Physica B 646 (2022) 414226

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Physica B: Physics of Condensed Matterjournal homepage: www.elsevier.com/locate/physb

Structure, electric transport, and magneto-transport properties of metallic
double-chain based Pr1−𝑥 Ca𝑥 Ba2 Cu4 O8 with low Ca substitution
Takehiro Teramura a , Michiaki Matsukawa a ,∗, Tatsuya Senzaki a , Haruka Taniguchi a ,Kazuhiro Sano b , Yoshiaki Ōno c , Makoto Hagiwara daFaculty of Science and Engineering, Iwate University, Morioka 020-8551, Japanb Department of Physics Engineering, Mie University, Tsu 514-8507, Japanc Department of Physics, Niigata University, Niigata 950-2181, Japand Kyoto Institute of Technology, Kyoto 606-8585, Japan

ARTICLEINFO

Keywords:
CuO double chain
Ca substitution
Carrier doping
Electrical transport
Magneto-resistance

ABSTRACTIn this study, we showed the crystal structure, electric resistivity, Seebeck and Hall coefficients, magnetoresistance, and magnetic susceptibility of Pr1−𝑥 Ca𝑥 Ba2 Cu4 O8 (𝑥 = 0.0, 0.02, and 0.05) are all relevant for
our understanding of physical properties along CuO double chains. The lattice parameters of Ca substituted
PrBa2 Cu4 O8 remained almost invariant up to 𝑥 = 0.05. Contrary to the Ca doping effect in the PrBa2 Cu3 O7−𝛿system, the significant increases in the Seebeck and Hall coefficients due to the Ca substitution indicate adecrease in the carrier number. The significant magneto-resistance effect in the parent sample (16% at 10K) was significantly reduced down to 5% in the 𝑥 = 0.05 composition. On the basis of the two types ofcarrier models, we discussed the influence of Ca substitution on the electrical transport and magneto-transport
properties.

1. Introduction
High-𝑇c cuprate materials have been widely studied from the different standpoints of science and engineering. Structurally, the Pr-based
cuprates, PrBa2 Cu3 O7−𝛿 (Pr123) and PrBa2 Cu4 O8 (Pr124), are identicalto their corresponding Y-based high-𝑇c superconductors, YBa2 Cu3 O7−𝛿(Y123) and YBa2 Cu4 O8 (Y124). Pr123 and Pr124 compounds haveinsulating CuO2 planes and are nonsuperconductive [1–3].
Pr124 system is a candidate material for a quasi one-dimensional(1D) metal. Pr124 compound has the CuO double-chains along the 𝑏axis sandwiched between insulating CuO planes along the 𝑐-axis, as
illustrated in Fig. 1(𝑎). For Pr124 single crystals, it has been reported
that the three-dimensional (3D) Fermi liquid state is realized at low
temperatures due to small interchain hopping energies [4,5]. With
increasing temperature, carrier hopping between chains is expected to
become incoherent, resulting in a dimensional crossover from 3D Fermi
liquid (FL) to 1D Tomonaga–Luttinger liquid (TLL) state [6]. However,
the temperature-induced FL to TLL crossover predicted in the Pr124
system remains a controversial issue [7]. In the Pr124 system, it ischallenging to control the oxygen stoichiometry because of its thermal
stability in the oxidation atmosphere. Our motivation is to vary the
carrier number along the CuO double chains due to the A-site partial

substitution of a divalent cation. There are numerous studies on the Bsite substitution effect in PrBa2 (Cu1−𝑥 Zn𝑥 )4 O8 to clarify the electronic
state of CuO double chains so far [7,8]. The A-site substitution effect such as Ca2+ substitution for Pr3+ has not been investigated on
structural and physical properties in the Pr124 system [9].
For Pr1−𝑥 Ca𝑥 Ba2 Cu3 O7−𝛿 (Pr1−𝑥 Ca𝑥 123) thin films (𝑥 = 0.4 and 0.5),
the partial substitution of Ca for Pr caused the hole doping in the
CuO2 plane and compensated for the suppression of superconductivity
because of Pr ion [10,11]. Furthermore, Luszczek showed that hole
doping is insufficient to compensate for suppressing superconductivity
in the Pr1−𝑥 Ca𝑥 123 bulk ceramic samples. The Ca atoms introduced
additional holes to the Pr123 system, but gave structural defects inthe case of high Ca concentrations [12]. In the Pr123 structure, asystematic study on PrBa2−𝑦 Ca𝑦 Cu3 O7−𝛿 (𝑦 = 0.1–0.4) showed that Ca
ions can replace Pr ions but cannot substitute for Ba ions [13]. This
result suggests that the ionic radius plays a more crucial role than thechemical properties since the ionic radius of Ca2+ (1.12 Å) is close tothat of Pr3+ (1.126 Å)[14].
For its related Y124 system, Miyake reported that the partial substitution of Ca for Y increases a superconducting transition temperature(𝑇c ), and 𝑇c ∼ 90 K is achieved for Y0.9 Ca0.1 Ba2 Cu4 O8 [15,16]. In
Y(Ba,Sr)2 Cu4 O8 , there are recent studies on the stable improvement in∗ Corresponding author.

