PHYSICAL REVIE% 8 VOLUME 17, Ã UMBER 3 1 FEBRUAR Y 1978

Jahn-Teller effect in the fluorescent level of Mn++ in ZnSe and ZnS

R. Parrot, C. Naud, and C. PorteUniversite P. et N. Curie, Laboratoire de Luminescence, "4 Place Jussieu, 75230 Paris Cedex 05, France

D. Fournier, A. C. Boccara, and J. C. RivoalLaboratoire d'Optique Physique, Ecole de Physique et Chimie 1ndustriells, f 10 rue Vauquelin, 75231 Paris Cedex 05, France

(Received 22 September 1976)

Uniaxial-stress experiments have been used to analyze the fine-structure lines of the lowest 'T, level ofMn++ in cubic ZnSe and in cubic ZnS containing Stacking faults. We show that the two fine-structure lines

due to the cubic centers in ZnSe and ZnS can be interpreted by Ham's model corresponding to a strong

Jahn-Teller coupling with E symmetry modes. In both cases, the observed lines correspond to transitions

from the i'A [) fundamental state to the almost degenerate states ~I,),(3/+10) ~ I,(3/2) )—(1/+10)jl,(5/2)) for the line at lower energy and ~16),(1/+10)~I,(3/2))+(3/v'10)~I, (5/2))for the line at higher energy. The influence of the Jahn-Teller effect on the axial Mn++ centers in stacking

faults of ZnS is also briefly considered. Finally a comparison is made of the Jahn-Teller efect in the low-

est 'T[ and 'T, states of Mn++ in ZnS and ZnSe.

I. INTRODUCTION

Although the Jahn-Teller effect has been exten-sively studied for a number of d ions either byelectron paramagnetic resonance or by opticalspectroscopy, ' very few detailed studies of this ef-fect for d' ions have been reported. Furthermore,to our knowledge, only Mn" has been studiedamong the d' ions.

Amongst the early studies on the Jahn-Teller ef-fect on Mn" ions, we can cite a theoretical studyof this effect on the fluorescent level of Mn" in'

MgOAl, O, and also a theoretical determination ofthe g factors of the fine-structure lines of thefluorescent 'T, level of Mn" in ZnS in the case ofa strong coupling to an E vibrational mode. ' How-

ever, no direct demonstration of the nature of thecoupling, either to E symmetry modes or T, sym-metry modes of both was undertaken at that time.

The first systematic study of the Jahn-Teller ef-fect on Mn" was made by Chen, McClure, andSolomon' and Solomon and McClure' who studiedthe orbital triplet levels 'T, and 'T, at lower ener-gy of Mn" in antiferromagnetic RbMnF, . Theseauthors interpreted all their experimental resultson the Zeeman levels using Ham's formalism cor-responding to a strong Jahn- Teller coupling to Esymmetry modes and to a small coupling to a T,vibrational mode for certain levels.

More recently, a study of the Jahn-Teller effectin the lowest 'T, level of Mn" in ZnSe and ZnShas been published. ' It was clearly shown that thezero-pressure spectrum could lead to the errone-ous conclusion that a strong coupling to 8 modesis present. By means of uniaxial stress experi-ments, it was demonstrated that the 'T, level issubjected to a medium Jahn- Teller coupling to anE symmetry mode and that the intensity of one

TABLE I. Dimensions and orientations of the crystals used in our experiments. & is the

cross-sectional area perpendicular to the applied pressure P. 8% of Mn++ ions in ZrB arein stacking faults, the other ions are in cubic sites.

SampleDimensions (mm)

(error + 0.01 mm) S (mm)Applied

pressure

ZnSe: Mn(Semielements)0.1-mol /o Mncubic

ZnS: Mn(Eagle Picher)0.01-mo1% Mn

cubic plus stackingfaults

1.50 x 2.75x 3.551 85x1.92 x4.872.70 x 3.45 x 3.55

1 61x1 95x4 50

0.82x 1.23 x 3.16

4.123.559.31

3.14

1.01

z [[oog& l[&u[I &C1113

p[I [&&olg

17 l 057

R. PARROT et al. l7

fine-structure line is transferred selectively toexcited vibronic levels. In fact, the selective in-tensity transfer has been rarely studied. Amongthe very few studies of this effect, we can cite,for example, the work of Ham and Slack' whodemonstrated the presence of an intensity transferto one-phonon sidebands in the 'T, state of Fe" inZnS.

