Qiu X.G. (Ed.) High Temperature Superconductors
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Electron-doped cuprates as high-temperature superconductors 231
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6.12 Ce doping dependence of T
c
in T
'
-Pr
2 – x
Ce
x
CuO
4
. The T
c
-vs-x by
the improved (solid line) and standard (dashed line) reduction are
compared. With the improved reduction, the superconducting window
expands down to x = 0.04 and there is a clear tendency of an increasing
T
c
with decreasing x. (Reprinted with permission from Brinkmann et al.
(1997), Physica C, 292, 104. © 1997 Elsevier.)
6.13 Correlation between residual resistivity and T
c
reduction, ‘the
larger
ρ
R
, the lower T
c
’. Different symbols represent different specimens:
filled squares and open circles are the data for two specimens with
x = 0.15 whereas filled diamonds and open triangles are the data for
two specimens with x = 0.07. (Adapted from Brinkmann et al., 1996.)
232 High-temperature superconductors
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window expands with lower x
opt
and higher T
c
max
for larger RE
3+
, and consequently
the T
c
-vs-x curve is not universal. This trend is not explained by the chemical
pressure effect since T
c
has almost no dependence on pressure in square-planar
cuprates. The trend seems to be related to the empirical trend of solid state chemistry
in T
'
cuprates that O
ap
removal is easier for larger RE
3+
(section 6.3.2).
6.5.3 Superconductivity in T
'
parent compounds
The parent compounds of high-temperature superconductors have long been
believed to be universally a Mott Hubbard insulator. T-La
2
CuO
4
is a Mott insulator
without doubt. T
'
-RE
2
CuO
4
has also been believed a Mott insulator since the
discovery of ‘electron-doped’ superconductors in 1989. In fact, not only early
6.14 T
c
-vs-x for MBE-grown T
'
-RE
2 – x
Ce
x
CuO
4
films with different RE
(La, Pr, Nd, Sm, and Eu). The superconducting window expands with
larger RE
3+
.
Table 6.7 RE dependence of the optimum doping level (x
opt
) and the
highest T
c
(T
c
max
) for MBE-grown T’-RE
2-x
Ce
x
CuO
4
RE x
opt
T
c
max
(K)
La 0.08 31.0
Pr 0.135 27.0
Nd 0.140 25.5
Sm 0.150 19.0
Eu 0.155 12.0
Gd – 0.0
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polycrystalline pellets but also single crystals of Nd
2
CuO
4
and Pr
2
CuO
4
showed
semiconducting behavior with high resistivity. However, it should be noted that T
'
parent compounds were not given ‘reduction’ for O
ap
removal in most cases. This
is because the parent compounds are much easier to decompose than Ce-containing
compounds (section 6.3.1). In fact, MBE-grown T
'
-RE
2
CuO
4
films of RE = La,
Pr, Nd are not highly insulating after careful ‘reduction’ but have
ρ
(300 K) of
2–10 mΩcm and metallic behavior (d
ρ
/dT > 0) down to 150–200 K (Tsukada
et al., 2002). However, they showed an upturn of resistivity at lower temperatures
and no superconductivity.
The first compounds Tsukada et al., (2005a) made superconducting without
electron doping were T
'
-(La,RE)
2
CuO
4
, grown by MBE. In these compounds,
La
3+
is substituted not by Ce
4+
but by isovalent RE
3+
(RE = Sm, Eu, Gd, Tb, Lu,
Y), and there is no effective dopant. Since then, further exploration on synthetic
routes for more complete O
ap
removal has taken place. Finally, superconductivity
in the parent compounds, T
'
-RE
2
CuO
4
(RE = Pr, Nd, Sm, Eu, Gd), by MOD was
achieved by Matsumoto et al. (2008, 2009a). Figure 6.15 shows a superconducting
transition of a Nd
2
CuO
4
film as one example. T
c
on
is as high as 33 K, which is
~10 K higher than T
c
~ 24 K of ‘electron-doped’ Nd
1.85
Ce
0.15
CuO
4
. Figure 6.16
compares the T
c
with and without Ce doping for each RE. It should be noted that
undoped T
c
is substantially higher than electron-doped T
c
for all RE. The most
remarkable is Gd
2
CuO
4
: there has been no report that electron-doped
Gd
2 – x
Ce
x
CuO
4
becomes superconducting whereas undoped Gd
2
CuO
4
has T
c
on
as
high as 20 K (Manthiram and Zhu, 1994).
