Raman spectroscopy on ternary transition metal chalcogenide Rb2Ni3S4

Journal of Alloys and Compounds 364 (2004) 199–207

Raman spectroscopy on ternary transition metal chalcogenide Rb2 Ni3S4 Takumi Hasegawa a,∗ , Mitsutaka Inui b , Katsuhiro Hondou a , Yishihiro Fujiwara a , Tetsuya Kato c , Katsunori Iio a a

Department of Physics, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan b Seiko Epson Corporation, 3-3-5 Owa, Suwa-shi, Nagano 392-8502, Japan c Faculty of Education, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba-shi, Chiba 263-8522, Japan Received 19 February 2003; accepted 7 April 2003

Abstract Raman scattering measurements were performed for the first time on the ternary alkali nickel sulfide Rb2 Ni3 S4 single crystal, in which nickel ions form a Kagome lattice. Factor-group analyses were made to determine the zone center vibrational modes for the crystal structure of the Cs2 Pt3 S4 -type with the space group of Fmmm, to which Rb2 Ni3 S4 belongs, and also for a unit stacked package layer with the point symmetry of 6/mmm piling up to the present layered sulfides. Raman active Ag (2) and Ag (1) + B2g modes were clearly observed as the subspecies modes which correlate to A1g and E2g of the stacked package. The Raman shift and line width of the observed modes, Ag s and B2g , exhibited a monotonic temperature dependence in the range between 4 K and 390 K. These thermal properties were discussed in terms of cubic and quartic lattice anharmonicity. Furthermore, observed decreases in their scattering intensities with increasing temperature were discussed heuristically by taking account of the thermal enhancement of extrinsic carriers with activation energy, which was found to be commensurate with the magnitude obtained from a previous resistivity measurement. © 2003 Elsevier B.V. All rights reserved. Keywords: Inelastic light scattering; Ternary metal chalcogenides; Rubidium nickel sulfide; Kagome lattice

1. Introduction Layered-structure sulfides have attracted considerable interest because of their technological applicability, for instance, as cathode materials of lithium ion cells [1,2] and because of the novel aspects of condensed matter physics specific to the low-dimensionality in the crystal structure of these compounds. Rb2 Ni3 S4 dealt with in the present paper is one of the ternary alkali nickel sulfides with two-dimensional characteristics [3]. A notable feature of this crystal is that the Ni ions constitute a Kagome lattice sandwiched by two S honeycomb lattices so as to form a [Ni3 S4 ]2− infinite layer. These layers are separated by two Rb triangular lattices, the lattice points of which are located above and below the honeycomb center of the S ∗ Corresponding author. Tel.: +81-3-5734-2367; fax: +81-3-5734-3542. E-mail address: [email protected] (T. Hasegawa).

0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0925-8388(03)00503-6

lattices [4]. This crystal has recently been identified with a nonmagnetic band insulator through magnetic measurements and LDA band-structure calculation [5]. Since alkali metals can be easily intercalated in or de-intercalated from layered chalcogenides [6,7], and even govern the dimensionality of the chalcogen lattice [8,9], the electric and nonmagnetic properties of Rb2 Ni3 S4 can be modified by either electron doping or hole doping. In particular, if the filling-controlled samples based on Rb2 Ni3 S4 are suitably prepared, some interesting properties, such as ferromagnetism or half-metallic behavior, are expected to emerge in them, because of the peculiar structure of the 3d-band of Ni2+ in the host Rb2 Ni3 S4 : the density of state spreads widely for about 8 eV owing to the covalency between Ni and S ions but the electronic states immediately below the Fermi energy are almost flat [5,10]. Additionally, if a possible modification in the valence electrons of Ni induces local magnetic moments on the Kagome lattices with an antiferromagnetic superexchange interaction between thus

