Conduction and localization in incommensurate misfit layer compounds

0022-3697(95)00404-l

Pergamon

CONDUCTION

TETSUO KONDOt,

J. Phys. Chem Solids Vol57, No. 6-8. pp. 110% 1108, 1996 Copyright 0 1996 Elscvier Science Ltd Printed in Great Britain. All rights reserved 0022.3697196 SI5.04 + 0.00

AND LOCALIZATION IN INCOMMENSURATE MISFIT LAYER COMPOUNDS KAZUYA SUZUKIS, TOSHIAKI ENOKIt, and TOSHIAKI OHTAg

HIROYUKI

TAJIMA$

TDepartment of Chemistry, Tokyo Institute of Technology, 2-12-1,Ookayama, Meguro-ku, Tokyo, 152, Japan IFaculty of Engineering, Yokohama National University, Tokiwa-dai, Hodogaya-ku, Yokohama, 240, Japan SDepartment of Chemistry, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113, Japan (Received 28 May 1995; accepted in revised form 3 1 May 1995)

Abstract-We investigated transport properties and optical reflectivity of incommensurate misfit layer compounds (LaS)t.t6VSz and (CeS)i,is(T&), (stage index n = 1,2). Electrical conduction measurements revealed that (CeS)l,is(TiS2),, is metallic while (LaS)i.i6VS2 is non-metallic. The existence of a short-range scattering process of the order of 10 A was indicated for both electrons and phonons in (CeS)i,19(TiS,),, suggesting that the local lattice modulation induced by the incommensurate structure has an important contribution to the conduction of electrons and phonons. Optical reflectance spectra for (LaS)I,t6VS2 exhibited the enhancement of the carrier scattering, indicating a different character of the conduction band of (LaS),,i6VS2 in comparison with metallic (CeS)i,,s(TiSs),. We propose the possibility of carrier localization in (LaS)i,u,V$ in relation to the incommensurate structure of these compounds. Keywords: A. incommensurate structure, A. layer compounds, D. electrical conduction, D. carrier localization

1. INTRODUCTION

2. RESULTS AND DISCUSSION

The titled materials are layered compounds comprising MS and TS2 sublattices with the chemical formula (MS),T& (M = rare earth metals, Pb, Sn, Bi: T = Ti, V, Cr, Nb, Ta). These belong to intercalation compounds of transition metal dichalcogenides. In the pristine state of the constituents, the structure of MS is cubic and TS2 has a hexagonal in-plane structure. When MS is inserted between the TSz layers, it forms MS double-layer slabs. Consequently, the difference in symmetry between the two constituent layers brings about the formation of lattice distortion in both MS and TS2 layers, leading to an incommensurate (misfit) structure in one direction in the in-plane structure [ 1,2]. The layer structure introduces two-dimensional&y in these compounds, while the incommensurate structure is expected to have an important effect on the in-plane transport of the conduction electrons and phonons in these compounds due to the local lattice modulation induced by the incommensurate structure. We have been studying the compounds of 3d transition metals (MS),TS2 (T = Ti, V, Cr) [3, 41. In this paper, we present studies of (CeS)l,19(TiS2), (n, stage index, n = 12) and (LaS)l,t6VS2. We performed experiments of transport properties and optical reflectivity in order to reveal the difference in the electronic structure between these compounds. We also discuss the effect of the incommensurate lattice on the conducting electrons and phonons in metallic (CeS)t,19(TiS2),.