The key step for superconductivity is to fire MOD films in a low-p
O2
atmosphere,
the aim of which is to minimize the amount of O
ap
impurities prior to the
post-reduction process. Figure 6.17 shows the effect of p
O2
during firing, which
6.15 Superconductivity in Nd
2
CuO
4
films prepared by MOD. The T
c
onset
is as high as 33 K.
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6.17 Superconducting versus nonsuperconducting Sm
2
CuO
4
films. The
film fired in p
O2
= 2.8 × 10
–3
atm at 850 °C became superconducting after
reduction whereas the film fired in p
O2
= 1 atm at 900°C never became
superconducting even after stronger reduction.
compares the resistivity of two Sm
2
CuO
4
films (A and B): film A fired at 900 °C
for 1 h in p
O2
= 1 atm, followed by vacuum reduction at 750 °C for 10 min, and
film B fired at 850 °C for 1 h in p
O2
= 2.8 × 10
–3
atm, followed by vacuum
reduction at 440 °C for 10 min. Film A is metallic down to 180 K with
6.16 Comparison of T
c
between undoped T
'
-RE
2
CuO
4
(solid circles) and
electron-doped T
'
-RE
1.85
Ce
0.15
CuO
4
(dashed line). Undoped T
'
-RE
2
CuO
4
has substantially higher T
c
than electron-doped T
'
-RE
1.85
Ce
0.15
CuO
4
.
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ρ
(300 K) ~ 100 mΩcm, but shows resistivity upturn at lower temperatures. In
contrast, film B is all metallic with
ρ
(300 K) ~ 900 µΩcm, and shows
superconductivity at T
c
on
= 28 K.
After low-p
O2
firing, films were ‘reduced’ in vacuum (< 10
–4
Torr) at different
temperatures (400 °C to 500 °C) for 5 to 60 min. The reduction is optimized based
on the c-axis lattice constant (c
0
) since the c
0
monotonically shrinks with reduction
until films decompose (Matsumoto et al., 2009c). Figure 6.18 plots the
ρ
(300 K)
6.18 T
c
and
ρ
(300 K) versus c
0
for Pr
2
CuO
4
films on DyScO
3
(110)
substrates prepared by MOD. (a) (T
c
-vs-c
0
): open and filled circles
stand for T
c
onset
and T
c
end
. (b) (
ρ
(300 K)
-vs-c
0
): crosses stand for films
not showing superconductivity, filled and open circles stand for
films showing superconductivity with and without zero resistance,
respectively. (Reprinted with permission from Matsumoto et al. (2009a),
Phys Rev B, 79, 100508(R). © 2009 by the American Physical Society.)
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(lower) and T
c
(upper) as a function of c
0
for MOD-grown Pr
2
CuO
4
films. One
can divide the range of c
0
into the following three regions.
I Insufficient reduction (12.23 Å ≥ c
0
≥ 12.20 Å): superconductivity improves
with reduction.
II Optimal reduction (12.20 Å ≥ c
0
≥ 12.19 Å): superconductivity is optimal.
III Excessive reduction (12.19 Å ≥ c
0
≥ 12.16 Å): superconductivity degrades
with reduction.
Figure 6.18 can be understood by assuming that the two effects, namely O
ap
removal and O1 loss, are involved in the reduction process. The predominant
effect in region I is O
ap
removal, which improves the film properties. In contrast,
the predominant in region III is O1 loss, which degrades the film properties
although O
ap
may be removed further as judged from the shrinkage of c
0
. The O
ap
removal is slightly quicker than the O1 loss, which realizes the situation with O
ap
atoms mostly cleaned up but with O1 atoms mostly preserved, and provides a
stage potential for high-T
c
superconductivity.
