We investigated thermoelectric properties for polycrystalline oxypnictide LaFePO_1-xF_x and LaFeAs_1-xF_x. The temperature (T) and F-doping dependences of resistivity (ρ) and Seebeck coefficient (S) are quite different between these compounds. In contrast to a monotonic T dependence and an absence of large F-doping dependences of ρ and S for LaFePO_1-xF_x, the S for LaFeAs_1-xF _x for 0 < x ≤ 0.14 take relatively large maximum absolute values of -60 to -150 μV/K around 90-180 K, while the T dependence of ρ dramatically changes and the ρ monotonically decreases with the F-doping, leading to a large power factor of about 37 μW/K² cm at 53K and a dimensinless thermoelectric figure of merit (ZT) of about 0.08 at 110K for LaFeAsO_0.89F_0.11. The non-monotonic behavior of S with the relatively large absolute value and the reported T dependence of Hall coefficient for LaFeAs_1-xF_x seem to evidence an instability of an orbital order accompanying a stripe-typeAF order even in the over F-doping region for LaFeAs_1-xF_x and indicate a possibility of a hidden mass enhancement of LaFeAs_1-xF_x.

Full text of DOI:10.1143/JPSJ.80.044704

Journal of the Physical Society of Japan 80 (2011) 044704
DOI: 10.1143/JPSJ.80.044704
FULL PAPERS
Thermoelectric Properties of LaFePO1ÀxFx and LaFeAsO1ÀxFx
—Possibility of the Hidden Mass Enhancement of LaFeAsO1ÀxFx—
ꢀ
1;2
3
3
3
Tetsuji OKUDA , Wataru HIRATA , Akira TAKEMORI , Shinnosuke SUZUKI ,
Satoshi SAIJO , Shigeki MIYASAKA3;4, and Setsuko TAJIMA
3
3;4
1Department of Nano-Structures and Advanced Materials, Kagoshima University,
1-21-40 Korimoto, Kagohisma 890-0065, Japan
2JST-PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
3Department of Physics, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan
4JST-TRIP, 5, Sanbancho, Chiyoda, Tokyo 113-0034, Japan
(Received October 8, 2010; accepted February 3, 2011; published online March 25, 2011)
We investigated thermoelectric properties for polycrystalline oxypnictide LaFePO1ꢁxFx and LaFeAsO1ꢁxFx. The
temperature (T) and F-doping dependences of resistivity (ꢀ) and Seebeck coefficient (S) are quite different between
these compounds. In contrast to a monotonic T dependence and an absence of large F-doping dependences of ꢀ and S
for LaFePO1ꢁxFx, the S for LaFeAsO1ꢁxFx for 0 < x ꢂ 0:14 take relatively large maximum absolute values of ꢁ60 to
ꢁ150 ꢀV/K around 90–180 K, while the T dependence of ꢀ dramatically changes and the ꢀ monotonically decreases
with the F-doping, leading to a large power factor of about 37 ꢀW/K2 cm at 53 K and a dimensinless thermoelectric
figure of merit (ZT) of about 0.08 at 110 K for LaFeAsO0:89F0:11. The non-monotonic behavior of S with the relatively
large absolute value and the reported T dependence of Hall coefficient for LaFeAsO1ꢁxFx seem to evidence an
instability of an orbital order accompanying a stripe-type AF order even in the over F-doping region for LaFeAsO1ꢁxFx
and indicate a possibility of a hidden mass enhancement of LaFeAsO1ꢁxFx.
KEYWORDS: Oxypnictide, Thermoelectric Property, Orbital Order, Antiferromagnetic Order
ꢃ 0:11 meV and a renormalization by a factor of 2.2, which
1. Introduction
indicate the itinerant ground state rather than the localized
The discovery of superconductivity in oxypnictide (Mott) ground state. On the other hand, the recent optical
LaFeAsO1ꢁxFx with the critical temperature (Tc) of about study9) reported electronic correlations in the metallic
26 K1) has caused great attentions of researchers on the LaFePO with the kinetic energy of the electrons reduced
related iron-pnictides and has led to the further discoveries to half of that predicted by the band theory and proposed that
of various new iron-pnictide superconductors with the the transport even in the most metallic superconducting
isostructures.2) The end compounds of the first iron-pnictide oxypnictide, LaFePO, lies between the itinerant and local
superconductors, LaFePO3) and LaFeAsO,1) have the so- magnetic moment extreme. However, such a quantitative
called 1111 structure, where the conducting FePn (Pn ¼ P agreement has not been observed in LaFeAsO by the ARPES
or As) layeres formed by the edge-sharing FePn4 tetrahe- measurements. The most remarkable discrepancy with the
drons and the insulating LaO layers are alternatively band calculations lies in the cross-shaped Fermi surface near
stacking. In LaFePO and LaFeAsO, the filling of electron the M-point, which is quite different from the small electron
can be controlled by substitutions of F for O1) or by the pocket observed in LaFePO. These results indicate that the
oxygen vacancy.4) Such conducting iron-pnictides having magnetic ordering, spin–orbit interaction, and orthorhombi-
natural super-lattice structures are expected to show a city should be taken into account in order to explain the
good thermoelectric property, as well as a higher Tc electronic structure for LaFeAsO.
superconducting state. Actually, after the discovery of the
superconductivity, some groups reported the relatively large of thermoelectric properties for LaFePO and LaFeAsO
thermoelectric propeties for some 1111 iron-pnictides.5,6)
and discuss an origin of a relatively good thermoelectric
In this paper, we investigate the F-doping dependences
According to the theoretical works,7) the electronic property of LaFeAsO1ꢁxFx by comparing the two systems.
