Transport and magnetic properties of a Mott-Hubbard system whose bandwidth and band filling are both controllable: R1-xCaxTiO3+y/2

Article abstract of DOI:10.1103/PhysRevB.56.10145

Transport and magnetic properties of R_1-xCa_xTiO_3+y/2 have been systematically investigated varying the one-electron bandwidth (W) and the band filling (n=1 - δ), which can be controlled by the R-dependent lattice distortion and by the Ca content x and/or oxygen offstoichiometry y (δ=x + y), respectively. The end compound RTiO₃ is a 3d¹ Mott-Hubbard insulator and its charge-gap magnitude increases with decreasing ionic radius of R, i.e., an increase of electron correlation (U/W) in proportion with (U/W)-(U/W)_c, where (U/W)_c is the critical value for the (hypothetical) n=1 Mott transition. Such a Mott insulator is transformed to a correlated metal by substitution of R with Ca (hole doping), and the nominal hole concentration required for the insulator-metal transition (δ_c) increases in proportion with (U/W)-(U/W)_c. Concerning magnetism, RTiO₃ with R=La, Pr, Nd, and Sm, shows the antiferromagnetic ordering and its Neel temperature (T_N) decreases with smaller R. T_N also decreases with Ca doping, but remains finite up to the metal-insulator phase boundary. On the basis of these results, electronic phase diagrams are derived for a series of titanates as an electron-correlated system with changes of two parameters, i.e., the strength of electron correlation and band filling. Possible origins of the insulating state with finite hole doping are also discussed in terms of the kinetic energy of doped carriers in the Mott-Hubbard insulator.

Full text of DOI:10.1103/PhysRevB.56.10145

PHYSICAL REVIEW B
VOLUME 56, NUMBER 16
15 OCTOBER 1997-II
Transport and magnetic properties of a Mott-Hubbard system whose bandwidth
and band filling are both controllable: R1؊xCaxTiO3؉y/2
T. Katsufuji, Y. Taguchi, and Y. Tokura
Department of Applied Physics, University of Tokyo, Tokyo 113, Japan
͑Received 14 May 1997͒
Transport and magnetic properties of R1ϪxCaxTiO3ϩy/2 have been systematically investigated varying the
one-electron bandwidth (W) and the band filling (nϭ1Ϫ␦), which can be controlled by the R-dependent
lattice distortion and by the Ca content x and/or oxygen offstoichiometry y (␦ϭxϩy), respectively. The end
compound RTiO3 is a 3d1 Mott-Hubbard insulator and its charge-gap magnitude increases with decreasing
ionic radius of R, i.e., an increase of electron correlation (U/W) in proportion with (U/W)Ϫ(U/W)c , where
(U/W)c is the critical value for the ͑hypothetical͒ nϭ1 Mott transition. Such a Mott insulator is transformed
to a correlated metal by substitution of R with Ca ͑hole doping͒, and the nominal hole concentration required
for the insulator-metal transition (␦c) increases in proportion with (U/W)Ϫ(U/W)c . Concerning magnetism,
´
RTiO3 with RϭLa, Pr, Nd, and Sm, shows the antiferromagnetic ordering and its Neel temperature (TN)
decreases with smaller R. TN also decreases with Ca doping, but remains finite up to the metal-insulator phase
boundary. On the basis of these results, electronic phase diagrams are derived for a series of titanates as an
electron-correlated system with changes of two parameters, i.e., the strength of electron correlation and band
filling. Possible origins of the insulating state with finite hole doping are also discussed in terms of the kinetic
energy of doped carriers in the Mott-Hubbard insulator. ͓S0163-1829͑97͒05640-3͔
I. INTRODUCTION
bond angle leads to a decrease of the one-electron bandwidth
of the conduction band.7 On the other hand, the substitution
of the trivalent R ion by the divalent A ion decreases the
number of electrons per Ti site (n) from 1 ͑nominal hole
doping͒, and drives the system metallic.8–12 There have been
various studies on this system, but few systematic studies of
transport and magnetic properties with changes of both the
two parameters, i.e., bandwidth and band filling.
