ABNORMAL POPULATIONS AND VIBRONIC PROPERTIES OF THE ELECTRONIC LEVELS OF Fe2+ IONS IN ZnS : 57 Co MÖSSBAUER SOURCES

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ABNORMAL POPULATIONS AND VIBRONIC PROPERTIES OF THE ELECTRONIC LEVELS OF Fe2+ IONS IN ZnS : 57 Co MÖSSBAUER SOURCES

C. Garcin, A. Gerard, P. Imbert, G. Jehanno

To cite this version:

C. Garcin, A. Gerard, P. Imbert, G. Jehanno. ABNORMAL POPULATIONS AND VI- BRONIC PROPERTIES OF THE ELECTRONIC LEVELS OF Fe2+ IONS IN ZnS : 57 Co MÖSSBAUER SOURCES. Journal de Physique Colloques, 1979, 40 (C2), pp.C2-413-C2-414.

�10.1051/jphyscol:19792144�. �jpa-00218517�

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JOURNAL DE PHYSIQUE Colloque C2, suppl6ment au n o 3, Tome 40, mars 1979, page C2-413

ABNORMAL P O P U L A T I O N S AND V I B R O N I C P R O P E R T I E S OF THE E L E C T R O N I C L E V E L S OF ~ e I O N S ~ + I N ZnS : 5 7 MOSSBAUER SOURCES ~ ~

C. Garcin, A. ~ e r a r d ~ , P. Imbert and G. Jehanno

i Dph-G/PSRM, CEN SacZay, B.P. ND2, 91190 a f - s / Y u e t t e , France

I n s t i t u t de Physique, Universitg de LiBge-Sart TiZman, B4000 LiBge, BeZgique

RQsum6.- LIQclatement hyperfin observe au-dessous de 4K dans les spectres&ssbauer de 5 7 ~ o dans ZnS est attribus 3 la contribution hors 6quilibre thermique des niveaux excites Ts et I's de Fe2" en presence d'effet Jahn-Teller dynamique. La coherence du modSle est examinse en presence de contraintes ou de champ magn6tique.

Abstract.- The hyperfine splitting of the Msssbauer spectra of 5 7 ~ o in ZnS below 4K is attributed to the contribution of the excited levels

rI,

^and^Tsof ~ e ~ + , which are populated out of thermal equilibrium and submitted to a dynamical Jahn-Teller effect. The coherence of this model is examined in the presence of strains or applied magnetic fields.

We have already described the abnormal beha- viour of the Msssbauer spectrum emitted by 5 7 ~ o at very low temperatures in the cubic phase of ZnS /l/ : the single line emitted by the Fe2+ ions in tetrahedral sites splits below about 4K, giving rise to 2 quadrupole doublets and a central line. In con- trast, such phenomena is absent in the Gssbauer absorption spectra of pe2+ impurities in ZnS at the same temperatures.

Following previous studies of ferrous ions in tetrahedral sites made by Ham / 2 / and Vallin 1 3 1 , we attributed these quadrupole doublets to the slow relaxation contributions of the two excited spin- orbit triplets

r4

^and^{r 5}of Fe2+ /l,&/, in the presence of both weak random strains which lift the degeneracy of these levels, and of a dynamical Jahn-Teller effect which reduces the corresponding quadrupole interaction.

Such an interpretation however requires an unu- sual assumption. As the Boltzmann populations of the triplets

r4

^and

rs

are negligeably small at such low temperatures, we are led to admit that the thermal equilibrium is not achieved at the observation time within the spin-orbit levels of the ferrous ion which results from the decay of the radio-active parent 5 7 ~ o . We have already shown that this hypo- thesis is reasonable, because of the low relaxation rates between spin-orbit levels at the temperatures under consideration /4/.

We examine here various aspects of the coherence of our interpretation.

1.

Fe2' in ZnS.- Starting from the calculation mad?

by Vallin for Fe2+ in CdTe 1 3 1 , we diagonalized

the linear Jahn-Teller Hamiltonian %T=~(~o U. +

QEUE) within the vibronic levels 141. These vibronic levels, which are the eigenstates of the Hamiltonian 16eO=x SO +Xvib, are products of a spin-orbit part

(corresponding t o x , ) and a vibrational part (cor- SO

responding toxvib). We limited the calculation to the vibrational states with 0,l and 2 phonons which are built with the phonon of the lowest energy (Hu=

70 cm-') which has been observed in ZnS /5/ and presents the correct symmetry for participating in the Jahn-Teller coupling with the orbital level I'3

of Fe2+. The solution is greatly simplified by the fact that

xJT

only couples those vibronic levels which belong to the same irreducible representation.