6.5.4 Generic phase diagram of T
'
cuprates
The same optimization in ‘reduction’ has been performed for Ce-containing
compounds (Matsumoto et al., 2009b). Figure 6.19 is a plot of T
c
-vs-x of resultant
T
'
-Nd
2 – x
Ce
x
CuO
4
films, which is compared with the one derived from past bulk
works and another from previous MBE works. The highest T
c
of the MOD films
6.19 T
c
-versus-x of Nd
2 – x
Ce
x
CuO
4
films prepared by MOD. For a
comparison, the data of bulk samples (dotted line) and MBE films
(triangles) are also plotted. Open and filled symbols represent T
c
onset
and T
c
end
. The solid line is a guide for the eye.
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is 29 K at x = 0.00, and T
c
monotonically decreases from 29 K to 24 K with
increasing x from 0.00 to 0.15. The T
c
of 24 K at x = 0.15 agrees with the
established bulk T
c
of Nd
1.85
Ce
0.15
CuO
4
. T
c
for x > 0.15 could not be determined
because of the solubility limit of Ce in the MOD process. In this region, however,
the data from MBE growth are complementary. The phase diagram derived from
MBE films shows a dome shape extending from x = 0.10 to 0.20. Although the T
c
of MBE films is always higher than the bulk T
c
, it is lower than the T
c
of MOD
films for x < 0.15. With the MOD and MBE data together, the T
c
of NCCO films
monotonically decreases from 29 K at x = 0.00 and disappears around x = 0.20.
This T
c
-vs-x, although it is quite different from the early bulk one, represents the
generic phase diagram for NCCO with O
ap
impurities removed.
6.6 Physical properties (1) – normal-state properties
6.6.1 Magnetism
The normal-state properties of T
'
cuprates are reviewed in this section, starting
with magnetism as it is the most closely related to the superconductivity in T
'
cuprates. The presence of O
ap
impurities greatly affects the magnetism in the CuO
2
layer as well as the superconductivity (T
c
-vs-x) in the previous section. One has to
pay attention to how carefully O
ap
impurities are removed in each article. The first
magnetic measurement on T
'
-RE
2 – x
Ce
x
CuO
4
was muon spin relaxation (µSR)
performed just after the discovery of ‘electron-doped’ superconductors. Since
then, magnetic studies on T
'
cuprates have been continuing, but experimental
results are sometimes contradictory and none of them are definitive, which is
somewhat similar to the situation for oxygen nonstoichiometry. The reason is, at
least in part, inhomogeneity of oxygen distribution in specimens. Neutron
diffraction experiments, especially, require large single crystals, in which
homogeneous oxygen distribution is hard to achieve.
The essence of the first result of µSR by Luke et al. (1990) is illustrated in
Fig. 6.20, and can be summarized as follows.
• The parent compounds show static magnetic order, which was later confirmed
by neutron diffraction to be antiferromagnetic order. The Néel temperature (T
N
)
for 3D static AF order is about 250 K, which is comparable to T
N
= 250–300 K
in T-La
2
CuO
4
.
• The initial decrease of T
N
with x is more gradual than in T-LSCO. There is an
abrupt drop of T
N
from ~80 K at x = 0.14 to <5 K at x = 0.15. Superconductivity
appears after long-range AF order disappears.
• In specimens not reduced, the AF order remains and no superconductivity
appears even at x = 0.15.
The electronic phase diagrams (T
c
-vs-x, T
N
-vs-x) of T
'
-Nd
2 – x
Ce
x
CuO
4
and
T-La
2 – x
Sr
x
CuO
4
in Fig. 6.20 appear to be roughly symmetric. One large difference
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is that electron-doped T
'
-Nd
2 – x
Ce
x
CuO
4
shows a much wider AF region and a
much narrower SC (superconducting) region than hole-doped T-La
2 – x
Sr
x
CuO
4
.