Very recently a theoretical investigation basedon the hypothesis of a strong Jahn- Teller couplingof several triplet levels of Mn" in various com-pounds has been made by Koidl. ' A study of theZeeman effect and of the magnetic polarization inthe fluorescent 'T, level of Mn" in ZnS has beenperformed by Fournier et al. '; their calculationsof the splitting and of the intensities of the zero-phonon lines computed in the hypothesis of a strongcoupling were in good accordance with the experi-mental data. The main purpose of this paper is toconfirm directly the hypothesis of a strong Jahn-Teller coupling to an E mode of the fluorescentlevel of Mn" in ZnS and to determine the natureof the coupling in the case of Mn" in ZnSe.

The excitation spectra under zero-pressure andthe uniaxial stress experiments are reported inSec. II. The splittings under stresses of the twofine-structure lines of the fluorescent 'T, level ofMn" in ZnSe and in the cubic sites of ZnS willshow that this level is strongly coupled to anF. vi-brational mode, the coupling to the T,. modes beingnegligible. In Sec. III, we briefly recall Ham's

model for an orbital triplet state coupled to an F.

vibrational mode, and we give several formulaspermitting convenient calculation for the second-order spin-orbit interaction (extended to the entired'" configuration) for the relative dipole strengthsand for the polarization effects under stresses. Itis shown in Sec. IV that all experimental results(stress and Zeeman experiment) for Mn" in ZnSeand in cubic ZnS are correctly described by as-suming an almost complete quenching of the first-order spin-orbit interaction. Finally, the couplingsof the lowest 'T, and 'T, states of Mn" in ZnSeand ZnS are compared in Sec. V.

II. EXPERIMENTS

A. Samples and apparatus

The origin, the concentration, and the crystal-lographic structure of the ZnSe: Mn and ZnS: Mnsamples used in our experiments are identical tothose described in preceding papers. '" Thesecharacteristics together with the dimensions andorientations of the crystals are given in Table I.

Owing to the small absorption coefficient of the'A. , 'T, band of Mn" in ZnSe and ZnS, we per-

10

Zn Se:Mn

6A1 4T1

Ell['I101. P=o

T= 1.7K

1N59 100 17050

Energy {cm')

10crn1

Ell [HO]

P = 17.108dyn/crn2

Pii [OOt]

«leo Energy (cni )

FIG. l. (a) Excitation spectrum of the fluorescentT& level of Mn" in ZnSe; (b) uniaxial stress effect

for the maximum applied pressure (P )}[001]) and (c)polar'ization effects. In (a) the linewidths of the twozero-phonon lines are 4.5 cm '. The phonon assistedline appears at 18075 cm ~. In (b) the linewidths of thezero-phonon lines are, respectively, 6 cm" ~ for thetwo lines at lower energy, and 4.5 cm" ~ for the two linesat higher energy. The splittings of the zero-phononlines and of the phonon-assisted line are equal to70 cm '. These spectra. were obtained for the electricfield F. of the excitation light parallel to a [110]axis.The vertical lines represent the calculated relativedipole strengths as given by the model of Secs ~ III and

IV. The broken-line spectra (c) were obtained for theelectric field of the excitation light parallel to a [llo]axis. The continuous line spectra correspond toE(( [001]. The vertical lines give the positions and thecalculated relative dipole strengths of the zero-phononlines. Only two lines are observed when E ~) [001] whilefour lines appear when E )) [110].

1B

JAH ELL

(a)

T HE F LAHORE EL OF

1602

Energy (cm')"

Appliedi pressure (1O['dynpcrtP)

Zn Se; Mn Pl [110)

6 — 4T

T- )7K

B. Ex im+nta]

The absorpt 1On S eCt~ero aPPlied

a of Mn

&ie»essure and fonSe for a

or the max, P=1VxlO' d n

c rum.

ag

'hnes are

in our exin isagreem

per1ment and 20ent of Lan

cm 'idR' ht

-ass sted 1 ise is observed at j.8 075 cm '

e is appli d along a [OO

onon line is spl't '1 into two c

1 axiscomponents.

