Person-to-person distribution by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Journal of the Physical Society of Japan 85, 124704 (2016)
http://doi.org/10.7566/JPSJ.85.124704

Eﬀect of Pressure on Magneto-Transport Properties in the Superconducting
and Normal Phases of the Metallic Double Chain Compound Pr2Ba4Cu7O15−δ
Masayoshi Kuwabara1, Michiaki Matsukawa2+, Keisuke Sugawara1, Haruka Taniguchi2,
Akiyuki Matsushita3, Makoto Hagiwara4, Kazuhiro Sano5, Yoshiaki Ōno6, and Takahiko Sasaki7
2

1
Graduate School of Engineering, Iwate University, Morioka 020-8551, Japan
Mathematical Science and Physics Course, Iwate University, Morioka 020-8551, Japan
3
National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan
4
Kyoto Institute of Technology, Kyoto 606-8585, Japan
5
Department of Physics Engineering, Mie University, Tsu 514-8507, Japan
6
Department of Physics, Niigata University, Niigata 950-2181, Japan
7
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan(Received September 7, 2016; accepted October 4, 2016; published online November 4, 2016)

To examine the electronic phase diagram of superconducting CuO double chains, we report the eﬀect of externalpressure on the magneto-transport properties in superconducting and non-superconducting polycrystalline samples of
Pr2Ba4Cu7O15−δ at low temperatures (1.8–40 K) under various magnetic ﬁelds (up to 14 T). In the as-sintered nonsuperconducting sample, the magneto-resistance (MR) follows a power law of H 3=2 at low temperatures, which is in noagreement with the H 2 dependence of MR in the PrBa2Cu4O8 system. The negative pressure dependence of thesuperconducting phase is qualitatively consistent with a theoretical prediction on the basis of the Tomonaga–Luttinger
liquid theory. The 48-h-reduced superconducting sample at ambient pressure exhibits no clear increase in MR for
T > Tc,on = 26.5 K. In contrast, with the application of pressure to the superconducting sample, the MR eﬀects reappear
and are also well ﬁtted by H 3=2. The model of slightly warped Fermi surfaces explains not only the MR eﬀect of thenon-superconducting sample, but is also related to the reasons for the pressure-induced MR phenomena of thesuperconducting sample.

1.

Introduction

Since the discovery of high-Tc copper-oxide superconductors, researches have focused on the unconventional superconductivity on the two-dimensional CuO2 planes in somecuprates. In quasi one-dimensional (1D) ladder system
without CuO2 planes, it is well known that the superconductivity at Tc ¼ 12 K appears only under the applicationof high pressure.1) In our previous study of Pr-based cuprates
with metallic CuO double chains and insulating CuO2 planes,
Pr2Ba4Cu7O15 is found to be a new superconductor with ahigher Tc (15 K) after a reduction treatment.2) A nuclear
quadrupole resonance study has revealed that the newly
discovered superconductivity is realized at the CuO doublechain block.3) Structurally, the Pr-based cuprates, PrBa2Cu3O7 (Pr123) and PrBa2Cu4O8 (Pr124), are identical totheir corresponding Y-based high-Tc superconductors, YBa2Cu3O7 (Y123) and YBa2Cu4O8 (Y124). Pr123 and Pr124
compounds have insulating CuO2 planes and are nonsuperconductive.4,5) The suppression of superconductivity
in the Pr substitutes has been explained by the hybridizationof Pr-4f and O-2p orbitals.6) The crystal structure of Pr124
with CuO double chains diﬀers from that of Pr123 with CuO
single chains. It is well known that CuO single chains inPr123 and CuO double chains in Pr124 show semiconducting
and metallic behaviors, respectively.7) The carrier concentration of doped double chains of Pr124 is diﬃcult to vary,because it is thermally stable up to high temperatures.
The compound Pr2Ba4Cu7O15 (Pr247) is an intermediate
between Pr123 and Pr124. In this compound, CuO singlechain and double-chain blocks are alternately stacked along
the c-axis such as {–D–S–D–S–} sequence8,9) (see Fig. 1).
Here, S and D denote CuO single-chain and double-chain
blocks along the b-axis, respectively. The physical propertiesof the metallic CuO double chains can be examined bycontrolling the oxygen content along the semiconducting
CuO single chains. Anisotropic resistivity measurements ofsingle-crystal Pr124 have revealed that metallic transportarises by the conduction along the CuO double chains.10) In
oxygen removed polycrystalline Pr2Ba4Cu7O15 , the superconductivity appears at an onset temperature Tc,on of ∼15 K.2)
Hall coeﬃcient measurements of superconducting Pr247
with Tc,on ¼ 15 K have revealed that at intermediate temperatures below 120 K, the main carriers change from holes toelectrons, as the temperature decreases. Accordingly, thiscompound is an electron-doped superconductor.11) In ourprevious study, we examined the eﬀect of magnetic ﬁeld
on the superconducting phase of Pr247.12) Despite of theresistive drop associated with the superconducting transition,
we found that the diamagnetic signal was strongly suppressed as expected in the 1D superconductivity of CuO
double chains. We also reported the temperature dependenceof the Hall coeﬃcient in superconducting Pr247 with ahigher Tc,on  27 K.13) Our ﬁndings indicated that thesuperconducting transition temperature increased because
the density of doped electron carriers became denser under
the reduction treatment, consistent with a theoreticalprediction.14)
In this paper, we demonstrate the magneto-transport
properties of the electron-doped metallic double-chain compound Pr2Ba4Cu7O15 , which has a higher Tc,on (26.5 K),
under the application of diﬀerent hydrostatic pressures (upto 1.6 GPa). Section 2 outlines the experimental methods,
and Sect. 3 presents the magneto-transport properties ofsuperconducting and non-superconducting polycrystalline
Pr247 samples under external pressures. These results are
discussed in the view point of topologies of Fermi surfaces,
which are varied from warped to straight form uponincreasing the carrier content. The ﬁnal section is devoted toa summary.