structures near the Fermi energy in the end compounds, We propose that the better thermoelectric property for
LaFePO and LaFeAsO, are quite similar and are consisted of LaFeAsO1ꢁxFx than that for LaFePO1ꢁxFx originates in an
five sheets mainly originating in five-fold degenerated Fe 3d instability of a 3dyz orbital order accompanying an instability
orbitals. However, their realized ground states are quite of the stripe-type AF order and in a hidden mass
different; the former compound shows a transition from a enhancement of LaFeAsO1ꢁxFx.
paramagnetic metallic state to a superconducting state and
2. Experimental Procedure
the latter compound becomes a stripe-type antiferromagnetic
(AF) metallic state at the ground state. According to the
results of the angle-resolved photoemission spectroscopy
Polycrystalline samples of LaFePO1ꢁxFx and LaFeAs-
1ꢁxFx were synthesized by using a two-step solid state
O
(ARPES),8) the electronic structure for LaFePO observed reaction.10) First, LaP and LaAs were prepared by reacting
by the ARPES well agrees with the LDA calculated band La elements and P or As chips in the evacuated silica tubes
dispersion with a shift of the calculated bands up to at 700 ꢄC for 10 h and 850 ꢄC for 15 h, respectively. The
mixtures of LaAs, LaP, dehydrated Fe2O3, Fe and FeF2 were
ꢀE-mail: okuda@eee.kagoshima-u.ac.jp
pressed into pellets, and they were annealed in the evacuated
044704-1
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J. Phys. Soc. Jpn. 80 (2011) 044704
FULL PAPERS
T. OKUDA et al.
2
(a)
LaFePO1-x
(b)
x = 0.02
F
x
10
1.5
1
x = 0.05
LaFeAsO1-x
F
x
ρ
ρ
5
x = 0
x = 0.1
x = 0.03
x = 0.05
x = 0.08
x = 0.1
0.5
0
x = 0.08
x = 0.14
x = 0.11
0
0
100
200
300
0
100
200
300
T (K)
T (K)
Fig. 1. (Color online) Temperature (T) dependences of resistivities (ꢀ) of (a) LaFePO1ꢁxFx and (b) LaFeAsO1ꢁxFx. The results of LaFePO1ꢁxFx for x ¼ 0,
0.03, and 0.05 are from ref. 10.
silica tubes at 1100 ꢄC for 40 h. All procedures were are 1.75 and 1:66 ꢅ 10ꢁ8 ꢀ cm/K2 for x ¼ 0:11 and 0.14,
performed in a highly pure Ar filled grove box. The respectively. Comparing with the previous results,11,12) the ꢀ
resistivity was measured by a standard four probe method for LaFeAsO1ꢁxFx does not seem to systematically change.
and the Seebeck coefficient and thermal conductivity were This is not only because the ꢀ for a polycrystalline
simultaneously measured by a steady state method.
anisotropic compound largely depends on the sample but
also because our polycrystalline samples are not so dense
and include some impurities (especially for the low F-doped
compounds).
3. Results
3.1 Resistivity, Seebeck coefficient, and power factor for
polycrystalline LaFePO1ꢁxFx and LaFeAsO1ꢁxFx
The A=ꢁ2n values deduced by using the reported electronic
Figures 1(a) and 1(b) show the T dependences of re- specific heat coefficients (ꢁn) of the normal state10,13) are
sistivity (ꢀ) of our polycrystalline samples of LaFePO1ꢁxFx 0.226, 0.385, and 0:353 ꢅ 10ꢁ3 ꢀꢀ cm/K2/(mJ/K2 mol)2
and LaFeAsO1ꢁxFx. In LaFePO1ꢁxFx, the end compound of for LaFePO1ꢁxFx for x ¼ 0, 0.03 and 0.05, and are 0.673
LaFePO already shows the low ꢀ of about 1.5 mꢀ cm at and 1:15 ꢅ 10ꢁ3 ꢀꢀ cm/K2/(mJ/K2 mol)2 for LaFeAs-
room temperature and shows the superconducting transition
O1ꢁxFx for x ¼ 0:11 and 0.14. These values are much
at about 5.8 K.10) The low-T ꢀ for LaFePO1ꢁxFx shows the higher than the value of a correlated metal obeyed by the
T2 dependence above Tc, as previously reported. In this Kadowaki–Woods law. It is noted that these values of
compound, the electron doping by the substitution of F for O polycrystalline samples must be overestimated. How-
does not significantly affect the absolute value of ꢀ and the T
ever, since the values of ꢀ for our LaFeAsO0:89F0:11 and
dependences, as shown in Fig. 1(a). Such an absence of the LaFeAsO0:86F0:14 are only a few times larger than those
large change of ꢀ with the F-doping is reported to originate for the high-density samples prepared by a high-pressure
in the absence of the F-doping dependence of structure synthesis technique,12) the deviation from the Kadowaki–
10)
in this compound.10) The observed Tc is 5.8, 7.8, 8.0, 7.8, Woods law is thought to be essential for these oxypnictides.