In 3d transition-metal oxides, strong electron-electron in-
teraction often localizes conduction electrons, and the system
becomes an insulator ͑a Mott insulator͒.1 In some cases, a
transition between a metal and a Mott insulator is observed
by a slight change of some parameters ͑a Mott transition͒. A
famous example that shows such a transition is V2O3,2 where
a metal-insulator transition at the lowest temperature occurs
with the application of pressure. This metal-insulator transi-
tion can be interpreted as one induced by changes of the
bandwidth of the conduction band arising from changes of a
lattice constant ͑a bandwidth-control Mott transition͒. On the
other hand, metal-insulator transitions observed in cuprate
superconductors are categorized another way. For example,
La2CuO4 is a Mott insulator with a Cu 3d9 electron configu-
ration, and becomes metallic with hole doping by the substi-
tution of the trivalent La ion with a divalent Sr ion.3 In con-
trast to the case of pressurized V2O3, the metal-insulator
transition of La2ϪxSrxCuO4 is induced by changes of the
band filling of the conduction band ͑a filling-control Mott
transition͒.4
Recently, R1ϪxAxTiO3 ͑R being a trivalent rare earth, and
A a divalent alkaline earth͒ has been studied as a prototypical
three-dimensional electron-correlated system.5–19 A unique
feature of this system is that both the bandwidth and the band
filling can be chemically controlled: The end compound
RTiO3, where the Ti atom is in the 3d1 electron configura-
tion, is a Mott insulator irrespective of the species of the rare
earth R.5,6 With a smaller ionic radius of R, the lattice struc-
ture becomes more distorted, and the Ti-O-Ti bond angle
decreases, with a greater departure from 180°. Since the con-
duction band of these compounds is composed of the Ti 3d
(t2g) and oxygen 2p orbitals, such a decrease of the Ti-O-Ti
In this paper, we report a systematic investigation of
R
1ϪxCaxTiO3ϩy/2 , with RϭLa, Pr, Nd, Sm, and Y, with a
finely controlled Ca concentration x and oxygen offstoichi-
ometry y. From this study, we can obtain detailed informa-
tion about the electronic and magnetic structures of this sys-
tem for wide ranges of the two parameters, bandwidth and
band filling. Such a study is expected to clarify generic fea-
tures of three-dimensional, doped, Mott-Hubbard systems.
We also focus on the critical behavior of the metal-insulator
phase boundary of this system.
The format of this paper is as follows: In Sec. II details of
the sample preparation and measurements are described. In
Sec. III, we describe the calculation of the bandwidth of the
conduction band, which characterizes the respective com-
pounds. Sections IV and V show the experimental results of
resistivity and magnetization, respectively, and Sec. V pre-
sents an electronic phase diagram of this system in a space of
bandwidth, band filling, and temperature. In Sec. VI some
features observed in the vicinity of the metal-insulator phase
boundaries are presented. In Sec. VII we discuss a possible
origin of the insulating state with finite hole concentration,
and Sec. VIII is devoted to a summary of the paper.
II. EXPERIMENT
All the samples investigated in this study were prepared
by the floating zone method, similarly to previous work.11
0163-1829/97/56͑16͒/10145͑9͒/$10.00
56
10 145
© 1997 The American Physical Society

10 146
T. KATSUFUJI, Y. TAGUCHI, AND Y. TOKURA
56
TABLE I. Ti-O-Ti bond angle and bandwidth of the conduction band of RTiO3. The values of the bond are from Ref. 13 except for
PrTiO3, whose bond angles ͑in parentheses͒ are obtained by the interpolation of LaTiO3 and NdTiO3 using their tolerance factors ͑see Ref.
21͒. O͑1͒ and O͑2͒ refer to the oxygens at two different sites of the GdFeO3 structure. W is the full width of the conduction band calculated
˜
with the tight-binding approximation. W is the ratio of W of each RTiO3 to that of LaTiO3.
La
Pr
Nd
Sm
Y
Ti-O͑1͒-Ti bond angle ͑degree͒
Ti-O͑2͒-Ti bond angle ͑degree͒
W ͑eV͒
157.5
156.9
2.45
͑152.8͒
͑152.3͒
2.33
150.7
150.3
2.27
0.93
146.8
147.0
2.16
0.88
140.3
143.7
2.04
0.83
˜
W
1
0.95
The starting materials are R2O3 ͑RϭLa, Pr, Nd, Sm, and Y͒,
TiO2, Ti, and CaTiO3. CaTiO3 was synthesized by firing
CaCO3 and TiO2 in air at 1000 C° for 24 h. Stoichiometric
amount of sources for R1ϪxCaxTiO3, which had been well
dried in advance, were mixed and pressed into rods with
ϳ5-mm diameter. To keep the stoichiometry of oxygen, we
omitted a sintering procedure, and directly melted the
pressed bar with use of a floating zone furnace equipped with
two halogen lamps and ellipsoidal mirrors. Atmosphere in
the furnace during the crystal growth was varied to control
the oxygen offstoichiometry of the samples (y), which was
determined by thermogravimetric analysis. The stoichio-
metric RTiO3.00 could be obtained in a gas flow of 30%
H2 /Ar, whereas the melting in a gas flow of Ar ͑6N͒ often
results in excess oxygen ͑y/2ϭ0.04 as a typical value͒. We
assume that the ratio of R, Ca, and Ti does not change from
the starting ratio. Thus the nominal hole concentration ␦ is
given by xϩy.
factor of LaTiO3 is 0.95, and that of YTiO3 is 0.89; the
difference is ϳ6%. On the other hand, the factors of
NdTiO3 and Nd0.8Ca0.2TiO3 are 0.92 and 0.93, respectively;
the difference is only ϳ1%. Thus, as long as properties in
the small-x region are discussed, the change of the bond
angle with Ca doping is negligible, and from now on we
ignore the change of the bandwidth with Ca doping.