124704-1©2016 The Physical Society of Japan

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J. Phys. Soc. Jpn. 85, 124704 (2016)

M. Kuwabara et al.
30(a) as-sintered

0.8 GPa
0 GPa

25

15

ZFC 5mT0χ (emu/gOe)ρ (mΩ cm)

20

-0.001

100GPa
0.8GPa1.2GPa-0.002-0.0035-0.004

0

0

50

0

5

100

10

15 20
T (K)

150

25

200

30

250

300

T (K)
15

(b) 48-h-reduced2.

ρ (m Ω cm)

Fig. 1. (Color online) X-ray diﬀraction patterns of as-sintered polycrystalline Pr2Ba4Cu7O15 . The (004) peak corresponds to one of typical Miller
indexes of Pr247. The calculated curve is obtained using the lattice parametersin the text. Inset shows the crystal structure of Pr247. S and D denote CuO
single-chain and double-chain blocks along the b-axis, respectively.

10

1.6 GPa
1.2 GPa
0.8 GPa
0.4 GPa
0 GPa

5Experiment

Polycrystalline samples of Pr2Ba4Cu7O15 (Pr247) weresynthesized by the citrate pyrolysis method.15) After several
annealing processes, the resulting precursors were pressed
into a pellet and calcined at 875–887 °C for an extended
period over 120–180 h under ambient oxygen pressure. The
oxygen in the as-sintered sample was removed by reduction
treatment in a vacuum at 500 °C for 48 h, yielding a
superconducting material. Typical dimensions of the pelletized rectangular sample were 9:9  2:4  1:7 mm3. X-ray
diﬀraction data revealed that the as-sintered polycrystalline
samples are an almost single phase with an orthorhombic
structure (Ammm), as shown in Fig. 1. The lattice parametersof the as-sintered sample are a ¼ 3:8753 Å, b ¼ 3:9107 Å,
and c ¼ 50:713 Å, which are in fair agreement with thoseobtained by a previous study.16) In a previous TEM imageof superconducting Pr247, we observed a regular stacking
structure of {–D–S–D–S–} along the c-axis direction.17)
The oxygen deﬁciency in the sample with Tc,on ¼ 26:5 K
prepared by the citrate method was estimated to be  ¼ 0:56
from gravimetric analysis. As a function of the oxygendeﬁciency, the Tc,on rises rapidly at  ≳ 0:2, then monotonically increases with increasing δ, and ﬁnally saturates around
26–27 K at  ≳ 0:6.18) Accordingly, the carriers in the present
sample are concentrated around the optimally doped region.
The electric resistivity in zero magnetic ﬁeld was measured
by the dc four-terminal method. The magneto-transport up
to 9 T was measured by the ac four-probe method using
a physical property measuring system (PPMS; Quantum
Design), increasing the zero-ﬁeld-cooling (ZFC) temperatures from 2 to 40 K. The high ﬁeld resistivity (up to 14 T)
was measured in a superconducting magnet at the High
Field Laboratory for Superconducting Materials, Institutefor Materials Research, Tohoku University. The electric
current I was applied longitudinally to the sample; consequently, the applied magnetic ﬁeld H was transverse to thesample (because H ? I). Hydrostatic pressures in the electric
resistivity measurement were applied using a clamp-type

