The center of orthorhombic symmetry in chromium doped Bi12GeO20 and Bi12SiO20 single crystals

J. Pbys. Chem. So/ids Vol. 45. No. 819. pp. 887-896. 1984 Printedin the U.S.A.

am-3697/64 53.00 + .oo Pcfgamoo PIed8 Ltd.

THE CENTER OF ORTHORHOMBIC SYMMETRY IN CHROMIUM DOPED Bi,,GeOm AND Bi,,SiOzo SINGLE CRYSTALS W. WARIEY%KZ and H.

SZYMCZAK

Institute of Physics, Polish Academy of Scieuces, 02468 W&saw, Poland (Receioed 13 Jmruary 1983; accepted in revisedform I December 1983) Abatmct-The absorption spectra of Bi,,GeO&r and Bi,,SiO,-Cr crystals were measured as a faction of temperature. A sharp no-phonon line and its vibrational structure were found. The width and the position of the sharp line as a function of temperature are analyzed on the basis of the theory of thermal broadening and thermal shifting due to Raman scattering processes. Uniaxial stmss measurements indicate that the center related to this line has orthorhombic symmetry. It is shown that there are interstitial positions in the crystal lattice of orthorhombic symmetry. It is argued that the center associated with the observed absorption is a chromium atom at such an interstitial position. INTRODUCMON

In the previous papers[l, 21 it was shown that in chromium doped Bi,,GeO~ (BGO) and Bi,,SiOzo (BSO) Cr impurities are located in the tetrahedral position. The absorption bands observed in these crystals were explained as due to the electron transitions in 3d” configuration, n being different for the state before and after donation. Near to liquid helium temperature a characteristic sharp line with pronounced phonon replica was found. The temperature dependence of these absorption spectra differs from that of d-electron absorptions. It was believed that the absorption spectrum of the sharp line and its phonon structure are due to tmnsitions in centers of unknown origin which involve chromium. The present paper presents the results of more detailed measurements of the sharp absorption line and its phonon replica, the temperature dependence of the absorption and also the results of uniaxial stress experiments. It is argued that the center responsible for the absorption is a chromium atom in the interstitial position of orthorhombic symmetry. Therefore in chromium doped bismuth germanium oxide and bismuth silicon oxide crystals, chromium is located in the tetrahedral position as well as in the interstitial position of orthorhombic symmetry. EXPERIMENTAL RESULTS

(a) Absorption measurements

Absorption of BGO-Cr and BSO-Cr measured at 1.8 K in the range from 9500 cm- k is shown in Figs. 1 and 2, respectively. Wavelengths of the observed line and bands are listed in Tables 1 and 2. Numbers of the consequent lines in the figures correspond to the numbers listed in the tables. The spectra of BGOCr and BSO-Cr differ only in small details. The spectrum of BSO-Cr is shifted compared to the spectrum of BGO-Cr to higher energies of about 30 cm-‘. As one can see from Tables 1 and 2 there is a

reasonable agreement between AE = EN - EO and the phonon energies observed in Refs. [3] and 141. The temperature dependence of the absorpof BGO-Cr in the range tion spectrum lO,OOOcm-‘-13,OOOcm-’ is shown in Fig. 3. The absorption band at 12,150 cm-’ is interpreted (see WardzytMi et al. [Z]) as due to 3A2-3T, [“a transition in Cr4+ ions. This absorption does not depend considerably on the temperature (see Fig. 3). The spectrum of the sharp line and its phonon replica, however, depend very much on the temperature. The temperature dependence of this spectrum in the vicinity of the zero phonon line is shown in Fig. 4. Absorption of the zero phonon line for different temperatures is shown in Fig. 5. The half width of the absorption line increases with increasing temperature. Th& position of the line is shifted toward lower energies with increasing temperature. According to the theory of thermal broadening of sharp zero-phonon linea[5], taking into account only Raman scattering processes, one can express the half width of the line as a function of the temperature by the equation:

(1) where Ho = half width of the line at T = 0 K, To = effective Debye temperature, and (Y= const. The dependence of the half width of the line on the temperature for BGO-Cr is given in Fig. 6. The solid line in this figure gives the best fit to formula (1) with the following fitting parameters: Ho = 1.7 cm-‘, 6 = 270 cm-‘, TD = 100 K. According to the theory of thermal line shifts [I the energy of the line as a faction of the temperature can be expressed by the following equation: (2)

887

W. WARDZYI;ISKI and H. SZYMCZAK

888

9-

l-

s-

3

1

c

I I I I II I II I II I I 01$9 11 I51719

%a

9600

il

loa

h cl'

Fig. 1. Absorption spectrum of no-phonon line and its vibrational structure in Bi,,GeQ,,-Cr crystals.