E-mail address: matsukawa@iwate-u.ac.jp (M. Matsukawa).
https://doi.org/10.1016/j.physb.2022.414226
Received 11 May 2022; Received in revised form 7 July 2022; Accepted 23 July 2022
Available online 20 August 2022
0921-4526/© 2022 Elsevier B.V. All rights reserved.

Physica B: Physics of Condensed Matter 646 (2022) 414226

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acid solution. After adding citric acid and neutralizing it with aqueous
ammonia, we obtained the porous products through the self-ignition
process using halogen-lamp stirrer. (Molar ratio of metal cations, citricacid, and nitric acid, PrCa124: C6 H8 O7 : HNO3 = 1:6:10) In the next
step, the precursors were ground and the resultant fine powders wereannealed under ambient oxygen pressure at 860 ◦ C–891 ◦ C for an
extended period over 110–120 h using three zones controlled electric
furnace to attain higher homogeneous temperature gradient.
For the scanning electron microscope (SEM) measurement, polycrystalline films on Ag substrates were fabricated using an electrophoretic
deposition approach, to show the microstructures of PrCa124 singlephase samples. The sample powders were suspended in an acetone andiodine bath and the electrophoretic deposition was performed in thebath under the application of an electric voltage of up to 100 V for
60–100 s, [23,24]. We set the Pt and Ag plates as anode and cathode,respectively.
We conducted X-ray diffraction measurements on the produced samples at room temperature using an Ultima IV diffractometer (Rigaku)
employing Cu-K𝛼 radiation. The lattice parameters were estimated fromthe X-ray diffraction data employing the least-squares fits. The composition was analyzed using an electron probe micro analyzer (EPMA,
JEOL). For the Ca substituted samples, we obtained Pr0.972 Ca0.027 Ba2.10
Cu3.81 O8.18 at 𝑥 = 0.02 and Pr0.944 Ca0.055 Ba2.13 Cu4.08 O7.94 at 𝑥 = 0.05.
Typical dimensions of the pelletized rectangular sample were 4.2 ×
3.4 × 1.0 mm3 . The electrical resistivity in a zero magnetic field wasmeasured using the 𝑑𝑐 four-terminal method. The magneto-transport
up to 9 𝑇 was measured by the 𝑎𝑐 four-probe method using a physicalproperty measuring system (PPMS, Quantum Design), elevating temperatures from 5 K to 40 K. The applied magnetic field was perpendicular to the applied electric current’s direction. The Seebeck coefficient(𝑆) was determined from thermal voltages along the measured sample’s
longitudinal direction [25] with a temperature difference of a few
Kelvins. Chromel-constantan thermocouples were used for measuringprobes. The absolute values of 𝑆 were calibrated using a referencematerial of high purity Pb rod. The Hall coefficient measurement atroom temperature was performed with the five-probe technique using
the PPMS, sweeping the applied field from +6 to −6 T. We measured
the temperature variation of the 𝑑𝑐 magnetization under zero-fieldcooling (ZFC) process of 0.1 𝑇 employing a superconducting quantum
interference device magnetometer (MPMS, Quantum Design).

Fig. 1. (Color online) (𝑎) Crystal structures of Pr123 with single-chain unit, Pr124
with double-chain unit, and Pr247 with single-chain and double-chain units alternately
stacked along the 𝑐-axis. (𝑏) Computed low-angle X-ray diffraction peaks showing theformation of Pr123, Pr124, and Pr247 phases. The indexed peak (002) in Pr124 is
responsible for (001) in Pr123 because of the doubling of lattices along the 𝑐-axis.
Similarly, the (004) peak in Pr247 corresponds to (002) in Pr124.

