Quantum oscillatory effects and band structure in graphite intercalation compounds

Synthetic Metals, 2 (1980) 353 - 360

353

© Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands

QUANTUM OSCILLATORY EFFECTS AND BAND S T R U C T U R E IN G R A P H I T E INTERCALATION COMPOUNDS

F. B A T A L L A N , I.R O S E N M A N

and C. S I M O N

Groupe de Physique des Solides de l'EcoleNormale Supdrieure, Tour 23, 2 place Jussieu, 75221 Paris Cedex 05 (France)

(Received May 19, 1980)

Summary Results for magnetothermal oscillations and the in situ deHaas-van Alphen effect in acceptor and donor graphite intercalation compounds are presented. The following intercalates have been investigated: C8,(NO3 H) s = 2, 3 and 4, C7,(SOsHF) s = 2, 3, C~ Br s = 2, C6,Li s = 2, C4,HgK s = 1, where s is the stage. The observed frequencies range between 40 and 1500 Tesla and the effective masses between 0.05 mo and 1 too. In acceptor compounds characteristic combinations of frequencies are present which are explained by the magnetic breakdown of the primitive orbits on the FS. A 2D FS model is proposed which includes the electronic structure proposed by Blinowski-Rigaux and the folding due to the periodicity of the intercalate layer. The results for the Ct6(NO3H) are analyzed in terms of a detailed FS. The charge transfer coefficient found is f = 0.6 and the Fermi level shift EF = - - 1 . 0 8 eV.

1. I n ~ o d u c f i o n Most of the features of the graphite intercalation c o m p o u n d s (GIC) should be related to the high density of charge carriers on the modified graphite layers. This high density comes from the charge transfer between the carbon layers and the intercalated molecules. The number of transferred carriers, which depends on the stage and the nature of the intercalate, can be determined only in an indirect way, since, in every case, the electronic structure must be known. So, in most cases, the transfer ratio, f, is treated as an adjustable parameter. One of the best tools to obtain the electronic structure, and a value of f, are the quantum effects of the deHaas-van Alphen (dHvA) type. In Section 2 we present the quantum oscillatory effects. In Section 3 we describe our results on graphite acceptor c o m p o u n d s (GAC). Section 4 is devoted to the electronic structure of the GAC, while in Section 5 we interpret our results in the GAC. In Section 6 we present some preliminary results on donors before concluding remarks.

354 2. Quantum oscillatory effects The three quantum oscillatory effects which have been used for the study of the GIC are: the Shubnikov-deHaas effect [ 1], the magnetothermal oscillations (MTO) [2], and the dHvA effect [3]. We have studied the MTO and the in situ dHvA effect, the MTO can be observed even in very small samples (3 mg) of arbitrary shape but need manipulation in a glove box and are thus suitable only for stable GIC, whereas in situ dHvA is best for compounds unstable against oxidation or desorption. In both methods we have used low frequency field modulation (11.1 Hz for MTO and 30.1 Hz for dHvA) in an 80 kOe superconducting coil and temperatures down to 1 K. The data are fed into a microcomputer (MINC Digital) through a programmable A - D converter and processed online to give the Fourier transform. We present here results on low stages GIC. Some of them, mainly acceptors can be interpreted in terms of a detailed electronic structure whereas others are only in a preliminary stage.

3. Results on graphite acceptor compounds

(i) N O s H We have observed MTO in stages 2, 3 and 4 of NOsH GAC of the low interplanar distance variety, the so called "residual graphite nitrate" (RGN) [4] of composition Cs,(NOsH) (s is the §tage). They are obtained by transforming the "normal graphite nitrate" (NGN) under a current of dry nitrogen for a week at room temperature. The structure of the samples is controlled by measuring their thickness, their mass, and the electrical resistivity as well as by X-rays. The RGN are particularly stable compounds at room temperature and this has been checked both by X-rays and by MTO which gave the same results after several months. We have studied five different samples, two of stage 2, one of stage 3 and two of stage 4. The samples were small discs of 3 - 4 mg with a diameter of ~ 4 mm and a thickness of ~ 0 . 2 mm. Experimental details have been given elsewhere [ 5]. Typical results are shown in Fig. 1 which present the MTO for stage 2 (a), and the corresponding Fourier transform (b). As can be seen, the dHvA spectrum is complex and contains a number of frequencies whose values range between 100 and 1200 Tesla. The complete results are summarized in Table 1 for the ~ direction parallel to the magnetic field. The effective masses range between 0.1 and 1.0 mo. The angular variation for the lowest frequency, the only one which we were able to study up to 35 ° from the ~ axis, fits well with a cylinder along the ~axis, i.e., a 2D Fermi surface. But given the uncertainty of the frequency (a few dHvA periods) an ellipsoidal FS of anisot r o p y larger than 10 would fit the observed variation as well. A feature of these results (see Table 1) is that the dHvA spectrum contains different frequencies for different stages, b u t the frequencies are the

