Band filling dependence of the electrical transport of Nd 1-xAxTiO3 ( A = Ca , Sr and Ba)

Article abstract of DOI:10.1016/j.jallcom.2003.11.021

We are here reporting the results of the studies of X-ray, electrical resistance (R) and thermoelectric power (TEP, S) on Nd_1-xA _xTiO₃ (A = Ca, Sr and Ba) over a wide temperature range as a function of 3d band filling n ( = 1-x). Depending upon the levels of band filling all the compounds studied show both insulating as well as metallic behavior thereby exhibiting a metal-insulator (M-I) transition. The filling level at which M-I occurs varies with the size of the divalent alkaline earth ions A. In the correlated metallic phase resistance data scales well with T ² suggesting that electron-electron scattering plays a major role governing the conduction mechanism. Analysis of the T-linear part of the TEP measurement reveals that the occurrence of the metal-insulator transition is due to the enhancement of the effective mass of the carriers.

Full text of DOI:10.1016/j.jallcom.2003.11.021

Journal of Alloys and Compounds 375 (2004) 15–23
Band filling dependence of the electrical transport of
Nd1−xAxTiO3 (A = Ca, Sr and Ba)
S. Das∗, A. Poddar, B. Roy
Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Calcutta 700064, India
Received 27 October 2003; received in revised form 14 November 2003; accepted 14 November 2003
Abstract
We are here reporting the results of the studies of X-ray, electrical resistance (R) and thermoelectric power (TEP, S) on Nd1−xAxTiO3
(A = Ca, Sr and Ba) over a wide temperature range as a function of 3d band filling n (=1 − x). Depending upon the levels of band filling all
the compounds studied show both insulating as well as metallic behavior thereby exhibiting a metal–insulator (M–I) transition. The filling level
at which M–I occurs varies with the size of the divalent alkaline earth ions A. In the correlated metallic phase resistance data scales well with
T2 suggesting that electron–electron scattering plays a major role governing the conduction mechanism. Analysis of the T-linear part of the
TEP measurement reveals that the occurrence of the metal–insulator transition is due to the enhancement of the effective mass of the carriers.
© 2003 Elsevier B.V. All rights reserved.
Keywords: Titanate; Metal–insulator transition; Resistivity; Thermopower
1. Introduction
lators. A Mott–Hubbard insulator can be transformed to
a correlated metal by enhancing the one-electron transfer
interaction and hence reducing the relative strength of the
electron correlation effect (U/W, where U is the on-site
Coulomb repulsion and W is the one-electron bandwidth of
the conduction band) with application of external pressure
such as observed in V2O3 [4] and PrNiO3 [5] or, with modi-
fication of the chemical composition as employed in RNiO3
(R being the rare-earth ion) [6]. The M–I transition induced
by changes of the bandwidth of the conduction band is
termed as bandwidth controlled insulator-metal transition.
In addition to the phase change associated with an opening
or, closing of the Mott-type or, CT-type gap due to variation
of U/W at a fixed integer valence of the constituent metal
element, there exists another type of insulator-metal (I–M)
transition induced by changes of the band filling of the
conduction band. This is termed as carrier doping or, filling
controlled I–M transition where the electronic process is
qualitatively different from the case of conventional doped
semiconductors with weak electron correlation. A typical ex-
ample of the doping-induced I–M transition is that observed
in layered cuprate compounds where drastic changes of
electronic structures and properties have been observed with
variation of the effective valence of Cu or, through filling of
the Cu–O related band. It is to be mentioned here that the
perovskite structure compounds are quite suitable for filling
Recently, intensive studies on the electronic properties of
the 3d transition metal compounds with perovskite related
structure have revealed a number of intriguing features [1,2]
of highly correlated electron system. Because of the strong
electron-correlation effect and resultant carrier localization,
most of these compounds undergo a metal–insulator (M–I)
transition as a function of temperature, carrier concentration,
bandwidth and so on [2]. In the Zaanen–Sawatzky–Allen
(ZSA) scheme [3], insulating properties arising from the
strong correlation between d electrons can be categorized
into two classes: Mott insulators (MI) and charge transfer
insulators (CTI). In Mott insulators the minimum charge gap
is formed between the d electron states i.e., the upper and
lower Hubbard bands whereas in CT insulators, the gap is
formed between the ligand (e.g., oxygen) p state and the un-
occupied d-like upper Hubbard band. According to the ZSA
scheme, the parent compounds for cuprate superconductors
with 3d9 configuration have been assigned to CT-type in-
sulators whereas some light transition metal oxides (e.g.,
V2O3) with localized d-electron states are the Mott insu-
∗
Corresponding author.
E-mail address: sailen@cmp.saha.ernet.in (S. Das).
0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.jallcom.2003.11.021