Fig. 2. Absorption spectrum of no-phonon line and its vibrational structure in Bi,,SiO,-Cr crystals.

Table 1. Energy of observed lines in BGO-Cr Line number N 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Energy cm-

Phonon energy

Raman[3] IR[4]

AE=EN-E,

cm-’ 9621 9657 9667 9671 9676 9679 9687 9691 9707 9745 9772 9808 9841 9848 9856 9866 9878 9920 9925 9970 9995 10,140 10,215 10,260 10,350

no-phonon line 36 46 50 55 58 66 70 86 124 151 187 220 227 235 245 257 299 304 349 374 519 594 639 729

The measured thermal line shift for BGO-Cr is shown in Fig. 7. The solid line is this figure gives the

best fit to formula (2) with the following parameters: I& = 9620.9 cm-‘, LY= -80 cm-‘, To = 100 K. The product of half width H and maximum absorption coeffmient amsx of the line determines the centers concentration. The dependence of the product on the temperature is given in Fig. 8. As one Ho,, can see, near the liquid helium temperature the

-

-

46.4 48.1 ; 52.4 54.6 57.5 67.7 89.4 124.0 153.0

123 154 190

236.5

232

305.0

254 281 303 355 372 600

concentration of centers is constant and then de creases rapidly with increasing temperature. Assuming that this decreasing of the centers concentration is due to thermal dissociation of the center, (Ha_), will be given by the following formula: (RZu_)r = (I%_&(1

- eeCwKm)

(3)

where AE is an activation energy. The solid line in Fig. 8 is given by formula (3) with (He,,JO = 19.5cm-*, AE = 25 cm-‘.

The center of orthorhombic

889

symmetry in chromium

Table 2. Energy of observed lines in BSO-Cr Line number N 0

1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ;: 23 24

Energy cm-’ 9651 9684 9690 9697 9700 9706 9717 9721 9736 9774 9805 9831 9873 9881 9887 9902 9930 9943 9954 10,008 10,026 10,175 10,260 10,310 10,379

AE=E,-E.

no-phonon line 33 39 46 49 55 66 70 85 123 154 186 222

230 236 251 279

292 303 357 375 524 609 659 728

Phonon energy Ban=n$ fN41

46.1

50.6 53.51 58.0 68.0 89.2

89

185.0

185

238.0 252.0

237 257

282.1 289 352.3 372.6

353 374 609

Fig. 3. The temperature dependence of the absorption spectrum of Bi,,GeO,~r in the range of 1o,OoOcm-‘-13,OOOcm-1.

Fig. 4. The temperature dependence of the absorption spectrum in the vicinity of no-phonon line.

(b) Uniaxial stress measurements Samples used for these measurements were oriented using X-rays. Stress was applied along [1001, [11 l] and [l lo] directions. The experiment was carried out at 4.2 K. Stress was applied to the samples using the arrangement described previously[a. Since the crystals are optically active and rotate the plane of the polarization, the polarization was set not exactly perpendicular or parallel to the stress direction, but

formed a small angle cp with these directions. The angle rp was selected according to the sample thicknesses to minimize the unwanted component of the polarization. The optical rotatory power for BGO at 962Ocm-‘wasmeasuredtobep=6.75deg~mm-’. Therefore for typical (in these measurements) sample thickness of 2-3 mm the optimum angle was P = (p-t)/(2) = 6-10 deg. The results of the splitting of the line by uniaxial

W. WAKOZYI+SKI and H.

890

Fig. 5. Absorption of no-phonon line at different temperatures.

