THE ELECTRONIC STRUCTURE AND ELECTRON CORRELATION EFFECTS STUDIED BY XPS

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THE ELECTRONIC STRUCTURE AND ELECTRON

CORRELATION EFFECTS STUDIED BY XPS

G. Sawatzky, E. Antonides

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C4, supplkment au no 10, Tome 37, Octobre 1976, page C4-117

THE ELECTRONIC STRUCTURE AND ELECTRON CORRELATION

EFFECTS STUDIED

BY XPS

G. A. SAWATZKY and E. ANTONIDES

Physical Chemistry Department of the Material Science Center University of Groningen, The Netherlands

RQum6. - Les interactions importantes pour la comprehension des transitions mBtal-non metal du type Mott-Hubbard sont les interactions Blectron-Blectron et les integrales B un electron. Les premikres conduisent h des effets de correlation et B la localisation tandis que les dernikres donnent la structure de bande B un electron et la dklocalisation. Dans cet article, nous etudions comment la XPS peut fournir des informations sur ces interactions. L'application de la XPS a 1'Ctude de la structure de bande a un electron est Bvidente et tout B fait directe. Comme exemple de ce cas, nous prksentons des resultats recents sur TaS2 intercalk avec Sn et montrons comment la XPS peut donner une description correcte des changements de structure electronique en intercalant de l'etain. Un autre exemple que nous discuterons est le changement de la nature de la bande d de V02 en franchissant la transition serniconducteur-metal. L'application de la XPS a l'ktude des effets des correlations 6lectroniques est moins Bvidente. Nous montrerons qu'a partir d'une Ctude dktaillk de la spectroscopie Auger B haute resolution et de Ia XPS, on peut obtenir les interactions coulombien- nes a un site reduites par une polarisation atomique et de bande ainsi que par des effets d'kcran. La reduction peut atteindre 90 % des valeurs correspondantes B I'atome libre.

Nous montrerons aussi, comment une Ctude dktaillke de la forme de raie des raies dues au ceur peut fournir des informations sur les effets des corr6lations. Par exemple, les raies de cceur de V02 sont fortement Blargies en franchissant la transition de l'Btat semiconducteur vers l't5tat mBtallique. Cet Blargissement est bien interpret6 en termes de transition de Mott-Hubbard. Nous discutons les dkcalages de la coupure du spectre de XPS a partir du niveau de Fermi en termes d'effets de correlation qui pourraient irnpliquer les 6lectrons ou les phonons. A partir de ces decalages, une valeur appro- chke de 1'6nergie de liaison du polaron dans Fe304 est obtenue.

Nous discuterons egalement une nouvelle sorte dYexpMence mettant en jeu les intensites des raies Auger, a partir desquelles on peut en principe obtenir le nombre de sites doublement occupes et par-18 donner des conclusions concernant le degre de correlations t5lectroniques.

Abstract. - The basic interactions which are of importance for an understanding of metal- non metal transitions of the Mott-Hubard type are the electron-electron interactions and the one electron integrals. The former leads to electron correlation effects and to localization and the latter results in the one electron band structure and delocalization. In this paper we want to investigate how XPS can yield information about these interactions. The application of XPS to a study of the one electron band structure is quite obvious and straight-forward. As an example of this we present recent results on Sn intercalated TaS2 and show XPS can give a very consistant picture of the changes in the electronic structure upon intercalation. Another example which will be discussed is the change in the d band of V 0 2 upon going through the semiconductor-metal transition. The application of XPS to a study of electron correlation effects is less obvious. We will show that from a detailed study of high resolution Auger spectroscopy as well as XPS one can obtain the on site coulomb interactions reduced by atomic as well as band polarization and screening effects. The reductions can be as much as 90 % of the free atom values.

