PERGAMON
Solid State Communications 112 (1999) 91–95
www.elsevier.com/locate/ssc
Optical study of the metal–nonmetal transition in Ni12dS
H. Okamura a,*, J. Naitoh a, T. Nanba a, M. Matoba b, M. Nishioka b, S. Anzai b,
I. Shimoyama a, K. Fukui c, H. Miura c, H. Nakagawa a, K. Nakagawa c, T. Kinoshita d
a
Department of Physics and Graduate School of Science and Technology, Kobe University, Kobe 657-8501, Japan
b
Department of Applied Physics and Physico-Informatics, Keio University, Yokohama 223-8522, Japan
c
Department of Electrical Engineering, Fukui University, Fukui 910-8507, Japan
d
UVSOR Facility, Institute for Molecular Science, Okazaki 444-8585, Okazaki, Japan
Received 17 November 1998; received in revised form 6 May 1999; accepted 4 June 1999 by H. Kamimura
Abstract
Optical reflectivity spectra of the hexagonal Ni12d S have been measured to study its electronic structures, in particular those
associated with the metal–nonmetal transition in this compound. Samples with d , 0.002 and 0.02 are studied, which have
transition temperatures Tt ,260 K and 150 K, respectively. Upon the transition, a pronounced dip appears in the infrared region
of the reflectivity spectra. The optical conductivity spectra suggest that the nonmetallic phase is a carrier-doped semiconductor
with an energy gap of ,0.2–0.3 eV. The spectra also show that the gap becomes larger with decreasing temperature, and
smaller with increasing d. It is found that the overall spectrum in the nonmetallic phase can be explained in terms of a chargetransfer semiconductor, consistent with recent theoretical and photoemission studies of NiS. q 1999 Elsevier Science Ltd. All
rights reserved.
Keywords: D. Optical properties; D. Phase transitions
The problem of the metal–nonmetal transition in the
hexagonal NiS has been studied for three decades, but the
transition mechanism is not completely understood yet [1].
The high temperature (HT) phase above the transition
temperature, Tt , 264 K, is a paramagnetic metal. Upon
cooling through Tt , the resistivity increases suddenly by a
factor of ,40, associated with a slight increase in the lattice
constants (0.3 % in a and 1 % in c) and the appearance of an
antiferromagnetic order [2–5]. Tt is lowered sharply with
increasing Ni vacancies, and the transition disappears when
the vacancy content exceeds ,4% [6]. Similar behavior is
observed also with an applied pressure, and the transition is
not observed at pressures above ,2 GPa [7]. These behaviors are summarized in the phase diagram of Fig. 1.
The nature of the low-temperature (LT) phase below Tt
has been studied by many experiments. The resistivity (r)
increases only slightly with cooling, with an activation
energy of several meV [6]. In contrast, the optical study
by Barker and Remeika [8] clearly showed the presence of
* Corresponding author.
E-mail address: [email protected] (H. Okamura)
an energy gap of about 0.2 eV. The Hall effect experiment
by Ohtani [6] has shown that the majority carrier in the LT
phase is the hole with a density of 1020 21021 cm23 , which is
proportional to that of Ni vacancies, with , two holes per Ni
vacancy. Namely, the LT phase can be described as a p-type
degenerate semiconductor, where the Ni vacancies act as
acceptors. Effects of substituting Ni or S sites by other
elements have also been studied in detail [9,10]. Recently,
two high-resolution photoemission studies [11,12] have
revealed a finite density of states (DOS) around the Fermi
energy (EF ) in the LT phase, but leading to contrasting
interpretations: Nakamura et al. [11] have concluded that
there is a small correlation-induced energy gap with an
unusually sharp band edge, and that the observed finite
DOS at EF is due to thermal and instrumental broadenings
of the edge. On the other hand, Sarma et al. [12] have
concluded that the LT phase is an “anomalous metal”.
Various models have been proposed to describe the phase
transition and the gap opening in NiS. At early stages, it was
proposed that the transition was a Mott-type transition [13].
In this model, the Ni 3d band splits into two bands separated
by a gap in the LT phase due to strong Coulomb interaction
0038-1098/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved.
PII: S0038-109 8(99)00277-X
92
H. Okamura et al. / Solid State Communications 112 (1999) 91–95
T
δ
Fig. 1. Schematic phase diagram of Ni12d S in terms of temperature
(T), Ni vacancy concentration (d), and external hydrostatic pressure
(P).
at Ni sites. Band calculations that take into account manybody effects via various approximations have been unable to
reproduce an energy gap with a reasonable magnitude [11].