𝑇c up to 90 K because of the partial replacement of Sr2+ for Ba2+ [17,18]. These results are related to the hole transfer from the CuO double
chains to the CuO2 planes by the chemical pressure effect due to thesmaller Sr substitution.
A citrate pyrolysis approach is similar to nitrate combustion synthesis approaches [19,20] and a unique route to preparing reactive
precursor mixtures through an ignition process of a concentrated aqueous solution including metallic ions of stoichiometric composition. For
YBa2 Cu4 O8 with 𝑇𝑐 = 80 K and its related cuprate oxide compounds,
high-quality single-phase polycrystalline materials are successfully synthesized under ambient pressure of oxygen gas at lower annealed
temperatures [21–23]. We expect that this procedure allows us toprepare highly homogeneous and fine powders for functional oxidematerials compared with conventional solid-state reaction approaches.
In this study, we try controlling the carrier number along themetallic CuO double chains through the partial substitution of Ca for
the Pr site in the Pr124 system. Despite Ca2+ replacement for Pr3+ ,our overall data suggest a significant reduction in the carrier number,which is in contrast with the Ca doping effect in the Pr123 system.
The experimental outline is described in the next section. In Section 3,
we show the experimental data, including the X-ray diffraction pattern,
the electrical resistivity, the Seebeck and Hall coefficients, the magnetoresistance effect, and the magnetic susceptibility. Particularly, the X-ray
data show that the Ca ion is incorporated into the crystal structure. For
our understanding of a carrier suppression due to the Ca substitution,
we discuss the transport properties of PrCa124 based on the two-typesof carrier models.

3. Results and discussion
3.1. Synthesis and structure
Chemical synthesis, including citrate pyrolysis preparation, ensures
the homogeneity, compared with conventional solid-state reaction synthesis. Furthermore, chemical synthesis can produce very fine powders.
All starting materials were dissolved in HNO3 to obtain nitrate mixtures. The citric acid (C6 H8 O7 ) was added to nitrate mixtures as achelating agent and appropriate amounts of aqueous ammonia (NH3 )were added to adjust the pH value to ∼6.9. After neutralizing the
mixture solution, the metal citrate complexes with stoichiometric composition and its associated ammonium nitrate (NH4 NO3 ) were formed.
NH4 NO3 was employed for facilitating the auto-combustion process.
The addition of excess ammonia over the neutralization probably
yields metal ammine complexes, instead of metal citrate complexes.
We expect that the excess ammonia prevents chelating respective metal
ions with C6 H8 O7 (complexant) and violates compositional homogeneity among the constituents, resulting in non-stoichiometric precursors.
Similarly, for spinel ferrite synthesis, the pH = 7 was adapted inRef. [20]. Finally, spontaneous combustion reactions occurred due to
NH4 NO3 through heating the resultant precursors using a halogen-lamp
type hot plate. (refer to a video file recording the typical combustion
process, which will be given as supplementary data in Appendix A.) For

2. Experiment
Polycrystalline samples of Pr1−𝑥 Ca𝑥 Ba2 Cu4 O8 (PrCa124) with 𝑥 =0.0, 0.02, and 0.05 were synthesized using the citrate pyrolysis approach. In the first step, at 70 ◦ C–80 ◦ C, stoichiometric mixtures ofhigh purity Pr6 O11 , CaCO3 , Ba(NO3 )2 , and CuO were dissolved in nitric2

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Table 1
Structural properties of Pr1−𝑥 Ca𝑥 Ba2 Cu4 O8 (𝑥 = 0.0, 0.02, and 0.05). The typical lattice parameters are
estimated from the experimental results in Fig. 4.
Ca content
𝑥Annealing
temp. (◦ C)

Orthorhombic phase(space group)

𝑎
(Å)

𝑏
(Å)

𝑐
(Å)

0.0
0.0

891
860

Pr247(𝐴𝑚𝑚𝑚)
Pr124(𝐴𝑚𝑚𝑚)

3.89253.88503.91003.900450.79327.261

0.02

860

Pr124(𝐴𝑚𝑚𝑚)

3.88233.901927.276

0.05
0.05

880
860

Pr123(𝑃 𝑚𝑚𝑚)
Pr124(𝐴𝑚𝑚𝑚)