(c)

Energy(cm4)l

ZnSe: Mn. Pll [111)

T =1.7K

rmed exc t1 ation ex e .

spectra wep 1ments.

re obtained b~ e exc1tation

pectra at va ~ bning the

tecting the 1»twith a dye ].ase

em1ss1on b~'g ~mitted by the

.r

CHand The excit

e tai] of the

H5 lase»sso '1 tion light js

ed by Coher (model 4gO

rhodamine lm)nt Radiatio~

is filtered b1ght emitted bThe 1.

n, the dye b~

e1ng

y an 1nterference fy the crystals

bandwidth: 26O' r (Matra HDL

e spl1ttings anr perm1tted m

Thand sh1fts of the

measuring

S Wereer»eS.

he experimente absorption 1'

ystals beinp rformed at 1.7

pressur' mersed in 11 u

' K the

e was appl dq ld hel1um. Th

1e as prev' sly described

A

1BND.

ggied pressure S d c( yn/cire)

0 1 2 6 9 1

ZnSe: Mn. S 1'

2 3 4 5 6 9 102 6 7 B 9 10

s ' ts in terms

A

s of the applied

ppiied pressure d m )

en in Sec. IV.

1

yn/c

aine E [( [110]ai . . The curves are[ l.

m the values of the pa-

106p

T- 1.7K

PII [1tp,

E II j11P(

PAg, 8Oy, ~

Energy (~~) Zn S . ldn P ll [110]

%,—4T

T -1.7K

17

ZnS. Mn

SA-~T1 2' T-1.7K

17000

17890

17950 Enact'gy Iqm 1)

Flo 3 c«a«on spectrum o 4

and 17890 cm-1o-p onon lines at 17900 cm-1

line at 17 905 cm- th fin cubic sites.

e wo lines centered at 1801 -1

zero phonon lines of M++ ~

5 cm are

rePresents the un'in stackin' g aults. The insert

umaxial stress effect on tli of " bin cu ic sites: Pt[ [110), EI) )ll0).

An overall view of thmaximum applied

e absorption s ep ctrum for there pressure (P=17X10' d

i . 1(). o ofo two lines sep-y cm ' are observed in this fi

Clear polarization ffin is figure.

'n e ects are observed

the smallest applied ress — . nr.e pressure (P=1.4X10' d n/m . igure 1(c) shows s e

P(~[100] and forspectra obtained for

and for the electric field of the e1 ht 11 1 to [100' axis and to a 110

The shifts and spl'ttare represented in t

p i ings of the zero--phonon lines

in Fig. 2. No splitt'e in terms of the ap liedp ie pressure

o sp itting and no broad

yn/cm [see Fig. 2(c)].In the case of ZnS:Mn, the ab o p o p

are identical to those re orrnier et al. (F' 2'

ose reported by Fou-ig. 3j. Two zero- ho

observed at 1V 90-p onon lines are

0 and 1'l 890 cm ' (these valose reported by Zigo

e5 cm ' and 17891 cm 'groups of lines cent d

h bn ere at 17990 and 1

associated with the zeasso ' t d' e zero-phonon lines of

n centers in stacking faults.The insert in Fig. 3 sh nc

pl&ed pressure P(~ ll ro-s ows the influenc

'gu r p e ents then sp ittings of the zero-

terms of thezero-phonon lines in

o e applied pressure.these lines '

The behavior ofs is analogous to that of Mn" '

the sense that each l 'peac ine is split into tw

ents. For I (([ill]ing of the cubic lines h, e o

, we observed a sli ht

ic ines, however, due to th

mp e used for this experiment (see

1788

17870.

0 4 5 i 7 8 10 11

Applied pressure (10 dynrcm')

Energy (cm')(b)

17010. ZnS: Mn. P [111]

T= 1.7K

17800.

17880.

Table I thishis broadening could be dueorientation of th e crystal.

e ue to a mis-

All these effecects clearly indicate that th

strong coupling of the 'T rel axed levels to a F.

e ler active mode.Uniaxial stress experiments performed o

zero-phonon lines of Mn" in stac 'on the

g ( 'g.a the two lines at 18012 and 18022

cm ' are split into two corne shifts and splittings being identical to those

17870.

