ELECTRONIC STRUCTURE OF Fe ION IN CuGaS2

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ELECTRONIC STRUCTURE OF Fe ION IN CuGaS2

K. Gondaira, T. Kambara, K. Suzuki

To cite this version:

K. Gondaira, T. Kambara, K. Suzuki. ELECTRONIC STRUCTURE OF Fe ION IN CuGaS2. Journal

de Physique Colloques, 1975, 36 (C3), pp.C3-145-C3-148. �10.1051/jphyscol:1975326�. �jpa-00216296�

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JOURNAL DE PHYSIQUE Colloque C3, supple'ment au no 9, Tome 36, Septembre 1975, page C3-145

ELECTRONIC STRUCTURE OF Fe ION IN CuGaS,

K. I. GONDAIRA, T. KAMBARA and K. SUZUKI The University of Electro-Communications, Chofu-shi, Tokyo 182, Japan

Resume. - La structure electronique autour d'un ion Fe dans CuGaS2 est etudiee en traitant le complexe forme par un ion Fe entoure tCtraCdriquemcnt par quatre ions de S et portant une attention particuliere au champ cristallin de faible symetrie et a l'interaction spin-orbite.

Les etats electroniques sont obtenus par la methode de Hcitler-London en tenant compte dcs differentes configurations ioniques. On remarque que tous les etats excitCs de basse energie consistent essentiellement en des configurations de transfert de charge Fe* '-(S4)7-.

Les valeurs de g et de la constante d'anisotropie uniaxiale de I'hamiltonien de spin sont calculCes pour I'etat de base 6A I . Ces calculs montrent que les valeurs obsewks de ces parametres, qui sont anormalement elevees, resultent de configurations de transfert de charge a la fois de 1'Ctat fonda- mental et des premiers etats excites.

Abstract. - The electronic structure around an Fe ion doped into CuGaS2 is investigated with a particular emphasis of the low symmetry crystal field and spin-orbit interaction, by dealing with a cluster consisting of an Fe ion and four S ions surrounding it tetrahedrally. The elctronic states are obtained based on the Heitler-London scheme with taking into account various ionic structures. It is pointed out that all the low energy excited states consist mainly of charge transfcr configurations FeZ'(S4) 7 - .

The g-values and uniaxial anisotropy constant D of the spin Hamiltonian for the ground state 6A ¹ are calculated. It is shown from the calculations that the anomalously large observed values of them are due to high mixing ratio of the charge transfer configurations into both the ground state and the lower excited states.

l . Introduction.

-

Recently, Teranishi et al. [l-31 have reported optical absorption and emission spectra of CuGaS, : Fe and CuAlS, : Fe in visible and infrared regions below the fundamental absorption edge. The absorption spectra [l, 21 show a very strong band with two peaks at about 1.2 eV and 1.9 eV for CuGaS,.

As regards the emission spectra [3], a sharp line of pretty low energy (4 942 cm-' for CuGaS,) has been found. The observation of its Zeeman effect shows that the ground state has

Q,

symmetry 131. It has been shown [4,5] that charge transfer among the impurity Fe ion and the ligand S ions plays a leading role in the strong optical absorption and such a low energy emission.

Schncider et al. [6] observed the ESR spectra of the Fe3+ ion in CuGaS,. The g value is found to be 2.024 and the zero-field splitting parameter D, 0.188 5 cm-'.

Such large positive g-shift and large zero-field splitting can hardly be expected for orbital singlet ions like Fe3+(3d)5 from the crystal field theory. Fidone and Stevens [7] and Watanabe [8j have shown qualitatively that a partial electron transfer through spin-orbit interaction from ligands to the orbital singlet ion is a reasonable source for the positive g-shift.