200

T. Hasegawa et al. / Journal of Alloys and Compounds 364 (2004) 199–207

induced nearest neighbors, a magnetic phase transition with spin frustration, which is a subject of recent magnetism, may occur in the modified systems [11–14]. The present authors have taken a tentative approach along this line by means of hole doping with Rb defects and electron doping due to the substitution of Sr for Rb on the host Rb2 Ni3 S4 . Some changes in electric and magnetic properties were preliminarily observed in these systems [15]. In the course of this investigation, information on the crystal lattice and lattice dynamics obtainable by methods other than X-ray diffraction has been required. The physical properties of the present system are quite similar to those of graphite intercalation compounds [16] and intercalated transition-metal chalcogenides Lix TX2 (T = Mo, Nd, etc. and X = S, Se) [17], in which light scattering has provided key insights into the physics of layer structures. Therefore, in addition to magnetic and electric measurements, the Raman spectroscopy measurement has been performed to clarify the lattice vibration of Rb2 Ni3 S4 as a host compound, because data on Raman scattering have so far been absent for the compounds related to Rb2 Ni3 S4 . In the present paper we show the results of factor–group analysis of the vibrational modes in Rb2 Ni3 S4 , the Raman scattering data at room temperature and the temperature dependence of the first order Raman spectra from 4 K to 390 K. A band structure attributable to the second order Raman spectra is also shown. The lattice anharmonicity responsible for the temperature dependence of Raman shift and line width and also the temperature dependence of Raman intensity are discussed for the modes observed.

2. Structure and vibration mode of Rb2 Ni3 S4 Rb2 Ni3 S4 crystallizes in a face-centered orthorhombic structure as shown schematically in Fig. 1. Four chemical formulae of Rb2 Ni3 S4 are included in one conventional unit cell, for which the lattice constants have been reported as a = 9.901 Å, b = 13.606 Å and c = 5.861 Å [3]. For characterizing this structure, it is helpful to note the atomic layers perpendicular to the b-axis. A composite unit of consecutive Rb–S–Ni–S–Rb layers along the b-axis stacks upon its predecessor layer, sliding over by half the translational period along the a-axis. The composite slab is a so-called stacked package and has a hexagonal symmetry 6/mmm. Crystal structures in ternary transition metal chalcogenides can be classified into several types according to the stacking of the packages. The present crystal belongs to the family of the Cs2 Pt3 S4 -type with the space group Fmmm, where the translational periodicity along the b-axis is twice the distance between the neighboring stacked packages. In order to obtain the vibrational modes of Rb2 Ni3 S4 , we performed factor-group analyses of the atomic displacements in a primitive Bravais lattice, of which a unit cell includes only one chemical formula. There are 27 vibrational modes, i.e. 3 acoustic modes and 24 optical modes, at each wave number k. We examined the vibrational modes for the zone center k = 0. Then a decomposition of the displacement of each atom into the irreducible representations gives: ΓRb = Ag + B1g + B1u + B2u + B3g + B3u

(1)

Fig. 1. Crystal structure of Rb2 Ni3 S4 . (a) A Bravais lattice with four chemical formulae. Dashed lines show sulfur honeycomb lattice. (b) A stacked package. Solid and dashed lines display nickel Kagome lattice and sulfur honeycomb lattice, respectively. (c) A way of stacking each layer as viewed down along the crystallographic b-axis.

T. Hasegawa et al. / Journal of Alloys and Compounds 364 (2004) 199–207 Table 1 Representations of Raman active phonons in mmm and 6/mmm and their atomic displacements along the a, c and b axes Representations in mmm

Representations in 6/mmm

Displacements

Ag

A1g

Ag

A1g

Rb Rb √1 (u 1 − u 2 ) b 2 b S S2 1 S1 (u + u − ub 3 b 2 b

Ag

S

− ub 4 )

S

S

S

S

S

S

1 S1 2 (ua

− ua 2 + ua 3 − ua 4 )

1 S1 2 (uc

− uc 2 + uc 3 − uc 4 )

E2g B2g

The superscript number of each sulfur is given in Fig. 2. For rubidiums, numbering is given for the atoms above and below the sulfurs honeycomb.