In the spirit of the Hubbard model, the electron-
correlation strength is given by U/W, where U is the on-site
Coulomb repulsion energy. Since the U value can be viewed
as constant among the RTiO3 series, we use the value of
Ϫ1
˜
W
in the following sections to represent the electron-
correlation strength below.
IV. TRANSPORT PROPERTIES
Figure 1 shows the temperature dependence of the resis-
tivity for R1ϪxCaxTiO3ϩy/2 , with RϭLa, Pr, Nd, and Sm,
and with various hole concentrations. Results for
X-ray powder diffraction was measured which showed
that the crystal structure of all the samples investigated here
is the GdFeO3 type. Resistivity measurements were carried
out by the conventional four-probe technique using indium
as an electrode. Magnetization measurement were performed
using a superconducting quantum interference device mag-
netometer.
Y
1ϪxCaxTiO3 ͑not shown͒ have already been published in
Ref. 10. For any R, the change of resistivity with hole dop-
ing is similar: With an increase of hole concentration ␦, the
temperature dependence of the resistivity varies from insu-
III. CALCULATION OF BANDWIDTH
The conduction band of this system is composed of Ti 3d
t2g and O 2p ␲ orbitals, and its bandwidth is governed by
the Ti-O-Ti bond angle. Complete structural parameters were
previously determined for RTiO3 in Ref. 13, and, with use of
their data, the one-electron bandwidth of the conduction
band for RTiO3 can be calculated by a tight-binding model,
where the Hamiltonian matrix, based on the Harrison’s
parametrization20 taking account of Ti 3d t2g and O 2p or-
bital with GdFeO3 lattice distortion is diagonalized. Details
of the calculation are shown in Ref. 7. The Ti-O-Ti bond
angle and the full width of the conduction band (W) from the
˜
calculation are listed in Table I. W is the ratio of W of each
RTiO3 to that of LaTiO3. Among these, the minimal band-
width of YTiO3 is 83% of the maximal one of LaTiO3.
Ca doping may also induce a change in the Ti-O-Ti bond
angle, and consequently in the bandwidth of the conduction
band. Since to our knowledge the Ti-O-Ti bond angle of
R
1ϪxCaxTiO3ϩy/2 with a finite value of x has not been de-
FIG. 1. Temperature dependence of resistivity in crystals of
termined so far experimentally we estimated the change of a
R
1ϪxCaxTiO3ϩy/2 for RϭLa, Pr, Nd, and Sm with various hole
tolerance factor21 instead of the bond angle. The tolerance
concentrations ␦ϭxϩy. The result of RϭY is shown in Ref. 10.

56
TRANSPORT AND MAGNETIC PROPERTIES OF A . . .
10 147
FIG. 2. Resistivity on a logarithmic scale vs the inverse of tem-
perature for RTiO3.
FIG. 4. Insulating crystals ͑closed circles͒ and metallic ones
͑open circles͒ are plotted in WϪ1-␦ space. For the definition of
˜
‘‘metallic’’ and ‘‘insulating’’ crystals, see text. The solid line is the
guide to the eyes, representing a linear relation that separates the
space into insulating and metallic regions.
lating with thermal activation to metallic ͑d␳/dT being posi-
tive͒. However, there are several R-dependent features. ͑1͒
The resistivity for the end compound (␦ϭ0) increases from
RϭLa to Sm ͑with a decrease of W͒. ͑2͒ The hole concen-
tration that is required to make the system metallic increases
from La to Sm. For example, ␦ϭ0.08 is sufficient to make
LaTiO3 metallic, whereas the sample with ␦ϭ0.09 is still
ductivity spectra for RTiO3.5 These experimental results in-
dicate that the relation between the magnitude of the Mott-
Hubbard gap (Eg) depends on the electron-correlation
strength (U/W) in such a way that EgϰU/WϪ(U/W)c .22
Here (U/W)c is a hypothetical point for a Mott transition
with nϭ1 (␦ϭ0) filling. We note that recent calculations of
the Hubbard model at infinite dimensions23 confirmed a
metal-insulator transition for nϭ1 with a finite value of
U/W, and quantitatively explained such a U/W dependence
of Eg .24
insulating for Nd1ϪxCaxTiO3ϩy/2
.