355

]

40 MAGNETIC

50 60 FIELD ( tesla )

200 dHvh

(a)

400 FREQUENCY

600

t,sla )

(b)

Fig. 1. (a) A typical MTO curve on fourth stage NO3H GAC at T = 1.2 K; (b) the corresponding Fourier transform. TABLE 1 MTO results on C ~ (NO3H): dHvA frequencies and relative cyclotron effective masses for stages 2, 3 and 4 Cas(NOaH) s=2

s=3

s=4

Label

F (T)

m*/m 0

Label F (T)

m*/m 0

Label

F (T)

m*/m 0

ot ~--3a -- 2o~ 7 --~

235 335 570 630 705 1040

0.15 0.8 0.25 0.3 -

9' 0~--/~ ~ a

<0.05 0.8 ~0.1 0.37 ~ 0.02 0.25 • 0.2

o~ /3 9, ~+~ "7+~ fi÷2~ 9, + 2~ + 3~

109 300 351 411 460 521 580 630

0.20 0.3 0.15 0.5 0.3 0.8 -

~- 0.02 ~0.3 :~ 0.05 ~ 0.3

40 240 421 662

~- 0.05 ~0.1 ; 0.1 ~ 0.1 ~ 0.1 ~ 0.2

same f o r t w o samples o f t h e same stage. This p o i n t , w h i c h is in c o n t r a d i c t i o n with o u r previous results o n SbC15 G A C [ 2 ] , will be i n t e r p r e t e d in detail later. A m o r e detailed e x a m i n a t i o n o f stage 2 results shows a main f r e q u e n c y , a, o f 2 3 5 Tesla with an effective mass o f 0.15 m0. All the o t h e r f r e q u e n c i e s e x c e p t the 9, f r e q u e n c y o f 6 3 0 T are o b t a i n e d b y s u b t r a c t i o n o f n times the f r e q u e n c y f r o m the ~ f r e q u e n c y o f 1 0 4 0 T. Also, f o r the third a n d f o u r t h stages, the f r e q u e n c i e s f o r m an a r i t h m e t i c series as s h o w n in Table 1. T y p i c a l results f o r Dingle t e m p e r a t u r e s are b e t w e e n 4 and 12 K. (ii) S 0 3 H F T h e G A C with S O a H F has a c o m p o s i t i o n o f f o r m u l a CT,(SOaHF) a n d we have observed M T O in stages 2 a n d 3. These c o m p o u n d s are also stable. T h e results are s u m m a r i z e d in Table 2. In stage 2 there are t w o isolated freq u e n c i e s o f 61 a n d 96 T a n d a set o f t h r e e f r e q u e n c i e s w h i c h f o r m an a r i t h m e t i c series with a step o f 1 3 0 T, w h i c h does n o t c o r r e s p o n d t o an o b s e r v e d f r e q u e n c y . F o r stage t h r e e we have f o u n d o n l y a f r e q u e n c y o f 1 8 8 T.

356

TABLE 2 MTO results on C7s(SO3HF): dHvA frequencies for stages 2 and 3 C7s(SO3HF) sffi3

s =2

Label

F (T)

a

61

Label

F (T)

a

188

96

9' 9' + e 7 + 2e

543 675 804

(iii) B r 2

We have already investigated the high stages (residual com pounds) o f bromine c o m p o u n d s [5]. F o r this study we used MTO. We present here some results on lowest stage bromine GAC, i.e., second stage CsBr. As this c o m p o u n d , very concent r a t e d in bromine, is unstable against desorption, we have used the in situ dHvA effect in order to prevent the desorption of the bromine. The sample is a disc of 4 m m dia. and 1.5 m m thickness maintained in a closed quartz tube, filled with an excess pressure of bromine, and in which the intercalation was made. Table 3 summarizes the frequencies t hat we have observed. Here, too, there is one isolated frequency, 7, of 860 T and an arithmetic series beginning with 180 Tesla and with a step, a, o f 250 Tesla. (iv) M a g n e t i c b r e a k d o w n