In addition we will show how a detailed line shape study of core lines can yield information about electron correlation effects. For example the core lines of V02 are strongly broadened as one goes through the transition from semiconductor to metal. This broadening is shown to be consistant with an interpretation in terms of a Mott-Hubbard type of transition. Shifts of the XPS cut off from the Fermi energy are discussed in terms of correlation effects which could involve either electrons or phonons. From these shifts an approximation to the polaron binding energy in Fe304 is obtained.

Also a new kind of experiment involving Auger intensities will be discussed from which one can in principal obtain the number of doubly occupied sites and thereby reach conclusions concerning the amount of electron correlation.

For a detailed understanding of metal-non metal tion (U) and the band width ( W ) which is the deter- transitions one has to have detailed knowledge of the mining factor for the material being a metal o r electron-electron interactions, the one electron' band non metal. For an s band and for U

$-

W the material structure and the electron phonon interaction. Start- will be a non metal for a half filled band and a strongly ing with the Hubbard hamiltonian for example it is correlated metal for other fillings. For U 4 W the the relative importance of the on site coulomb interac- material will behave like a n ordinary metal. In the

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C4-118 G. A. SAWATZKY AND E. ANTONIDES

Hubbard hamiltonian we should use an effective interaction (Ue,3 which can be written as I-A where I is the ionization potential and A the electron affinity of a singly occupied site. It is however difficult to obtain a good estimate of U,,, since it is strongly reduced from the free ion value by polarization and screening effects. We will show below that a value for

U,,, for transition metal compounds can be obtained

from a combination of XPS and Auger spectroscopy (AS) studies. As far as the one electron band width is concerned one can obtain this from XPS measurements. Here however one must be careful to correct for all symmetry splittings in for example d bands caused by crystal Jields, spin-orbit coupling and exchange

splittings in order to obtain the one electron band width which is to be compared to U,,,. In 3d transition metals for example like Cu the major portion of the observed d band width comes from symmetry splittings and only a small portion is due to one electron transfer integrals. This is quite obvious when one looks at the very narrow lines appearing in the LMM Auger spectra.

A very important property of XPS measurements is that they usually involve very short characteristic measurement times, typically of the order of 10-l6 seconds depending somewhat on the nature of the measurement and on the interactions involved. This means that all processes which take place in much less than 10-16 s are essentially static in an XPS measure- ment. In a metal then with a one electron band width of less than one electron volt the conduction electrons can be considered as frozen during the course of the measurement. If the conduction electrons are uncorre- lated as for U,,, 4 W the core lines will be broadened or even split because of the statistical distribution of conduction electrons on the ions. On the other hand if the conduction electrons are strongly correlated as for example in a Mott insulator the core lines will be narrow because each ion will have the qverage number of conduction electrons. It should be noted here that the binding energy of core electrons are quite strongly dependent on the occupation of the outer shell. Because of the above mentioned effect one should see a large change in the core line width if a material undergoes a Mott-Hubbard transition.

Another point worth mentioning about XPS measurements in conjunction with the fast measuring time concerns the Fermi level. The Fermi level is defined as the thermodynamic potential for all electrons and is therefore only defined in a thermodynamic equilibrium state. If the material to be measured is in good electrical contact with a good metal the Fermi levels will coincide. In an XPS measurement one measures only the occupied'states. This means that we should see a sharp cut off a t the Fermi energy of a good metal. This is the case for metals like Ag, Au and many others. If however correlation effects in the material are important the sudden removal of one electron will leave the material behind in an excited state of the

N - 1 electron system and the cut off in the XPS measurement need not coincide with the Fermi level. As an extreme example we could consider a small polaron material. In a slow measurement the phonon or lattice polarization cloud will have a chance to relax during the measurement and a cut off corresponding to the Fermi energy will be found. In a fast measurement however the polarization cloud will not have a chance to relax and the material will be left in an excited state and the cut off will be shifted from the Fermi energy by an amount of the order of the polaron binding energy. The same sort of shift can also occur if electron correlations are important. The amount of shift and the width of the cut off will depend on the interaction of the electron with the polarization cloud and the relaxation time of the polarization cloud which in turn is determined by the excitation spectrum of the polarized system.