In this paper we make detailed calculation of the electronic structure around an Fe ion in CuGaS, and estimate quantitatively the g-shift and zero-field splitting of the ground 6 A , state. For this purpose we

take a chlster constituted by an Fe ion and four S ions surrounding the Fe ion tetrahedrally. The electronic states of the cluster are calculated based on the Heitler-London scheme with taking into account five ionic structures Fe3+(s4)'-, Fe2+(S4)7-, Fe+(S4)6-, Fe(SJ5-, and Fe-(S4)4-.

Our main results are briefly summarized here. The main term of the ground 6Al state is not the pure d5 configuration (Fe3 ⁺(S,)'-) but the one-electron transferred configuration (FeZ+(SJ7

-).

Several excited sextet states which do not contain the pure d 5 configuration appear in the very low energy regions compared to the charge transferred states of many other transition metal compounds. These features of the electronic structure are essentially responsible for the large positive g-shift and the large zero-field splitting.

2. Methods of calculations.

-

The energy levels and the corresponding eigenfunctions of the [FeS,]

cluster are calculated as rigorously as possible.

Although the tetrahedrons of [FeS,] clusters are slightly distorted in the actual crystal, we deal with an undistorted cluster in the present treatment. The surroundings of the cluster are regarded as a source of a field acting on it and a suitable boundary condition is imposed upon the electron distribution in the cluster.

The orbitals from 1s to 3p of Fe and those from Is to 2p of S are dealt with as rigid cores so that electrons

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975326

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C3-146 K . I. GONDAIRA, T. KAMBARA AND K. SUZUKI occupying them do not participate in the binding

with other ions. The sp3-hybridized orbitals are constructed from 3s and 3p orbitals of sulfur ions and among them the orbitals pointing outward are consi- dered also doubly occupied and rigid ; they are taken into account simply as the Coulomb potential. This is our boundary condition for the charge distribution. We explicitly consider the 3d orbitals of Fe and the four hybridized orbitals X,,

X,,

X,, and X, directed to the center Fe ion. Ncither 4s nor 4p orbitals of Fe are taken into account for simplicity.

In a tetrahedral symmetry field, d orbitals span two irreducible subspaces belonging to the represcntations E and T, of the point group T, and the hybridized orbitals X,, X,, x3, and

x4

span also two subspaces A I and T,. The 3d orbitals with E symmetry are denoted as

(Prcu and

v,,,

and those with T, symmetry, as qFCc,

(pFc,,, and ^(p,,<, where u cc 3 ^{z 2}

-

r2, ^li^ccx 2 - y Z ,

<

^E^{y z ,}¹¹^K^zx,^and ^ccxy. The symmetrized mole-

cular orbitals for sulfur ions are dcnoted as

v,,

for A, symmetry and (pse,

vs,,,

and

vs!

for T2 symmetry, where these ~nolccular orbitals are described with appropriate linear combinations of X,, X,, x3, and x4.

As the basis orbitals for the Heitler-London calculation WC adopt the molecular orbitals vs., and qSa (a =

5, v , c)

and the 3d orbitals

( p

⁼^U,v ) and

(R =

5 , v ,

c). Here,

v;,,

are the orbitals orthogo- nalized to v,,, that is,

where S,

<

^qsa

I

yFea

>

⁼0.1 10 51. The use ofthe orthogonal orbitals greatly simplifies the calculations.

By distributing thirteen electrons among these basis orbitals in various manners, we construct the basis functions CD of the total system which form the bases of the Heitler-London calculation ; @ are expressed as antisymmetrized products (or linear combinations of them) constructed from the basis orbitals.

We are concerned with sextet states

6r

( r ⁼A , , A2, E, T,, and T,). The ionic structures leading to the sextet states are FeN+ (S4)("+ ^{5 ) -} for N = 3, 2, 1, 0, and

-

1, and the electronic configurations belonging to the FeN'(S,)(Nf ionic structure are expressed as [em t2,e8-N-n' a l n t2s5+N-n] (max (0.2

-

N)

5

m

5

4, max (0, N - 1)

5

n

5

2), where the basis orbitals (@Feu, ( ~ ~ e v ) , (&eC, &em d e < ) , Vsn, and ($?S<, vs,,, PS:) are simply denoted as e, tZFc, a l , and t,,, respectively.