To discuss the former point more quantitatively, in Fig. 2
we show an Arrhenius plot of the resistivity for the end com-
pound RTiO3. All the data approximately follow the
activation-type function ␳(T)ϭ␳ exp(⌬act /kBT), where the
0
activation energy ⌬act ͑the slope of the line͒ decreases from
YTiO3 to LaTiO3. We estimate the ⌬act value of RTiO3 from
the high-temperature part, and plot 2⌬act as a transport gap
The critical R dependence of the transport properties also
emerges when hole doping ͑␦͒ into the end compound,
RTiO3, causes the insulator-metal transition. In Fig. 4, insu-
lating and metallic samples are plotted by closed and open
Ϫ1
˜
against the inverse bandwidth W in Fig. 3. The 2⌬act value
decreases linearly with the decrease of WϪ1. The solid line
˜
˜
in Fig. 3 is the result of a least-square fitting of the data with
circles, respectively, in a WϪ1-␦ space. Here we define an
a linear function. This fitting suggests that 2⌬act becomes
insulator as a sample whose d␳/dT is negative over the
whole temperature range. It is clear from this figure that the
nominal hole concentration that is needed to cause the
insulator-metal transition (␦c) increases with increase of
Ϫ1
˜
zero at a finite value of W (ϳ0.95). We have observed a
Ϫ1
˜
similar W
dependence of the energy gap in optical con-
Ϫ1
Ϫ1
˜
˜
electron-correlation strength W . The W dependence of
␦c appears to be a linear function, as indicated by the solid
Ϫ1
˜
line. Moreover, the W
value at which ␦c becomes zero
approximately coincides with the one at which 2⌬act be-
comes zero in Fig. 3. This indicates a close interrelation be-
tween ␦c and the magnitude of the Mott gap in the end
compound. That is to say, ␦c increases in proportion with the
transport gap in the end Mott insulator. On the basis of a
simple three-dimensional Hubbard model that takes account
of only the on-site Coulomb interaction, the system should
become metallic with nonzero ␦. The insulating phase with
finite ␦ in R1ϪxCaxTiO3ϩy/2 is perhaps caused by some com-
bined effect of the electron correlation and others ͑static dis-
order or electron-lattice interaction͒, which was discussed in
Sec. III.
Ϫ1
˜
FIG. 3. 2⌬act vs W for RTiO3. ⌬act is the activation energy of
resistivity and W is the bandwidth of RTiO3 normalized to that of
V. MAGNETIC PROPERTIES AND PHASE DIAGRAMS
˜
The end compounds RTiO3 with relatively large ionic ra-
dius for R are known to show antiferromagnetism with slight
LaTiO3. The solid line is the result of least-square fitting with a
linear function.

10 148
T. KATSUFUJI, Y. TAGUCHI, AND Y. TOKURA
56
FIG. 5. Magnetization of RTiO3 at 100 Oe in a warming run,
after the cooling the sample under 50 000 Oe. Arrows correspond to
the antiferromagnetic ordering temperatures.
FIG. 7. Magnetization curves at 5 K measured at 100 Oe for ͑a͒
PrTiO3 and ͑b͒ NdTiO3.
spin-canting, giving rise to
a
small spontaneous
magnetization.14 To determine the antiferromagnetic ͑AF͒
ordering temperature TN of each sample, magnetization mea-
surements were carried out by the following procedure: The
sample was first cooled down to 5 K with the application of
a magnetic field of 50 000 Oe; then the magnetic field was
decreased to 100 Oe, and the magnetization of the sample
was measured in a warming run. The temperature depen-
dence of the measured magnetization of RTiO3 is shown in
Fig. 5, where TN for each compound is indicated by an ar-
row. The results for RϭLa, Pr, and Nd are consistent with
those previously reported.8,15,12 As far as we know, the AF
ordering of SmTiO3 is observed for the first time in the
present study. On the other hand, YTiO3 shows a ferromag-
netic ordering below TCϳ30 K.10,14
Ϫ1
˜
increase of Y concentration ͑increase of W ͒ down to zero,
and subsequently a ferromagnetic ordering appears and the
Curie temperature (TC) increases with a further increase of
Y concentration. The result of RTiO3 in the present study
also shows a similar behavior. However, it should be noted
that a simple one-band Hubbard model hardly explains such
a rapid decrease of TN and the appearance of ferromagnetic
ordering with an increase in WϪ1. In RTiO3, conduction
˜
electrons are accommodated in nearly triply degenerate Ti
3d t2g orbitals, and the degenerate ͑multiband͒ Hubbard
model seems appropriate to describe the experimental re-
sults. Recently, Mizokawa and Fujimori26 investigated the
spin structure of RTiO3 by a Hartree-Fock calculation, and
found that ferromagnetic ordering is favored when the de-
generacy of the 3d orbitals is taken into account. However,
they claimed that the change of W alone does not explain the
change of the spin structure from antiferromagnetic to ferro-
magnetic ordering, and that a Jahn-Teller distortion is impor-
tant. In any case, the ferromagnetic ordering is accompanied
by the ordering of the degenerate 3d orbitals. In fact, such an
orbital ordering has recently been confirmed by polarized
neutron-scattering experiments.27 Moreover, a recent band
calculation of YTiO3 ͑Ref. 28͒ by the generalized gradient
approximation, taking account of its GdFeO3 distortion, suc-
ceeds in reproducing a ferromagnetic spin state with orbital
ordering.