Luke et al. explained this difference by dilution versus frustration of Cu spins by
electron versus hole doping. A doped electron resides at the Cu site and compensates
a Cu spin, leading to the dilution of the Cu spin density, whereas a doped hole
resides at the oxygen site and forces the neighboring two Cu spins to align,
introducing frustration in the AF order. The influence of doping on the AF order is
weaker in electron doping than in hole doping, hence the AF phase remains until
higher x in electron doping, and touches the SC phase. According to Fig. 6.20, the
superconductivity in T
'
cuprates suddenly appears at the SC–AF boundary with
maximum T
c
, which points toward the competition between the SC and AF orders.
The first experiments by Luke et al. were performed on Nd
2 – x
Ce
x
CuO
4
samples
that were not well-characterized, especially in oxygen homogeneity, but the
results were basically supported by later µSR experiments (Kadono et al., 2003;
Fujita et al., 2003a). There are a few reports claiming that the SC and AF orders
coexist in Nd
2 – x
Ce
x
CuO
4
with x = 0.14 – 0.15 (Watanabe et al., 2001), but the
inhomogeneity of samples is suspected.
The results of µSR were also supported by neutron diffraction. The early neutron
diffraction experiment by Matsuda et al. (1990, 1992) on single crystals of
6.20 Electronic phase diagram of hole-doped T-La
2 – x
Sr
x
CuO
4
and
electron-doped T
'
-Nd
2 – x
Ce
x
CuO
4
based on the µSR experiments. The
electron-hole symmetry appears to hold roughly. However, note that the
structure is different in the hole- and electron-doped sides. Since the T
N
of
T
'
-Nd
2 – x
Ce
x
CuO
4
depends crucially on the amount of O
ap
impurities, the
phase diagram in the electron-doped side will change dramatically after
complete removal of O
ap
impurities. (Adapted from Luke et al., 1990.)
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Nd
2 – x
Ce
x
CuO
4
and Pr
2
CuO
4
is one of the most extensive works on the magnetism
of T
'
cuprates. In the parent compounds, Nd
2
CuO
4
and Pr
2
CuO
4
, the Cu
2+
spin has
a magnetic moment of ~ 0.4
µ
B
, and the AF order develops below T
N
= 255 K. The
Cu
2+
spin structure in Nd
2
CuO
4
shows complex behavior at low temperatures due
to the interaction with Nd
3+
. moments whereas the spin structure in Pr
2
CuO
4
is
unchanged with temperature owing to the singlet ground state of Pr
3+
. In the parent
compounds, no significant change in the magnetic behavior was observed by heat
treatment in Ar or in O
2
. In Ce-doped compounds, however, a large change was
observed by heat treatment. In as-grown samples with Ce doping of x = 0.15, the
AF order remains with T
N
varying from 125 K to 160 K. After reduction (950 °C/
Ar/20 hr followed by 500 °C/O
2
/20 hr), the SC phase was predominant at x = 0.15
but with the AF order remaining in 10% or more volume of a specimen, which
corresponds to the region in which O
ap
impurities remain.
From the viewpoint of the mechanism of high-temperature superconductivity,
the crucial issue is whether dynamic AF fluctuations exist in superconducting
samples or not. In fact, in T-La
2 – x
Sr
x
CuO
4
, it has been claimed that dynamic AF
fluctuations are observed in superconducting samples. On clarifying this issue in
T
'
cuprates, however, high background magnetic scattering by Nd
3+
moments is
one obstacle in obtaining the detailed information on the dynamics of Cu spins in
Nd
2 – x
Ce
x
CuO
4
. In the above work by Matsuda et al., no inelastic magnetic peak
clearly above the background was observed in the superconducting samples.