2.1. Properties of metallic (CeS),,,9(TiS2), The temperature dependence of the in-plane resistivity is presented for (CeS)1,1s(TiS2), (n = 1,2) in Fig. 1. The resistivities are metallic for these compounds. Stage 1 and stage 2 (CeS)l,19(TiS2), show antiferromagnetic orderings at TN = 2.8K, but no anomaly was observed around TN. This suggests that the CeS layers do not contribute to the electrical conduction. Consequently, we only consider the conducting carriers in Ti!$ layers in the following discussion. The residual resistivities pres are 450 and 350,u~cm for the stage 1 and stage 2 compounds, respectively, which are larger than the reported value of Li,Ti$ (x < 1; 8 5 pres 5 85@cm) where the incommensurate structure is absent [5]. Therefore, the large residual resistivity indicates that the local lattice modulation induced by the incommensurate structure plays a significant role in the carrier scattering processes. The resistivity shows a linear temperature dependence above 50 K, suggesting the important contribution of the acoustic phonons to the carrier scattering process in the high temperature region. Optical reflectance spectra were measured at room temperature by a microphotometric technique between 700 and 25000 cm-t. Figure 2 represents the reflectance spectra for stage 1 and stage 2 (CeS)&TiS2), (n = 1.2). The spectra show typical Drude type free carrier reflectance below the Drude

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T. KONDO et al.

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Table 1. Summary of Drude parameters: plasma frequency wPj,optical relaxation time 7 and optical conductivity ui for carriers j (= A, B) in stage 1 and stage 2 (CeS)i,,s(T&), (n = 1,2)

g

(CeSh isTiS2

8

9

2.2 1.3 x 2.6 1.2 x 1.3 x 1.6 x

6

‘0

c Q

4

(CeShdTW2

0

01 0

1

I

200

100

1 1

300

T(K) Fig. 1. Temperature dependence of the in-plane resistivity p for stage 1 (CeS)i,isTiS2 (closed circles) and stage 2 (CES)1.19(TiS2)2(open circles).

edge (92OOcm-’ for (CeS),.,9TiS2, 74OOcm-’ for (CeS),.r9(TiS2)Z). The Drude edges are different between the two compounds, indicating the difference in the degree of charge transfer from CeS to TiS2 layers. We analyze these spectra using the DrudeLorentz model. The dielectric function E(W)expressed in terms of the core contribution cc, the Drude contribution with conduction electrons (second term) and the inter-band transition (third term) are given by,

(1) where j and k are the labels of the carriers and the interband transitions, respectively, Upj is the plasma frequency, 9 is the optical relaxation time, fik is the oscillator strength, wok is the Lorentz resonant

I

I

I

- 80

z 80

- 60

2 .; 60 '5 2 40

- 40

cz

- 20

20

2.7 4.2 x 1.2 1.5 x 7.6 x 5.2 x

lo-‘4 10-15 lo4 lo3

10-15 10-15 IO3 IO2

frequency and rk is the damping factor. In order to achieve optimum fitting to the experimental results, we have to introduce two types of carriers for both stage 1 and stage 2 compounds, and 4 and 5 inter-band transitions for the stage 1 and stage 2 compounds, respectively. The estimated Drude parameters and optical conductivities are summarized in Table 1. The parameters in the Drude term in eqn (1) give the optical conductivity through the relationship 0 ,+ = +/4r. The thermoelectric power S is presented in Fig. 3 for the stage 1 and stage 2 compounds as a function of temperature. In the stage 1 compound, the thermoelectric power exhibits contributions of both electron and hole carriers, which are compensating each other. The two-carrier conduction of the stage 1 compound is consistent with the result of optical reflectivity that requires the two types of carrier with different conductivity. Contrary to this, the stage 2 compound contains only a contribution of electron carriers judging from the negative thermoelectric power. This seems to be inconsistent with the optical reflectivity, however, the consistency is achieved based on the difference in the contributions of the two carriers to 10

1 100

100

(CeS)i.is(TiS&

I

I

o (CeSh.d%

0

.I0

-0

Ot-----10 0

0

20

100

200

300

30

Wave Number (1 03cmm’) Fig. 2. In-plane optical reflectance spectra for stage 1 (CeS)i,isTiS2 (squares), stage 2 (CeS)1.is(TiS2)2 (open circles), and (LaS)i,ir,VS2 (closed circles) at room temperature.