and 6.2 K, the observed residual resistivity ꢀ0 are about Such a behavior seems to be similar to that of Sr1ꢁxLax-
14)
0.0676, 0.0771, 0.0788, 0.117, and 0.203 mꢀ cm, and the T2 TiO3ꢁꢂ
,
whose ꢀ at the low temperature is also well
coefficients A of ꢀ (¼ ꢀ0 þ AT2) are about 2.31, 2.78, 2.43, proportional to T2 but the A=ꢁ2n values are 927, 11.2, and
3.31, and 3:14 ꢅ 10ꢁ8 ꢀ cm/K2, for x ¼ 0, 0.03, 0.05, 0.08, 1:34 ꢅ 10ꢁ3 ꢀꢀ cm/K2/(mJ/K2 mol)2 for the carrier conce-
and 0.1, respectively.
tration n ¼ 0:0052, 0.022, and 0.061 1/Ti, although the
In contrast to the results of LaFePO1ꢁxFx, the ꢀ for magnetic states are different. These results may indicate that
LaFeAsO1ꢁxFx is much affected by the F-doping. As shown another correlation, such as an electron-phonon coupling or
in the Fig. 1(b), the ꢀ dramatically decreases and the a phonon-mediated electron-electron interaction, is domi-
T-dependence significantly changes with the increase in x. nant at the low temperature in these compounds.
For x ¼ 0 and 0.02, our samples show no superconducting
transition till about 4 K, while for x ꢆ 0:05 the super- Seebeck coefficient (S) for LaFePO1ꢁxFx and LaFeAs-
conducting transitions occur at 14.5, 22.8, 25.2, 22.9, and
1ꢁxFx. As shown in Figs. 2(a) and 2(b), the sign of S are
Figures 2(a) and 2(b) show the T dependences of the
O
12.9 K for x ¼ 0:05, 0.08, 0.1, 0.11, and 0.14, respectively. negative except for the S at the low T for LaFeAsO,
With the increase of x above 0.11, the ꢀ becomes as small as indicating the n-type characteristics of these compounds. As
those of LaFePO1ꢁxFx and becomes to be well fitted to the well as the T dependences of ꢀ, the T dependences of S are
relation that ꢀ ¼ ꢀ0 þ AT2. The residual resistivity ꢀ0 are quite different between two compounds. The observed T
0.0501 and 0.0481 mꢀ cm and the observed T2 coefficients dependence of S for LaFePO is consistent with the previous
044704-2
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J. Phys. Soc. Jpn. 80 (2011) 044704
FULL PAPERS
T. OKUDA et al.
(b)
LaFeAsO1-x
F
x
50
0
T
N T
-50
x = 0
S
-100
0
(a)
LaFePO1-x
F
x
10
-50
0
-10
-20
-30
0
x = 0.02
x = 0.05
-100
0
x = 0
-50
-100
0
-10
-20
-30
0
μ
x = 0.03
-50
-100
0
x = 0.08
x = 0.1
μ
-10
-20
-30
0
x = 0.05
x = 0.08
x = 0.1
-50
-100
0
-10
-20
-30
-50
x = 0.11
x = 0.14
-100
0
0
-10
-20
-30
-50
-100
0
100
200
300
0
100
200
300
T (K)
T (K)
Fig. 2. (Color online) T dependences of Seebeck coefficients (S) of (a) LaFePO1ꢁxFx and (b) LaFeAsO1ꢁxFx.
result;15) the absolute value decreases with the decrease of T
always negative above Tc and the S takes a maximum
from room temperature to about 90 K and shows the broad absolute value (S ꢃ ꢁ150 ꢀV/K) around Ts and TN. Even
peak structure around 40 K. The 3% F-doping slightly if both Ts and TN disappear with the further F-doping,
changes the T dependence; the S becomes to monotonically the maximum absolute values of S remain large, ꢁ60 to
decrease with the decreases of T down to Tc, although it also ꢁ150 ꢀV/K around 90–180 K, in spite of the dramatic
shows the broad peak structure around 40 K. However, as decrease of ꢀ, leading to a large power factor at the low
well as in the case of ꢀ, the further F-doping little changes temperature.
the T dependence of S. The observed broad peak structure
Figures 3(a) and 3(b) show the T dependences of power
around 40 K may be due to the phonon drag effect, as factor (PF ꢇ S2=ꢀ) for LaFePO1ꢁxFx and LaFeAsO1ꢁxFx.
14)
observed in Sr1ꢁxLaxTiO3ꢁꢂ
be discussed, later.
.
Another possible origin will Reflecting the differences of the T and F-doping depen-
dences of ꢀ and S, the T and F-doping dependences of the
On the other hand, the LaFeAsO1ꢁxFx compounds show PF are quite different between two compounds. For the F-
quite different T and F-doping dependences of S from those doped LaFePO, the PF values at room temperature are about
of LaFePO1ꢁxFx. Our result of S for LaFeAsO is also 0.8 ꢀW/K2 cm and are slightly enhanced above Tc. On
consistent with the results reported by some groups.2,6) As the other hand, the PF values for the F-doped LaFeAsO
shown in the Fig. 2(b), the sign of S for LaFeAsO is take broad peak structures around 50–110 K, as shown in
negative at room temperature. The absolute value slightly Fig. 3(b). In this study, the observed maximum PF is about
increases with the decrease of T near a structural transition 37 ꢀW/K2 cm at 53 K for LaFeAsO0:89F0:11, which is
temperature (Ts), and around Ts it starts to largely decrease. comparable to the reported value6) for LaFeAsO0:86
With the further decrease in T, the sign of S changes from
negative to positive just below an AF transition temperature 3.2 Thermal conductivity and dimensionless
.