5 15

Applied pressure (10 dyn/crnr)

FIG. 4. ZnS: Mn. Splittin s andgs o n in cubic sites in terms

appl&ed pressure P )( [11 )lines represent th h'

0 and P) ill ]. The dotteden e shifts due to the e A st

curves are drawn f h&) strains. The

wn rom the values of the

given in Sec. Pf.e parameters

JAHN-TELLER EFFECT IN THE FLUORESCENT LEVEL OF. . . 1061

not split but shifted, while the two other lines aresplit into two components.

III. JAHN-TELLER EFFECT

p 26.10 dyn/cm2

()o Errrrr&ry(cni')

FIG. 5. ZnS:Mn. Uniaxial stress effects on the zero-phonon lines of Mn" in stacking faults. The behaviorof the lines centered at 18015 cm ' is identical to thatof the lines of Mn" in cubic sites (for P=2.6xl0 dynjcm, the splittings and shifts are identical to thosereported in Fig. 3 for the same pressure). The be-havior of the four lines centered at 17990 cm ~ is morecomplicated. The two lines at 17 983 and 17992 cm ~

are split and shifted, while no splitting of the two otherlines is observed.

observed for the cubic lines. The behavior of thefour lines centered at 17980 cm ' is more compli-cated; the two lines at 17983 and 17992 cm ' are

A. Jahn-Teller coupling to an E vibrational mode.

Energy levels in Td symmetry

Since the case of a strong coupling to an E vibra-tional mode has been extensively studied by Ham, '"we will only recall the main results of the theoryand give the relevant formulas for the lowest T,level of d' ions in cubic symmetry.

The first-order spin-orbit interaction X so actingon the fundamental vibronic state can be replacedby the following equivalent operator X'so acting onthe electronic states:

X~'& =e ~T" Xso SO y

where E,T is related to the strength of the Jahn-Teller coupling Vz and to the angular frequency ofthe effective mode of E symmetry by

F.» = V'/2g&o',

p. being the mass of the effective phonon.The matrix elements of the second-order spin-

orbit interactions in the fundamental vibronic levelare given by

&'T„,ool x'sole, ~, oo& = — ~' 2 &'T,~ I x„l'T„&&'T,& I x„l'T„&

k4V

j I xs&)lss+ h & ( s+

lsI xs&) I T

W( T,) —W( +'h)

for the diagonal matrix elements, and

('T„,ool l' oooo)y= —(~o')('r„lro„l'r j('r„lro„l'r,.)W(oT, ) —W(' "h)

for the off-diagonal matrix elements;oo

f, = e G(x), with x=3F. ,T/Ro, G(x)=g, , and f, = e *G(sx).yr

Following the method previously described, ' the diagonal and off-diagonal matrix elements of Xso (in thereal tetragonal component system 's"hMO defined by Griffith" ) were calculated in terms of the classicalmatrix elements in Td* by the following relations:

« I xlolr. &„=l «.I xylo lr.&+ ~«.(l)I x' lr.(l) & + l &r.(l) I xl lr.(~)&+ l &r.(l) I xl lr. (l)&,

«.Ixsolr, &c; = l&r, lxsolr, &+i «.(s)lxsolr. (s)&+ h&r. (l)lxsolr. (l)& -i «.(-:)Ixsolr.(s)&,

(r, (-,')I x'„Ir,(-', )&„„=~ (r, lx'„Ir, &+ —'(r,

lx'„Ir, &

+ P&r, (-', )Ix'„Ir,(-', )&+ ~&r, (-'.)Ix'„Ir,(-,')& ——;,&r, (-', )Ix'„Ir,(-'.)&,

(r,(-', )I x'„lr, (-'. )&„„=~&r, lx'„Ir,&+ —,', (r, lx'„Ir, &

+ ' (r (')lxsolr (')&+ &r (')lxsolr (')&+ " &r (')lxsolr (')&

1062 R. PARROT et al. l7

and

«.(-')Ise'oIr. &-')&,;., = —~&r.l36lolr. &+ ~«.I36'oIr. &

—.,«.(l)I36solr, (l) &+.,«,(l)136solr.(l)&+ „&r.(l}13elolr.(l) &,

««I &',o I «~'&.„~;~= &«&I 36'sol f s J'& —&«& I 36sol «&'&s.s ~

In the case of the lowest orbital triplet level 'T,of a d' ion, 39 multiplets are involved in the cal-culation of the second-order spin-orbit interac-tion; they are" 'A„'T, (3), 'T,(3},'E(2), 'A, (1),'T, (8), 'T, (10), sE (7), 'A, (4) (the numbers in paren-theses are the numbers of multiplets of given spinand symmetry) Of.course, the contribution of thesecond-order spin-orbit coupling between differentelectronic states is identical to that obtained by themethod of equivalent operators used, for example,by Koidl. '