We write the basis function with

6r

symmetry arising from a configuration [em t2,e8-N-m a

,"

t2s5+N-"] as

den'

^t ^~8 - N - n ~ ^~ ^e a l n t2Ss+N-n

. .

6 r ) .

The Hamiltonian of the system, in atomic units, is

13

where ~ y ( i ) is the Coulomb potential due to the nucleus and the core electrons of the K-th ion in the cluster, n,(x) are the hybridized orbitals pointed outwardly, and Vo,,(i) represents the effects of the surroundings.

The eigcnfunctions !P,(") of the total system are represented by linear combinations of 41(~r). The eigenvalues and cxpansion coefficients are determined by the secular equation of the energy matrix based on

@(('T). The matrix elements of X are expressed in terms of the integrals of atomic orbitals, where the atomic orbitals used are the Hartree-Fock solutions of a free F e Z + and S-, taken from Clcmenti's tables [9]. We evaluate the integrals using Matsuoka's program which is based on the Gaussian type orbital expansion method. In this calculation we put

where ~L'and R , are the effective nuclear charge and the position vector of the K-th ion, respectively. We

eff eff

assume ZFc = 8 and Z s = 6 and treat the matrix elements of

as adjustable parameters.

3. Calculational details and discussions.

-

3. I ENERGY ^LEVELS.- The secular equations were solved for the sextet states of each symmetry A,, A,, E, T , and T,. Then the adjustable parameters were determined so that the calculated energy differences E,(6T,) - E,(6Al) and E,(6T2) - El(6Al) fit to the two peaks (at 1.2 eV and 1.9 eV) of the absorption band in CuGaS, : Fe [2], because it has been shown [ 5 ] that the two peaks arise mainly from the allowed transitions to the lowest Y1(6T2) and the next lowest eigenstates Y#T,) from the ground eigenstate

'j"1(6A1).

The calculated energies and wavefunctions of the eigenstates whose energy is below the fundamental absorption edge 2.5 eV of CuGaS, are as follows :

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ELECTRONIC STRUCTURE OF Fe ION IN CuGaSz

It is one of the noticeable results of our calculation that the one-electron transferred configuration [e2 t 2 2 a: t2:] is dominant in the ground state Y 1 ( 6 ~ 1 ) , instead of the none transferred configuration [e2 t,,", a; t2t]

corresponding to the Fe3+ (S4)'- ionic structure. It should be remember, in this respect, that the Fe ion often prefers the divalent state. Another feature is that the charge transferred eigenstates ('E, 6T1, 6T2) lie in such low energy regions compared to those of many transition metal compounds.

3.2 SPIN HAMILTONIAN. - The spin Hamiltonian appropriate to the ground state [6] has D,, symmetry and is denoted, up to the order of S:, as

The g-values and the zero-field splitting parameter D are calculated by second-order perturbation theory as

and

4 ²

D

=

-E]

₂₅

<

Y*I(~AI, 512)

1

H,,

I

'Y.('T,, 512 Z )

> I

^x

(

¹

^-

¹

n E , ( ' T ~ ) - ( ~ / ~ ) A ~ ( ~ T ~ ) E , ( ~ T ~ ) + A , ( ~ T , )

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C3-148 K. I. GONDAIRA, T. KAMBARA A N D K. SUZUKI

where H,, is the spin-orbit interaction and 312 An(6Tl) is the energy splitting of the !?',(6~1) state due to the low symmetry (D,,) crystal field. This D,, crystal field arises from the small deviation of the chalcopyrite crystal from zincblende structure, and it is the origin of the uniaxial anisotropy of the spin Hamiltonian.

By using our calculated eigenvalues Ei(6r) and eigenfunctions Y,(6r), we evaluate eq. (6), (7), and (8).