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S. Das et al. / Journal of Alloys and Compounds 375 (2004) 15–23
control since their structure is very tough in withstanding
chemical modification on the perovskite A-site. In the filling
controlled systems as the I–M phase change is approached
from the metallic side many unconventional phenomena
have been unravelled, for instance charge and spin ordering
[7], colossal magnetoresistance [8,9], antiferromagnetism
[10], ferromagnetism, high temperature superconductiv-
ity [11–13] and so on. Recently an intense attention has
been devoted to the perovskite-type system R1−xAxTiO3
(R being a trivalent rare earth and A is a divalent alkaline
earth) where both the bandwidth and the band filling can
be chemically controlled [14–16]. The end member RTiO3,
where the R atom is in the 3d1 electron configuration, is
a Mott insulator irrespective of the rare-earth R. Here the
one-electron band width (W) of the conduction band can be
varied [17] by changing R. On the other hand, substitution
of the trivalent R ion by the divalent A ion decreases the
number of electrons per Ti site or, the band filling n (=1−x)
and drives the system metallic. In the metallic regime of
R1−xAxTiO3 many of the characteristic fingerprints for
Fermi liquid, such as T-squared resistivity, T-independent
Pauli-like susceptibility and the T-linear coefficient of the
specific heat have been observed [14,18]. Additionally the
carrier effective mass is found [19] to be critically enhanced
as the I–M transition is approached from the metallic side
indicating a strong role of electron correlation for the M–I
transition. Apart from the recent extensive studies, however,
not so much has been known about the doping induced
I–M transition in the Mott–Hubbard systems. Moreover,
there is scarce report for the thermoelectric power on this
system although this experiment is a sensitive probe of the
degree of itineracy of the carriers and an investigation of the
thermoelectric response in the regime where large mass en-
hancement has been observed is highly desirable. In view of
this we have undertaken a systematic study of the electrical
transport and thermoelectric power (TEP, S) measurement
of the perovskite-type solid solution system Nd1−xAxTiO3
(A = Ca, Sr and Ba) where one can control the effective Ti
valence from 3+ (x = 0) to 4+ (x = 1) or band filling while
essentially maintaining the original lattice structure. In the
parent NdTiO3 insulator partial substitution of Nd3+ sites
with A2+ ions drives the phase change from a Mott–Hubbard
insulator to a correlated metal. We observed a transitional
behavior from the doped Mott insulator to the narrow band
metal with increasing x (or decreasing the band filling n).
ric mixture of prefired ATiO3, prefired Nd2O3 and Ti2O3
were mixed homogeneously and pressed into pellets. The
pelletized mixture was then melted in an arc furnace in ar-
gon atmosphere with repetitive turnings. To obtain a single
phase the samples were remelted several times with inter-
mediate grindings. The samples thus prepared were found
to be brittle and preserved in a dessicator purged with argon
gas to avoid oxidation.
The crystal structure and the phase purity of the samples
were checked by powder X-ray diffraction with Cu K␣ radi-
ation using a Philips APD 1877 X-ray diffractometer. Due to
the irregular shape of the samples precise determinations of
the resistivity was not possible. Temperature dependence of
the electrical resistance and thermopower were measured us-
ing methods as described elsewhere [25]. The thermopower
of the samples was measured using a differential technique
where a temperature gradient is created across the sample
and the voltage developed between the hot and cold ends
of the thermocouple formed by the sample and Cu wires is
measured. The details of the set up and measurement tech-
nique have been reported earlier [20].
3. Results and discussions
3.1. X-ray diffraction
Fig. 1 depicts a representative X-ray diffraction pattern
of Nd1−xAxTiO3 (A = Ca, Sr and Ba). Analysis of the
X-ray data of the compounds shows that the samples stud-
ied are single phase. The Ca- and Sr-doped NdTiO3 shows
perovskite crystal structures with orthorhombic distortions
(GdFeO3-type) throughout the concentration range studied.
The X-ray pattern of Nd1−xBaxTiO3 can be well fitted with
cubic symmetry. Thus it is found that the incorporation of
the small size Ca2+ (rCa = 1.48 Å) and Sr2+ (rSr = 1.58 Å)
ions produces an orthorhombic distortion throughout the
whole concentration range whereas the largest Ba ion (rBa
1.75 Å) produces cubic symmetry.
=
3.2. Resistivity
In Figs. 2–4 we show the temperature dependence of
the normalized resistance Rn (=R/R300) of Nd1−xAxTiO3
(A = Ca, Sr and Ba). For the Nd1−xCaxTiO3 (x = 0.1–0.8)
system Fig. 2 shows that the normalized resistance Rn of
the x = 0.1 sample increases with the decrease of tem-
perature similar to that of a semiconducting sample. The
upturn in Rn at low temperature may originate from the ef-
fect of carrier localization. The nature of the Rn(T) curves
of all samples with x = 0.2–0.8 are quite similar. With
decreasing temperature starting from room temperature Rn
decreases like a metallic sample and then after crossing a
certain temperature it decreases very slowly with lowering
of temperature. The metallic nature of Rn is consistent with
earlier reported results [21]. Thus samples with low filling
2. Experimental
TiO2 powder was prefired at 1000 ◦C for 24 h. Poly-
crystalline ATiO3 (A = Ca, Sr and Ba) were prepared by
heating the mixture of TiO2 and ACO3 (A = Ca, Sr and Ba)
in air at 1000–1200 ◦C for 48 h with intermediate grindings
and pelletization. The structure of ATiO3 was confirmed by
X-ray diffraction. Neodynium oxide (Nd2O3) was heated
at 1000 ◦C in air for 12 h prior to use. The stoichiomet-