ΓNi = Au + 3B1u + 2B2u + 3B3u

(2)

ΓS = 2Ag + Au + B1g + 2B1u + B2g + 2B2u + 2B3g + B3u

(3)

The displacements corresponding to Ag and B2g modes are listed in Table 1 and those for S’s are illustrated in Fig. 2. It should be noted that the displacements of the Ag modes given here do not correspond to the real eigenmodes, because the actual modes are given as a linear combination

201

of the displacements of the same representations. Only the B2g mode represents the eigenmode because there is only one B2g . The acoustic modes are B1u +B2u +B3u . Infrared active modes must have the same symmetry as the acoustic ones, and therefore 13 modes, ΓIR = 5B1u + 4B2u + 4B3u

(4)

are infrared active. Nine modes, ΓRaman = 3Ag + 2B1g + B2g + 3B3g

(5)

are Raman active, where the vibrations associated with the Ni Kagome lattice are not included. Since all Ni atoms locate on the sites with the center of inversion, the lattice modes associated with Ni cannot be observed through Raman scattering. The Raman tensors R␣␤ for the relevant representations are listed in Table 2 in accordance with the notation by Loudon [18], where they are specified with two-dimensional matrix elements with respect to the a- and c-axes for the backscattering. To understand further the lattice dynamics of the present system, we examined a comparative analysis of the vibrational modes for one stacked package with the point symmetry of 6/mmm, neglecting the stacking along the b-axis

Fig. 2. Raman active vibrational modes of sulfur. The numbers beside the atoms indicate atomic numbers used in Table 1. In the A1g mode in 6/mmm displacements are along the b-axis and in the E2g mode sulfurs move in the ac plane. As a remaining A1g mode in 6/mmm (Ag mode in mmm), the rubidium pair located above and below the sulfur honeycomb move antiparallel to each other along the b-axis. Table 2 List of the Raman tensor matrices R␣␤ of the observed phonon modes for the representations in mmm and 6/mmm; the magnitudes of the components are evaluated relative to the ‘a’ element for Ag (1) and the observed phonon energies at room temperature Representations in mmm
 ‘a’ 0 Ag (2) 0 ‘c’
 ‘a’ 0 Ag (1) 0 ‘c’
B2a

0

‘e’

‘e’

0



A1g

Representations in 6/mmm
 ‘a’ 0


E2




0

‘a’

‘d’

0

0

−‘d’

0

‘d’

‘d’

0





Magnitude of tensors
 1.12 0





0

0.58 

1

0

0

−1.10

0

0.82

0.86 0

Energy (cm−1 ) 361.8

284.8  278.7

202

T. Hasegawa et al. / Journal of Alloys and Compounds 364 (2004) 199–207

[19]. Then, we obtain: ΓRb = A1g + A2u + E1g + E1u

(6)

ΓNi = A2u + B1u + B2u + 2E1u + E1u

(7)

ΓS = A1g + A2u + B1u + B2g + E1g + E1u + E2g + E2u (8) In this hypothetical case some previous modes are degenerated and some Raman tensor elements become identical. Therefore, if the binding force between the stacked-package layers of Rb2 Ni3 S4 is weak, probable differences in both mode energies and Raman tensor elements will be small. Both kinds of symmetry considerations are applicable for assigning observable phonon modes. The atomic displacements and the Raman tensors for the single stacked package are also listed in Tables 1 and 2, respectively.

3. Experimental results 3.1. Mode assignment Single crystals of Rb2 Ni3 S4 were grown by the flux method as described in a study by the present authors [15]. Prepared samples were sheet-like in shape, having ac-plane surfaces. Raman scattering data were obtained by using an Ar+ laser with an excitation wavelength of 514.5 nm, a triple polychromator T64000 (Jobin Yvon Inc.) with a CCD counter cooled with liquid nitrogen and a microscope in order to find a fault-free area in the surface. After the Raman scattering measurements, the direction of the crystalline axes a and c on the surface was ascertained by taking an X-ray Laue pattern.