0
0

50

100

150
T (K)

200

250

300

Fig. 2. (Color online) (a) Temperature dependences of electric resistivitiesof the as-sintered non-superconducting Pr2Ba4Cu7O15 compound measured
under 0 and 0.8 GPa. (b) Temperature dependences of electric resistivities of
the 48-h-reduced superconducting Pr2Ba4Cu7O15 compound measured
under various pressures (0, 0.4, 0.8, 1.2 and 1.6 GPa). Inset plots lowtemperature dependences of magnetic susceptibilities χ of the 48-h-reduced
superconducting sample measured under several pressures (up to 1.2 GPa).

CuBe=NiCrAl cell up to 1.6 GPa. Fluorinert was used as apressure transmitting medium. Inner and outer cylinders weremade of NiCrAl and CuBe alloys, respectively.
The dc magnetization was performed under ZFC in acommercial superconducting quantum interference device
magnetometer (Quantum Design MPMS). The magnetization
measurement under applied pressure was conducted using astandard clamp-type pressure device. A simple clamp cellconsists of a ZrO2 piston and cylinder made of a CuBe alloy.
The M=H values of the clamp-type cell are estimated to be108 emu=g and are considerably smaller than the values of
M=H for all samples.
3.

Results and Discussion

Figure 2 shows the temperature dependences of electric
resistivities of the as-sintered non-superconducting and 48-hreduced superconducting samples measured under variouspressures [(a) 0.GPa and 0.8 GPa, (b) 0, 0.4, 0.8, 1.2, and
1.6 GPa]. For comparison, inset of Fig. 2 plots low-temperature dependences of magnetic susceptibilities χ of thesuperconducting sample under various pressures (up to 1.2
GPa). First of all, the superconductivity of the 48-h-reduced
sample was suppressed with increasing the applied pressure.
When applied pressures exceed 0.8 GPa, zero-resistance state

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J. Phys. Soc. Jpn. 85, 124704 (2016)

M. Kuwabara et al.

15(a) as-sintered 0 GPa

9T
0T
5

0 GPa
0.8 GPaΔρ /ρ (0) (%)ρ (mΩ cm)

1010

μ0 H =9 (T)

5

10

0

0

5

10

15

20
T (K)

30

25

30

20

40

35

40

T (K)
8

(b) as-sintered
0 GPa (30K)
0.8 GPa (30K)
0 GPa (40K)
0.8 GPa (40K)6Δρ /ρ(0) (%)