S. Das et al. / Journal of Alloys and Compounds 375 (2004) 15–23
17
Nd0.6Ca0.4TiO3
Nd0.5Sr0.5TiO3
Nd0.2Ba0.8TiO3
0
20
40
60
80
2θ
Fig. 1. X-ray diffraction pattern of Nd0.6Ca0.4TiO3, Nd0.5Sr0.5TiO3 and Nd0.2Ba0.8TiO3.
(x ≤ 0.1) shows semiconducting like behavior whereas
those with x ≥ 0.2 exhibit metallic properties. This result
suggests that a transition from insulator to metal (I–M)
should occur in the range x = 0.1–0.2. Furthermore partial
replacement of Nd by Ca convert the Mott–Hubbard insu-
lator NdTiO3 (x = 0) with 3d1 configuration to a metallic
state thereby resulting to a M–I transition near x ∼ 0.15
[21].
Nd1-x Cax Ti O3
1.0
0.8
0.6
0.4
0.2
0.0
1.3
1.2
1.1
1.0
0.1
0.5
0.8
0.4
0.3
0.7
0.6
0.2
0
50
100
150
200
250
300
T(K)
Fig. 2. The temperature dependence of the normalized resistance Rn (=R/R300) for Nd1−xCaxTiO3 (x = 0.1–0.8).

18
S. Das et al. / Journal of Alloys and Compounds 375 (2004) 15–23
70
60
50
40
30
20
10
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Nd1-xSrxTiO3
0.1
0.6
0.8
0.5
0.4
0.3
0.2
0.9
0
0
5 0
100
150
200
250
300
T (K)
Fig. 3. Plot of Rn as a function of temperature for Nd1−xSrxTiO3 (x = 0.1–0.9).
1.5
1.4
1.3
1.2
1.1
1.0
1.0
0.9
0.8
0.7
0.6
0.5
Nd1-x Bax Ti O3
0.1
0.4
0.6
0.5
0.4
0.3
0.9
0
50
100
150
200
250
300
T (K)
Fig. 4. Thermal variation of Rn of Nd1−xBaxTiO3 (x = 0.1–0.9).