With attention to these rather general introductory remarks we will now discuss in more detail and with the aid of several examples how one can obtain information about the band structure and electron correlation effects from XPS.

We start with the valence and conduction band structures. As an example we take the 2 H phase of TaS, and various Sn intercalates. These materials exhibit superconductivity and the superconducting transition temperature can be influenced by intercalation. By intercalation we mean the addition of atoms or molecules in positions inbetween the TaSz layers. The structures of these compounds are described in detail in other papers of this conference. It is of funda- mental importance to know how the electronic structure of the materials change upon intercalation and in which ionization state the intercalates appear.

In figure 1 we show XPS spectra, obtained with

monochromatised A1-Ka radiation of the valence band region for TaS2, Sn,,,TaS, and Sn,TaS2. The sharp peak close to the Fermi level is the Ta 5d band and the

FIG. 1. - XPS spectra of the valence band region of 2 H-TaS2 (drawn line) and SnzTaS2 (X = 113

...

; x = 1

- -

-). The zero of

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THE ELECTRONIC STRUCTURE AND ELECTRON CORRELATION EFFECTS STUDIED BY XPS C4-119

broad peak below it is the S 3p band. It is quite obvious from these spectra that the number of Ta 5d electrons increases upon Sn intercalation. In fact if we compare the areas under the 5d part of the spectrum to the S 3p part we find that the number of 5d electrons I for

TaS, 1.8 $- 0.2 for Snl,,TaS, and 2.2

+

0.2 for Sn,TaS,.

We can conclude from this that every Sn donates 2 electrons to the 5d band of Ta up to an upper limit of a total of about I electron per Ta. More Sn intercalation does not increase the number of 5d electrons so that the rest of the Sn probably goes into the lattice as neutral Sn. This can be checked by looking at the Sn 3d core lines shown in figure 2. We see indeed that

l I I I I I l I I I l

L81 0 L830 L85 0 L870 L91 0

BINDING ENERGY l EVl

FIG. 2. - XPS spectra of the Sn 3d,,, region of SnzTaS~

( X = 113

...

; X = l - - -).

for Snl,,TaS2 there is only one kind of Sn present whereas for SnlTaS, there are 2 kinds of Sn present

corresponding approximately to Sn2 + and Sn neutral.

The presence of 2 types of Sn in Sn,TaS, seems to be in contradiction to Mossbauer effect [ l ] and NMR [2]

results in which only one type of Sn was found. This apparent discrepancy can be explained when one considers the effective measurement times. For Moss- bauer effect and NMR this is of the order of 10-' S. while for XPS it is of the order of 10-l6 S. It is also

concluded from the Mossbauer effect experiments that the Sn atoms are quite loosely bound having a large mean square displacement in the plane of the layers and that the isomer shift lies between Sn2+ and neutral Sn. We conclude therefore that there are two types of Sn which however exchange rapidly in a characteristic time between I O - ~ and 10-16.

XPS experiments can also give information about the non occupied states of the system. In figure 3 we show the 4f lines of Ta in the 3 above mentioned samples. These lines are very asymmetric which is a result of the material being left behind in an excited state. From the shape of the asymmetry one can at least qualitatively

l I I I I

22 0 U 0 26 0 280 30 0 320

BINDING ENERGY l E V l

FIG. 3.

-

XPS spectra of the Ta 4f region in 2 H-TaS2 (drawn line) and SnzTaSz (X = 113 ... ; x = 1

-

-). The energy scale

was shifted so as to make the peaks coincide.

obtain the excited states of the systems which we have shown to be in good agreement with the band structure as calculated by Mattheiss [3].

From these experiments we can also obtain the shift of the 4f lines as a function of the number of 5d electrons. This is of importance for determining the amplitude of the charge density waves in these materials at low temperature [4]. We find a shift of about 0.8 eV per 5d electron. For a more detailed description of these experiments we refer you to ref. [5].