(TN). These behaviors perhaps originate in the multi-band
nature of the electronic state of LaFeAsO. In contrast to
the case of LaFePO1ꢁxFx, the 2% F-doping dramatically
thermoelectric figure of merit for polycrystalline
LaFePO1ꢁxFx and LaFeAsO1ꢁxFx
Thermal conductivities (ꢃ) for LaFePO1ꢁxFx and
changes the T dependence;2) the sign of S becomes to be LaFeAsO1ꢁxFx are shown in Figs. 4(a) and 4(b) where the
044704-3
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T. OKUDA et al.
(b)
20
10
LaFeAsO1-x
F
x
x = 0.14
(a)
LAFePO1-x
F
x
0
30
20
10
0
0.8
x = 0.1
0.4
0
0.8
x = 0.08
x = 0.05
0.4
x = 0.11
x = 0.1
0
0.8
μ
10
0.4
μ
0
10
0
0.8
x = 0.08
x = 0.05
0
10
x = 0.03
0.4
0
0.8
× 10
× 10
0
10
0.4
x = 0
x = 0.02
0
0
0
100
200
300
0
100
200
300
T (K)
T (K)
Fig. 3. (Color online) T dependences of power factors (PF) of (a) LaFePO1ꢁxFx and (b) LaFeAsO1ꢁxFx.
dotted lines show the electronic contributions (ꢃel) to ꢃ 100–150 K, because of the enhancement of S around 100–
deduced by the Wiedemann-Franz law and the solid lines 150 K in spite of the relatively low ꢀ, as shown in Figs. 2(a)
show ꢃ ꢁ ꢃel. Since our polycrystalline samples are not and 2(b). The observed maximum ZT is 0.08 at 110 K for
so dense, the ꢃ is perhaps largely affected by the grain LaFeAsO0:89F0:11, which is the largest value among the ZT
boundary especially for the low F-doped LaFeAsO1ꢁxFx. values6) ever reported for iron-pnictides.
Therefore, the observed ꢃ values are smaller than the
previous results for the high-density samples.6,12,16)
4. Discussion
As shown in Fig. 4(a), the ꢃ for LaFePO1ꢁxFx are 2–3 4.1 Origin of the T dependences of Seebeck coefficients
W/Km at room temperature and do not show a dramatic
The differences between the ZT values of LaFePO1ꢁxFx
change down to about 50 K. On the other hand, the ꢃ for and LaFeAsO1ꢁxFx mainly come from the differences of the
LaFeAsO shows an abrupt increase at Ts (not at TN), as electronic transport properties such as ꢀ and S as discussed
shown in Fig. 4(b), which is consistent with the previous in x3.1. Such differences of the transport properties
results.6,16) The F-doping blurs the change around Ts and a apparently come from the existence of the AF and structural
distinct anomaly has not been observed for x ꢆ 0:05. For transitions for LaFeAsO1ꢁxFx.2,18) The LaFePO1ꢁxFx com-
x ¼ 0:05, 0.08, and 0.1, the ꢃ dose not show a distinct pounds are in a paramagnetic (PM) state and the structure
T dependence, while, for x ¼ 0:11 and 0.14, it clearly belongs to a tetragonal lattice with a space group of P4=nmm
increases with the decrease of T down to about 50 K. Such below room temperature.15) The lattice parameters little
differences are perhaps due to the ꢃel. Actually, for x ꢆ 0:05, change with the F-doping. Such an absence of the large
the T dependences of ꢃ ꢁ ꢃel do not largely change with the crystallographic change is proposed to cause the small
F-doping, as shown in Fig. 4(b). As previously reported,17) change of Tc and the physical properties for LaFePO1ꢁxFx,10)
for all superconducting compounds in LaFeAsO1ꢁxFx, which is consistent with the absence of the large F-doping
there is no distinct decrease of ꢃ below Tc, although the dependence of S in this study.
simultaneously measured S becomes zero at Tc as shown in
Fig. 2(b).
In contrast to LaFePO1ꢁxFx, the low F-doped LaFeAsO
compounds show the transition from the PM state to the
Figures 5(a) and 5(b) summarize the T dependences stripe-type AF state and the structural transition from a
of dimensionless thermoelectric figure of merits (ZT ꢇ tetragonal lattice with a space group of P4=nmm to an
S2=ꢀꢃ ¼ PF=ꢃ) for LaFePO1ꢁxFx and LaFeAsO1ꢁxFx. As orthorhombic lattice with a space group of Cmma,18) as
shown in Fig. 5(a), the ZT values for LaFePO1ꢁxFx at room shown in Fig. 6(a). According to the previous reports,18) the
temperature are less than 0.009 and monotonically decrease AF transition temperature TN is just below a structural
with the decrease in T down to 100 K. On the other hand, the temperature Ts, and slightly decreases from about 140 K
ZT values for the F-doped LaFeAsO are 0.02–0.08 around to about 120 K with an increase of x. The AF transition
044704-4
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(b)
LaFeAsO1-x
F
x
4
3
2
1
0
3
2
1
0
x = 0.14
(a)
LaFePO1-x
F
3
x
2
1
x = 0.1
-
el
el
x = 0.11
el
0
2
1
el
x = 0.08
2
1
x = 0.1
0
2
1
0
2
x = 0.08
x = 0.05
x = 0.03
x = 0
1
0
2
0
2
1
x = 0.05
x = 0.02
x = 0
1
0
2
T
N
0
1
0
2
2
1
T
S
1
00
100
200
300
0 0
100
200
300
T (K)
T (K)
Fig. 4. (Color online) T dependences of thermal conductivities (ꢃ) of (a) LaFePO1ꢁxFx and (b) LaFeAsO1ꢁxFx. The dotted lines show the electronic
contributions (ꢃel) to ꢃ deduced by the Wiedemann-Franz law and the solid lines show ꢃ ꢁ ꢃel.