3.87103.88403.92973.898811.72727.293annealing temperature regions of 880 ◦ C–891 ◦ C, and 860 ◦ C–868 ◦ C,
respectively, as shown in X-ray diffraction patterns of Fig. 4 (𝑐). Near
the intermediate annealing temperature of 873 ◦ C, the Pr123 phase
was primarily detected accompanied by a minority phase of Pr124, as
evidenced from the magnified data in the inset of the lower panel on
the left-hand side (Fig. 4 (𝑐)). For instance, we noticed three satellite
peaks of Pr124 near 30◦ and identified one low-angle peak around 6.5◦
with (002) index of Pr124. It was hard to separate the main peaks of
the Pr123 and Pr124 phases from the observed data since they werecompletely overlapped near 30◦ .
In Fig. 3(𝑑), we show the enlarged X-ray data around 30◦ for the
Ca5% samples were annealed at 880 ◦ C, which agrees well with thecomputed patterns of the BaCuO2 cubic phase. Judging from theirmeasured intensities, we give a rough estimation of several weighpercentages for the impurity phase. In the case of light Ca substitution,
we detected no impurity phase of calcium oxides such as Ca2 CuO2
besides BaCuO2 .
Now, we plot, in Fig. 5(𝑎), (𝑏), and (𝑐), the lattice parameters as afunction of annealing temperature for the 𝑥 = 0.0, 𝑥 = 0.02 and 𝑥 = 0.05
samples, respectively. Here, the lattice parameters were estimated fromthe X-ray diffraction data employing the least-squares fits. These values
are in fair agreement with the published data [30–32] for the Pr124,
Pr247, and Pr123 compounds. The gray areas represent the stableformation of the Pr124 phase. The Ca substitution at Pr sites suppresses
the phase boundary between Pr124 and Pr123 (or Pr247) down to thelower temperature side. For the YCa124 system, it has been reported
that the synthesis boundary between the Y124 and Y123 phases shifts
the lower annealing temperatures with increasing Ca content [33].
However, the lattice parameters of the Ca substituted Pr124 (or Pr123)
remain nearly constant compared with these values of the Ca-freeparent samples. This result is probably related to the fact that the ionicradius of Ca2+ (1.12 Å) is close to that of Pr3+ (1.126 Å), as mentioned
in Ref. [13]. For the Ca lightly substituted Y1−𝑥 Ca𝑥 Ba2 Cu4 O8 (𝑥 = 0.0,
0.05, and 0.1) system, it has been reported that upon increasing the Cacontent, the 𝑐-axis slightly elongates but both the 𝑎 and 𝑏-axes remainunchanged [15]. For the oxygen concentration in PrBa2 Cu3 O7−𝛿 , weevaluate from the lattice parameters in Fig. 5 that 7 − 𝛿 is around
6.9, which is located around the optimal region [32]. From the EPMA
analysis, the oxygen contents of the Ca substituted Pr124 samples areabout the nominal value as mentioned before.

Fig. 2. (Color online) SEM images of Pr1−𝑥 Ca𝑥 Ba2 Cu4 O8 polycrystalline films fabricatedfrom single phase powders prepared by the citrate pyrolysis . (𝑎) 𝑥 = 0.0 and (𝑏) 0.05.

the SEM measurement, polycrystalline films on Ag substrates were prepared from the PrCa124 powders using an electrophoretic deposition
approach. The SEM images of Fig. 2 showed that the polycrystalline
grains with a few micron sizes are homogeneously dispersed.
As shown in Fig. 1(𝑎), we show the crystal structures of Pr123
with a single-chain unit, Pr124 with a double-chain unit, and Pr247
with single-chain and double-chain units alternately stacked along the𝑐-axis. Additionally, the computed low-angle X-ray diffraction curves(Fig. 1(𝑏)) are made clear, to identify their existing phases with theformation of Pr123, Pr124, and Pr247. Furthermore, we computed
the main and satellite peaks for Pr123, Pr124, and Pr247 near 2𝜃 =30–35 ◦ C using the published data (Fig. 3(𝑎)–(𝑐)).
Next, Fig. 4 shows X-ray diffraction patterns of Ca substituted
polycrystalline samples as a function of oxygen annealing temperature between 860 ◦ C and 891 ◦ C ((𝑎) 𝑥 = 0.0, (𝑏) 𝑥 = 0.02, and(𝑐) 𝑥 = 0.05). For the parent samples, the Pr124 phase was stably
formed within all annealing temperature ranges, except for the Pr247
phase prepared at a high temperature of 891 ◦ C. For both the Ca2%and Ca5% substituted samples, the Pr124 phase was established atlower annealing temperatures, while the Pr123 phase was formed at
higher temperatures. The X-ray diffraction curves for Pr123, Pr124,
and Pr247 were computed using the corresponding lattice parameters,
which will be given in Table 1 and Fig. 5. Additionally, for Ca5%
substituted compounds, the Pr123 and Pr124 phases were formed at the3.2. Resistivity and Seebeck coefficient
Next, we analyzed the effect of Ca substitution on the electricaltransport properties of Pr124. In Fig. 6(𝑎), the electrical resistivities for
Pr1−𝑥 Ca𝑥 Ba2 Cu4 O8 (𝑥 = 0.0, 0.02, and 0.05) are shown as a function oftemperature. With increasing the Ca content, the electrical resistivities
gradually increased over various temperatures accompanied by suppression in a maximum peak temperature from 190 K at 𝑥 = 0.0 down
to 138 K at 𝑥 = 0.05. Despite Ca2+ replacement for Pr3+ , the increased
resistivity data for PrCa124 imply a decrease in the carrier number.
Inset of Fig. 6 (𝑎) shows 𝜌 vs. 𝑇 for the Ca 5% substituted samples
annealed under three different conditions. A Ca 5% substituted sample
annealed at 880 ◦ C (Pr123 phase) showed a semiconducting behavior
like pure Pr123. However, 𝜌 of the 𝑥 = 0.05 sample annealed at 873 ◦ C
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Fig. 3. (Color online) Calculated X-ray diffraction patterns of Pr124 (𝑎), Pr247 (𝑏), and Pr123 (𝑐) near 2𝜃 = 30◦ –35◦ . (𝑑) Enlarged X-ray data around 30◦ for the Ca5% samples
annealed at 880 ◦ C. They are well fitted by the simulated curve of the BaCuO2 cubic phase.
Table 2
Physical properties of Pr1−𝑥 Ca𝑥 Ba2 Cu4 O8 (𝑥 = 0.0, 0.02, and 0.05). The typical data are collected from theexperimental results in Figs. 6–8.
Ca content𝑥𝜌 (300 K)(mΩcm)