More recently, it has been proposed, based on cluster-model
calculations and resonant photoemission experiments, that
the energy gap in NiS is a charge-transfer gap between the
upper 3d and the S 3p bands [1,14–16].
In this work, we have performed optical reflectivity
experiments of Ni12d S in wide ranges of temperature (8–
300 K) and photon energy (0.008–30 eV), to study changes
in the electronic structures upon the metal–nonmetal transition. Around Tt we observe a sudden decrease in the reflec-
Fig. 2. Infrared reflectivity spectra (R) of Ni0:998 S and Ni0:98 S
measured at several temperatures. The inset shows R of Ni0:998 S
at 295 K up to 30 eV.
tivity [R…v†] and the formation of an energy gap of ,0.2 eV
in the optical conductivity [s…v†]. Although a gap formation
in s…v† of NiS was reported previously by Barker and
Remeika [8], their work was done in limited ranges of
temperatures and photon energies for samples with Tt .
220 K only. In contrast, our present work provides more
detailed temperature dependence of the energy gap, and a
comparison between samples having different values of Tt
(and d). We find that the energy gap becomes larger with
decreasing temperature, and smaller with increasing d. In
addition, we show that the overall spectrum in the LT phase
can be explained in terms of a charge-transfer semiconductor, consistent with cluster-model calculations and photoemission experiments [14–16].
The samples used in this work were polycrystalline
Ni12d S prepared as follows. Ni and S powders were
mixed with molar ratios of [Ni]:[S] ˆ 1:1 and 0.98:1, and
melted at 10008C in an evacuated quartz tube. Then they
were annealed at 7008C for two days and at 5008C for one
week, and quenched in iced water. The 1:1 mixture resulted
in an ingot with Tt . 260 K, and the 0.98:1 mixture with
Tt . 150 K. Comparing these Tt values with those in
previous works [9,10] the vacancy contents in these samples
are estimated as d , 0:002 (or Ni0:998 S, Tt ˆ 260 K) and
d , 0:02 (Ni0:98 S, Tt ˆ 150 K). 1 The ingots were cut into
disk-shaped samples, and the surface was mechanically
polished with alumina powders. Then the samples were
annealed at 5008C for three days in an evacuated quartz
tube, followed by a quench in iced water. This re-annealing
process is necessary because the mechanical cutting and
polishing suppress the phase transition in the sample surface
[8]. After this annealing process, the sample surface
appeared less shiny and the reflectivity decreased by 10–
25% depending on the wavelength. This was due to small
roughness on the sample surface caused by the annealing.
To correct for the roughness, we first measured the reflectivity of the annealed sample with respect to a flat mirror,
then evaporated Au or Ag on the entire sample surface and
measured the reflectivity again with respect to the same flat
mirror. We divided the former spectrum by the latter to
obtain a reflectivity spectrum corrected for the roughness.
This method has been shown to be quite efficient in measuring the reflectivity of a rough surface [19]. A standard nearnormal incidence configuration was used for the reflectivity
measurements, using a rapid-scan Fourier interferometer
(Bruker Inc. IFS-66v) and conventional sources for
measurements below # 2:5 eV, and using synchrotron
radiation source at the beamline BL7B of the UVSOR Facility, Institute for Molecular Science [18] for measurements
between 1.5 eV and 30 eV. The correction for roughness
was done only for the Fourier interferometer data, to which
the synchrotron data were smoothly connected. s…v† spectra
1
It is possible that even carefully prepared sintered NiS with
Tt . 264 K has a sizable amount of Ni vacancies, d # 0:002. See
[17].
H. Okamura et al. / Solid State Communications 112 (1999) 91–95
93
(a)
Ω
ECT (eV)
0.2
Ni0.98S
(Tt=150 K)
0.1
1
Ω
σ
Ni0.998S
(Tt=260 K)
0.3
σ
Tt
0
0
100
Tt
200
300
T (K)
σ
1
Ω
( b)
Fig. 3. Optical conductivity spectra (s) of Ni0:998 S and Ni0:98 S
below 2.0 eV at several temperatures. The arrows indicate the
“onset” discussed in the text, and the dashed straight lines are fitted
to the linearly rising portion of s. The inset shows s of Ni0:998 S at
295 K up to 25 eV, and the arrow indicates the peak due to d–d
transition discussed in the text.
were obtained from the measured R…v† spectra using the
Kramers–Kronig relations [20]. The Hagen–Rubens
p
(1 2 a v) and v24 extrapolation functions were used to
complete the lower- and higher-energy ends of the reflectivity spectra.