SZYMCWK

2*s! ,(,,,,,

2.0

.05

L 1

.I

Fig. 8. The dependence of H~Q, on the temperature for 9621 cm-’ line.

IO

I

20

I

30

I

40

I

50

OK

Fig. 6. Thermal broadening of 9621 cm-’ line. Solid linetheory with & = 270 cm-‘, T,, = 100 K.

stress for stress applied paralled to[lOO] direction are shown in Fig. 9, for stress parallel to [l 1l] direction in Fig. 10 and for stress parallel to [l lo] direction in Fig. 11. The characteristic feature of the observed splitting pattern is the pronounced broadening of some components when the stress is applied parallel to [lOO] direction and the only very small shifting and ahnost no broadening of the line when the stress is applied in [l 1 l] direction (see Fig. 12). Also for stress applied parallel to [l lo] direction, the low energy component is much sharper than the higher energy component although in this case the picture is not so clear because of the overlapping of both components allowed for both polarization. DISCUSSION

As one can see from Fig. 13, at 5 K the shape of the no-phonon line observed in BGO-Cr is closer to a Lorentzian than to a Gaussian as expected for Raman broadening. However the small wing deviations seem to indicate some influence of a random distribution of strains.

cm’ 9625

i/i

PII i?ool

4 11

+

9615 *I

Fig. 7. Thermal shift of 9621 cm-’ line. Solid line-theory with 01 = 80

cm-‘, To =

100 K.

Fig. 9. Splitting of the 9621 en-’ line by uniaxial stress applied parallel to [lOO]direction.

The center of orthorhombic

L

9620

l&/cd

200 400

Fig. 10. Splitting of the 9621 cm-’ line by uniaxial stress applied parallel to [ 11l] direction.

pll El01

&’

1

II 1

891

symmetry in chromium

The constants a and E are related to the strength of the phonon-impurity interaction. Fbr sharp optical transitions of 3d ions in ruby and MgO a and a’ were found, depending on impurity concentration and nature of the center, to be from - 15Ocm-’ to -4OOcm-‘[7l and from 1681cm-’ to 415cn-‘, respectively. These values should be compared with a = -8Ocm-’ and CT=27Ocm-’ found in the present work for BGO-Cr. The BGO-Cr values are closer to values found for sharp optical transitions of 4f ions (E from 3Ocn-’ to 31Ocm-‘)[8]. The results of uniaxial stress measurements can be explained assuming that a splitting is brought by the removal of the orientational degeneracy of the anisotropic center. The theory of such a splitting was developed by Kaplianski[9]. Because for stress applied in [loo] direction we observed 3 components and for stress in [ 11 l] 1 component, the center should be of orthorhombic II [loo] C, type [lo]. According to this theory the relation between the energy change A and the strain uti is given by: A = A,,a,, + AyyayV+ Azzczz + 2(A*J&y + A#,,

Fig. 11. Splitting of the 9621 cm-’ line by uniaxial stress applied parallel to [l lo] direction.

-

p-0

Eli P EIP

n A,

,/’

.... El

P

(4)

The piezospectroscopic tensor for the orthorhombic II [lOO] C, center will have the form: A,

0

0

A2

0

0

0

A3

pit [IO01 ~-565~Y~,?

+ AZXG).

0 (9

--- ELP

For stress applied in [loo] direction components be given by:

will

I’

A, = Ag observed for polarization I to the stress, A2 = AQ observed for polarization 11to the stress, As = Ag observed for polarization J_ to the stress, p

is the compressive stress. For stress applied in [ll l] direction A = (A, + A, + A,)p/3 observed for both polarization and for stress applied in [l lo] direction if light is propagated along [ 1001 direction Fig. 12. The splitting pattern for p([ [lOO] and pII [Ill].

A, =(A, +A,$

42

=

(A2

+

A&

/I“L 1 : : ;

: I

:

I

:

:

51:

j

/j

___4.. , ”

9615

6, \ .‘._

_-:,*‘* j *

.\

i

”

observed for both polarization. Solid lines were drawn in Figs. 9-11 according to the theory with the following parameters:

i

t

A, = +0.0112

cm-‘/kg/cm2

A2 = -0.0132

cm-‘/kg/cm2

As = -0.0035

cm-‘/kgjcm2.