Another quite interesting material is VO,. As is well known this material exhibits a semiconductor-metal transition at about 70 OC. A very important question which has not yet been satisfactorally answered is that of the driving force for the transition and what is the nature of the ground state in the two phases. The question really is are the electron phonon or the electron electron interactions the most important for describing the properties of this system.

We have studied the electronic structure of VO, in both phases with XPS [6]. The spectra of the valence

band region are shown in figure 4 for both phases. In

I

L

-

2 0 - 2

b~ndlng energy (eV)

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(3-120 G. A. SAWATZKY AND E. ANTONIDES

general the band structure consists of a V 3d band close TABLE I to the Fermi level and a deeper lying broad 0 2p band.

These spectra were obtained with MgKa radiation which has a width of about 0.7 eV. If we correct for this width the 3d band of the semiconducting phase is about 1 eV wide and lies about 2 eV above the top of the 0 2p band.

The 3d band gap was found to be slightly temperature dependent and is about 0.3 eV at 300 K if we assume the Fermi level to be pinned to the bottom of the conduction band. 'Upon going through the transition to the metallic phase the band gap closes and the highest occupied states now are at the Fermi level. In addition the 3d band is seen to broaden somewhat although the total number of occupied d states stays the same as can be concluded from the areas under the 3d portion of the spectrum. From these results we still cannot distinguish between the two possible mechti- nisms mentioned above for the semiconductor-metal transition. A broadening and shift of the band is expected in both cases.

Perhaps we can learn more from the core lines. In figure 5 we show the V 2p and 0 1s core lines in both

FIG. 5. - XPS spectra of the V 2p and 0 Is region taken above (uppercurve) and below (lower curve) the transition temperature, after correction of the background. The arrows indicate the positions of the V and the 0 lines and also the positions of the

0 1s lines of some possible surface contaminants.

phases. A careful measurement of the peak positions shows that the binding energy difference between the V 2p3,, and the 0 1s lines is slightly larger in the metallic phase indicating a slightly more ionic bond. The differences are however very small and could also be due to Madelung energy changes. In table I we have listed some of the peak positions and widths of these core lines. For comparison we also listed the corresponding lines for V205 and V metal. We see that the VO, lines are first of all much broader and secondly

Peak positions and Widths of XPS lines of V 2p3,, and 0 1s lines of various V compounds

Mate- T (K) rial - v02 273 293 393 393 v205 293 V 293

position width position width

- -

-

529.6 2.4 515.7 3.2 529.6 2.35 515.7 3.1 529.35 3.0 515.75 4.2 529.45 3.0 515.7 4.25 529.9 1.7 516.8 2.0 512.7 2.0

that the V 2p lines broaden considerably upon going to the metallic phase. A possible explanation of this could be the following. The binding energy of a core electron depends on the oxidation state of the ion and therefore of the number of 3d electrons. The shift of the V 2p lines per 3d electron added is about 0.8 eV. The 3d band width in the metallic phase is about 1 eV. As discussed above in an instantaneous picture the 3d electrons will be distributed statistically over the sites in a manner given by the binomial distribution. This means that 0.5 of the V ions will be 4 + and 0.25 will be 3

+

and 5

+

.

This would result in a symme- trically broadened line. The amount of braodening will depend on the measurement time as compared to the one electron band width and will also be reduced by correlation effects. In the semiconducting phase the lines are relatively narrow which indicates that here each V ion has the average number of 3d electrons even in an instantaneous picture. This interpretation would be in excellent qualitative agreement with a picture in which VO, is a Mott insulator at low temperatures and goes through a Mott-Hubbard transition to a high temperature metallic phase. We see from this example that core line shapes can yield information about electron correlation effects and the nature of metal non metal transitions.