Fig. 2 shows the infrared R…v† of Ni0:998 S and Ni0:98 S
measured at several temperatures, with the inset showing
R…v† of Ni0:998 S at room temperature up to 30 eV. The
peaks in R…v† above 8 eV are due to higher-lying interband
transitions. For both samples the most significant spectral
change upon the transition is a large decrease of R…v† in the
infrared region, accompanied by a dip near 0.15 eV. These
spectral changes occurred over a temperature width of a few
K around Tt , as observed on our rapid-scan spectrometer
while cooling down slowly. With cooling further in the
LT phase, the dip undergoes a slight blue shift, which is
seen much more clearly for Ni0:998 S. For Ni0:998 S, a sharp
peak is observed at ,0.04 eV in the LT phase, but for
Ni0:98 S such a peak is not observed. This peak is likely to
result from optical phonons [5], and is not observed for
Ni0:98 S probably due to disorder caused by the larger density
of Ni vacancies or due to a stronger screening caused by the
larger density of free holes. The overall spectral shapes for
Ni0:998 S at 295 K and 80 K are very similar to those given by
Fig. 4. (a) Energy gap magnitude (ECT ) in the LT phase of Ni0:998 S
and Ni0:98 S as a function of temperature (T). The solid curves are
guide to the eye. (b) Illustration of optical excitations for a chargetransfer insulator and a Mott–Hubbard insulator. The upward
arrows indicate the gap excitations.
Barker and Remeika [8] using single crystalline samples.
This shows that our procedure to correct for the sample
roughness has functioned properly, i.e. our reflectivity spectra result from the intrinsic electronic structure of NiS.
Fig. 3 shows s…v† obtained from R…v†. Both samples have
a sharp rise in s…v† toward lower energy in the HT phase,
which is typical of a good metal. Below Tt , however, the
spectral weight below ,0.3 eV is strongly depleted with an
“onset” of s…v† at ,0.15 2 0.2 eV, which is indicated by
the arrows in Fig. 3. Above the onset energy, a broad absorption band is observed, extending up to ,2.5 eV. Below the
onset, s…v† rises toward the lower-energy end. This metallic, Drude-like spectral component indicates that there are
small amounts of free carriers in the LT phase. These spectral features suggest that the LT phase is a semiconductor
with an energy gap of ,0.2 eV and excess carriers, or
equivalently a carrier-doped semiconductor. This is consistent with the Hall effect result, [6] which shows that there
are ,1021 ‰cm23 Š holes in the LT phase. Another possible
interpretation for the LT phase from these optical spectra is
a semimetal, that has a low carrier concentration and a
strong reduction in the DOS around EF (a pseudogap). In
94
H. Okamura et al. / Solid State Communications 112 (1999) 91–95
any case, the above-mentioned broad absorption peak can be
regarded as the gap excitation peak. Later we will show that
the gap excitation results from optical transitions between S
3p-derived band and Ni 3d-derived (upper Hubbard) band.
Although the hexagonal NiS has an anisotropic crystal structure, the optical anisotropy in NiS is not large: according to
the polarized reflectivity experiments on single crystalline
NiS by Barker and Remeika [8], the gap opens in s…v† for
both E k c and E ' c polarizations with similar sizes. We,
therefore, assume that the temperature- and compositionvariations of the gap in the present work do not result
from changes in the optical properties along a particular
direction.
The onset in s…v† undergoes a blue shift with decreasing
temperature, as shown by the straight broken lines in Fig. 3.
These lines are fitted to the linearly rising portion in s…v†
above the onset. We attribute this blue shift to an increase in
the gap size. As a measure of the gap size, we take the
energies where the straight broken lines in Fig. 3 reach
s…v† ˆ 0, which are plotted as a function of temperature
in Fig. 4(a) together with data measured at additional
temperatures not indicated in Figs. 2 and 3. Clearly, the
gap becomes larger with decreasing temperature, and it is
much smaller for Ni0:98 S than that for Ni0:998 S. Note that the
edge of the gap excitation band for Ni0:98 S has a smaller
slope (as indicated by the broken lines in Fig. 3). Namely,
the narrower gap for Ni0:98 S is associated with a broader
band edge. One possible reason for the narrower gap in
Ni0:98 S is the shrinkage of lattice caused by the larger d in
Ni0:98 S,[5] since smaller atomic distances can lead to
broader bands. In addition, an increase in d introduces a
higher density of acceptor-related states near the top of
occupied band as well as a larger degree of vacancy-induced
disorder, both of which may lead to a broadening of the
absorption band around the band edge. In reality, the
observed gap narrowing and the lowering of Tt with increasing d is probably a result of complicated interplay among
these effects.