S. Das et al. / Journal of Alloys and Compounds 375 (2004) 15–23
19
The variation of Rn as a function of temperature in
Nd1−xSrxTiO3 (x = 0.1–0.9) is shown in Fig. 3. Here
also we have noticed that with replacement of Nd by Sr
the functional dependence of Rn follows a similar fashion
as that observed in Nd1−xCaxTiO3. For example, x = 0.1
sample shows semiconducting behavior whereas samples
with x ≥ 0.2 exhibits metallic nature. From the functional
dependence of the resistivity with temperature it appears
that in this case the insulator-metal transition occurs in
between x = 0.15 and x = 0.2 [22].
of Rn can be described quite satisfactorily by the relation
Rn = Rn0 + AT2, where Rn0 is the residual normalized
resistance and A is a constant. In order to determine the
nature of metallicity we have plotted Rn as a function of
T2 in Fig. 5 for Nd1−xAxTiO3 (A = Ca and Sr) over
a temperature range 20–300 K. In the case of Ba-doped
NdTiO3 we also observed a similar type of T2 dependence
for Rn. For all the compounds the linear nature of the
curve suggests that strong electron–electron scattering plays
an important role in governing the electrical conduction
in these materials. This T2 behavior of Rn is one of the
characteristic fingerprints of a Fermi liquid [23,24]. In the
metallic Nd1−xCaxTiO3 compounds it has been reported
[21] that the effective mass of the carrier increases as the
M–I boundary (x = 0.15) is approached.
In Fig. 4 we show plots of Rn as a function of temperature
for the Nd1−xBaxTiO3 (x = 0.1–0.9) series. For x = 0.1,
Rn increases with decrease of temperature like a semicon-
ducting material. Similar semiconducting type of electrical
transport has also been observed in other titanate systems
in the vicinity of the parent insulating state. Moreover, as
one approaches the insulating state from the metallic side
the carrier effective mass is found [18] to be critically en-
hanced owing to the electron correlation effect. Observation
of the insulating state with finite doping may be ascribed to
the carrier localization effect arising from a combined ef-
fect of the correlation enhanced effective mass and the ran-
dom potential induced from the ionic A-sites of the ABO3
perovskite structure (Nd/Ba mixture). For x > 0.1, Rn(T)
shows metallic behavior as observed in Ca- and Sr-doped
NdTiO3 systems mentioned above.
From the above discussions on the variation of resistance
with temperature in Nd1−xAxTiO3 (A = Ca, Sr and Ba) as
a function of 3d conduction band filling n (=1 − x) we may
arrive at the following results. Partial substitution of Nd with
divalent alkaline-earth A ions (Ca, Sr and Ba) transforms
the Mott–Hubbard insulator NdTiO3 with 3d1 configuration
into a correlated metal thereby leading to an insulator-metal
transition. However, depending upon the size of the dopant
ion A, the M–I transition occurs at different levels of band
filling. For instance when the size of the A ion is large (e.g.,
Ba), a 20% Ba substitution is sufficient to induce the M–I
transition in NdTiO3 whereas for dopants of smaller size
(e.g., Sr and Ca) it takes place at 20% Sr substitution and
In the metallic regime of Nd1−xAxTiO3 (A = Ca, Sr
and Ba) we have observed that the temperature dependence
1.0
Nd1-x Ax Ti O3
A = Ca
x =
0.8
0.6
0.4
0.5
0.8
0.4
A = Sr
0.4
0.2
8
4
6
2
-2
0
10
T2 (104 .K2 )
Fig. 5. Variation of Rn as a function of T2 for Nd1−xAxTiO3 (A = Ca; x = 0.4, 0.5, 0.8 and A = Sr; x = 0.2, 0.4).