Fe304 is another material which has caused a lot of controversy. Photoelectron studies of this material have been done by Bishop and Kemeny [7]. Among other things there is something quite interesting happening at the Fermi level. The photoelectron cut off seems to be about 0.4 eV below the Fermi level. As mentioned before this is a strong indication that the high temperature phase of Fe,O, is not a simple metal.

We have also done studies below the transition temperature and find no shift in this cut off. This probably means that the conductivity in the high temperature phase is due to small polarons and that the transition has to do with an ordering or localization of these polarons. Such an ordering will of course also result in a change in the crystal structure.

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THE ELECTRONIC STRUCTURE AND ELECTRON CORRELATION EFFECTS STUDIED BY XPS (24-121

covalency effects in these compounds must be modi- fied to include the band structure effects. Covalency effects and the consequences thereof like superexchange, transfered hyperfine interactions and crystal field splittings have usually been described in ti local cluster approximation neglecting all band structure effects. An examination of XPS spectra of TaS, (Fig. l), V 0 2 (Fig. 4), VS [g] and many others clearly shows that the valence band region is composed of a rather broad (5-8 eV) ligand band structure and a rather sharp transition metal d band (1 eV). The local cluster model is only valid if the band width of the states to be covalently mixed is small compared to the separation in energy of the bands. This is clearly not the case in these compounds. We have shown [9] that band structure effects will lead to long range superexchange interactions. In these materials a better approach would seem to be to consider the anions to form a lattice with rather broad energy bands resulting in a semiconductor. The cations are then introduced in the large holes in the anion lattice and have sharp d levels. The material would then behave like a high impurity concentration semiconductor. The d levels will broaden into bands because of the covalent mixing and long range effects will be observed in the superexchange and transfered hyperfine interactions.

We now turn to the problem of how one can measure the effective on site electron-electron interaction. We will show that a combination of Auger spectroscopy and XPS provide a quite simple way of doing this for transition metal compounds. By the effective coulomb interaction (U,,,) we mean the interaction with all the screening and polarization corrections made. We will show that the polarization corrections are especially important as. has been suggested in several other contributions in this conference

[IQ,

1 l]. The most important Auger processes in the 3d transi- tion metal ions are the LMM processes. In Auger spectroscopy one first ionizes say a 2p,,, electron. The ion will now decay to a lower energy state either by x-ray fluorescence or by the Auger process. In the Auger decay we can distinguish 3 dominant processes :

1) The 2p hole is filled up with a 3p electron and another 3p electron is ejected the final state being 2 holes in the 3p shell. 2) The 2p hole is filled up with a 3p electron and a 3d electron is ejected the final state being I hole in 3p and one in 3d. 3) The 2p hole is filled up with a 3d electron and another 3d electron is ejected the final state being 2 holes in the 3d shell. The kinetic energy of the ejected Auger electron will depend on the energy of the 2p hole and on the energy of the final state of the ion left behind. The energy of the 2p hole as well as other one electron or hole states can be measured with XPS. We can then write for the Auger process with 2 holes in the 3d shell :

where E,, and E,, are the one electron energies and E,

is the kinetic energy of the Auger electron. From this we can determine U,,,. In Auger spectroscopy it is customary to split up U,,, into an atomic coulomb interaction and a reduction of this due to relaxation or polarization effects as follows :

Here F ( X ) is the atomic coulomb and exchange inte-, grals corresponding to the various final state terms and R is the relaxation or polarization reduction. The relaxation energy R is a result of the interaction of the one hole with the polarization cloud of the other and visa versa. The interaction of a hole with its own polarization cloud is included in the measured values for the one partical energies E,,, and Before we go on a word about the measurement time. The polarization correction measured in this way is the high frequency correction corresponding to hw I. l eV.

Any relaxation effects which are much slower than this will not contribute. This means that for example relaxation of the lattice will not be included completely. This would then be comparable to the polarization energy reduction expected for d electrons moving in a band of width 1 eV. We could call this the electronic pdarization reduction to distinguish it from the static mainly lattice polarization reduction in the Anderson bi-polaron [12].