(b)
LaFeAsO1-x
F
x
0.06
0.04
0.02
x = 0.14
(a)
LaFePO1-x
F
0.008
0.004
0
0.08
0.06
x
x = 0.1
0
x = 0.11
0.04
0.02
0.008
0.004
x = 0.08
x = 0.05
0
0.04
0
0.008
x = 0.1
0.02
0.004
0
0.04
x = 0.08
0
0.02
0.008
0
0.04
x = 0.03
0.004
x = 0.05
x = 0.02
× 2
× 2
0.02
0
0
0.04
0.008
0.004
0.02
x = 0
00
100
200
300
00
100
200
300
T (K)
T (K)
Fig. 5. (Color online) T dependences of dimensionless figure of merits (ZT) of (a) LaFePO1ꢁxFx and (b) LaFeAsO1ꢁxFx.
044704-5 #2011 The Physical Society of Japan

J. Phys. Soc. Jpn. 80 (2011) 044704
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T. OKUDA et al.
200
-150
(a)
0
-0.1
-0.2
-0.3
LaFePO1-xFx
(a)
LaFeAsO1-xFx
0.15
0.1
0.05
0
TS
P4/nmm
TSmax
150
100
50
μ
-100
-50
0
x = 0
x = 0.03
x = 0.05
x = 0.08
x = 0.1
TN
μ
μ
xz
yz
xz, yz
t
2g
xy
0
100
200
300
Fe
T (K)
3z2-r2
x2-y2
P4/nmm
Tc
e
g
As
(b)
Cmma
SC
0
15
0
100
200
300
T (K)
10
5
5
4
3
2
1
0
LaFeAsO1-xFx
(b)
LaFePO1-xFx
0
x = 0
-1
x = 0.02
x = 0.05
x = 0.08
x = 0.1
x = 0.11
x = 0.14
0
μ
0
0.05
0.1
0.15
F doping x
-2
-3
μ
Fig. 6. (Color online) (a) The F-doping dependences of the structural
(Ts, open circles), AF (TN, open squares), and superconducting (Tc, closed
circles) transition temperatures with that of the maximum S (Smax, closed
squares). The presented Ts, TN, and the structures in the phase diagram are
from ref. 18. The closed downward triangle expresses the temperature
(TSmax) where the S take maximum values. The solid and dotted lines are
guide to eyes. The insets show the expected intermediate spin state
(spin = 1) of Fe2þ ions in the FeAs4 tetrahedrons. (b) The F-doping
dependences of the electronic specific heat coefficient of the normal state
(ꢁn) for LaFePO1ꢁxFx and LaFeAsO1ꢁxFx. The closed diamonds, the
closed downward triangles, and the closed upward triangles show ꢁn for
LaFePO1ꢁxFx reported in refs. 10, 15, and 20, espectively. The close circles
show ꢁn for LaFeAsO1ꢁxFx reported in ref. 13. The chain and dotted lines
are guide to eyes.
LaFeAsO1-xFx
0
100
200
300
T (K)
0
100
200
300
T (K)
3=2
Fig. 7. (Color online) The T dependences of ðjSj=TÞ
for (a) LaFeP-
O
1ꢁxFx and (b) LaFeAsO1ꢁxFx. The insets show the T dependences of S=T
for these compounds.
disappears above x ¼ 0:03, while the structural transition determined by the formal valences and the observed large S
persists till x ¼ 0:05.18) For x ꢆ 0:05, the LaFeAsO1ꢁxFx values for LaFeAsO1ꢁxFx originated in mꢀ, the electronic
compounds are also in the PM metallic state above Tc with a specific heat coefficients (ꢁn) for LaFeAsO1ꢁxFx would be
P4=nmm tetragonal lattice, but the orthorhombic structural larger than those for LaFePO1ꢁxFx corresponding to the S
distortion is reported to be left18) in this regime. Figure 6(a) values, because ꢁn / mꢀn1=3 in the framework. However, as
13)
superposes our results of the maximum S (Smax) on the phase shown in Fig. 6(b), the ꢁn for LaFeAsO1ꢁxFx is smaller
diagram. For x ꢂ 0:03, the S take maximum at TSmax near Ts than that10,15,20) for LaFePO1ꢁxFx, and it monotonically
and TN, while it keeps taking a relatively large maximum decreases with the F-doping although the maximum S (Smax
)
values around 90–180 K after the disappearance of the shows the critical-like behavior around x ꢃ 0:1. Therefore,
structural and AF transitions with the increase of x above if the framework is held, the n must not be determined by
0.05. Comparing the results of LaFePO1ꢁxFx, these results the formal valence. Then, we plot the T dependences of
3=2
strongly suggest that the correlation of AF order and the ðjSj=TÞ
and S=T in Fig. 7 and their insets. It is quite
3=2
residual orthorhombic structural distortion much affect the S interesting that the T dependences of ðjSj=TÞ
for both
as well as the ꢀ.10)
LaFePO1ꢁxFx and LaFeAsO1ꢁxFx are qualitatively similar to
In order to understand the origin of the differences of those of the Hall coefficients (RH).10,21,22) These results
the S between the two compounds and the observed large S strongly suggest that the overall T dependences of the S for
for the F-doped LaFeAsO, in the first approximation we the F-doped LaFePO and LaFeAsO are mainly governed by
make a rough analysis of the results by using a conventional the T dependences of the n.