In Fig. 6 the magnetic-ordering temperatures of RTiO3 are
plotted by closed circles together with the results reported by
Greedan,14 as a function of WϪ1. In the same figure results
˜
for La1ϪxYxTiO3 from Refs. 25 and 7 are also plotted for
´
comparison, where the Neel temperature (TN) decreases with
As shown in Fig. 5, the magnitude of the magnetization
below TN differs by several orders of magnitude depending
on the species of R. We measured the magnetization curves
at 5 K for PrTiO3 and NdTiO3 as shown in Fig. 7. For
PrTiO3,9 a large hysterisis was found with magnetic field,
whereas almost no hysterisis was found for NdTiO3.
Neutron-scattering measurements of these compounds indi-
cate that PrTiO3 ͑Ref. 16͒ and NdTiO3 ͑Ref. 17͒ have quali-
tatively the same spin configuration both at the Ti site and
the rare-earth site below TN . At present it is not clear why
the M-H curve below TN behaves differently with different
species of rare earth. We speculate, however, that such a
´
FIG. 6. Neel (TN) and Curie (TC) temperatures of RTiO3
͑closed circles͒ and LaxY1ϪxTiO3 ͑open circles͒ as a function of
Ϫ1. The data from literature ͑Refs. 7, 14, and 25͒ are also shown.
The dashed lines are the guide to the eyes.
˜
W

56
TRANSPORT AND MAGNETIC PROPERTIES OF A . . .
10 149
FIG. 10. The electronic phase diagram of R1ϪxCaxTiO3ϩy/2 in a
space of the electron-correlation strength U/W, nominal hole con-
centration ␦, and temperature T.
FIG. 8. Temperature dependence of magnetization for ͑a͒
Pr1ϪxCaxTiO3ϩy/2 and ͑b͒ Sm1ϪxCaxTiO3ϩy/2 . The measurement
condition is the same as in Fig. 5.
scribed above. The AF phase extends to near the metal-
insulator phase boundary for any R, which goes to a higher ␦
position in varying R from La to Sm. In other words, the AF
phase survives as long as doped holes are localized. Such a
correlation between the AF state and the carrier localization
is also seen in cuprates such as La2ϪxSrxCuO4 ͑Ref. 3͒ and
variety in the magnetism of RTiO3 arises from the 3d-4f
interaction between Ti and R.
We measured the magnetization of R1ϪxCaxTiO3ϩy/2 with
finite ␦(ϭxϩy). The results for Pr1ϪxCaxTiO3ϩy/2 and
Sm1ϪxCaxTiO3ϩy/2 are exemplified in Fig. 8. The magneti-
zation of Nd1ϪxCaxTiO3 was also measured, and found to
agree with that previously reported.12 Irrespective of R, TN
decreases and finally disappears with an increase of ␦ for the
respective compound. Figure 9 is a plot of TN as a function
of ␦. Dashed lines correspond to the metal-insulator phase
boundary determined by resistivity measurements, as de-
R
2ϪxCexCuO4,29 and other transition-metal oxides such as
La1ϪxSrxVO3.30 This phenomenon is qualitatively under-
stood as follows: If doped holes are localized, they will act as
impurities with Sϭ0, and such impurities do not effectively
destroy the AF ordering as in a diluted spin system. But if a
doped hole becomes movable, it will affect many sites with
fairly short time scale, and will destroy the long-range AF
ordering.
Figure 10 shows the electronic phase diagram of the
present R1ϪxCaxTiO3ϩy/2 system as a function of U/W,
␦ϭxϩy, and T. The T-U/W plane at ␦ϭ0 indicates that TN
decreases with increase of correlation strength U/W for the
end compound. The T-␦ plane indicates that TN decreases
with an increase of hole concentration ␦. The U/W-␦ plane
at Tϭ0 indicates that both the insulating phase and the an-
tiferromagnetic phase survive up to larger ␦ with larger
U/W.