of the 48-h-reduced sample then disappeared. Second, thehigh-temperature metallic properties of the reduced superconducting sample were changed to the semi-conducting
behaviors at applied pressures above 0.8 GPa, accompanied
by a rapid increase in ρ. The onset temperature of superconducting transition Tc,on is suppressed from 26.5 K underambient pressure through 24.1 K under 0.8 GPa to 18.0 K
under a maximum pressure of 1.6 GPa (Tc,on versus pressure
at a zero ﬁeld as displayed in inset of Fig. 7).
The normal–superconducting phase diagram of CuO
double chains has been investigated on the basis of theTomonaga–Luttinger liquid theory.14) When the distance
between the two single chains of a CuO double-chain block
shrinks along the c-axis, the hopping energies tpp and tdd are
expected to increase. Here, tpp and tdd represent the hoping
term between 2p orbitals at the nearest neighbor oxygensites and that between 3dx2 y2 orbitals at the nearest neighborcopper sites, respectively. The application of the externalpressure on the CuO double chains causes an enhancement of
the hopping terms, resulting in a phase transition from thesuperconducting to normal phase. This theoretical prediction
is qualitatively consistent with the superconducting properties suppressed by the pressure eﬀect.19)
As shown in Fig. 2, the pressure eﬀect on the electronictransports of the as-sintered non-superconducting sample isquite weak, in both its magnitude and temperature dependence, in comparison with that of the 48-h-reduced
superconducting sample. (These behaviors of the present assintered Pr247 are almost similar to the eﬀect of pressure on
the temperature dependence of as-sintered Pr247 compound
prepared by high-pressure synthesis technique.20))
Next, let us show in Fig. 3 the temperature dependences ofelectric resistivities of the as-sintered non-superconducting
Pr2Ba4Cu7O15 compound measured under a zero ﬁeld andan applied ﬁeld of 9 T. Inset of Fig. 3 plots the magnetoresistance (MR) data of the as-sintered sample =ð0Þversus T (between 4 and 40 K) under 0 and 0.8 GPa. The
value of =ð0Þ taken at 9 T reaches a maximum of about
12% near 10 K under either 0 or 0.8 GPa. Moreover, themagneto-resistance curves as a function of applied ﬁeld
follow similar ﬁeld dependences in the both cases of 0 and
0.8 GPa. Accordingly, we infer that application of pressure
on the as-sintered sample gives rise to no considerable
variation in the magneto-resistance eﬀect.
Here, we try to ﬁt the ﬁeld dependence of the MR eﬀect
=ð0Þ by using a power law of H. As shown in Fig. 4, we
found out that =ð0Þ of the as-sintered Pr247 sample atambient pressure is well scaled with H3=2 over a wide rangeof temperatures (2–40 K). In a similar way, the MR data of
the as-sintered sample recorded at 0.8 GPa are well describedby a power law of =ð0Þ / H3=2 . Our ﬁndings are notconsistent with the MR eﬀect of polycrystalline Pr124
compounds with metallic double-chains. In Pr124 system,
=ð0Þ / H2 for H ? I.21) These discrepancies in magnetic
ﬁeld dependences of MR between Pr124 and Pr247 are
originated from the diﬀerences of their crystal structures. In
the latter compounds, we believe that CuO double chains
stacked along the c-axis are separated by CuO single chains,resulting in a suppression of carrier hopping between
individual double chains along the c-axis. Furthermore, aphotoemission spectroscopy study22) has revealed that the

4

2

0
0

2

4

6

μ0H (T)

8

10

Fig. 3. (Color online) (a) Low-temperature dependences of electric
resistivities of the as-sintered non-superconducting Pr2Ba4Cu7O15
compound measured under a zero ﬁeld and an applied ﬁeld of 9 T. Inset
plots the magneto-resistance data of the as-sintered sample =ð0Þ versus T(below 40 K) under 0 and 0.8 GPa. Here,  ¼ ðHÞ  ð0Þ. In (b), themagneto-resistance data of the as-sintered sample =ð0Þ are plotted as afunction of H (up to 9 T) at T ¼ 30 and 40 K under both P ¼ 0 and 0.8 GPa.

CuO double chain in Pr247 has a better one dimensionality
than that in Pr124, which is probably close to the suppressionof c-axis carrier hopping.
In Pr124 system, it is well known that the inter-chaintransport at low temperatures is destroyed by a high magnetic
ﬁeld applied perpendicular to the CuO double chains.23) The
ﬁeld-induced dimensional-crossover causes the weak ﬁeld
dependence of the c-axis magneto-resistance of Pr124 when
the applied ﬁeld exceeds the decoupling ﬁeld of 11 T.
Furthermore, in Y124 system, the ﬁeld dependence of thec-axis magneto-resistance is changed from H2 to H-linear
dependence at high ﬁelds, suggesting the ﬁeld-induced
dimensional crossover.24) An anomalous ﬁeld dependenceof the c-axis MR ( / H3=2 ) has been reported in the 1D
organic conductor (TMTSF)2PF6 once the inter-chain transport becomes incoherent.25) For Pr124 or Y124 with {–D–D–
D–D–} sequence, the c-axis hopping of carriers between
CuO double chains is suppressed by the application of highly
magnetic ﬁeld. In Pr247 system, the c-axis carrier transport isoriginally incoherent because of regular stacking structuresof {–D–S–D–S–} along the c-axis direction, as depicted inFig. 1.