- .I_

“.‘,

9620 cni’

Fig. 13. The shape of the 9621 cm- ’ line at 5 K.

892

W. WARDZ&XI and H. SZYMCZNC

The reasonably good agreement of the theory with the experiment indicates that the center responsible for the no-phonon line is a center invoIving chromium impurity in surroundings of local orthorhombic symmetry. The problem that now arises is, where in the crystal lattice of BGO could such a center be formed. BGG crystallizes in a body centered cubic structure-space groups 123(T3)[lI, 121. For crystals of such a symmetry there will be several equivalent interstitial positions of orthorhombic symmetry in the unit ce11[13]. These positions will be located for example at the center of faces of the cell. One can show that there is a very large empty space from the center of the elementary cell through the center of the face to the center of the neighboring fell. The impurity atom as an interstitiai atom can occupy the center of the face of the elementary cell as shown in Fig. 14. This figure also presents the scheme of the atomic arrange ment around such interstitial, showing orthorhombic symmetry of the interstitial. The projection of ions on the ZX, zy and XY plane are shown in Fig. 15. The ionic radii of 1.40 8, for 02-, 0.53 8, for Ge4’ and 0.74 A for B?+ were used in this construction. It is possible to see that the free space for an interstitial impurity forms a cylinder with diameter of about 2.24A and height of about 4.06w. This place is so large that it can hold atoms or ions of large dimensions. It is very probable that such impurities like for example rare earth ions will occupy this place. There is also enough place even for a neutral chromium atom. It is therefore possible to assume that the chromium involved in the center is a neutral atom. In principle the center responsible for the 9621 cm-’ line could be due to some 0”” ion in tetrahedral coordination. The sharp line, could arise as a no-phonon line of a broad band or could be due to a spin forbidden transition like 4Xr--2T2 or 4T,-2T, in Cr3+ or 3A2-‘E in Cr4+. Sharp lines in chromium doped GaAs and GaP were observedfl41 in the 6600 cm- ‘-8500 cm -I region. In the case of

D2 (m) A

0

0

,

L/

Ge infersfitiot

Fig. 14. The position and symmetry of ir&rstitial (&_I in Bi,@eO,.

k.251”= Fig. 15. The dimension of interstitial place in Bi,,GeG,.

GaAs some of these lines were interpreted as due to the no-phonon lines of the ‘T2-‘E transition of C# + ion in tetrahedral coordination (maximum of a broad band at 726Ocm-‘). This possibility should be excluded because: (a) Such an assumption requires D,, = 1100 cm-‘, a value which is too high comparing with - 73Ocm-’ in the case of GaAs[l4] and - 550 em-’ in the case of ZnTe[lS] and CdS[l6$ (b) In the cubic center the uniaxial stress will remove only electronic degeneracy, unless the static Jahn-Teller effect wiIl be taken into account. The observed splitting is not consistent with the expected splitting pattern due to a uniaxial stress which lifts electronic or electronic + o~~~tion~ degeneracy (see Table 1, in Ref. [ 171). Similar arguments rule out the possibility of other Cr”+ centers in tetrahedral coordination. Let us take into account the chromium impurity located in the interstitial position. Such a center will have orthorhombic symmetry and an approximate analysis of the energy levels due to the electron transition in the 3d” configuration should be carried out for octahedral coordination. From all possible charge states for this ease only Cr4 + and perhaps also Cr3 + and Cr2 + will give fairly acceptable values of B and D@parameters for the 9621 em-’ line. Further arguments for our assignment comes from the &axial stress experiment. For example, for a C?+ center the 9621 cm-’ line should be assigned to the transition 5E-3T,. The ground state will be split by the crystal field of orthorhombic symmetry 4 giving two [, levels and the excited state will be split into r 2, r 3 and r 4 levels. Therefore we should have 6 lines allowed for both polarization because of the orientational degeneracy of the center. Even if possible termalization effects at low temperatures would be present one should expect three lines. Furthermore the spin-orbit interaction in such a low symmetry crystal field should split the excited state (S = 1) into three levels removing all degeneracy except of the