Later, the improved statistics enabled Yamada and co-workers to observe inelastic
magnetic signal at (1/2 1/2 0) in superconducting Nd
1.85
Ce
0.15
CuO
4
samples,
indicating the presence of commensurate AF fluctuations. More recently, further
efforts have been performed employing Pr
1 – x
LaCe
x
CuO
4
single crystals in order
to reduce the background magnetic scattering. However, the role of dynamic AF
fluctuations to superconductivity has not been settled.
As mentioned above, at x = 0.15, T
N
is 125 K – 160 K in the as-grown state
whereas T
N
is 0 K in the reduced state. Hence the T
N
of the AF order in T
'
cuprates
depends not only on the Ce doping level but also (or more crucially) on the amount
of O
ap
impurities. This statement may also be true for lightly doped or parent
compounds, and the AF order is expected to be substantially suppressed or even
disappear when O
ap
impurities are fully removed. Taking account of the competition
between the SC and AF orders, the expansion of the superconducting window down
to x = 0.0, as mentioned in sections 6.5.3 and 6.5.4., seems to indicate that the AF
order may not be intrinsic at any of x but extrinsic, namely induced by O
ap
impurities.
6.6.2 Resistivity
The best transport properties can be obtained with epitaxial thin films as mentioned
in section 6.4.1. MOD growth provides better results than MBE growth in
x < 0.15 whereas the opposite is true in x ≥ 0.15. Figure 6.21 shows the
ρ
-T curves
of MBE-grown RE
2 – x
Ce
x
CuO
4
films with different RE (Naito et al., 2002). The
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room-temperature resistivity,
ρ
(300 K), of best Nd
1.85
Ce
0.15
CuO
4
films is as low
as 100 µΩcm, which is 1/3 to 1/4 of the lowest value reported for single crystals.
The resistivity becomes the most metallic at around x = 0.175, slightly ‘overdoped’:
ρ
(300 K) ~ 100 µΩcm,
ρ
(30 K) ~ 10 µΩcm, and RRR (≡
ρ
(300 K)/
ρ
(30 K)) ~10.
The anisotropy (
ρ
c
/
ρ
ab
) of resistivity is reported to be ~10
4
from the data of
Nd
1.85
Ce
0.15
CuO
4
single crystals (Hidaka and Suzuki, 1989).
The resistivity is nearly proportional to temperature in most hole-doped cuprates,
whereas the resistivity appears to follow a T
2
dependence in T
'
-(RE,Ce)
2
CuO
4
.
Tsuei et al. (1989) ascribed the T
2
dependence to electron–electron scattering.
However, the coefficient of the T
2
dependence is 2–3 orders of magnitude larger and
the temperature range is much wider than electron-electronic scattering observed in
conventional metals. Brinkmann et al. (1997) reported resistivity up to 700 K,
as shown in Fig. 6.22, which is not greatly different from the temperature depend-
ence of conventional metals, but with a substantially higher Debye temperature
(~ 500 K). The T
2
dependence in T
'
-(RE,Ce)
2
CuO
4
appears to be a conclusion
derived from the data in a limited temperature range below room temperature.
The behavior of the low-temperature resistivity should be commented on. T
'
cuprates often show a resistivity upturn at low temperatures (Fournier et al., 1997;
Sekitani et al., 2002). Figure 6.23 shows two examples: nonsuperconducting
Pr
2 – x
Ce
x
CuO
4
film with x ~ 0.10 and superconducting Nd
2 – x
Ce
x
CuO
4
with x ~
0.15, both grown by MBE. In the latter film, the normal-state behavior is revealed
by suppressing superconductivity in magnetic fields. The upturn has a log T
dependence below the resistivity minimum but saturates to a finite value toward
lowest temperatures. In addition, the upturn is suppressed in magnetic fields
6.21
ρ
-T curves of MBE-grown RE
2 – x
Ce
x
CuO
4
films with different RE.
The triangles, squares, and circles represent RE = La with x = 0.09,
RE = Pr with x = 0.135, RE = Nd with x = 0.140, respectively.