Δ𝜌∕𝜌 (10 K)(%)

𝑆 (290 K)(𝜇V/K)

𝑅𝐻 (270 K, 300 K)(10−3 cm3 /C)

𝜇𝑒𝑓 𝑓
(𝜇𝐵 )

0.0
0.02
0.05
0.0[26]

2.1
2.8
3.1
1.2

16
–
5
16

20
26
29
27

1.2, 1.1

3.07

1.9, 1.6–, 0.4a

2.95
3.11c

∼400
∼80

–
–

93
77

(Pr1−𝑥 Ca𝑥 123)
0.0 [12]0.1 [12]a–, 6.7bRef. [27]b Ref. [28]c Ref. [29]calculation, assuming the energy dispersion 𝐸(𝑘) of the CuO doublechain model proposed by Habaguchi et al. [37]. These results provide(1/𝑁)(𝑑𝑁/𝑑𝐸) > 0 for the hole-doped region (𝑛 > 0.5). An increasein the hole number (decreasing the electron number from 1) yields adecrease in (1/𝑁)(𝑑𝑁/𝑑𝐸) reducing 𝑆 in Eq. (1). Thus, the improvement of 𝑆 due to Ca substitution also suggests a decrease in the carrier
number along the CuO double chains. Furthermore, the temperature
variation of 𝑆 for the parent sample showed a quick decrease from∼200 K and then reached quite a small value (∼1𝜇V/K) at lower
temperatures below 100 K. Particularly, the latter behavior has a deep
relationship with crossover from 1D to 2D in the low-temperatureelectronic states, as mentioned by Terasaki [26]. In the 2D electron
system, it has been well accepted that the density of states becomes aconstant. Therefore, assuming that Seebeck coefficient is proportional
to the energy derivative of DOS, then 𝑆 approaches a zero value. This
trend was a common future for all samples studied.
The magnetic field dependence of the Hall voltage for the 𝑥 = 0.0
and 0.05 samples at 270 K is plotted in the inset of Fig. 6 (𝑏). Applying
a linear fit to the Hall data, we obtained the Hall coefficient (𝑅𝐻 ) for
the 𝑥 = 0.0 and 0.05 samples, as listed in Table 2. The Ca substitution
at Pr site affected 𝑅𝐻 at 270 K from 1.2 × 10−3 cm3 /C at the 𝑥 = 0.0
sample to 1.9×10−3 cm3 /C at the 𝑥 = 0.05 sample. This finding suggests

