Ligand-field model for the electronic structure of the fluorescent levels of d5 ions in II–VI compounds

JOURNAL

OF

LUMINESCENCE ELSEVIER

Journal of Luminescence

72-74

(I 997) 637-639

Ligand-field model for the electronic structure of the fluorescent levels of d5 ions in II-VI compounds D.Boulanger

a, R. Parrot b,*

a UniversitP de Puris-Sud, Laboratoire d’lnfirmatique, M&rise de Sciences Physiques, Bitiment 479, 91405 Orsay Cedex, France b Universitk des Antilles Guyune. Institur Universitaire de Formation des Maitres et Fact& de Technoloyie de la Guyane BP 792, 97337 Cayenne Cedes, Guyane Francaise, French Guiana

Abstract An analysis of the first-order spin-orbit (SO) interaction for the fluorescent levels of Mn ‘+ in the common cation series ZnS, Z&e, ZnS and also in CdTe shows that, with respect to the results of the crystal-field model, the SO interaction is strongly reduced for the fluorescent state of Mn in ZnS and strongly enhanced and of opposite sign for ZnSe, ZnS and CdTe. It is shown that, for ligands Se and Te, the molecular SO interaction is primarily controlled by the large SO coupling constants of the electrons 4p(Se) and Sp(Te) of the ligands. Keywords:

Fluorescence;

d5 ions; II-VI compounds

1. Introduction

2. Ligand-field model for the first-order spin-orbit interaction in orbital triplet states

It will be shown that covalency effect on the spinorbit splittings of the orbital triplets of d5 ions is much more important than expected in earlier covalent models [ 11. In the proposed molecular model for the first-order SO interaction in the fluorescent state of Mn*+ in II-VI compounds, we will use the molecular orbitals which were previously used to interpret the orbitlattice coupling constants (OLCC) of the orbital triplet states 14Tl) and i4T2) at lower energies of Mn2+ in ZnS and ZnSe [2] and the spin-lattice coupling coefficients (SLCC) of Mn*+ in ZnS, ZnSe, ZnS, and CdTe [3].

* Corresponding

author. Tel.: 594 304200;

fax: 594 30 79.53

0022-23 13/97/$17.00 Published by Elsevier Science B.V. PZi SOO22-23 13(96)0017 i -8

The molecular spin-orbit interaction Hsom which describes the spin-orbit interaction in a covalent model, is that defined by Misetich and Buch [4]: HSO~

=

C

i

cM(riM)l;M

Si + C C
where &M and 1,~ are one electron orbital operators for the metal and the ligands, respectively. CM and i~ are the spin-orbit coupling constants, defined by Blume and Watson [5]. In the following, the relevant spin-orbit coupling constants will be those of the electrons 3d of the metal and of the electrons np of ligands (n = 3 for S, 4 for Se, and 5 for Te). It can be noted that Hso,,, depends on interatomic distances and angles.

638

D. Boulanger,

R. Parrot J Journal of Luminescence

72-74 (1997)

637639

It is convenient to write Hso,,, in terms of the molecular angular momentum r: of electron i and the complex components of the spin operators [6] as

elements of r for the monoelectronic 2e and 4t2 are

H som --c

let2 = -(e+,It2i)

wave functions

i

7:;s;.

2

4;

In this expression, u =x or y if q = f 1 and u = z if q = 0. The operators rb are

and 02t2

0’ being the total angular momentum of electron i of the ligands. The relevant monoelectronic molecular orbitals 4t2 and 2e (of the half-filled shell) which are linear combinations of atomic orbitals 3d and 4p of Mn, and the valence orbitals 3s and 3p of sulfur, are described in detail in Ref. [2]. They are written in terms of the monoelectronic orbitals of the electrons 3d and 4p of metal, and in terms of the orbitals (ss, op, and rep of ligands as: Jt2y) = adldt2y) + aP]pt2y) + a0S((Sst2y) + a’JPIopt2y) + a”PlxPt,Y), where y = 5, y or [ refers to the components molecular monoelectronic level 4t2, and, ley’) =bdIdey’)

of the

+ bqlrtpey’),

where y’ = 6’ or t’ refers to the components of the molecular monoelectronic level 2e. The a’s for the orbitals 4t2 and the b’s for the orbitals 2e result from the diagonalization of the molecular Hamiltonian. The levels It,, 2t2, 3t2 and le are filled, and the levels 4t2 and 2e are half-filled. The multielectronic wave functions for the orbital triplet states are obtained by diagonalizing the matrix of Sugano et al. [7] for the three (4Ti)-states at lower energy. Explicitly we get 14Tp,) = aTj4Tfl,(4ti2e))