Let us define two coordinate systems; one is referenced to the crystalline axes (a, b, c) and the other to the experimental coordinate (X, Y, Z) of a backward scattering geometry. The Z-axis is taken along the ‘b’-axis parallel to the incident laser beam. Four configurations, Z(XX)Z, Z(XY)Z, Z(YX)Z and Z(YY)Z, were examined. Supposing that the system has the symmetry 6/mmm, E2g being the progenitor of Ag + B2g in mmm might be possible to observe. Thus, an Ag + B2g pair is expected to have nearly equal energy. The energy of Ag , however, will be larger than that of B2g , because in Ag S’s move in the plane perpendicular to the c-axis towards Rb’s on the adjacent stacked package, while in B2g they take a displacement in such a way that S avoids Rb. A typical Raman spectrum at room temperature is shown in Fig. 3. There are three main peaks attributable to the first order phonon Raman scattering. As expected, a pair of peaks can be seen at 278.7 cm−1 and 284.8 cm−1 . According to the above discussion, we can assign these two modes to B2g and Ag , respectively, and the mode with a peak at 361.8 cm−1 to Ag , because all remaining modes are expected to belong to Ag . To confirm these assignments, we examined the symmetry of Raman tensors and evaluated its relative magnitudes from the experimental data. To do so, the intensities of three peaks for all of the configurations indicated above were measured as a function of the angle θ between the incident light polarization X and a certain crystallographic orientation on the ac plane, by rotating a specimen around the b-axis step by step. At each angle we took care not to give rise to trivial variations of the experimental conditions, e.g. focusing position on the specimen, lens focus, laser power, and so on. The scattering intensities of the phonon modes were calculated by fitting a Raman profile with a Lorentzian curve, I(ω) =

I0 Γ π (ω − Ω)2 + Γ 2

(9)

Fig. 3. Typical Raman spectrum at room temperature, where the X-axis specifying the incident light polarization is nearly parallel to the crystallographic a-axis.

T. Hasegawa et al. / Journal of Alloys and Compounds 364 (2004) 199–207

where I0 is the integrated intensity, Ω the phonon energy and Γ their line width or lifetime. In this paper the relation between I0 and R␣␤ is taken as  2   es␣ R␣␤ ei␤ , (α, β = x, y, z) (10) I0 =   ␣␤ where es and ei are the polarization vectors of the electric field of scattered and incident lights, respectively, and the coordinate (x, y, z) corresponds to the crystalline (a, c, b). According to this definition, this Raman tensor including a square root of the Bose factor (n+1)1/2 and an inverse of the dielectric constant ε−1 differs from the conventional one. The magnitude of intensity was determined typically to an accuracy of a few %, which was due to a cumulative error in the measurement of I(ω). The angular dependence of I0 for the Z(XX)Z configuration is shown in Fig. 4, where the effective Raman tensors for a given angle of θ are ‘a’cos2 θ + ‘c’sin2 θ

(11)

for Ag and 2‘e’cosθsinθ

(12)

for B2g . The tensor elements determined relative to the aa component ‘a’ of Ag at 284.8 cm−1 are listed in Table 2. Through a Laue pattern observation, the orthogonal principal axes found at the angles of 21◦ and 111◦ from the present angular dependence were confirmed to correspond to the crystalline a- and c-axes, respectively. The relative difference between the factor of (n + 1)1/2 involved in these Raman tensors at 278 cm−1 and that involved at 362 cm−1 is only ∼6% at 300 K. In addition to the energy values, the connectivity of the Ag + B2g modes in mmm symmetry to the Eg mode in 6/mmm symmetry was also confirmed from