was strongly suppressed and it followed a metallic property at lower
temperatures below ∼100 K. As mentioned in Section 3.1, the 𝑥 = 0.05
sample annealed at 873 ◦ C contained the Pr124 minority phase withmetallic properties, which contributes to a substantial decrease in the
low-temperature resistivity.
Fig. 6 (𝑏) illustrates Seebeck coefficients (𝑆) as a function of temperature for Pr1−𝑥 Ca𝑥 Ba2 Cu4 O8 (𝑥 = 0.0, 0.02, and 0.05). For theparent and Ca substituted samples, the values of 𝑆 at high temperatures
were improved due to Ca substitution. In the 1D electron correlated
system, such as a quasi 1D organic conductor, the Seebeck coefficientis well described by the Heikes formula 𝑆 = (𝑘𝐵 ∕𝑒)ln[2(1 − 𝑥)∕𝑥](𝑥:carrier concentration) at high temperature limit [34,35]. Following
the simple model, 𝑆 shows a monotonous increase with decreasing thehole concentration from 𝑥 = 0.5, indicating that larger magnitudes of
S offer lower carrier contents. In a conventional metal, the Seebeckcoefficient is given in such a way,{}
(𝜋𝑘𝐵 )2 𝑇
1 𝑑𝑁(𝐸)(1)
𝑆(𝑇 ) =
3𝑒
𝑁(𝐸) 𝑑𝐸
where 𝑁(𝐸) represents the density of electronic state (DOS). In ourprevious study [36], we computed the energy derivative of the DOS
as a function of the electron density using density functional band4

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Fig. 4. (Color online) X-ray diffraction patterns of polycrystalline samples as a function of oxygen annealing temperature (860∼891 ◦ C). (𝑎) 𝑥 = 0.0, (𝑏) 𝑥 = 0.02 and (𝑐) 𝑥 =0.05. The X-ray diffraction curves for Pr123, Pr124, and Pr247 were computed using the corresponding lattice parameters, which will be given in Table 1 and Fig. 5. For theparent samples, the Pr124 phase was stable except for Pr247 phase formed at 891 ◦ C. For both Ca2% and Ca5% substituted samples, the Pr124 phase was established at lower
annealing temperatures, while the Pr123 phase was formed at higher temperatures.

a substantial drop in carrier density due to the Ca substitution, whichis almost consistent with the enhancement of the Seebeck coefficientat higher Ca content. For comparison, the published data for the Pr123
system are cited in Table 2. The Ca substitution at the Pr site suppressedboth the electrical resistivity and the Seebeck coefficient through hole
doping in the CuO2 plane of the Pr123 phase. However, the effect of Ca
substitution in the Pr124 system caused a significant increase in both 𝜌and 𝑆 accompanied by a drop in the carrier density. Thus, considering
the main conduction channel along the CuO double chains in the Pr124
phase, the suppression in the carrier number is probably attributed to
CuO double-chain block.
5

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Fig. 6. (Color online) Temperature dependences of electrical resistivities and Seebeckcoefficients, (𝑎) and (𝑏), for Pr1−𝑥 Ca𝑥 Ba2 Cu4 O8 (𝑥 = 0.0, 0.02, and 0.05). Inset of(𝑎) shows 𝜌 vs. 𝑇 for the Ca 5% substituted samples annealed under three different
conditions. Magnetic field dependence of the Hall voltage for the 𝑥 = 0.0 and 0.05
samples at 270 K is plotted in the inset of (𝑏). Applying a linear fit to the Hall data
gives rise to Hall coefficient (𝑅𝐻 ) for the 𝑥 = 0.0 and 0.05 samples as listed in Table 2.