20
S. Das et al. / Journal of Alloys and Compounds 375 (2004) 15–23
15% Ca substitution, respectively. This result is consistent
with our recent observation [25] in the strongly correlated
Y1−xAxTiO3 (A = Ca, Sr and Ba) where also the 3d band
filling level (x) for the occurrence of M–I transition depends
on the size of the A-ion. For A = Ca, YTiO3 requires a
higher hole doping (40% Ca) while for A = Sr or, Ba, it re-
quires comparatively less hole doping (35% Sr or, 20% Ba)
to induce the M–I transition. It is to be mentioned here that a
∼5% Sr substitution is sufficient to induce the metallic phase
in the weakly correlated LaTiO3 [14]. Thus NdTiO3 which
is intermediate between LaTiO3 and YTiO3, requires a lower
amount of substitution of A for Nd than in the strongly cor-
related YTiO3 to induce the M–I transition. A systematic
investigation of the electronic properties in Nd1−xCaxTiO3,
La1−xSrxTiO3 [14] and Y1−xCaxTiO3 [16] systems reveals
that on the verge of the M–I transition the carrier effec-
tive mass increases. Furthermore, on approaching the I–M
phase from the metallic side the observed enhancement of
the carrier effective mass may be due to the filling dependent
change of the correlation effect. In the vicinity of the M–I
transition the combined effect of the correlation enhanced
effective mass and the random potential arising from the per-
ovskite A-sites gives rise to localization of charge carriers.
The Fermi liquid type behaviors observed in the correlated
metallic phase seems to be a common features of the diva-
lent alkaline earth ion doped titanate systems.
versa have recently received new interest in the thermopower
of correlated materials. Thermoelectric power (TEP, S) is a
very useful probe to study the semiconducting and metal-
lic behavior of compounds since it offers a characteristic
difference in the two cases. We have measured the TEP of
Nd1−xAxTiO3 (A = Ca, Sr and Ba) in the correlated metal-
lic phase. The metallic TEP has a low value at room tem-
perature and varies linearly with temperature. The sign of
the TEP describes (not always) the type of majority carriers
present in the compound at a certain temperature.
In Fig. 6 we present the temperature variation of S in
Nd1−xCaxTiO3 (x = 0.2–0.9). For all the samples S is found
to be negative indicating electronic charge carriers. Fig. 6
shows that S varies linearly with temperature irrespective of
the 3d conduction band filling level. This is consistent with
the observed correlated metallic behavior of the electrical
transport in this range of band filling. Thermal variation
of S for Nd1−xSrxTiO3 (x = 0.3–0.8) and Nd1−xBaxTiO3
(x = 0.1–0.8) for different band filling are shown in Figs. 7
and 8, respectively. Both the systems exhibit S(T) curves
which are quite similar in nature to those observed in
Nd1−xCaxTiO3.
It is to be pointed out here that monovalent metals, no-
ble metals and some other metals [26] also exhibit a linear
dependence of S on T similar to that observed in doped ti-
tanate oxides mentioned above. Considering the nearly free
electron model, Mott [27] has given an expression for the
characteristic diffusion thermopower of a metal as
3.3. Thermoelectric power
ꢀ
ꢁ
ꢂ
ꢃ
π2kB2 T
d( ln σ(E))
dT
Thermoelectric effects which are responsible for the di-
rect conversion of heat energy into electrical energy and vice
S(T) =
(1)
3e
E=E
F
0
20
10
0
0.7
-40
-80
0.8
0.9
-10
0.2
0.5
-120
-160
-20
Nd1-xCaxTiO3
0.6
50
100
150
200
250
300
350
T (K)
Fig. 6. The temperature dependence of the thermopower (S) of Nd1−xCaxTiO3 for different x. Solid line represents the theoretical fit following the
expression (3) described in the text.

S. Das et al. / Journal of Alloys and Compounds 375 (2004) 15–23
21
T (K)
50
100
150
200
250
300
0
-20
-4
-8
-40
-60
0.8
0.5
-80
-12
-16
0.3
-100
-120
Nd1-xSrxTiO3
0.7
50
100
150
200
250
300
350
T (K)
Fig. 7. Plot of S as a function of temperature for Nd1−xSrxTiO3 along with the fitted curve (solid line).
where kB is Boltzmann’s constant, EF the Fermi energy
and e is the charge of the carriers. Assuming that the con-
ductivity is proportional to the energy and that there is a
T-independent mean free path for the carriers, expression
(1) becomes
Eq. (2) is derived considering a spherical Fermi surface to-
gether with a T-independent relaxation. This approximation
limits the validity of Eq. (2) to low temperatures. From the
above relation S is linear with T and is extremely sensitive on
the nature of the Fermi surface. Experimental data belong-
ing to the linear region of the S(T) curve for Nd1−xAxTiO3
(A = Ca, Sr and Ba) can be fitted quite satisfactorily
π2kB2 T
S(T) ≈
(2)
3eEF
0
0
-10
-20
-30
-40
-50
0.1
-20
0.3
-40
-60
-80
0.6
0.7
0.8
Nd1-xBaxTiO3
50
100
150
200
T(K)
250
300
350
Fig. 8. Thermal dependence of S for Nd1−xBaxTiO3. Solid line is the fitted curve.