203

the empirical magnitude of the tensor components as listed in Table 2, where the relations, i.e. ‘a’∼–‘c’ and ‘a’∼‘e’, for the components of the Ag and B2g modes were approximately proved and so this Ag mode consists of the vibration shown in Fig. 2. These results imply that interlayer interactions between the stacked packages relevant to the lattice vibrations are weaker than intralayer interactions. In contrast to these pair modes, the tensor components of the other Ag mode do not exhibit good connection to the Ag mode in 6/mmm. This result is due to interlayer charge transfer since in this mode, the distances between layers are changed as seen in the left mode of Fig. 2. This effect enhances ‘a’ more than ‘c’ as a result of the larger polarization induced by the longer shift between adjacent layers along a-axis when the displacement of this mode occurs. For convenience, we designate the peak at 284.8 cm−1 as Ag (1) and the peak at 361.8 cm−1 as Ag (2) from now on. Also, we consider a remaining Ag mode, which characterizes the vibration of Rb’s moving along the b-axis. Judging from the crystal structure, energy of this Rb mode seems to be low, probably less than 100 cm−1 . No Raman shift assignable with it was observed in this region, probably because the perturbation of this vibration on the electronic states of sulfurs and nickels locating near the Fermi energy is so weak that it does not yield an observable Raman intensity. 3.2. The temperature dependence of Raman scattering Raman shift, line width and scattering intensity of the optical phonons were measured as a function of temperature for the range of 4 K–390 K. The specimens were mounted in vacuum on a heat exchanger inside the Microstat (Oxford Inc.) in which the temperature was controlled with liquid He flow and a heater. Temperatures of samples were recognized

Fig. 4. Angular dependence of Raman intensities at room temperature for the Z(XX)Z configuration. Solid lines are curves calculated with the parameters in Table 2. In this specimen, the a- and c-axes are located at 21◦ and 111◦ , respectively.

204

T. Hasegawa et al. / Journal of Alloys and Compounds 364 (2004) 199–207

Fig. 6. Second order Raman spectra with the Z(XX)Z configuration at various temperatures.

Fig. 5. First order Raman spectra for three main Raman peaks at various temperatures.

as nominal values at a position on the heat exchanger close to the sample. An output power of the incident laser was reduced below 30 mW, in order to avoid an increase in the temperature of the scatterer. Note that the true temperatures of the scatterer would be somewhat higher. In the present study, it was clarified that Rb2 Ni3 S4 does not undergo any structural transition below the measured range, and thus obtaining further precise thermometry was not considered important. In Fig. 5 the three main peak positions observed are shown as a function of temperature, where the angle between X and the a axis was 72◦ in this measurement. Although the energies of these peaks decrease slightly as the temperature is raised, no anomaly was recognized. All peaks were fitted very well with the Lorentzian line profile of Eq. (9), where a window function deduced from the plasma lines of the Ar+ laser was used for deconvolution, since at low temperature the line widths were reduced to be comparable with the slit width (about 0.5 cm−1 ). The parameters representing these profiles, i.e., the Raman shift Ω, line width Γ and integrated intensity I0 , are discussed in the next section. The Raman profiles in a higher shift region are shown in Fig. 6, where a detailed Raman profile can be clearly observed at low temperatures.

4. Discussion The thermal effects of Raman shift and line width are caused by the anharmonicity of the vibrational potential energy, which is usually described by the cubic and quartic

terms of lattice vibration energy. It is better, of course, to carry out a first-principle calculation of the frequency shift and damping constant arising from both cubic and quadratic anharmonicity in the present crystal. However, such a calculation is by no means trivial, because a simple model such as a nearest-neighbor model is inadequate to describe either the harmonic or the anharmonic properties of crystal. Thus we will follow an intuitive discussion about the anharmonic effects in light scattering due to optical phonons performed successfully by Balkanski et al. in silicon, where the processes of an excited phonon decaying into two or three phonons with equal energy are taken into account [20]. In this approach, Raman shift Ω and line width Γ varying with temperature are described for a mode with a harmonic phonon frequency Ω0 as follows,

 

2 3 3 Γ(T) = A 1 + x +B 1+ y + e −1 e − 1 (ey − 1)2 (13)