Fig. 3. Thermoelectric power S for stage I (CeS),,i9TiS2 (open circles) and stage 2 (CeS),,,s(TiS& (squares). The calculated S for (CeS), 19(TiSz)z (stage 2) is presented by solid line with the contributions of the electron diffusion term (S,,) and the phonon drag term (Sri,).

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Misfit layer compounds

the transport process. Namely, the difference in the optical conductivities between the two types of carriers is estimated at 15 times, so that the contribution of minority carriers to the transport properties is expected to be negligibly small. Then we can treat the stage 2 compound as a nearly-single carrier system. Now in order to clarify the difference between the electronic structures of stage 1 and stage 2 compounds, we discuss the electronic structure of conducting TiS2 layers in (CeS),,,s(TiS2), on the basis of the rigid band model, where we consider the charge transfer from the CeS layers to the t2, conduction band of Ti$. The degree of charge transfer is expected to be large for the stage 1 compound in comparison with the stage 2 compound. Band structure calculation of the host TiSz suggests that the t2r conduction band is split into two sub-bands with a zero energy gap [6]. The coexistence of two types of carriers in the stage 1 compound requires the overlap of the two sub-bands at the Fermi energy. Then it is suggested that the large charge transfer pushes up the Fermi energy for the stage 1 compound in the region of the band structure where the two sub-bands induced by the split of the t2g band overlap. For the stage 2 compound, the Fermi energy is expected to be located on the lower side of the lower sub-band, resulting in the presence of single type of electron carrier. Therefore, the coexistence of two types of carrier observed in the optical reflectivity will arise from the detailed structure of the energy band. Next we analyze the thermoelectric power for the stage 2 compound on the basis of a single carrier model to reveal the scattering process of conducting carriers and phonons in this system. Under the single carrier model, thermoelectric power S is described in terms of the contributions of the electron diffusion terms S, and the phonon drag effect S,, (S = S, + S&. We introduce the two-dimensional parabolic energy dispersion. Then Sd is given as follows 171:

where ka is the Boltzmann constant, e the charge of an electron, and I+ the Fermi energy, SPt, is given by [7]:

transfer ratio for the acoustic phonon, R(q), is written as a function of phonon momentum in the following equation, R(q) =

a’ b+aq+cqT3’

(4)

where b, aq, cqT3 are the numbers of the collisions per unit time in the phonon scattering processes through (i) domain-boundaries; (ii) electron-phonon interactions; and (iii) phonon-phonon interactions, respectively. The parameter fitting of the experimental result to eqns (2) and (3) gives EF = 0.68 eV, b/aq,,, = 2.9, c/a = 2 x lo-’ s, and krv,l.2 x lOI SC’. The free electron model gives kF = 4.2 x lo9 m-’ (kF = (2EFm,/h2)“2, m,: the mass of a free electron) and then the sound velocity becomes U, = 2.3 x lo2 m SC’. Here, on the basis of the above discussion, we estimate the mean free path of the conduction electrons at low temperatures where the scattering process of conduction electrons is governed by the lattice irregularity. The mean free path 1, of the conducting electrons is given by the relation I, = wr7 where or is the Fermi velocity of the electrons (~1~= hk,/m*), and 7 is the relaxation time of the electrons. Thus, using the relaxation time obtained from the residual resistivity preSand the estimated value of kF, 1, is estimated at 9 A, which is several times larger than the in-plane lattice constant of the TiSz and CeS sublattices. This finding proves the presence of short-range scattering of conduction electrons where the in-plane lattice periodicity associated with the incommensurate structure plays an important role. Indeed, the existence of the local lattice modulation induced by the incommensurate structure is evidenced by the observed satellite spots along the incommensurate direction in the in-plane electron diffraction patterns [ 1,2]. Meanwhile, from the estimated value of term b in the phonon drag effect, the domain size in the domainboundary scattering for the acoustic phonons is estimated at lb = 11 A [8,9], which is of the same order of magnitude to 1,. Therefore, considering that the domain scattering originates from the incommensurate long lattice periodicity, it is indicated that the local lattice modulation has a significant contribution not only for the scattering process of conducting electrons but for phonons. 2.2. Properties of non-metallic (LaS)t,t6VS2