Before any detailed interpretation in terms of Fermi surface structure, the following remark must be made. With the exception of stage 3 of SO3HF GAC, where only one f r e que nc y is observed, in all the c o m p o u n d s we not e the presence o f a combination of frequencies by the addition or subtraction TABLE 3 dHvA results on C4sBr: dHvA frequencies for stage 2 CsBr (s = 2) Label a

~+a + 2a 7 + 4a

+ 5a

F (T) 180 250 435 670 860 116o 1420

357 of a given frequency. Moreover, for the N O s H GAC where we have measured the effective masses, a combination rule for the effective masses exists. This implies the presence of a coupling mechanism between the orbits on the Fermi surface, mainly the magnetic breakdown between closed orbits separated by small gaps which can be overcrossed in the presence of a high magnetic field. If we know the frequencies and the effective masses of a set of frequencies we can determine the primitive orbits between which the magnetic breakdown occurs. Indeed, they correspond to the two smallest effective masses. By the way, we obtain the relative character of the two orbits (electron or hole). This is very important if we want to correlate the FS results with an electronic band structure.

4. The electronic structure We shall interpret our results with a 2D band structure model for the graphite acceptor compounds. The 2D properties of the GAC have their origin in the nature of the charge transfer. Indeed, the holes created in the graphite are delocalized within the carbon layers, whereas the electrons accepted by the intercalate are localized on the molecules. These charged intercalate layers produce an electrostatic screening which prevents the m o v e m e n t of the delocalized holes across this potential barrier. The GAC can then be described as a sequence in the c direction of 2D Unit Zones (UZ) made of the s carbon layers b o u n d b y the t w o intercalate layers. The dynamical properties are those of the carriers in a 2D UZ. The electronic structure of such a zone has been c o m p u t e d by Blinowski and Rigaux ( B - R ) [6, 7]. They assume that the 2D UZ is made of s interacting carbon layers differently charged with holes, and they consider the intercalate layers as a homogeneous distribution of electrons. We will discuss here only our results for the second stages, in this case B - R find four bands (two of valence and t w o of conduction) with the following dispersion relations: 1 Ec~ = --Evl = ~

(x/712+ 972b2k2 - - 7 1 )

(1)

1 Ec2 = --Ev2 = ~ (x/72 + 9702b2k2 + 71).

(2)

The t w o parameters 70 and 71 are overlapping integrals for the nearest atoms of, respectively, the same carbon layer and of adjacent carbon layers, k is the m o m e n t u m vector c o m p u t e d from the U and U' points (the corner of the 2D graphite BZ). b, the distance between the nearest carbon atom, = 1.42 A. Usually IEFI > 71 so that the FS consists of two circles centered around U and U' and of radii kF1 and kf2.

358 Actually, the charge of the localized electron is n o t homogeneously distributed b u t has the periodicity of the intercalate lattice; the resulting periodic potential introduces a new periodicity in the band structure of the GAC. Energy gaps will then appear at the Bragg diffraction planes given by the equation. (~) = (£ + lG + m~') {~) is the star of the ~ vector, G and ~ are the 2D basic reciprocal lattice vectors corresponding to the carbon layer and the intercalate layer, I and m are arbitrary integers. This equation is valid for every value of q, either commensurate or incommensurate with G. In the commensurate case -~ = ( n / q ) G , which is the only case that we will consider; it is possible to define a new periodicity which includes both the 2D graphite lattice and the intercalate lattice periodicities. The FS of the GAC is then obtained by folding the isoenergy surface for E = E F , defined in the 2D graphite BZ, into the 2D BZ of the GAC.