+ aTj4TyU(4t:2e2))

+ ai/4TpU(4ti2e3)), where q = 1,2,3 refers to the three levels 4Ti. u =x, y or 2. The matrix elements of the molecular spin-orbit interaction can now be expressed in terms of the matrix elements of the operator r. The relevant matrix

=

-

i(t2514t2v)

Explicitly [et2 and jt2t2 are given in terms of the mixing coefficients of the monoelectronic wave functions and of the spin-orbit constants of the metal and of the ligands by

let2 =adbdh+ lb~P@rP (2J3)

+

QGPJ2)IL

and, jt2t2 = (adad - aPaP)cM + uXP(a0PJ2 - a”P/2)[L. We can note here that in the CF-model restricted to the configuration d5, = 1353 + 297(Q~ + l), and [L (Te)=3444 + 756(Q~ f 1). Then, by using the mixing parameters for the triplet states obtained from the values of the Racah parameters B, C, and of the cubic field coefficients Dq (reported in Ref. [2]), we obtained x in terms of a linear combination crjtztz + jI[etz of the matrix elements [t2t2 and {et2. The a’s and ,8’s are given in Table 1 for the studied /4T,)-fluorescent states. Finally, x has been computed by using the molecular orbitals which correctly accounted for the OLCCs [2] and SLCCs [3] of Mn. The values for x, as given by the proposed molecular model and by the CF-model, are in Table 1.

639

D. Boulanger, R. Parrot 1 Journal of’ Luminescence 72-74 (1997) 637639 Table 1 Values for c(,/I, [tztz, jetz, and 1 as given by the LF-model.

XCF is obtained

from the CF-model. [et2

w.

B

02t2

ZnS

0.1438

-0.0848

f131

f205

ZnSe

0.1448

-0.0880

-321

+125

ZnTe

0.1382

-0.0898

-774

f82

CdTe

0.1386

-0.0898

-689

+45

3. Conclusions

it2t2, [etz, 1 and XCF are in cm-’

ants

cL(Se),

%

and

XCF

+ I .42

f17.7 +17.1

-57.5

fl4.5

-114

+14.7

-99.1

cL(Te)

are

much

greater

than

L(S). Table 1 shows that for ZnS : Mn, x is strongly reduced with respect to the value XCF of f17.7 cm-] as deduced from the CF-model (by taking i3d = 300 cm-‘), this is due to the fact that x depends on two terms having approximately the same magnitude and opposite signs. In Z&e, ZnS, and CdTe, x is negative and its modulus is much greater than the value given by the CFmodel restricted to the dS configuration. The values for [tztz and [et* are very different when passing from ZnS to ZnSe, ZnTe, and CdTe primarily because the spin-orbit coupling const-

References [I] J.S. Griffith, The Theory of Transition Metal Ions (Cambridge University Press, London, I97 1). [2] D. Boulanger and R. Parrot, J. Chem. Phys. 87 (1987) 1469. [3] R. Parrot and D. Boulanger, Phys. Rev. 47 (1993) 1849. [4] A.A. Misetich and T. Buch, 1. Chem. Phys. 41 (1964) 2524. [5] M. Blume and R.E. Watson, Proc. R. Sot. London Ser. A 271 (1963) 565. [6] J.S. Griffith, The Irreducible Tensor Method for Molecular Symmetry Groups (Prentice-Hall, Englewood Cliffs, NJ, 1962). [7] Sugano, Y. Tanabe and H. Kamimura, Multiplets of Transition Metal Ions in Crystals (Academic Press, New York, 1970).