VI. BEHAVIOR NEAR PHASE BOUNDARIES
As seen in Fig. 9, there exits a metallic region where the
AF state persists to at low temperature.11 Figure 11 shows
resistivity ͑␳͒, the second T derivative of the resistivity
(d2␳/dT2), and magnetization (M) at 100 Oe ͑signaling the
AF ordering with slight spin canting͒ for Pr1ϪxCaxTiO3ϩy/2
with ␦ϭ0.14, as a typical example in such a region. TN is
ϳ80 K for this sample, and the slope of ␳(T) changes from
positive to negative at this temperature. A sharp peak is ob-
served for d2␳/dT2 at the same temperature, indicating a
steep change of the slope of ␳(T) at TN . In spite of such a
critical change of resistivity with magnetic ordering, the re-
sistivity does not diverge ͑i.e., the conductivity does not be-
come zero͒ but remains finite at the lowest temperature ͑2 K͒
of the present measurement, as shown in the inset of Fig. 11
´
FIG. 9. Neel temperature for R1ϪxCaxTiO3ϩy/2 as a function of
␦. The solid lines are the guide to the eyes. The dashed lines indi-
cate the insulator-metal phase boundary determined from resistivity
measurements.

10 150
T. KATSUFUJI, Y. TAGUCHI, AND Y. TOKURA
56
FIG. 13. ␳Ϫ␳ vs T2 for ͑a͒ Pr1ϪxCaxTiO3ϩy/2 and ͑b͒
0
Sm1ϪxCaxTiO3ϩy/2 with various ␦. ␳ is the residual resistivity and
0
the ␳Ϫ␳ values are normalized, so that the slope becomes the
0
same for all the data.
anomaly does not correspond to that of magnetic ordering,
since TN is much lower than this temperature. A similar re-
sistivity change has also been observed for Y1ϪxCaxTiO3
with xϳ0.40,18 and these can be regarded as a transition
from a high-temperature PI ͑HTPI͒ phase to low-temperature
metallic ͑LTM͒ phase. Therefore, the phase boundary be-
tween the PI and metallic state shown by dashed lines in
Figs. 9 and 10 is not completely parallel to the T axis, but is
slightly inclined ͑going to larger ␦ with higher T͒. Such an
electronic phase diagram is quite similar to those of V2O3
͑Ref. 2͒ and NiS2ϪxSex ,33 though the abscissa is different
for these systems; namely, the band filling for
FIG. 11. Magnetization (M) at 100 Oe, resistivity ͑␳͒, and sec-
ond T derivative of ␳ as a function of temperature (T) for
Pr1ϪxCaxTiO3ϩy/2 , with ␦ϭ0.14.
where conductivity is plotted as a function of T. This indi-
cates that the phase below 80 K is an AF metallic phase.
Thus we may call this the transition from a high-temperature
metal ͑HTM͒ to the low-temperature-antiferromagnetic
metal ͑LTAFM͒. Such an AF metal has been observed for
V2O3 with slight V vacancy,31 where a spin-density wave
with an incommensurate wave vector was observed by neu-
tron diffraction.32 It would be interesting to investigate
whether such an incommensurate spin ordering also exists in
these titanates.
The crystals near the border between the metallic phase
and paramagnetic insulating ͑PI͒ phase also show a novel
behavior. Figure 12 shows the temperature dependence of ␳
for Sm1ϪxCaxTiO3ϩy/2 with ␦ϭ0.24. The ␳ value at room
temperature is ϳ10 m⍀ cm, and around 200 K it sharply
decreases with decrease of temperature down to
ϳ0.2 m⍀ cm. Note that the temperature for the resistivity
R
1ϪxCaxTiO3ϩy/2 and the bandwidth for V2O3 or
NiS2ϪxSex . Recent numerical calculations19,34 based on the
Hubbard model in infinite dimensions have reproduced the
HTPI-LTM transition, which can be interpreted as the disap-
pearance of the coherent peak in the density of states, which
is responsible for the metallic conduction, with an increase in
T.
In the metallic phase of La1ϪxSrxTiO3, the resistivity ␳
follows T2 relation from the lowest temperature to fairly
high temperature (ϳ300 K).9 Such a T2 dependence of the
resistivity ␳ is also observed for the metallic phases of other
R systems. In the vicinity of the metal-insulator phase
boundary; however, a deviation from this T2 relation is ob-
served. In Fig. 13 we plot ␳ as a function of T2. Here the
residual resistivity (␳0) is subtracted, and the values of
␳Ϫ␳ are normalized for the respective compounds, so that
0
the slope appears the same. For Pr1ϪxCaxTiO3ϩy/2 , the ␳
value for ␦ϭ0.21 shows a T2 relation down to the lowest
temperature, whereas, as ␦ decreases, ␳ begins to deviate
from the T2 relation at low temperatures. This deviation is
apparently related to the HTM-LTAFM transition described
above. For ␦ϭ0.14, TN is 80 K ͑approximately correspond-
ing to the temperature for the minimum resistivity͒ but the
deviation from the T2 relation is observable up to higher
temperature ϳ140 K. This implies that strong antiferromag-
netic fluctuations persist well above TN in the doped system,
which gives rise to an additional carrier-scattering process
other than that contributing to the normal T2 dependence. On
the other hand, the deviation from the T2 relation is observed
for Sm1ϪxCaxTiO3ϩy/2 ͑and also Y1ϪxCaxTiO3ϩy/2͒ at
higher temperatures, which would be related to the HTPI-
LTM transition. For these smaller-W systems, the tempera-
ture range where ␳ follows the T2 relation is suppressed to
FIG. 12. Temperature (T) dependence of resistivity ͑␳͒ for
Sm1ϪxCaxTiO3ϩy/2 with ␦ϭ0.24 and 0.40. The inset shows the T
dependence of ␳ for Sm1ϪxCaxTiO3ϩy/2 with ␦ϭ0.20 and 0.24 on a
logarithmic scale.