B. Uniaxigl stress effects

»r pil[l&o], pll[100], and %II[III], the nonzerolinear combinations of the strain tensor are, re-spectively, '6

s (A,) = (s„+2s»)P,

e( „)=-(s„-s»)P, e(Tst)=ss«P;e(Aq) = (sq~+s»)P) s(E„)= 2(sqq -s»}P;s(A,) = (s»+2s»}P, e(Tss) =c(T») =s(Tst) = ss«P, -where the s,&'s are elastic compliance constants.

In the case of a strong Jahn-Teller coupling to anE vibrational mode, the matrix elements of the vi-

brations'n,

V(T„) (s=$, q, p) of the crystal field arereduced by a factor e ~» ' and will be neglected.

I

However, the matrix elements of n. V (E„) are notaffected by the coupling to an F- mode. The effectof E„strains mill be described in the following interms of the parameter:

C. Polarization effef'. ts under pressure

As in the case of the lowest 'T, level, '" numer-ous schemes contribute to the dipole strengths ofthe fine-structure lines of the lowest 'T, level.However, being primarily interested by the rela-tive dipole strengths (RDS) we will use an equiva-lent operator to calculate these dipole strengths.For electric dipolar transitions, the simplestequivalent operator relating the A, and '7, levelsls

~(ll) 2 g7(11)3

where the 8"s are mixed tensor operators of rank1 for spin and for the orbital momentum. By usingthese operators, the polarization effects can besimply calculated in terms of the components (f7')of the eigenvectors of the matrix describing thestress effects, for example. The RDS's

Q(E II[001]), $(E II[110]), and $(EII [110])corres-ponding, respectively, to light polarized along a[100], [110], and [110] axis are given by

@(E II [ooi])= (I/z') [ I (I/~s) (r, —,') —(I/~is) (r, —,', —,') + (2/~is) (r, —,', —,') I'

+ I—(2/v 15)(I', —') +—'&3 (r, -'„--',) —(I/sv 3)(r, -'„--,') I'

+ I(2/~15)(rs s) + (I/5~3)(r. s s) + (I/5~3)(r. s~ s) I'j

o(E II [»0])=@(EII [Iio])= (I/2N') [I (~2/&3)(1', -') + (I/M30)(r, -'„-') —(~2/~15)(r, -'„-') I'

+ I (I/~io) (r, -'„--',) —(W2/Ws) (r, -'„--',) I'

+I -(W2/Mls }(I' —) +—', (v 3 /W2) (I', —', ——') + (v 2 /5&3) (I' —', ——')

I

+ I-(~~/Ws)(r, -'. )+(I/vY)(r. s )I'

+ I( v 2/~15)(I', s) + (I/5&6)(I', -'„s) —(W2/5&3)(rs-'„s) I'

+ I-(~2/~5)(r, -') —(I/~2)(r. l --') I']

The above formulas have been obtained by neglect-ing the small splitting I',('A, ) —r, ('A, ) = 3a of thefundamental level. (3a = 23.6x 10 ' cm ' for Mn"in's ZnS and 59.1X 10 ~ cm ' for Mn" in's ZnSe. )

They are valid in the case of a negligible, a medi-um, or a strong Jahn-Teller effect. [The import-ant problem is to determine the relevant (t7J)'s.]

In the case of a negligible or strong Jahn- Teller

JAHN-TELLER EFFECT IN TH'E FLUORESCENT LEVEL OF. . . 1063

TABLE O. Nonreduced first-order {superscript a) and second-order {superscript 5) con-tributions of the spin-orbit interaction to the splittings and shifts of the 47~ level of Mn++ inZnSe and Zns. Spin-orbit parameter: f3~ ——

, 300 cm '. The T~ level is taken as reference.