3D parabolic band model with a single carrier14,19) (see
Appendix). In this model, the S is proportional to mꢀnꢁ2=3T, 4.2 Possibilities of the instability of orbital order and the
where the mꢀ is an effective mass and n is a carrier density.
When the mꢀ and n are constant, the relation expresses the
hidden mass enhancement of LaFeAsO1ꢁxFx
In order to understand the origin of the T dependences of
well-known T-linear dependence of S for a metal. If the the S for these compounds, it is necessary to understand the
densities of electrons doped into these compounds were origin of the T dependences of the RH. According to the
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J. Phys. Soc. Jpn. 80 (2011) 044704
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T. OKUDA et al.
results in ref. 21, the RH for LaFeAsO increases and shows
an abrupt increase around Ts with the decrease of T,
indicating that the structural transition from the tetragonal
structure to the orthorhombic one dramatically suppresses
the n although the ꢀ drops below Ts.1,2) To explain the
experimental results, the mobility of carrier (ꢄc) must
dramatically increase, i.e., something to disturb the electro-
nic transport is dramatically suppressed by the structural
transition. It is natural to think that the origin of this increase
of ꢄc is due to the suppression of fluctuations of the Fe 3d
orbital by the orbital order associated with the structural
transition proposed by some theoretical predictions23–25) on
the base of an intermediate spin state of Fe2þ ion as shown
in the inset of Fig. 6(a). The electrons participating in the
orbital order are localized, so the n dramatically decreases,
while the ꢄc of the itinerant carriers that do not participate in
the orbital order dramatically increases because of the
suppression of the orbital fluctuation.
3
2
1
0
LaFeAsO1-x
F
x
LaFePO1-x
F
x
0
0.05
0.1
F doping x
0.15
Fig. 8. (Color online) The F-doping dependences of the effective mass
(mꢀ) normalize by the mꢀ for LaFePO. The solid circles and the solid
squares are the normalized mꢀ for LaFePO1ꢁxFx and LaFeAsO1ꢁxFx,
respectively (see text).
The electron doping by the substitution of F for O
suppresses the orbital order as evidenced by the disappear-
ance of the structural transition and that of the associated AF
transition [Fig. 6(a)]. However, the instability of the orbital
order may persist in the over F-doped region especially near
5. Summary
In this study, we systematically investigate the thermo-
the phase boundary, as partially supported by the residual electric properties for polycrystalline LaFePO1ꢁxFx and
orthorhombic structural distortion in the tetragonal phase.18) LaFeAsO1ꢁxFx and discuss an origin of a relatively good
This instability may cause the T dependences of the RH thermoelectric property of LaFeAsO1ꢁxFx by comparing the
for the over F-doped LaFeAsO; the development of the properties of these compounds. The observed maximum
correlation of the orbital order gradually reduces the n of the power factor is about 37
itinerant electrons with the decrease of T, leading to the 0:89F0:11 and the maximum dimensionless thermoelectric
with the decrease of T. It is figure of merit (ZT) is about 0.08 at 110 K for LaFeAs-
ꢀ
W/K2 cm at 53 K for LaFeAs-
O
13,22)
reported increase of RH
noted that the slight enhancement of the RH and S observed
at the low temperatures in LaFePO1ꢁxFx may be also due to
O
O
0:89F0:11 which is larger by an order than those for LaFeP-
1ꢁxFx. This observed relatively large ZT at the low
the instability of this orbital order rather than phonon drag temperature for LaFeAsO0:89F0:11 is due to the low resistivity
effect. Such a residual instability of the orbital order in the (ꢀ) and the large Seebeck coefficient (S). According to our
metallic state may cause the deviation from the Kadowaki– rough analysis by using a 3D parabolic band model with a
Woods law.
single carrier, the low ꢀ in the over F-doped region in
Lastly, we make a rough estimation of the mꢀ for LaFeAsO1ꢁxFx is perhaps not only due to an increase of an
LaFePO1ꢁxFx and LaFeAsO1ꢁxFx by using the 3D parabolic electron density (n) by the F-doping, but also due to a
metallic band model with a single carrier (electron) on the suppression of an orbital fluctuation of Fe ions by the residual
assumption that the suppression of the n due to the instability instability of the orbital order proposed in LaFeAsO by some
of the orbital order actually occurs. In this simple model, theoretical works. Furthermore, the relatively large S for the
3=2
2=9
S=T / mꢀnꢁ2=3 and ꢁn / mꢀn1=3, so ½ðjSj=TÞ ꢁ3nꢈ / mꢀ. over F-doped LaFeAsO may originate not only in the smaller
3=2
By using the maximum ðjSj=TÞ values at about 25 K for n than that expected from the formal valence due to the
LaFePO1ꢁxFx in Fig. 7(a) and the reported values of ꢁn10) for residual instability of the orbital order, but also in the
LaFePO1ꢁxFx, we deduce the mꢀ for LaFePO1ꢁxFx. As for mass enhancement around the structural and magnetic phase
LaFeAsO1ꢁxFx, we calculate the mꢀ by using the maximum boundary due to the renormalized spin or orbital fluctuations.