56
TRANSPORT AND MAGNETIC PROPERTIES OF A . . .
10 151
FIG. 15. Spectral weight of the in-gap state (Ningap) as a func-
tion of ␦ for R1ϪxCaxTiO3ϩy/2 . Closed symbols represent insulat-
ing crystals and open symbols the metallic ones. Circles, squares,
rhombuses, and triangles represent RϭLa, Pr, Nd, and Sm, respec-
tively. The dashed line indicates the critical value of Ningap (ϳ0.03)
for the insulator-metal transition.
FIG. 14. ͑a͒ ␳ vs TϪ1 for Nd1ϪxCaxTiO3ϩy/2 with ␦ϭ0, 0.09,
and 0.20, and ͑b͒ optical conductivity spectra ␴͑␻͒ for the corre-
sponding crystals.
where m0 is the free-electron mass, and N the number of Ti
lower temperature as the system approaches the metal-
insulator ͑MI͒ transition.
atoms per unit volume. The cut-off frequency ␻ is the isos-
c
betic point of the spectra against the change of ␦, which is
1.0–1.5 eV depending on the R species.5 The Ningap value
proportionally increases with hole concentration,
VII. INSULATING STATE WITH FINITE DOPING
N
ingapϭC␦.
͑2͒
As pointed out above, the insulating phase exists not only
at half-filling but persists in the finite-doping region for the
present Ti oxide. For example, in Nd1ϪxCaxTiO3ϩy/2 , the
␦ϭ0 sample shows thermal-activation-type carrier conduc-
tion, and a clear gaplike structure in the optical conductivity
spectrum, as indicated in Fig. 14. Such an insulating state
comes from the on-site Coulomb interaction ͑i.e., is a Mott
insulator͒, as described above. When the 9% holes are doped
to this Mott insulator, the resistivity keeps increasing with a
decrease of temperature, but its temperature dependence de-
viates from the activation type.35 In the optical conductivity
spectrum,5 the spectral weight increases inside the Mott-gap
structure of the ␦ϭ0 spectrum ͑forming the in-gap state͒, but
the magnitude of the conductivity at zero energy remains
almost zero. Such an insulating state, with a finite hole con-
centration, cannot be explained by a simple Hubbard model
that takes account only of on-site Coulomb interaction. For
the 18% doped sample, the resistivity decreases with a de-
crease of temperature, and the magnitude of conductivity at
The coefficient C, i.e., the evolution rate of in-gap-spectral-
weight, depends on the correlation strength of the system as
Ϫ1
Cϰ U/W͒Ϫ U/W͒
͓͑
.
͑3͒
͑
͔
c
Such an in-gap state, however, does not contribute to the
␻ϭ0 conduction, i.e., the system remains insulating, up to
the critical hole concentration (␦c) for the metal-insulator
transition. The ␦c value depends on the strength of electron
correlation ͑Fig. 4͒ approximately as
␦ ϰ U/W͒Ϫ U/W͒ .
͑4͒
͑
͑
c
c
In fact, the experimental value for (U/W)c in Eqs. ͑3͒ and
͑4͒ is nearly identical, as seen for the comparison between
Figs. 3 and 4. Thus we can derive a simple law from these
empirical relations,
NcϭC␦cϭconst.
͑5͒
zero energy ␴(␻ϳ0) becomes finite, i.e., the sample is
͓
͔
The value of Nc corresponds to the spectral weight of the
in-gap state that is required for metallic conduction. In other
words, the in-gap state caused by hole doping does not con-
tribute to the metallic conduction if its spectral weight is less
than a certain value. In Fig. 15, we plot Ningap as a function
of ␦ for several R. Here, we plot insulating samples ͑in
which d␳/dT is negative at all temperatures͒ as closed sym-
bols, and metallic ones as open symbols. This figure clearly
shows the existence of the critical value Nc (ϳ0.03) that
separates the insulating and metallic regions, and does not
depend on R, or the critical hole concentration ␦c .