5. Interpretation of results As we have seen, the general features of our results, i.e. the structure of the frequency spectrum and its range, are the same in all the GAC. We will, therefore, interpret in detail only the results for the second stage of the NOaH GAC for which they are the most exhaustive. We take as unit cell for this c o m p o u n d C8 x 2(NOaH), a cell containing four acid molecules which is 16 times larger than that of graphite. The unit vector is parallel to, and four times larger than, that of graphite. In order to obtain the FS of the GAC we have to fold the isoenergy surfaces given by the BR model into the BZ of the GAC. In this case, the two isoenergy circles centered at the U and U' points of the graphite BZ come to the U and U' points of GAC BZ. The construction is represented in Fig. 2. If we adjust the a area to obtain a frequency of 235 Tesla we obtain for the second area a frequency of 1014 T, in good agreement with the/3 frequency of 1040 T. The/3 frequency corresponds to a star with six branches centered at F. The original circle has a hole character (acceptor c o m p o u n d ) so that the a orbit has a hole character and the/3 orbit has an electron character. All the experimental frequencies of the a;/~ set are obtained by magnetic breakdown of the a and/~ orbits. They fit the relations: F~-na = F a --nFa m a _ , , ~ = m a + nm,~.

The Fermi m o m e n t u m corresponding to the primitive circle is kF, = 0.265 A -1.

359

0

Fig. 2. Fermi surface and Brillouin zone for the second stage NO3H GAC. The three primitive orbits ~, ~ and 7 are also shown. There is also an isolated frequency 7, Fv = 630 T which corresponds to an isolated smaller circle of Fermi m o m e n t u m . kF2 = 0.138 A -1. For the kind of FS shown in Fig. 2, the existence of two different sets of frequencies: ~;3 and 7 implies the conditions: kF1 + kF2 < D 2kFl > D where D is the side of the GAC BZ, which are indeed verified in our case. Once kF1 and kF2 are known we obtain several physical quantities by using the dispersion relations, eqns. (1) and (2): the charge transfer factor f, the shift of the Fermi energy E F and the band masses for every orbit. For f, we find: 3x/3

f= 47r lb2(k21+ k22) where I is the number of carbon atoms in the layer by the intercalate molecule. Here l = 8. This gives f = 0.60. As can be seen, when the unit cell is known we need only the kFl and kF2 values to compute f. The Fermi energy relative to the band crossing of pure graphite is given by the formula 3b EF = - ~---/~ 70 4k2F1 + k2F2 then E F = --0.45 3'0. B - R takes 70 ~ 2.40 eV; with this value we find E F -- --1.08 eV. This estimate is of the same order as the 0.7 eV for second stage C13Fe GAC [S]. The other physical quantities such as the band masses, can be deduced from our data, but depend on the choice of the 70 and 71 parameters. A detailed discussion including an extension of the B ' R model will be published elsewhere [9].

360

6. Results on GDC We now present our results on graphite donor compounds (GDC). We have made some preliminary observations of quantum effects in GDC using MTO, but in situ dHvA experiments would be more appropriate in this case because of the high reactivity of the GDC. Even a very small partial pressure of oxygen in the glove box is sufficient to oxidize the alkali metal and to destroy the signal. This is probably the reason why our results are less satisfactory in this case than in the GAC. We are n o w undertaking in situ dHvA experiments for these compounds. We have observed the MTO in C12Li (s = 2) and C4KHg (s = 1) for c I[ B. For the C12Li only two frequencies are present: 220 and 247 Tesla. For the C4KHg there are three frequencies: 177, 194 and 637 T. These results are t o o incomplete to be interpreted in terms of Fermi surface. Nevertheless, one should mention that the GDC unlike the GAC, are 3D. This is a consequence of the presence of free electrons in the intercalated metal, resulting in carriers delocalized in the whole crystal space. We can say that the metal makes a bridge between the carbon layers on each side of the intercalate and enhances the electrical conductivity along the c axis. Consequently, no 2D electronic structure can be used to describe the properties of the GDC.

7. Conclusion

We have observed MTO and in situ dHvA effects in acceptor and donor GIC. In acceptor compounds, characteristic combinations of frequencies are present which are explained by the magnetic breakdown of the primitive orbits on the FS. A 2D FS model is proposed which includes the electronic structure given by Blinowski and Rigaux and the folding due to the periodicity of the intercalate layer. The results of the second stage C16(NOsH) comp o u n d are analyzed in terms of a detailed FS. The charge transfer coefficient found is f = 0.6 and the Fermi level shift E F = --1.08 eV.

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