(3) where kF is the Fermi wave number, v, the sound velocity of acoustic x = fiusq/kBT, phonons, 4max- 2kF (the maximum phonon wave number available for the phonon drag effect). The momentum

Contrary to the metallic behavior of the compounds of Ti, the resistivity p shows a semiconductor-like behavior as we presented in a previous paper [3]. In Fig. 2, the in-plane optical reflectance spectra at room temperature for (LaS)t,16VS2 is presented in comparison with (CeS)1,19(TiS2),. The spectra of (LaS)l,16VS2 show a Drude-type free carrier contribution below

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T. KONDO et al.

8200 cm-’ , suggesting the existence of free carriers. The contribution below the Drude edge is reduced to a large extent in comparison with that for metallic (CeS),,,s(TiSz),. According to the Drude model in eqn (l), this implies that the relaxation time of (LaS),.,sVSz is considerably shorter than that for (CeS),,,s(TiSz),. In other words, the carrier scattering process is strongly enhanced in the compound of V in comparison with the compound of Ti. According to the rigid band scheme, (LaS)t,rsVSz is expected to be metallic when we assume that the electronic structure in VSz is similar to that of TiSz layers in (CeS)t,,s(TiSz),. This is inconsistent with the non-metallic conduction of (LaS),,t6VSz, suggesting that the conduction band in VSz layers is significantly different from that of(CeS)l.r9(TiSz),. The non-metallic properties of (LaS)t,tsVSz will be explained by two alternative possibilities: (i) the formation of an energy gap at I+, and (ii) carrier localization with a mobility edge. A split of the tzr conduction band is suggested in TiSz layers as mentioned in the previous section. The split originates from the deformation of the octahedral coordination of sulfur atoms in the TiSz layer. This situation is considered to be present also in the electronic structure of VSz. Moreover, the increase of the number of 3d electrons for (LaS),.,sVSz in comparison with (CeS),.,s(TiSz), yields the narrower conduction band in VSz layers due to the larger interaction between the core charge of the V atom and 3delectrons than in TiSz layers. In the case that the large deformation of the octahedral coordination exists, a direct energy gap between the split sub-bands appears. However, in the actual case, VSz layers in (MS),V.Q retain the slightly deformed octahedral coordination of VS2 layers [2]. Therefore, we consider that the modification of the octahedral coordination of sulfurs makes the two sub-bands overlap slightly in (LaS),,,sVS2. Since the lowest flying sub-band of (LaShr6VS2 is almost filled by the charge transfer, the Fermi energy of (LaS)1,16VS2 is expected to be located at the slightly overlapped

region of the conduction bands, where the density of state for conducting carriers is small. In addition, the incommensurate lattice causes random potential in the electronic structure. We suppose that the random potential is strong enough to make the carrier localization with the mobility edge. As a consequence, among all (MS),TSz, the carrier localization is present only in VSz based compounds, which is associated with the narrow conduction band width in (LaShVS2.

Finally, we mention the relation between the carrier localization and the observed optical reflectivity. The existence of the free carriers which is revealed in the optical reflectance spectra seems to be inconsistent with the semiconducting behavior of the in-plane resistivity. However, in the optical reflectivity, the energy of photons is large enough to induce plasma oscillation for the conducting carriers. This makes the Drude type behavior observable in the optical reflectivity in spite of the presence of carrier localization. Acknowledgements-We are grateful to Prof. K. Sugihara for valuable discussions. One of the authors (T.K.) has been supported by a Research Fellowship for Young Scientists of the Japan Society for the Promotion of Science.

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