This coupling introduces a linear combination of 1

and 2 phonon wave functions into the zero phonon levels r4 and r 5 leading to a reduction of the spin and orbital observables and particularly of the quadrupole interaction. The only two adjustable parame- ters in this problem are, first, the pure spin-orbit separation K =6 (h2/a+p), which lies between 15 cm-'

0

(the reduced separation observed between the actual levels) and about 24 cm-' (the free ion value), and

v2

I secondly the Jahn-Teller energy EJT=

- -

/ 3 / .

2a2

With the values K619.5 cm- and EJT=15.6 cm-', we can account for the Jahn-Teller reduction factors q(r4) and q(rs) observed in the two corresponding quadrupole doublets, and also for the energies of the levels rt,,r3 and

rs

from optical measurements 161. (see the.£igure I).

2. Strain broadening of the ~Essbauer lines.- Whe- reas the calculation of § I consisted in diagonalizing the Hamiltonian

so

⁺^$LJT,we add here a '

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19792144

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C2-414 JOURNAL DE PHYSIQUE

strain Hamiltonian

2

S = E U + EEUE.

8 8 actual vibronic levels r b and rs. However this type

Fig. 1 : a

-

pure zero-phonon vibronic levels, without Jahn-Teller coupling; b- the same levels after one-and two-phonon admixture through the Jahn- Teller coupling, and calculated values of the quadrupole reduction factors q(I-4) and q(T5); c

-

opti- cally measured levels from reference /6/, and experimental values of q(rr,) and q(Ts).

It can be shown that the total Hamiltonian

Xo +W

JT

+g

acts separately within the following S

groups of representations

(rl + r2 + r38 +

(r4X.+

^rs~),

(rky

⁺^r~,,),

(rsz

⁺^rs5),

which gives 1 matrix 24 X 24 and 3 matrices 12 X 12.

to be diagonalized within the 0,l and 2 phonon vibronic wave-functions. We thus calculated the quadrupole interaction in the ground singlet

rl

and in the triplets rs and F5 as a function of strains of various symmetries and magnitudes. As the strain de- creases to zero, the quadrupole interaction disap- pears in l'l, whereas it reaches a finite value common to the 3 sublevels in each triplet r4 or

rs .

^{We can}

thus predict the relative broadening of each compo- nent of the Mijssbauer spectrum (central line due to rl, quadrupole doublets due to I't, and I's ) when a given strain is applied. The relative broadenings are found to be relatively insensitive to the syme- try of the strain. They are in good agreement with the experimental broadenings which are observed in samples having different strains following the pre- paration conditions.

3. Influence of an applied magnetic field.-

3.1.- Low field cogp&igg.- The calculation consists in diagonalizing the Zeeman Hamiltonian inside the vibronic triplets r b and

rS

resulting from the Jahn- Teller coupling (1.1). Compared to the pure spin- orbit levels

rt,

and rs, we found that the hyperfine field (or the magnetic moment) is reduced respecti- vely by factors r(r4)=0.97 and r(r5)=0.86 in the

of calculation implies that the Zeeman perturbation is much less than the spin-orbit separation but much higher than the strain splittings, a condition which is hardly realized for the actual samples where the strains are always too important.

3.2. High-field alogg-iggL> directions.- We diagonalized here the total Hamiltonian

x = x

+ +

0 JT

J'eZeeman

within the 0,l and 2 phonon vibronic wave functions. When H is applied along <001> directions, the matrix of 2 factorizes into 1 matrix 24 X 24 (rsx + + r55 + rsn) and 2 matrices 18 X 18 (Ti + rsz + r 3 8 ) and (r2 + rsr + raE). We completed the calculation in this case and predicted the corresponding Sssbauer line shape. The experimental veri- fication on single crystal 5 7 ~ o / ~ n ~ sources is in progress. But we have already checked that the calculated Zeeman sublevels of the vibronic triplets Tr, and r s are in agreementwith those experimentally obtained from optical measurements in an applied field by Vallin et al. /6/.

As a conclusion, our interpretation of the abnormal Mijssbauer spectra of "CO in ZnS is con- sistent with the various experimental data which are now at our disposal.

References

/l/ Garcin, C., Imbert, P., and Jehanno, G., Solid State Commun.

21

(1977) 545.

/2/ Ham, F.S., J. Physique Colloq.

2

(1974) C6-121 /3/ Vallin, J.T., Phys. Rev. (1970) 2390.

/4/ Imbert, P., reserved lecture, Internat. Conf.

Gssbauer Spectroscopy, Bucharest (1977).

/5/ Ham, F.S. and Slack, G.A., Phys. Rev. (1971) 777.

/61 Vallin, J.T., Slack, G.A. and Bradley, C.C., Phys. Rev. (1970) 4406.