discussed later in terms of the two types of carries model. We give somecomments on the magneto-resistance effect of disordered Pr124 single
crystals using Kohler’s plot. Narduzzo measured the 𝑏-axis magnetoresistance data for Pr124 crystals with different levels of disorder andexamined their MR behavior using Kohler’s plot [38]. For disorderedsamples, it was revealed that the positive MR effect is more enhanced
accompanied by deviations from Kohler’s rule. The suppressed MR
data for PrCa124 are in contrast to those for the disordered Pr124
crystals. In Fig. 7(𝑐), we plotted MR data at selected temperatures asa function of (𝐻∕𝜌(0))2 . For both the Ca0% and Ca5% samples, weunderstand that Kohler’s plots follow no single curve at temperature
region above 15 K, indicating violation of Kohler’s rule. Our MR data
for the Ca5% substituted sample is not explained by the same scenario
as the anomalously enhanced MR in Pr124 single crystals. In the initial
fields, the weakly negative MR effect appeared for both the 𝑥 = 0.0 and
0.05 samples, which seems to be related to a suppression of carrier
scattering by Pr 4f spin. The low-temperature magnetization data were
measured under ZFC of 0.1 𝑇 for both the 𝑥 = 0 and 0.05 samples,
as illustrated in the inset of Fig. 8. The antiferromagnetic transition
temperature 𝑇𝑁 = 17 K of the 𝑥 = 0 sample remains constant due to the
Ca substitution, resulting in a similar trend in the low field negative MR
effect. Applying the Curie–Weiss law to the magnetic susceptibility data
illustrated in Fig. 8, we evaluated the magnetic moment 𝜇𝑒𝑓 𝑓 = 3.07
𝜇𝐵 at Ca0% and 2.95 𝜇𝐵 at Ca5%. The value decreased by about
4% due to the Ca5% substitution. The magnitude of the magnetic
moment for the Ca5% substituted sample is reduced by 5% because
the nonmagnetic ion of Ca2+ is partially replaced with the Pr3+ ion.
This experimental estimation is not so far from the suggested value.
The estimated value (3.07 𝜇𝐵 ) is smaller than the magnetic moment ofFig. 5. (Color online) Lattice parameters vs annealing temperature. (𝑎) 𝑥 = 0.0, (𝑏) 𝑥= 0.02 and (𝑐) 𝑥 = 0.05. The gray areas represent the stable formation of the Pr124
phase. The closed symbols ( : 𝑎-axis,■: 𝑏-axis, ▴: 𝑐-axis) represent the publisheddata [30–32]. (Pr124:Horii, Pr247:Yamada, Pr123:Lopez-Morales).

∙3.3. Magneto-resistance
Additionally, we demonstrated magneto-resistance (MR) effect,𝛥𝜌∕𝜌(0)= (𝜌(H)-𝜌(0T))/𝜌(0T), measured at selected temperatures for
Pr1−𝑥 Ca𝑥 Ba2 Cu4 O8 (𝑥 = 0.0 and 0.05) (Fig. 7). First, the MR data were
almost fitted by 𝐻 2 solid curves. In Ref. [26], the low-temperature
positive MR effect in Pr124 is explained by the classical model, in whichelectron orbitals are distorted by Lorentz force in the 2D electronic
state. Secondly, a large MR effect observed in the parent sample(∼16% at 10 K) was strongly suppressed down to ∼5% in the Ca 𝑥
= 0.05 substituted case. This suppression in the MR effect will be
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T. Teramura et al.

Fig. 8. (Color online) Temperature dependence of magnetic susceptibility measured
under ZFC of 0.1 𝑇 for both the 𝑥 = 0.0 and 0.05 samples. The arrows in the inset
represent the antiferromagnetic transition temperature 𝑇𝑁 =17 K.

where 𝜎𝑖 , 𝑛𝑖 , and 𝜇𝑖 (i=1 and 2: electron and hole) represent the
conductivity, the carrier number and the mobility, respectively. Thus,
the total Seebeck coefficient is expressed using the electron and hole
conductivities, 𝜎1 and 𝜎2 [40],𝑆=

𝜎1 𝑆 1 + 𝜎2 𝑆 2
𝜎1 + 𝜎2(2)where 𝑆1 (< 0) and 𝑆2 (> 0) are responsible for the electron and holecomponents, respectively. Additionally, the Hall coefficient for the two
types of carrier models is given by the following formula,𝑅𝐻 =𝜇22 𝑛2 − 𝜇12 𝑛1𝑒(𝑛1 𝜇1 + 𝑛2 𝜇2 )2Here, we assume that the number of electron carriers is smaller thanthat of hole carriers, 𝑛1 < 𝑛2 , keeping the electron and hole mobilities
such as 𝜇1 ∼ 𝜇2 . However, we set the number of electron carrier 𝑛1 tobe zero and that of hole carrier 𝑛2 to be constant. For clarification, we
represent the corresponding conductivity, Seebeck coefficient, and Hall
coefficient as 𝜎 ′ , 𝑆 ′ , and 𝑅′𝐻 , respectively. For the former and lattertransport coefficients, we have 𝜎 > 𝜎 ′ , 𝑆 < 𝑆 ′ , and 𝑅𝐻 < 𝑅′𝐻 as follows,
𝜎 = 𝑒𝜇2 (𝑛1 + 𝑛2 ) > 𝜎 ′ = 𝑛2 𝑒𝜇2𝑆=𝑛1 𝑆1 + 𝑛2 𝑆2< 𝑆 ′ = 𝑆2 (𝑆1 < 0, 𝑆2 > 0)
𝑛1 + 𝑛2and𝑅𝐻 =Fig. 7. (Color online) Magneto-resistance effect, 𝛥𝜌∕𝜌(0)= (𝜌(H)-𝜌(0T))/𝜌(0T), at selected temperatures, (𝑎) 𝑥 = 0.0 and (𝑏)𝑥 = 0.05, for Pr1−𝑥 Ca𝑥 Ba2 Cu4 O8 . MR data
beyond 2T are almost fitted by 𝐻 2 solid curves. Inset of (𝑏) shows 𝛥𝜌∕𝜌(0)= (𝜌(9T)𝜌(0T))/𝜌(0T), as a function of temperature for both compositions. In (𝑐) 𝑥 = 0.05, weplotted MR data at selected temperatures as a function of (𝐻∕𝜌(0))2 . Inset of (𝑐) shows
Kohler’s plot for the parent sample.