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J. Phys. Soc. Jpn. 85, 124704 (2016)

M. Kuwabara et al.

2.5

12

(a) 0 GPa
2K
5K
10K
15K
20K
30 K
40 K

8
6
4

2
1.5

14 T
10 T
6T
3T
0T

1

9T

2
0

(a) 48-h-reduced
0 GPa
Tc, on =26.5K

ρ (mΩ cm)Δρ /ρ(0) (%)

10

0.5

0

5

10

15

20

μ0H)

3/2

3/2

(T

25

30

0
0

)

5

10

15

20

25

30

35

40

12

14

T (K)

25

(b) 0.8GPa

2.5 (b) 48-h-reduced 0 GPa

6K

2

30K
15

40K

ρ (mΩ cm)Δρ /ρ(0) (%)

20

10
14T
5
9T
0

0

10

20

30K
20K
4K

1

3K
1.7K

0.5

30

40

μ0H)

3/2

3/2

1.5

(T

50

60

0

)

0

2

4

6

8

μ0H (T)

10

Fig. 4. (Color online) Magneto-resistance eﬀect =ð0Þ of the assintered non-superconducting Pr2Ba4Cu7O15 compound. In (a), the MRdata (up to 9 T) under ambient pressure are plotted as a function of H3=2 at
the selected temperatures (T ¼ 2{40 K). In (b), the MR data (up to 14 T)
under 0.8 GPa are plotted as a function of H3=2 at the selected temperatures of
T ¼ 5, 30, and 40 K.

Fig. 5. (Color online) (a) Low-temperature dependences of electric resistivities of the 48-h-reduced superconducting Pr2Ba4Cu7O15 compound
measured at the several applied ﬁelds (H ¼ 0{14 T). In (b), the magnetoresistance data of the superconducting sample are plotted as a function ofmagnetic ﬁelds (up to 14 T) at the selected temperatures (T ¼ 1:7{30 K).

Figure 5(a) plots the low-temperature dependences ofelectric resistivities of the superconducting Pr2Ba4Cu7O15
compound with Tc,on ¼ 26:5 K in several applied ﬁelds (0, 3,
6, 10, and 14 T). Even at high ﬁelds above 10 T, the resistive
drop associated with the superconducting transition isobserved but the diamagnetic signal is strongly suppressedat low ﬁeld below 1 T. This observation is closely related to
the 1D superconductivity of CuO double-chains as highlighted in our previous paper.12) The magneto-resistance eﬀect(up to 14 T) of the 48-h-reduced superconducting sample in
the normal sate temperature region above Tc,on ¼ 26:5 K isvery small in comparison to the large MR eﬀect of the assintered sample. = of the as-sintered sample recorded at
30 K attains ∼7% up to 9 T while for the 48-h-reduced sample
the MR eﬀect rapidly decreases below ∼1% at 9 T. The
suppressed MR eﬀect in the normal phase of the 48-h-reduced
superconducting sample is probably explained by the topology of Fermi surfaces of CuO double chains,26,27) where theFermi surfaces are changed from their warped to straightforms upon increasing carrier contents (as mentioned below).
Figure 6 plots the low-temperature dependences of electric
resistivities of the superconducting Pr2Ba4Cu7O15 compound measured in the several applied ﬁelds (0–14 T) undervarious hydrostatic pressures [(a) P ¼ 0:4 GPa, (b) P ¼ 1:2
GPa, and (c) P ¼ 1:6 GPa]. For the superconducting sample
without magnetic ﬁeld, the superconducting transition
temperature reaching zero-resistance state Tc,zero is sup-pressed from 16 K at 0 GPa down to 6 K at a low pressure of
0.4 GPa. At high ﬁelds above 10 T, the low-temperature data
under 0.4 GPa remain the resistive drops associated with thesuperconducting transition, upon decreasing temperature.
These tendencies still appear for the high-ﬁeld resistive data
(up to 10 T) under both 1.2 and 1.6 GPa.
For temperatures close to Tc,on , we are concentrated on
the magneto-transport properties in the normal state of the
48-h-reduced superconducting sample. As mentioned before,
although the strong MR eﬀect is observed in the as-sinterednon-superconducting sample, the 48-h-reduced annealing
procedure for it causes a considerably suppression of thenormal-state MR accompanied by the appearance of thesuperconductivity with Tc,on ¼ 26:5 K. The application ofpressure on the superconducting sample gives rise to a
substantial decrease of Tc,on from 26.5 K at 0 GPa down to
18 K at 1.6 GPa, as shown in inset of Fig. 7. On the other
hand, the ﬁnite magneto-resistance eﬀect reappears forT  Tc,on when the applied pressure to the superconducting
sample is increased.
Figure 7 plots the magneto-resistances (up to 14 T) of the
48-h-reduced superconducting sample, =ð0Þ, measured
under a maximum pressure of 1.6 GPa. For T > Tc,on ¼ 18 K,
=ð0Þ curves initially start to increase in the the downward
convey forms with applied ﬁelds. On the other hand, the MRdata recorded at T below Tc,on ¼ 18 K tend to increase
according to the upward covey behaviors at low ﬁelds.