1 s {a) I's {5)

I'7

I'sh)

-42.6'-i0.4"

29 6&

y7 06& 23 8& 2.53'

+25.6'-25.8'

~s { )

~s 4)

-44.25 -10"+26.55 -29.2

-i7.7'-23.5' -~-2.62"

+ 26.55 —25.3"

effect, the above formulas give the followingRDS's:

N['a, - r, ('T,)] = 48, @['a,- I',('T,)] = 20,

e['W,- I', (-', )('T,)] =83, @['a,- r, (-', )('T,)] =22

for the transitions from the 'A, level to the fine-structure lines of a 'T, state in T~ symmetry (P= 0).

IV. COMPARISON WITH EXPERIMENTS

For Mn" in ZnSe, the electronic structure ofthe lowest 'T, level was calculated from the foQow-ing values of the Racah parameters and of the cubicfield parameter". 8 = V40 cm ', C=2V40 cm ',and Dq = -405 cm '. The nonreduced first-orderand second-order spin-orbit contributiogs aregiven in Table II, and the dipole strengths aregiven in Sec. DIC. Qbviously this structure is indisagreement with experiments.

As suggested by the experimental results, wewill now consider a strong coupling to an ~ vibra-tional mode. In that case, f„ f~, and e" are ap-proximately zero and the theoretical spectrum isreduced to two "zero-phonon lines" correspondingto transitions from the 'A. , state to the almost de-generate vibronic states:

~I'„00) and (3/&10)~I', (—'), 00)

-(I/4 10)( I,(-,'), 00)

for the states at lower energy, and

~I'„00) and (I/~10 ) ) I', ( —'), 00)

+ (3/v 10)II'8( a), 00)

for the states at higher energy. The splitting ofthe two "zero-phonon lines" is due to the nonre-

duced matrix elements of the second-order spin-orbit interactions. Taking into account all therelevant multiplets of the d' configuration, thissplitting is calculated to be 7.4 cm '." (This valuewas obtained by nulling f„f„and e 't' )The .bestargument in favor of this model is ttutt it predictscorrectly the uniaxial stress effects.

The pressure effects reported in Fig. 2 werecorrectly fitted by taking Q z„s„=4800 cm ' per unitstrain(see Table 1II), the shift commonto all linesbeing 17 800 cm 'per unit strain. (The used elasticconstants were those of the pure crystal determinedby Berlincourt et al. ' at, 25 'C: s yy 2 26 x 10 'cm'/dyn, and s» =-0.85 x10 "cm'/dyn. )

The calculated RDS's for a zero applied pressureand the polarization effects under pressure re-ported in Fig. 2 are in good agreement with experi-ments. In fact, it is necessary to be aware of thedifferent linewidths of the two lines at higher ener-gy and of the two lines at lower energy before com-paring the calculated RDS's to experiments. Theslight broadening of the lines at lower energy isobviously due to the greater sensitivity of theselines to uniaxial strain (see Fig. 2).

In the case of Mn" in ZnS, the chosen values of8, C, and Dq are 8 = V30 cm ', C =2880 cm ',and Dq = -420 cm '. ' The first- and second-orderspin-orbit contributions are given in Table II. Inthe limit of a strong Jahn- Teller coupling to an Evibrational mode, the calculated spectrum consistsof two lines separated by V.V cm '." Of course thewave functions of the fundamental vibronic statesare identical to those of Mn" in ZnSe.

The shifts and splittings of the lines in terms ofthe applied pressure (Fig. 4) are correctly fittedwith 8 = 5400 cm ' per unit strain, the shift com-mon to all levels being 23 600 cm ' per unit strain

1064 R. PARROT et al.

(s»=1.786X10 ' cm'/dyn, s»=0.685x10 "cma/dyn at 77 K).

As pointed out in Sec. II 8, the behavior understress of the two lines centered at 18015 cm ' dueto the Mn'" centers in stacking faults is identicalto that of cubic centers (same shift and same 8parameter). The Mn" centers giving the fourzero-phonon lines centered at 17990 cm ' are ob-viously not as strongly coupled to the lattice as thecubic centers. Actually, the nature of these Mn"centers is not well known enough to permit an an-alysis of the Jahn-Teller effect.

The experimental data obtained on cubic centerssupport the hypothesis of a strong Jahn-Tellercoupling with an E mode made by Fournier et al.in order to explain the Zeeman splitting aniso-tropy of the 'T, relaxed excited state. ' Although thepresent formalism carried in cubic symmetry isparticularly able to express the wave functionswhen going from intermediate to strong coupling,the stress data could also be easily interpretedusing the tetragonal anisotropic centers in cubiccrystals formalism" in order to represent, as inRef. 9, the three tetragonal distortions in the sta-tic limit.