3=2
ðjSj=TÞ
values at about 30 K in Fig. 7(b), the reported Such a mass enhancement may be related to the mechanism of
13)
values of ꢁn
extrapolated values of ꢁn for x ¼ 0:08 and 0.1 in Fig. 6(b). thermoelectronic properties in these iron-pnictides.
Appendix
for x ¼ 0:05, 0.11, and 0.14, and the the superconducting state as well as the relatively good low-T
Figure 8 summarizes the F-doping dependences of the
deduced mꢀ normalized by that for LaFePO in the tetragonal
phase. This rough analysis shows that the mꢀ around
According to the previous reports,8) both LaFePO and
x ¼ 0:05{0:1 of LaFeAsO1ꢁxFx are larger than those of LaFeAsO have multiple bands (three hole-like bands and
LaFePO1ꢁxFx, LaFeAsO0:89F0:11
,
and LaFeAsO0:86F0:14 two electron-like bands) and multiple Fermi surface sheets,
.
As observed around a Mott transition,26–29) such a mass so both hole and electron should contribute to the transport
enhancement (in Fig. 8) with the absence of the enhance- properties for LaFePO1ꢁxFx and LaFeAsO1ꢁxFx. In this
ment of ꢁn [in Fig. 6(b)] is perhaps due to the renormalized paper, in order to capture the overall picture of the origin
spin or orbital fluctuation of Fe ions around a critical region of the difference of the S between two series, we make a
above x ¼ 0:05, and should be related to the mechanism of following discussion on the basis of experimental results and
the superconducting state30–32) as well as the relatively good make a rough analysis in the text by using a 3D parabolic
low-T thermoelectric properties in these iron-pnictides.
bnad model with a single carrier.
044704-7
#2011 The Physical Society of Japan

J. Phys. Soc. Jpn. 80 (2011) 044704
FULL PAPERS
T. OKUDA et al.
3=2
Both end compounds, LaFePO and LaFeAsO, are of ðjSj=TÞ quite resemble those of RH, as shown in Fig. 6.
assumed to have three hole bands and two nearly degenerate Paradoxically, the consistency seems to strongly suggest that
electron bands. Their Seebeck coefficients, S, are expressed the transport properties for these oxypnictides are governed
as follows:
by the contribution of the electron bands.
Sh1ꢅh1 þ Sh2ꢅh2 þ Sh3ꢅh3 þ Se1ꢅe1 þ Se2ꢅe2
S ¼
ꢅh1 þ ꢅh2 þ ꢅh3 þ ꢅe1 þ ꢅe2
ðSꢅÞh þ 2Seꢅe
1) Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono: J. Am. Chem.
Soc. 130 (2008) 3296.
ꢉ
:
ðAꢊ1Þ
ꢅ
2) K. Ishida, Y. Nakai, and H. Hosono: J. Phys. Soc. Jpn. 78 (2009)
062001.
where
3) Y. Kamihara, H. Hiramatsu, M. Hirano, R. Kawamura, H. Yanagi, T.
Kamiya, and H. Hosono: J. Am. Chem. Soc. 128 (2006) 10012.
4) 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 (2008) 083704.
ðSꢅÞh ¼ Sh1ꢅh1 þ Sh2ꢅh2 þ Sh3ꢅh3;
ꢅ ¼ ꢅh1 þ ꢅh2 þ ꢅh3 þ ꢅe1 þ ꢅe2;
Se1 ꢉ Se2 ꢉ Se;
ðAꢊ2Þ
ðAꢊ3Þ
ðAꢊ4Þ
ðAꢊ5Þ
ꢅe1 ꢉ ꢅe2 ꢉ ꢅe:
´
5) L. Pinsard-Gaudart, D. Berardan, J. Bobroff, and N. Dragoe: Phys.
For LaFeAsO, the absolute value of S (ꢁ10 to 30
ꢀ
V/K) is
Status Solidi: Rapid Res. Lett. 2 (2008) 185.
6) K. Kihou, C. H. Lee, K. Miyazawa, P. M. Shirage, A. Iyo, and E.
Eisaki: J. Appl. Phys. 108 (2010) 033703.
much smaller than the maximum absolute value of S (about
ꢁ150 V/K) for LaFeAsO1ꢁxFx and the sign changes with
ꢀ
7) D. J. Singh and M.-H. Du: Phys. Rev. Lett. 100 (2008) 237003.
8) D. H. Lu, M. Yi, J. G. Analytis, J.-H. Chu, A. S. Erickson, D. J. Singh,
Z. Hssain, T. H. Geballe, I. R. Fisher, and Z.-X. Shen: Physica C 469
(2009) 452.
the decrease of T, which is perhaps due to the competition
between the contributions of hole and electron. Then, we
roughly assume that S ꢉ 0 for LaFeAsO, so ðSꢅÞh þ
2Seꢅe ꢉ 0. In the case of LaFeAsO1ꢁxFx, we also assume
that the changes of the transport properties come only from
the increase of electron densities in the electron bands. Then,
the ꢅ for LaFeAsO1ꢁxFx is expressed by ꢅ ꢉ ꢅh þ 2ðꢅe þ
ꢁꢅeÞ, where ꢅh ¼ ꢅh1 þ ꢅh2 þ ꢅh3 and ꢁꢅe is the increase
of the contribution of electron to the conductivity. The ꢅ for
LaFeAsO1ꢁxFx much increases with the F doping as shown in
Fig. 1(b), so ꢅh þ 2ꢅe ꢋ 2ꢁꢅe. Then, the Seebeck coefficient
for LaFeAsO1ꢁxFx is approximately expressed as follows,
9) M. M. Qazilbash, J. J. Hamlin, R. E. Baumback, L. Zhang, D. J. Singh,
M. B. Maple, and D. N. Basov: Nat. Phys. 5 (2009) 647.
10) S. Suzuki, S. Miyasaka, S. Tajima, T. Kida, and M. Hagiwara: J. Phys.