𝑛2 − 𝑛1𝑒(𝑛1 + 𝑛2 )2< 𝑅′𝐻 = 1∕𝑒𝑛2 .

These rough estimations qualitatively reproduce the high-temperature
improvements for the resistivity, the Seebeck coefficient, and the Hall
coefficient due to Ca substitution. We note that a significant decrease in
the electron density after the Ca substitution at the Pr site is an essential
assumption.
Furthermore, we give some comments on the effect of magnetoresistance for Pr1−𝑥 Ca𝑥 124 (𝑥 = 0.0 and 0.05). According to the transport coefficient classical theory, we obtain the magneto-resistance formula at small magnetic fields 𝐻,

the Pr3+ free ion (3.58 𝜇𝐵 ), which is closely related to the crystal field
effect or hybridization effect of Pr-4f and O-2p orbitals [28].
Finally, we discuss our high-temperature experimental data for the
Seebeck and Hall coefficients, applying the two types of carrier models
with electrons and holes [39]. First, the total conductivity is written as
the sum of electron and hole components𝛥𝜌∕𝜌(0) =𝜎1 𝜎2 (𝛽1 + 𝛽2 )2 𝐻 2(𝜎1 + 𝜎2 )2(𝛽𝑖 = 𝑒𝜏𝑖 ∕𝑚𝑖 )(3)

where 𝜏𝑖 and 𝑚𝑖 represent the relaxation time and effective mass forthe corresponding carrier (𝑖 = 1 and 2: electron and hole). Generally,𝜎 = 𝜎1 + 𝜎2 = 𝑛1 𝑒𝜇1 + 𝑛2 𝑒𝜇2
7Physica B: Physics of Condensed Matter 646 (2022) 414226

T. Teramura et al.

the existence of magneto-resistance in metal is evidence for different
types of carriers [39]. When the two types of carriers such as different
masses or different charges are deflected by different amounts in themagnetic field, it is impossible to find an electric field that will keep
both components of the current going in the same direction. The given
formula (3) for the two types of carrier models supports that 𝛥𝜌 is
proportional to 𝐻 2 . Furthermore, if the electrons are removed (𝑛1 ∼ 0),
we then obtain that 𝛥𝜌 ∼ 0. This simple estimation is consistent withthe suppressed MR effect for the Ca substituted sample. If we assume
that the electron carriers are removed because of the Ca substitution,
our overall experimental results are well explained on the basis of thetwo types of carrier transport classical model.
In conclusion, we tried controlling the carrier number along themetallic CuO double chains through the partial substitution of Ca for
the Pr site in the Pr124 system. The Pr/Ca124 compounds with low
Ca substitution were successfully synthesized using the citrate pyrolysis
approach. The lattice parameters remained almost constant for the Cacontent, and the Ca ion was incorporated into the crystal structure.
Despite the addition of a divalent ion, our overall data suggest asignificant reduction in the carrier number, which is in contrast with
the Ca doping effect in the Pr123 system. We discussed the influenceof Ca substitution on the electrical transport and magneto-transport
properties based on the two types of carrier model.

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CRediT authorship contribution statement
Takehiro Teramura: Investigation, Writing – original draft, Investigation. Michiaki Matsukawa: Writing – review & editing, Investigation. Tatsuya Senzaki: Investigation. Haruka Taniguchi: Investigation. Kazuhiro Sano: Investigation. Yoshiaki Ōno: Investigation.
Makoto Hagiwara: Investigation.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared toinfluence the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgments
We would like to thank K. Honnami and K. Toyota for sample preparation, and M. Nakamura for his assistance in the PPMS experiments.
This work was supported in part by the Japan Society for the Promotionof Science (KAKENHI Grants No. JP19K04995).
Appendix A. Supplementary data
Supplementary material related to this article can be found online
at https://doi.org/10.1016/j.physb.2022.414226.
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