V. COMPARISON OF THE JAHN-TELLER EFFECT IN

THE LOWEST 4T1 AND 4T2 STATES OFMn++ IN ZnS AND Zn5e

Although the adopted structure for the fluores-cent 'T, levels of ZnSe: Mn and cubic ZnS: Mn per-mits a very good interpretation of all experimentalresults, several difficulties arise when comparingthe Jahn- Teller effect in the lowest 'T, and 'T,levels. [For the lowest 'T, levels of Mn"' in ZnSeand ZnS, the values of the Huang-Rhys factors Sand of the strengths of the couplings to an E vibra-tional mode are'. S('T,) = 1.2 for ZnSe; S('T,)= 0.6 for ZnS; V~ = A. z„q, = -3650 cm for ZnSe: Mn;and &s =Azns =-3100 cm ' for ZnS: Mn. j

In fact, in the case of a very strong Jahn-Tellercoupling, uniaxial stress experiments alone do notpermit a precise determination of the strength ofthe coupling. Stress and magnetic circular dichro-ism experiments performed on the zero-phononlines and on the broad bands could have given theHuang-Rhys factor S and the frequency of the ef-fective phonon. Unfortunately, given the small ab-sorption of the 'A, - 'T, bands, the dichroism ex-periments performed on the crystals at our dis-posal failed to give an experimental estimate for S.

However, it is possible to evaluate S for thefluorescent levels by assuming that the nearest-neighbor cluster model is valid and that the fre-quencies of the effective phonons are equal in the'T, and 'T, states (so that Scc Vs). From these

TABLE III. Matrix elements of the pressure-inducedcrystal field for P)[[100]. The c." (t vt) and P' (t ~J)are, respectively, the diagonal and off-diagonal {in Td*}matrix elements of the spin-orbit interaction. The para-meter 8 is defined in Sec. III.

12 s(2) I's (-,')+ y

r, +~I's (-'2) + a

I's (y) +-'

2

{-)+ys(y}+ 2

7 2

O.' (I 7)

+(1/2v 5) 8'[I s(-', )]+ &8

I' (-', ) &

~(3/2v 5) 8&'~l s (p)]- 5 8

+(3/2v S) 8p'- -' 8

10

~ tl.s(25}]-~2 8

I', (&),+-+ {1/2&5) 8

(5)] ~2 8

hypotheses and the values of S and V~ for the 'T,states, we get S('T,) =2 for ZnSe: Mn, and S('T,)= 1.8 for ZnS: Mn. These values represent a lowerlimit of S to account for the strong quenching of thespin-orbit splittings in the studied fluorescent lev-els; in fact, they are in agreement with a crudeestimate of the lower limit of S obtained from theratio of the unquenched spin-orbit splitting to thelinewidth [this estimate gives S('T,) - 1.8 forZnSe:Mn, and S('T,) 1.9 for ZnS: Mnj. Highervalues for the Huang-Rhys factors in the 'T, statescould be obtained by assuming that the frequenciesof the effective phonons are smaller in the 'T,states than in the 'T, states; however, no experi-mental proof of this hypothesis is actually avail-able.

Finally, the coupling parameters for the 'T, and'T, states have been calculated in a crystal-fieldmodel (see Appendix). We obtained

8z„, =-604 cm ' (exp: -5400 cm '),

Sz~, =-484 cm ' (exp: -4800 cm ')

for the 'T, levels, and

Az„, =-1757 cm ' (exp: -3100 cm ')',

&znse = -1475 cm (exp: -3650 cm )

for the 'T, levels. These values show that thecrystal-field model gives no more than an order-of-magnitude agreement between the calculated andthe measured coupling parameters so that thismodel is of little help in'predicting the strength ofthe coupling to an E vibrational mode. Further-more, this model predicts that the coupling of the'T, state to the T, vibrational modes should bestronger than the coupling to the E mode in thecase of ZnSe: Mn and ZnS:Mn, although the exper-

17 JAHN-TELLER EFFECT IN THE FLUORESCENT LEVEL OF. . . 1065

imental results show that the coupling to the T,modes is negligible.

and

VI. CONCLUSION where

As a preliminary result, the zero-phonon linesof the fluorescent level of Mn" in ZnSe were ob-served unambiguously for the first time. Thenfrom a very detailed experimental study understress of the fluorescent 'T, states of Mn" inZnSe and ZnS (cubic centers) it was shown directlythat these states are strongly coupled to an E vi-brational mode. A structure for the observed lineswas established permitting us to interpret all ex-perimental results (splitting under stresses, rela-tive dipole strengths, and polarization effects un-der stresses).