 2 Ω(T) = ω0 + C 1 + x e −1

 3 3 +D 1 + y + y e − 1 (e − 1)2

(14)

where x = h ¯ ω0 /2kB T and y = h ¯ ω0 /3kB T. In these expressions, A and C correspond to cubic terms and B and D to quartic terms. For each mode, the numerical curve based on Eq. (13) did not fit well with the experimental Γ (T), whereas that based on Eq. (14) did fit well with the experimental Ω(T). This discrepancy can be ascribed to the probable presence of defects and stacking faults giving rise to a broadening of the line width. This factor compels us to modify Eq. (13) by adding a certain constant E and replacing intrinsic ω0 by other extrinsic ω 0 . Nevertheless, we regarded an average of ω 0 in Eqs. (13) and (14) as the intrinsic fre-

T. Hasegawa et al. / Journal of Alloys and Compounds 364 (2004) 199–207

Fig. 7. Raman shift vs. temperature. Solid curves give theoretical fits by using Eq. (14) with the parameters in Table 3.

Fig. 8. Line width vs. temperature. Solid curves give theoretical fits by using Eq. (13) with the parameters in Table 3, where a constant E specifying an inhomogeneous width is added to Eq. (13).

quency and thus an amendment to Γ was made only to add a constant E to the right-hand side of Eq. (13). Such modified equations demonstrate the experimental data fairly well as shown in Figs. 7 and 8. The fitting parameters A, B, C, D, E and ω0 are listed in Table 3. These values clearly indicate that the anharmonicity in the Ag (2) mode is governed normally by the three phonon process, but that in the subspecies modes Ag (1) and B2g is dominated by the four phonon process instead. This means that the density of phonon states at about 140 cm−1 is very small, because, for example, this energy region is located between the interlayer and intralayer vibration energies. On the basis of these results the lattice instability invoking metal-insulator-like transitions is presumed to be absent from this chalcogenide compound over the temperature range measured. Table 3 Harmonic energy Ω and anharmonic coefficients of the observed three phonons

B2g Ag (1) Ag (2)

ω0

A

B

C

D

E

281.4 288.0 366.0

0.000 0.085 0.63

0.041 0.081 0.000

0.091 −0.060 −1.090

−0.181 −0.188 −0.150

0.738 0.858 0.280

All magnitudes are measured in the unit of cm−1 .

205

Fig. 9. Temperature variation in the effective Raman tensor deduced from the integrated intensity from Eq. (10) for observed modes. Solid curves are those fitted by Eq. (15) with an activation energy ∆ of 48 meV. The other parameters are listed in Table 4.

The Raman tensor coefficients defined by Eq. (10) may also depend on temperature. In Fig. 9, the coefficients deduced from the integrated intensities are illustrated as a function of temperature. Their magnitudes, except for ‘c’ of Ag (2), decrease as the temperature is raised. If the electron–phonon interaction responsible for light scattering is independent of temperature, the Raman intensity should increase in proportion to the population factor n+1. This inconsistency is ascribed to a probable decrease in the spatial correlation of relevant phonons brought about by thermally excited carriers as a reflection of the semiconductive character of Rb2 Ni3 S4 . If the correlation length l becomes shorter than the characteristic length of a scattering volume, the Raman intensity is proportional to l3 . A similar effect is observed in opaque materials in association with a reduction of the scattering volume perpendicular to a sample surface. In the latter case the momentum conservation becomes ambiguous within an order of ∼l−1 . However, in the present case, since such a correlation length is sufficiently large in comparison with the atomic scale, this effect is not considered to be serious. We presume that the correlation length is strongly affected by the carrier concentration which is −∆/kT described by l−3 = N0 (1 + nc eB ), where N0 is a phenomenological constant depending on the correlation length at zero temperature, nc denotes a ratio of reduction caused by thermally excited carriers, and ∆ an activation energy of these carriers. Then the temperature dependence of the present effective Raman tensor R␣␤ (T) can be expressed as:

12 1+n 0 (15) R␣␤ (T ) = R␣␤ 1 + nc e−∆/kB T where R0 ␣␤ is the Raman tensor at 0 K. As shown in Fig. 9, this equation can be fitted to the experimental data with a common ∆, which is extracted to be 48 meV. Other parameters are tabulated in Table 4. In this treatment, nc ’s for different elements belonging to a certain vibration mode must have the same value, but two nc ’s for the Ag (2) mode are significantly different from each other, whereas nc ’s of the Ag (1) mode have a similar value. A previous resistivity

206

T. Hasegawa et al. / Journal of Alloys and Compounds 364 (2004) 199–207

Table 4 The coefficients of Eq. (15), where R0 is Raman tensor coefficient at 0 K, nc a coefficient representing a ratio of reduction caused by thermally excited carriers, and ∆ an activation energy of these carriers

R0 nc

Ag (1) a

Ag (1) c

Ag (2) a

Ag (2) c

B2g e

1.92 18.80

2.09 19.80

2.54 25.80

0.54 0.94

1.41 13.40

∆ = 48 meV.

measurement revealed that the temperature dependence of resistivity ρ(T) in the present system exhibits different characteristics over a broad temperature region, i.e. ρ(T) with an activation energy of 50 meV at low temperatures (∼ 100 K), ρ(T) with a crossover of resistivity at intermediate temperatures (∼ 250 K) and ρ(T) with an activation energy of 400 meV which is regarded as the intrinsic gap energy at higher temperatures [5]. ρ(T) at temperatures below the intermediate region was proposed to be governed by the impurity conduction due to the defects inevitably introduced through the single crystal growth. Therefore, a fair agreement between the extrinsic energy gap of 48 meV estimated from the present Raman scattering and that of 50 meV obtained from the electric transport supports the adequacy of the heuristic scenario proposed for R␣␤ (T). Finally, we comment on the Raman spectra at 4 K for the shift energies higher than 400 cm−1 shown in Fig. 10. Some broad peaks, narrow hollows and sharp peaks are seen from 430 cm−1 to 730 cm−1 . These structures are ascribed to the second order Raman process. If the process in which two phonons of the same branch are emitted (overtone) is taken into account, the resulting Raman spectrum has the same shape as the density of one phonon state with a doubled energy and has mainly Ag -like polarization. In Fig. 10, where the angle between the X and the a-axes was 72◦ , the Raman shifts for the Z(XX)Z configuration are governed mainly by the coefficient ‘c’ of Ag and those for the Z(YY)Z and Z(XY)Z are governed by ‘a’ of Ag and ‘e’ of B2g , respectively. This indicates that these peaks were assigned to the Ag -like mode and were due to the overtone Raman process. However, at present we only have information on three op-

tical phonon frequencies so that the one-phonon density of states cannot be constructed. Only the following insight is deduced. The sharp peak at 730 cm−1 has a nearly two-fold value of 368 cm−1 for the Ag (2) mode energy and belongs to the same branch. Similarly, the broad peak around 560 cm−1 is related to 287 cm−1 of Ag (1) and 281 cm−1 of B2g . Other spectra including a very sharp peak around 636 cm−1 may also correspond to the intralayer modes branch of sulfurs and nickels. Detailed analyses based on an appropriate model of lattice dynamics remain to be performed to gain an understanding of the structure of the second order spectra and the temperature dependence of the first order spectra.