22
S. Das et al. / Journal of Alloys and Compounds 375 (2004) 15–23
-0.04
-0.06
-0.08
-0.10
-0.12
-0.14
Nd1-xBaxTiO3
0.0
0.2
0.4
0.6
0.8
x
Fig. 9. Variation of the coefficient S1 as a function of the filling level (x) for Nd1−xBaxTiO3.
considering the expression
currence of the observed MI transition is associated with
an enhancement of the effective mass of the carriers caused
by the strong correlation effects. In our case a very simpli-
fied model for the thermopower also indicates a mass en-
hancement though the factor of enhancement obtained by
other experimental techniques is higher. It is felt that for
a true analysis of the thermopower data a very precise ex-
pression for S is needed on the basis of the actual band
structure.
S(T) = S0 + S1T
(3)
and the fit is shown by solid lines in Figs. 6–8, respectively.
Here S0 (=S at T = 0) can be obtained from the extrap-
olation of the high temperature fit of S. This term has no
physical origin and is inserted to overcome the problem of
truncating the low temperature data. Thus from the slope of
the S(T) curve one can obtain knowledge about how S1 varies
with filling level (x). In Fig. 9 we have plotted S1 as a func-
tion of x for Nd1−xBaxTiO3. Now comparing Mott’s relation
(2) with expression (3), the coefficient S1 of the T linear term
can be written as S1 = π2kB2 /3eEF. According to the free
4. Conclusion
electron theory EF is given by EF = h¯ 2/2m∗(3π2nf)2/3
,
Analysis of the X-ray data reveals that NdTiO3 doped
with Ca and Sr belongs to the orthorhombic structure and
when doped with Ba shows cubic symmetry. Analysis of
the electrical transport of Nd1−xAxTiO3 (A = Ca, Sr and
Ba) suggests that for all the compounds the nature of charge
conduction depends sensitively on the 3d band filling level
n (=1 − x). For each compound as the filling level varies
the electrical conduction changes from insulating to metal-
lic type leading to a M–I transition. Moreover, the filling
level at which the insulator-metal transition occurs depends
on the size of the divalent alkaline earth A-ion. In the cor-
related metallic phase the Fermi liquid description seems
to be a common feature of the divalent alkaline earth-ion
doped titanate systems. In this regime of filling, the electri-
cal transport data indicates that the electron–electron scat-
tering plays a major role governing the conduction process.
Analysis of the TEP data belonging to the linear region of
the S(T) curve reveals an enhancement of the carrier effec-
tive mass.
where h¯ = h/2π, h being Planck’s constant, m∗ the ef-
fective mass and nf is the free electron density. Theoreti-
cal estimations of nf have been made using values of the
mass density obtained from X-ray diffraction data under
the assumption of four formula units per cell [28]. For the
Ba-doped samples, nf is taken as 1.615 × 1022(1 − x). The
best theoretical fit to the experimentally evaluated S1 ver-
sus x data (open symbol) obtained with m∗ = 5m0 (where
m0 is the free electron mass) is shown in Fig. 9 by solid
line. Such an enhancement of mass (m∗/m ∼ 10) has also
been reported [21] from the analysis of the resistivity data
of Nd0.4Ca0.6TiO3. Similar enhancement in the effective
mass of the charge carriers has been obtained by analyz-
ing the thermoelectric power data in La1−xSrxTiO3 [29] and
Y1−xAxTiO3 (A = Ca, Sr and Ba) [25]. In La1−xSrxTiO3
Tokura et al. [14] observed an increase of the T-linear term
in the low temperature specific heat with band filling indi-
cating an enhancement of the effective mass. Thus the oc-

S. Das et al. / Journal of Alloys and Compounds 375 (2004) 15–23
23
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