A comparison with the results previously ob-tained for the lowest 'T, states of Mn" in ZnSeand ZnS, ' has shown that the structure of the 'T,and 'T, states are very different, although thespectra of the zero-phonon lines (for 8= 0) areidentical in the case of ZnSe: Mn and differ only bythe energy separation of the zero-phonon lines inthe case of ZnS: Mn. This comparison led us todetermine a lower limit for the Huang-Rhys param-eters in the fluorescent levels of Mn" in ZnSe andZnS, and to emphasize the problems encounteredwhen trying to compare the Jahn-Teller couplingsin the 'T, and 'T, states.

ACKNOW( LEDGMENTS

Thanks are due to Dr. M. D. Sturge for a verycritical reading of the manuscript. We are alsoindebted to Dr. R. Romestain for giving us theZnSe: Mn crystals used in this work and toN. Machorine, A. Vandenborghe, and P. Villermetfor cutting and polishing the samples used in ourexperiments.

APPENDIX

The coupling parameters for the 'T, and 'T, lev-els are defined by

nV(g„)=~ D +nB [D —(v 7/v 10)(D,' +D', ] .The D~ ~'s are electronic operators defined in termsof radial integrals and spherical harmonics by

D& &= [4w/(2k+ 1)]'~'&3d~r'~3d) y'i"&

The ~,'s are stress-induced crystal-field param-eters linear in e (E„).

By writing the 'T, and 'T, states in terms ofspectroscopic terms, we obtain

8 = -(41 el/3~5)r(»+fi)X [~ /f (~,)'] &3dlr'Il&

and

A =+ (41 eI /31&~)P'(2~'+ ~& r')

x ([6nB,/e(Z„)] &3dlr'13d&

—[~,/~ (E.)] &3dlr'I3d&]

where the mixing parameters n, p, y and n', p', Z'

are defined by

I'T,& =~I'P& P+l'&&+rl'G&

I'T2& = ~'I'D& fi+'I'+& + r'I'&& .By evaluating ~, and ~B, in a point-charge

model restricted to the nearest neighbors we get

».= -I eI (3/3ft')e(&. )

and

~,=+ ~e~(40/3'if'')~(Z„),

where R is the nearest-neighbor distance.The values for 9 and A given in Sec. V were ob-

tained from the following data: &3d~r'~3d&= 5.513ao (ao is the first Bohr radius), &3d~r'-'~3d&

1 54 for I ++ R 4 43 3 0 112 39= 0.200 99, y' = 0.973 13 for ZnS: Mn, and R=4.638@ . ~'=0.10462, P'=0.19515, and y'

=0.97518 for ZnSe: Mn.

*Equipe de Recherche associate au CNRS.fEquipe de Recherche No. 5 du CNRS.~See, for example M. D. Sturge, in Solid State Physics,

edited by F. Seitz and G. Turnbull (Academic, New

York, 1967), V'ol. 20; A. Abragam and B. Bleaney,Electron Paramagnetic Resonance of Transition MetalIons (Clarendon, Oxford, 1969); R. Englman, TheJahn-Teller Effect in Moleclles and Crystals(Wiley, New York, 1972); F. S. Ham, in Electron Para-

magnetic Resonance, edited by S. Geschwind (Plenum,1972).

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~~In Hef. 6, p. 3753, replace the sentence: "The com-plete calculation must be performed by taking intoaccount all 35 relevant multiplets T,{3), T2(3), E(7),'"T&{8), T&(10), A &(3), A &(1) of the d configuration

. . ." by "The complete calculation must be per-formed by taking into account all 37 relevant multi-plets 4E{2), T({3), T2(3), E(7), T i(8), T2(10), A2(3),A&(l) of the d configuration . . . ."

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