metallic, although the shape of ␴͑␻͒ is not a simple Drude-
type. Such an insulating phase away from the integer filling
is widely observed in other transition-metal oxides, such as
perovskite-type vanadates30 and manganites.36
Systematic optical studies of the present titanates5 could
clarify a characteristic feature of the insulating phase and the
insulator-metal transition at fininte ␦ as follows. We define
the spectral weight of the in-gap state,
␻
2m0
␲e2N
c
Keeping such a feature in mind, let us consider the pos-
sible origin of the insulating state with finite doping. One
N
ingapϭ
␴ ␻͒d␻,
͑
͑1͒
͵
0

10 152
T. KATSUFUJI, Y. TAGUCHI, AND Y. TOKURA
56
possibility is that the random potential might localize the
conduction carriers, i.e., Anderson localization.1 Such an ef-
fect is observed in doped semiconductors, where the dopant
itself acts as a random potential and the sample remains in-
sulating up to critical doping concentration. In the present
correlation͒ and band filling can both be controlled by the
change of the ͑R, Ca͒ composition. The charge-gap magni-
tude (Eg) of the end compounds, RTiO3, as well as the hole
concentration required to make the sample metallic (␦c),
change with the correlation strength in a way that
ϰU/WϪ(U/W)c .
R
1ϪxCaxTiO3ϩy/2 system, the trivalent R and divalent Ca
forms a solid solution, which could act as a random potential
for the conduction carriers. Another possible origin for the
insulating state is the electron-phonon interaction, by which
conduction carriers could be localized as small polarons. In
both cases, localization or delocalization of the conduction
carriers depends on whether the transfer energy ͑bandwidth͒
for conduction carriers is smaller or larger than a critical
value. In fact, Millis, Moeller, and Shraiman37 recently in-
vestigated the effect of electron-phonon interaction on con-
duction carriers by a dynamical mean-field method, and
found that the resistivity shows a semiconducting behavior
when a dimensioless parameter ␭ϭg2/kt ͑t is the transfer
energy of electrons, g the coupling constant of electron-
phonon interaction, and k the elastic force constant͒ is larger
than a critical value. Such scenarios are consistent with the
above-mentioned feature ͑existence of Nc͒, provided that the
spectral weight of the in-gap state Ningap represents the
‘‘renormalized’’ bandwidth for the carriers with strong elec-
tron correlation. In other words, doping controls such renor-
malized bandwidths, which increase proportionally with dop-
ing concentration, and the system becomes metallic when the
hole concentration ͑the renormalized bandwidth͒ is larger
than the critical value. Therefore, the in-gap spectral weight
Ningap measures the effective kinetic energy of the conduc-
tion carriers that governs their localization-delocalization
transition.
´
The Neel temperature (TN) in RTiO3 decreases from La
to Sm ͑with decreasing bandwidth W͒, and YTiO3 becomes a
ferromagnet at low temperature. Such a decrease of TN and
the appearance of the ferromagnetism should be attributed to
the degeneracy of the Ti 3d t2g orbital as well as the orbital
ordering. TN also decreases with hole doping, but remains
finite as long as the compound remains insulating.
The R1ϪxCaxTiO3ϩy/2 crystals near the MI phase bound-
ary show characteristic behaviors. One is the transition from
a high-temperature-metallic phase to a low-temperature-
antiferromagnetic phase. The resistivity shows an upturn at
the transition temperature but, its value remains finite at the
lowest temperature ͑2 K in this experiment͒, indicating the
existence of the antiferromagnetic metallic state. The other is
the transition from
a
high-temperature-paramagnetic-
insulating phase to a low-temperature-metallic phase. In both
cases, a deviation from a T2 dependence is observed for the
resistivity in the metallic phases near the phase boundary. It
was also found that the insulator-metal transition at a finite
hole doping level in a series of R1ϪxCaxTiO3ϩy/2 takes place
when the spectral weight of the in-gap state in the optical
conductivity spectrum, which represents the effective kinetic
energy of the mass-renormalized carriers, reaches the com-
mon critical value.
Another possible candidate for the origin of the insulating
state is the long-range Coulomb interaction, which would in
cases induce the ordering of doped holes. This kind of hole
ACKNOWLEDGMENTS
ordering is in fact observed for the K2NiF4-type cuprate with
1
hole concentration,38 or for the K2NiF4-type nickelate with
8
1
4
1
13 , and ͑Ref. 40͒ hole concentrations, but has not been
39
We thank Y. Okimoto for his collaboration for the optical
measurement and calculation of the bandwidth. We are also
grateful to Y. Okada for his collaboration at the early stage
of this study, and to M. Imada and N. Nagaosa for enlight-
ening discussions. The present work was supported by a
Grant-In-Aid for Scientific Research from Ministry of Edu-
cation, Science, and Culture, Japan, and by NEDO.
,
2
observed for the present Ti oxides.
VIII. SUMMARY
We have investigated transport and magnetic properties of
R
1ϪxCaxTiO3ϩy/2 whose bandwidth ͑or strength of electron
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1
4
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