The results are

where

c,

is the spin-orbit parameter for the 3d orbital of Fe and the two center integrals of H,, are ignored since H,, is approximately proportional to r F 3 and appreciable only a t the vicinity of the origins. In the above expressions for the g-values and D we omit the terms arising from the higher 6Tl states since they are very small. The expressions (9), (10), and ( 1 1) involve three parameters, the spin-orbit

c,

and the low symmetry crystal field d 1 ( q T , ) and A,(~T,). For the

c,

^{we take}

the value 410 cm-' for a free Fe2+ ion, since the main configurations of the Y l ( 6 ~ l ) , Yl(6Tl), and Y2(6T1) states belong to the Fe2+(sJ7- ionic structure. No precise values are available for Al(6T,) and A2(6Tl).

Ignoring the second term of eq. (1 l), however, we can obtain such a value of A l ( 6 ~ l ) as the observed value of D is derived. We obtain Al(6Tl) = 830 cm-' in this way and then the low symmetry crystal field splitting of the Yl(6Tl) state becomes 1 320 cm-'. This value of the splitting is reasonable : it should be compared with the cubic field splitting 10 Dy, which is nearly the same as the energy difference

E2(6T,)

-

E,(6T,) = 6 162 cm-'

.

of the large g-shifts can be clearly seen from eq. (6) and (7) and the features of our calculated eigenfunctions. The matrix elements

<

y1(6A1)

i

^{H s o}

I

YnPT1)

>

and

in the equations are expressed in terms of the basis functions ~ ( ~ r ) . Among these the matrix elements between the ~ ( ~ r ) belonging to the same ionic structures, which are reduced to one-center integrals, are overwhelmingly large compared with those between the c D ( ~ ~ ) belonging to different ionic structures, which are mainly two-center integrals. The dominant term of Y ~ ( ~ A I ) is @(e2 t2 2 a? t2:) which belongs to the F ~ ~ + ( S , ) ~ - ionic structure, the same as the main terms of ~ ~ ( ~ 7 , ) and YJ2(6T1). If the main term of Y , ( ~ A , )

3 2 6 6

were @(e2 t2Fe a, tzs : A,) as one might expect usually for a ~e~~ ion in ionic crystals, such large g-shifts would not result.

Furthermore, the denominators in eq. (6) and (7) Using A , ( ~ T , ) = 880 cm-' and omitting the second become relatively small compared with those in case terms of eq. (9) and (IO), we obtain g,, = 2.033 of many other com~ounds.

and g, ⁼2.038.

Acknowledgments.

-

We would like to express 3 . 3 Drscussio~ OF g-SHIFTS. - Note that the above our sincere thanks to Dr. Teranishi for allowing fre- calculated g-shifts are large, positive, and rather iso- quent (sometimes over-night) use of a computer tropic in harmony with the observation [6]. The source which has enabled us to make the whole of this work.

References

[l] KONW, K., TERANISHI, T . and SATO, K., J. Phys. Soc. Japan ^[6]SCHNEIDER, J., R ~ U B E K , A. and BKAWDT, G., J. Phys. Chem.

36 (1974) 311. Solids 34 (1973) 443.

[21 TE~ANLSZII, T., SAT% K. and KoNr>o, K., J . Phys. Soc. Japan _FlnoNE,I. and s T E " ~ N S , I(. W . H., proc. Phys. sot. 73, 36 (1974) 1618.

[3] SATO, K. and TEKANISHI, T., J. Phys. Soc. Jupun 37 (1974) 415. (1956) 116.

[4] KAMBARA, T., J. Phys. Soc. Japan 36 (1974) 1625. ^[S] WATANARE, H., J. Phys. Chem. Solids 25 (1964) 1471.

[5] KAMBARA, T., SUZUKI, K. and GONDAIKA, K. I., to be publish- [9] CLEMEKTI, E., IBM J. Res. Developm. Suppl. 9 (1965) 2.

ed in J. Phys. Soc. Japan (1975).