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J. Phys. Soc. Jpn. 85, 124704 (2016)

M. Kuwabara et al.
15(a) 48-h-reduced
0.4 GPa

3.5(a) 1.6 GPac, on=25.3K

2

14T
12T
6T
3T
0T

1.5
1
0.5
0

5

5

4.3 K
15K

15

1/3*Δρ/ρ(0)

c, on

9

5

8

0

20

T

c, on

=18.0K
14T
10T
6T
3T
0T

7
6

10

15

20
25
T (K)

30

35

SC

10
0

5

Normal30

10T(c) 48-h-reduced
1.6 GPa

0

15

20

14T
10T
6T
3T
0T

3

5

10

μ0H (T)(b) 1.6 GPa

6
5

0

25

Tc, on =20.1K

Δρ /ρ(0) (%)ρ (m Ω cm)

7

4

ρ (m Ω cm)

100(b) 48-h-reduced
8
1.2 GPa

20K
25K
30K
40K

(K)

T

Δρ /ρ(0) (%)ρ (m Ω cm)

3
2.5

0

5

μ0H (T)

0

0.4

10

0.8 1.2 1.6
P (GPa)15

Fig. 7. (Color online) Magneto-resistances (up to 14 T) of the 48-hreduced superconducting sample for temperatures close to Tc,on ¼ 18 K
under a maximum pressure of 1.6 GPa. For T > Tc,on and T < Tc,on , the MRdata are presented in (a) and (b), respectively. Inset plots Tc,on versus pressure(up to 1.6 GPa).

40

Fig. 6. (Color online) Low-temperature dependences of electric resistivities of the 48-h-reduced superconducting Pr2Ba4Cu7O15 compound
measured at several applied ﬁelds under hydrostatic pressures of (a) 0.4
GPa, (b) 1.2 GPa, and (c) 1.6 GPa. For H ¼ 0 Tesla, Tc,on is decreased from25.3 K at 0.4 GPa through 20.1 K under 1.2 GPa to 18.0 K under a maximum
pressure of 1.6 GPa.

In a similar way to the MR of the as-sintered sample,
the MR data of the superconducting sample recorded under
1.6 GPa are well described by a power law of =ð0Þ /H3=2 over the normal state region between 20 and 40 K, as
shown in Fig. 8(a). For comparison, Fig. 8(b) shows the MRdata at T ¼ 30 K under P ¼ 0:4, 1.2, and 1.6 GPa. The
application of pressures on the superconducting sample
enhances the MR at 14 T from 2.2% at 0.4 GPa through 5.8%
at 1.2 GPa up to 8% at 1.6 GPa. Furthermore, the MR data
under pressures are well ﬁtted by using =ð0Þ / H3=2
[Fig. 8(b)].
Now, we try to discuss the pressure-induced magnetoresistance eﬀect of the 48-h-reduced superconducting sample.
First of all, we assume that the Fermi surfaces of the double
chains of the superconducting Pr247 are almost straight aspredicted by the band calculation.28) In an ideal 1D conductor
with straight Fermi surfaces without the wave numbers
perpendicular to the conducting direction, the orbitals ofitinerant carries are not bended by the Lorentz force, resulting
in no MR eﬀect. In the case of warped Fermi surfaces, theitinerant carriers have the ﬁnite component of wave number