Before we can actually measure U,,, however we must be able to interpret the Auger spectra in detail and identify the peaks with the various final state terms. We have recently done this for Cu, Zn, Ga, and Ge with remarkable success [13]. To display this we show the part of the Auger spectrum of Ga corresponding to 2 holes in the' 3d shell in figure 6. The terms which can occur with two holes in 3d are 'S,

'G, ,P, 'D, ,F. We have calculated the transition

probabilities and fit the spectrum using the theoretically determined transition probabilities. The fit is shown as the solid line and it is obvious that we now fully

43L L3 M45 M45

-

f l t o o o exper>mentol

-

30- X

-

U)

-

_c₃

8

17- K ~ n e t ~ c Energy i eV l

RG. 6.

-

The L3M45M45 Auger spectrum of Ga. The dots are the experimental values and the curve is the fit to five final state terms 'S 1G, 3F, 3P, and ID. The intensities were taken from theoretical transition probability calculations and the widths of

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C4- 122 G. A. SAWATZKY AND E. ANTONIDES

understand these spectra. In table I1 we have listed the free atom coulomb integrals involved in the 'G final state as well as the relaxation energy and the U,,. We see indeed that the U,,, is strongly reduced from the

TABLE I1

The coulomb interaction as determined

from atomic calculations and the measured relaxation energies and U,,, for the L3M45M45 Auger lines

F R U,,,

-

- Cu 27.0 19.0 8.0 Zn 30.2 22.5 7.7 Ga 33.3 22.2 11.1 Ge 36.2 23.3 12.9 Fe304 U,,,

=

3-4 eV v02 U,,, 1-2 eV

free atom value. We have only just begun the measurements on the transition metal compounds so only a few results are known. From these however we can conclude that for the beginning of the 3d series Ti and V the polarization reduction can reduce U to about

10% of the free atom value. An interesting question now is : where does this relaxation come from ?

We can distinguish 2 processes : 1) atomic relaxation coming from the core electrons of the atoms, 2) extra atomic relaxation coming from mainly the valence electrons. We can determine the atomic contribution from free ion electronic structure calculations ; for Zn we find a value of only 6 eV. The dominant contribution to the polarization reduction is therefore from the valence electrons which are delo- calized into a band in the solid. The U,,, will therefore be quite sensitive to the state of the material. For a metal we expect U,,, to be lower than for a semicon- ductor because of the lower dielectric constant of the latter due to the band gap. This has been observed in Zn as compared to ZnO. In ZnO U,,, is a b ~ u t 2.0 eV higher than in Zn metal. This kind of polarization reduction is exactly what we proposed in a recent paper in which it was argued that U,,, will be different in the semiconducting state than in the metallic state of a material undergoing a semiconductor-metal transition [14].

It would be interesting to do this kind of study on impurities in glasses. As discussed by Anderson [l21 there should be a bap in the one electron spectrum which would show up in the XPS of the valence band. In the two electron spectrum however no gap should appear because U,,, is attractive. Perhaps an example of an attractive U,,, is the one dimensional compound K2Pt(CN),Br,,,2.3 H 2 0 . In figure 7 we show the 4f core lines of Pt in this compound. The spectrum is fit with 2 doublets and can be fit very satisfactorally in this way. The peak positions of the

I l l t

62 68 7 L 8 0

ELECTRON B I N D I N G EDERGY ( e V )

FIG. 7. - XPS spectra of the Pt 4f and the Br 3d region. 1) K2Pt(CN)4n(H20) ; 2a) KzPt(CN)4Bro,sn(HzO) at

-

120 C ;

2b) same as 2a) but at -50 C so without crystal water; 3) K2Pt(CN)4Brz. The lines drawn are the least squares fits to

the spectra.

two doublets correspond to Pt2+ and Pt4+ and the intensities are in the expected ratio corresponding to the chemical formula. This is indicative of a strongly correlated system with an attractive Hubbard U the electrical conductivity being provided by 2 electron processes as well as one electron processes but then with an energy gap as given by Anderson. Another indication that this is the case is the XPS valence band spectrum. In this spectrum we find a gap of about 1.5 eV as would be expected in the one electron excitation spectrum. A word of caution however. We have not as yet been able to conclusively exclude the possibility that the spectrum arises from a surface layer of a frozen solution in which case Pt2+ and Pt4+ would be expected. A detailed discussion of this work can be found in ref. [15].