5. Conclusion Raman scattering were measured for the first time on the ternary alkali nickel sulfide Rb2 Ni3 S4 single crystal. Factor-group analyses of the vibrational modes were performed for the Cs2 Pt3 S4 -type (Fmmm) structure which characterizes Rb2 Ni3 S4 . Three Raman active optical modes Ag (1), Ag (2) and B2g associated with the displacements of sulfurs are observed as the first order Raman scattering. A pair mode of Ag (1) +B2g was recognized as the subspecies mode correlating with E2g in a stacked package layer, but the Ag (2) mode had some discrepancy caused by the interlayer charge transfer. The remaining Raman active mode with Rb vibration could not be observed probably because this mode does not have a sufficient magnitude of Raman polarizability. The observed temperature dependence in the Raman shifts and the line widths for three modes in the temperature range from 4 K to 390 K are discussed from a viewpoint of lattice anharmonicity. The cubic term for the pair modes was found to be weak and this fact indicated that there is a low density of phonon states around 140 cm−1 , i.e. about a half of their energy, and this energy is regarded as a rough separator between the low-energy interlayer and Rb modes and the high-energy intralayer S and Ni modes. The integrated Raman intensity exhibiting an anomalous decrease with increasing temperature was discussed by taking into account the thermal enhancement of extrinsic carriers which reduces the phonon correlation length.

Acknowledgements

Fig. 10. Second order Raman spectra at 4 K for three configurations. Z(XY)Z is equivalent to Z(YX)Z.

The authors are indebted to M. Usuda and N. Hamada of Science University of Tokyo for offering us their LDA calculation and to S. Nawai and A. Fujimori of Tokyo University for performing the photoemission spectroscopy experiment. These were useful in clarifying the electronic band structure of the 3d electron of Ni2+ in Rb2 Ni3 S4 . They also thank A. Saiki of Tokyo Institute of Technology for observing the Laue pattern of the present samples.

T. Hasegawa et al. / Journal of Alloys and Compounds 364 (2004) 199–207

References [1] K. Mizushima, P.C. Jones, P.J. Wiseman, J.B. Goodenough, Mater. Res. Bull. 15 (1980) 783. [2] C. Delmas, I. Saadoune, Solid State Ionics 53–57 (1992) 370. [3] W. Bronger, J. Eyck, W. Rüdorff, A. Stössel, Z. Anorg. Allg. Chem. 375 (1970) 1. [4] W. Bronger, R. Rennau, D. Schmitz, Z. Anorg. Allg. Chem. 597 (1991) 27. [5] K. Hondou, Y. Fujiwara, T. Kato, K. Iio, A. Saiki, M. Usuda, N. Hamada, J. Alloys Comp. 333 (2002) 274. [6] W. Muller-Warmuth, R. Schollhorn, Progress in Intercalation Research, Kluwer Academic Publishers, Boston, 1994. [7] S.H. Elder, S. Jobic, R. Brec, M. Gelabert, F.J. DiSalvo, J. Alloys Comp. 235 (1996) 135. [8] Y.-J. Lu, J.A. Ibers, Comments Inorg. Chem. 14 (1993) 229.

207

[9] W. Bronger, P. Müller, J. Less-Common Met. 100 (1984) 241. [10] M. Usuda, in: Lead at annual meeting of Physical Society of Japan, Tokushima, 2001. [11] A. Mielke, J. Phys. A 25 (1992) 4335. [12] T. Kato, K. Hondou, K. Iio, J. Magn. Magn. Mater. 177 (1998) 591. [13] H. Asakawa, M. Suzuki, Physica A 205 (1994) 687. [14] A. Kuroda, S. Miyashita, J. Phys. Soc. Jpn. 64 (1995) 4509. [15] K. Hondou, Y. Fujiwara, T. Kato, K. Iio (unpublished observations). [16] M.S. Dresselhaus, G. Dresselhaus, Light Scattering in Graphite Intercalation Compounds, in: M. Cardona, G. Guntherodt (Eds.), Light Scattering in Solids III, Springer–Verlag, Berlin, 1982, pp. 3–57. [17] T. Sekine, C. Julien, I. Samaras, M. Jouanne, M. Balkanski, Mat. Sci. Eng. B3 (1989) 153. [18] R. Loudon, Adv. Phys. 13 (1964) 423. [19] M. Inui, Masters Thesis, Tokyo Institute of Technology, 1999. [20] M. Balkanski, R.F. Wallis, E. Haro, Phys. Rev. B 28 (1983) 1928.