Recently, Sarma et al. [12] have reported a high-resolution photoemission study of NiS. They observed a metallic
electronic structure in the LT phase, where the DOS at EF
was nearly flat and smoothly varying, and was also slightly
smaller than that in the HT phase. Contrasting the metallic
electronic structure around EF to the weakly temperaturedependent r and the large optical gap, they argued that the
LT phase was an “anomalous metal”. However, a metallic
DOS within the close vicinity of EF is not necessarily inconsistent with a small variation in r…T† and a large gap in the
LT phase, since these behaviors can be viewed as typical of
a p-type, degenerate semiconductor [6,21]. Namely, in a
degenerate p-type semiconductor, EF is located near the
top of the occupied band, where a large acceptor-related
DOS is present. Then it is possible to have a metallic
(continuous) DOS around EF which is smaller than that
for the HT phase (good metal). For such case, the activation
energy measured by r…T† at low temperatures probes the
activation of holes to these acceptor-related states near EF ,
and it is not directly related to the (larger) intrinsic gap [21].
It has been demonstrated convincingly that the LT phase of
NiS is a p-type, degenerate semiconductor by Ohtani [6],
and the present optical result gives further support to this
picture.
Fujimori et al. [14–16] have performed cluster-model
calculations for NiS that take into account many-body and
inter-configuration interactions. Comparing the calculated
results with the measured photoemission spectra, they
have concluded that the energy gap in NiS is a charge-transfer (CT) gap that opens between the upper Ni 3d- and the S
3p-derived bands, rather than a Mott–Hubbard (M–H) gap
between the correlation-split 3d bands. The two situations
are illustrated in Fig. 4(b). For gap excitations in the M–H
case, the optical transitions occur from the lower Ni 3d band
to the upper 3d band. Hence, the situation is close to an
intra-atomic transition between the d orbitals at a Ni site,
which is optically forbidden in the dipole approximation. In
reality, symmetry breaking effects caused by defects and
hybridization make the transition partially allowed, but the
transition is still weak. For typical M–H insulators such as
V2 O3 [Ref. [22]], RTiO3 [Ref. [23]], and RVO3 [Ref. [24]]
(R: rare earth elements), the intensity of the gap excitations
in s…v† is in the range 300–500…V21 cm21 †. The observed
intensity for NiS, ,4000…V21 cm21 †, is an order of magnitude larger, and difficult to reconcile with a M–H gap. In
contrast, for a CT gap optical transitions occur from the
spatially-extended S 3p band 2 to the Ni upper 3d band.
These bands have a large spatial overlap of wave function,
and also the p ! d transitions have no symmetry restriction
for dipole transitions. This explains quite naturally the
observed strong intensity of the gap excitation, and also
demonstrates convincingly that the energy gap in NiS is a
CT gap. According to Fujimori et al. [14–16], the on-site
Coulomb repulsion energy at a Ni site in NiS is U ˆ 4:0 ^
0:5 eV. This value agrees well with the position of the weak
peak at ,4.5 eV in s…v†, which is marked by the arrow in
the inset of Fig. 3. Hence we attribute this peak to optical
transitions from the lower Ni 3d band to the upper Ni 3d
band. This agreement gives a further support to our interpretation of the observed spectra in terms of a CT gap.
We have shown that the optical spectra of Ni12d S show
large changes in the infrared region upon the metal–nonmetal transition, and that the spectra for the LT phase can be
described as those of a carrier-doped semiconductor with an
energy gap of ,0.2–0.3 eV. The magnitude of the energy
gap becomes larger with decreasing temperature, and smaller with increasing d. The overall spectrum including the
violet region can be explained in terms of a charge-transfer
semiconductor, consistent with previous photoemission
results and cluster-model calculations. We point out that
2
Note that the “3p band” here is not purely derived from S, but
there can be a strong mixing with the Ni 3d band, since the gap is
much smaller than the width of the gap excitation band.
H. Okamura et al. / Solid State Communications 112 (1999) 91–95
the holes in the LT phase are probably under the influence of
strong on-site Coulomb interaction, not showing simple
free-particle behaviors. In this respect, the behaviors of
the holes in the LT phase are very interesting and deserve
further studies.
Acknowledgements
We would like to thank S. Kimura for useful discussions
and for providing the Kramers–Kronig analysis software
used in this work. We acknowledge financial support from
Grants-in-Aid from the Ministry of Education, Science and
Culture.
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