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THE ELECTRONIC STRUCTURE AND ELECTRON CORRELATION EFFECTS STUDIED BY XPS C4-123

low temperature the electrons are localized so that each V has the average number of d electrons namely one. In the high temperature metallic phase we consider for illustration purposes the material to be an uncorrelated metal. As discussed above an instantaneous picture will then show V with zero, one or two 3d electrons with a probability ratio 1 : 2 : 1.

It is obvious that in a fast measurement the Auger process corresponding to 2d holes in the final state will not be present in the low temperature phase but will appear in the high temperature metallic phase. By measuring the intensity of this Auger line one can obtain the average number of doubly occupied sites and reach conclusions concerning the amount of electron correlation in the two phases. The experiment is however not as simple as it may appear. Aside from the usual surface contamination and oxidation

problems nature has for V02 and Vz03 provided for another more serious problem. The V Auger line of interest falls almost exactly under a very strong 0

Auger line. This means long measurement times and a very careful subtraction of the 0 Auger contribution. These experiments are now in progress on VOz, V203, V4O9, V and V20, as well as a series of Ti oxides.

In conclusion we can say that a careful study of line shapes, Fermi level shifts and Auger peak positions and intensities can yield quite a lot of information concerning the nature of metal non metal transitions and electron correlation effects.

This investigation was supported by the Netherlands Foundation for Chemical Research (S. 0. N.) with financial aid from the Netherlands Organization for the Advancement of pure Research (Z. W. 0.).

References

[l] HERBER, R. H. and DAVIS, D. F., J. Chem. Phys. 63 (1975) 3668 and J. Chem. Phys. to be published (1976). [2] GOSSARD, A. C., DI SALVO, F. S. and YASUOKA, H., Phys.

Rev. B 9 (1974) 3965.

[3] MATTREISS, L. F., Phys. Rev. B 8 (1973) 3719.

[4] POLLAK, R. A. and HUGHES, H. P., J. Physique Colloq.

37 (1976) C4-151.

[5] EPPINGA, R., SAWATZKY, G. A., HAAS, C. and VAN BRUG- GEN, C. F., J. Phys. C to be published.

[6] BLAAUW, C., LEENHOUTS, F., VAN DER WOUDE, F. and

SAWATZKY, G. A., J. Phys. C. 8 (1975) 459. [7] BISHOP, S. G. and UMENY, P. C., Solid State Commun. 15

(1974) 1877.

[8] FRANZEN, H. F. and SAWATZKY, G. A., J. Solid State Chem.

15 (1975) 1 .

[9] SAWATZKY, G. A., GEERTSMA, W. and HAAS, C., J. ofMagn.

and Magn. Materials 3 (1976) 37.

[l01 BERGGREN, K. F. and SERNELIUS, B., J. Physique Colloq. 37 (1976) C4-315.

[l11 GHAZALI, A. and LEROUX-HUGON, P., J. Physique Colloq. 37 (1976) C4:321.

[l21 ANDERSON, P. W., Phys. Rev. Left. 34 (1975) 953 and J. Physique Colloq. 37 (1976) C4-337.

1131 ANTONIDES, E., JANSE, E. C . and S A ~ A T Z K Y , G. A. (to be published).

[l41 SAWATZKY, G. A., KUINDERSMA, P. I. and KOMMANDEUR, J., Solid State Commun. 17 (1975) 569.

[l51 KUINDERSMA, P. I., Thesis University of Groningen 1975