Soc. Jpn. 78 (2009) 114712.
11) C. Hess, A. Kondrat, A. Narduzzo, J. E. Hamann-Borreo, R. Klingeler,
J. Werner, G. Behr, and B. Buchner: Europhys. Lett. 87 (2009) 17005.
¨
12) S. Ishida, M. Nakajima, Y. Tomioka, T. Ito, K. Miyazawa, H. Kito,
C. H. Lee, M. Ishikado, S. Shamoto, A. Iyo, H. Eisaki, K. M. Kojima,
and S. Uchida: Phys. Rev. B 81 (2010) 094515.
13) Y. Kohama, Y. Kamihara, M. Hirano, H. Kawaji, T. Atake, and H.
Hosono: Phys. Rev. B 78 (2008) 020512(R).
14) T. Okuda, K. Nakanishi, S. Miyaksa, and Y. Tokura: Phys. Rev. B 63
(2001) 113104.
ðSꢅÞh þ 2ðSe þ ꢁSeÞðꢅe þ ꢁꢅeÞ
S þ ꢁS ꢉ
15) T. M. McQueen, M. Regulacio, A. J. Williams, Q. Huang, J. W. Lynn,
Y. S. Hor, D. V. West, M. A. Green, and R. J. Cava: Phys. Rev. B 78
(2008) 024521.
ꢅ þ 2ꢁꢅe
ðAꢊ6Þ
2ꢁSeꢅe þ 2ðSe þ ꢁSeÞꢁꢅe
ꢉ
ꢉ Se þ ꢁSe
2ꢁꢅe
16) M. A. McGuire, A. D. Christianson, A. S. Sefat, B. C. Ssles, M. D.
Lumsden, R. Jin, E. A. Payzant, D. Mandrus, Y. Luan, V. Kappens, V.
Varadarajan, J. W. Brill, R. P. Hermann, M. T. Sougrati, F. Grandjean,
and G. J. Long: Phys. Rev. B 78 (2008) 094517.
where ꢁS and ꢁSe is the change of S and Se with the
F-doping, respectively. The total Seebeck coefficient for
LaFeAsO1ꢁxFx can be approximated by the contribution of
the electron band.
17) A. S. Sefat, M. A. McGuire, B. C. Sales, R. Jin, J. Y. Howe, and D.
Mandrus: Phys. Rev. B 77 (2008) 174503.
In the case of LaFePO1ꢁxFx, the same approximation
cannot be done, because LaFePO is already a good metal
without the F-doping and the conductivity little changes
with the F-doping, as shown in Fig. 1(a). Then, we roughly
assume that S ꢉ Se ꢉ Sh ꢉ 0, comparing with the maximum
absolute value of S (about ꢁ150 ꢀV/K) for LaFeAsO1ꢁxFx.
Furthermore, the ꢅ for LaFePO is assumed to be governed
by the electron conductivity, ꢅ ꢉ 2ꢅe, which is partially
supported by the facts that the RH and S are negative and the
mobility of electron is estimated to be much higher than that
of hole by the ARPES. Then, the total Seebeck coefficient
for LaFePO1ꢁxFx becomes as follows:
18) Q. Huang, J. Zhao, J. W. Lynn, G. F. Chen, J. L. Luo, N. L. Wang, and
P. Dai: Phys. Rev. B 78 (2008) 054529.
19) G. D. Mahan: Solid State Phys. 51 (1998) 81.
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Hosono: J. Phys. Soc. Jpn. 77 (2008) 094715.
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Balakirev, T. Atake, M. Jamie, M. Hirano, and H. Hosono: Phys. Rev.
B 79 (2009) 144527.
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¨
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1039.
ðSꢅÞh þ 2ðSe þ ꢁSeÞꢅe 2ðSe þ ꢁSeÞꢅe
S þ ꢁS ꢉ
ꢉ
27) T. Okuda, A. Asamitsu, Y. Tomioka, T. Kimura, Y. Taguchi, and Y.
Tokura: Phys. Rev. Lett. 81 (1998) 3203.
2ꢅe
2ꢅe
ꢉ Se þ ꢁSe:
ðAꢊ7Þ
28) S. Miyasaka, T. Okuda, and Y. Tokura: Phys. Rev. Lett. 85 (2000) 5388.
29) H. Kato, T. Okuda, Y. Okimoto, Y. Tomioka, K. Oikawa, T.
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It can also be approximated by the contribution of the
electron band.
In the above discussions, the assumptions and approxima-
tions are rather rough and may partially be incorrect.
However, the above conclusions are consistent with the facts
that both S and RH are negative and that the T dependences
31) K. Kuroki, S. Onari, R. Arita, H. Usui, Y. Tanaka, H. Kontani, and H.
Aoki: Phys. Rev. Lett. 101 (2008) 087004.
32) H. Kontani and S. Onari: Phys. Rev. Lett. 104 (2010) 157001.
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#2011 The Physical Society of Japan