across the conducting chain direction and the Lorentz force
can bend their orbitals, giving the classical MR eﬀect. For thesuperconducting Pr247, a model of straight Fermi surfaces
for the CuO double chains at ambient pressure is consistent
with the absence of MR eﬀect observed. On the other hand, if
the Fermi surfaces of the double chains under the externalpressures are changed to their warped structures with ﬁnite
values of ka , then it is naturally understood that the MR
eﬀects reappear with increasing the applied pressure. In
particular, the lattice shrinkage due to the hydrostaticpressure enhances not only charge transfer across two single
chains of a CuO double chain but also increase the couplings
between neighboring CuO double chains along the a-axis. As
mentioned before, the suppressed MR eﬀect of the superconducting sample under ambient pressure is closely related
to the topology of Fermi surfaces of CuO double chains,which are varied from their warped to straight forms uponincreasing carrier contents. Accordingly, we expect that themodel of warped Fermi surfaces is not only applicable to theorigins of the MR eﬀect of the non-superconducting sample,
but is also related to the reasons for the pressure-induced MR
phenomena of the superconducting sample.
4.

Summary

We demonstrated the magneto-transport properties ofsuperconducting and non-superconducting Pr2Ba4Cu7O15
compounds under the application of diﬀerent hydrostatic

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J. Phys. Soc. Jpn. 85, 124704 (2016)

M. Kuwabara et al.

15Δρ /ρ(0) (%)(a) 1.6 GPa
20K
25K
30K
35K
40K

10

ple, but it also is closely related to the reasons for thepressure-induced MR phenomena of the superconducting
sample.

9T
14T

Acknowledgment
The authors are grateful for M. Nakamura for his
assistance in PPMS experiments at Center for Regional
Collaboration in Research and Education, Iwate University.

5

0

0

10

20

30

40

50

60
+

μ0H) 3/2 (T 3/2 )10(b) 30K
0.4GPaΔρ / ρ(0) (%)

8

14T
9T

1.2GPa6

1.6GPa

4
2
0

0

10

20

30

40

50

60

μ0H) 3/2 (T 3/2 )Fig. 8. (Color online) The corresponding MR data (up to 14 T) are plotted
as a function of H3=2 . The data of (a) and (b) are collected under P ¼ 1:6 GPa
at T ¼ 20, 25, 30, 35, and 40 K, and at T ¼ 30 K under P ¼ 0:4, 1.2, and
1.6 GPa, respectively.

pressures (up to 1.6 GPa). We found out that =ð0Þ of theas-sintered Pr247 sample at ambient pressure is well scaledby using H3=2 over a wide range of temperatures (2–40 K).
In present Pr247 system, crystal structures of {–D–S–D–S–}
along the c-axis direction probably make inter-chain
couplings between CuO double chains incoherent, resulting
in the H3=2 dependence of MR. This result of Pr247 is notconsistent with the H2 dependence of MR in Pr124 systemwith stacking structures of {–D–D–D–D–} along the c-axis.
The superconducting properties suppressed by the pressure
eﬀect is qualitatively explained by the normal–superconducting phase diagram of CuO double chains on the basis of
the Tomonaga–Luttinger liquid theory. The 48-h-reduced
annealing procedure for the as-sintered sample causes a
considerably decrease in the normal-state MR accompaniedby the appearance of the superconductivity with Tc,on ¼
26:5 K. The suppressed MR eﬀect of the superconducting
sample is probably explained by the topology of Fermi
surfaces of CuO double chains, where the Fermi surfaces arechanged from their warped to straight forms upon increasing
carrier contents. In contrast, for T > Tc,on , the applicationof pressure (up to 1.6 GPa) on the superconducting sample
results in a substantial MR eﬀect of 8% at 14 T. In a similar
way to the MR of the as-sintered sample, the MR data of thesuperconducting sample recorded under 1.6 GPa are welldescribed by a power law of =ð0Þ / H3=2 over thenormal state region between 20 and 40 K. The model ofslightly warped Fermi surfaces explains not only themagneto-resistance eﬀect of the non-superconducting sam-matsukawa@iwate-u.ac.jp
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