893

The center of orthorhombic symmetry in chromium

Kramers degeneracy and we should see without stress much more lines than one. In the experiment we see only one line in ~n~a~~on to the above expectation. These arguments should be applied similarly to the Cr’+ and Cr4+ centers. Further dithculties arise if one attempt to explain the observed broadening of some components with the stress (see Fig. 12). One can understand such a broadening assuming the spin-lattice interaction which will remove the spin degeneracy. If the splitting is comparatively small and the components number is high (high spin value) one can expect the pronounced broadening of the line with the stress. We believe that because without stress we are able to observe only one line while we should expect at least three, and because there are difficulties in explaining the observed broadening of some lines with the stress, we should look for some other explanations. This leads us to the assumption that our center involves chromium in the 3d5s1 configuration. It should be mentioned here that for an in~rstiti~ impurity, 4s electrons are expected to fall into the d shell, and therefore the d6 besides the d’s configuration should also be taken into account for Cr’. For a d6 configuration the 9621 cm-’ line should be treated as a no-phonon line of the 5T2-‘E band. This leads to Q, - 1000 cm-’ a value which is fairly acceptable for the center of octahedral coordination. Since the actual symmetry of our interstitial is orthorhombic, the low symmetry crystal field will split the 5T2 level into three, and the ‘E into two components (neglecting spin-orbit interaction) and we should observe without stress at least two lines. The expected splitting should be as large as 850 cm- ’ (Fe2 + in ZnS) to 3400 cm-’ (Co’+ in Li,CoF,). From Figs. l-4 and Tables 1 and 2 one can see, that the largest distance from the 9621 cm-’ line to some comparatively narrow structure is about 73Octn’. Therefore it is possible that the line (weaker and broader than no-phonon line) at about 10,35Ocm-’ appears as a result of the splitting of the ‘E level in the low symmetry crystal field, we believe however that this structure is rather a phonon structure of the 9621 cm - * line and we should discuss the possibility of the 3d%’ configuration. The lowest energy levels of atomic chromium is shown in Fig. 16. Energy of the transition from the ground state ‘S3(3d54s) to ‘S2(3d54s) is 7593.1 cn- ‘. Very close to the 5S, level there are ‘D levels. The next excited state lies much higher at about 20,060 cm-‘. We assume that the observed (in the present work) sharp no-phonon line in BGGCr at 9621 cm-’ and in BGUCr at 9651 cm -I is due to the transition 7S3-5S, in interstitial chromium atom which form a center of orthorhombic D2 symmetry. As one can see the transition energy for the free atom is smaller than the transition energy in the crystal. There is an opinion that Racah parameters for ions in crystals should he smaller than those of the free ions. But there are known experimentally determined values of

s

-

5

-

4

-

a 2

-

1

3d5(*S)4s

-

‘Ss

Fig. 16. The diagram of lowest levels in atomic chromium.

I&ah parameters in crystals which do not conform to this rule[l8]. Such cases can be explained on the basis of the theory of Koide and Pry@ 191. They showed in the frame of molecular orbital theory that a reduction of I&ah parameters occurs if the covalency parameters are larger than the corresponding overlap integrals. This assumption also gives a qualitative explanation of the broadening of some components in the observed splitting pattern. Let us notice at first that the transition ‘S,-‘S, is strongly forbidden because of parity and also because both ground and excited levels belong to states with different values of spin (S = 3+S = 2). IIowever at the site with a 4 symmetry there is no inversion center and the selection rule connected with parity is partly broken both by odd crystal field and by odd vibrations. Similarly the spin-forbidden transitions can be partly allowed by spin-orbit coupling of the ground state with the excited state, Analogically it is possible to explain why the uniaxial stress could influence the 7S and ‘S levels. In the ideal case when both states are pure S states (L = 0) there is no spin-lattice coupling and the uniaxial stress cannot influence the position of the energy levels. The presence of the 5D levels in the vicinity of the 5S level is essential. Also, the admixture of sD states to 5S state enables us to assume that the uniaxial stress will influence first of all the excited state of the center leaving the ground state practically unchanged. Still there is a problem of how much will the crystal field change the energy of the excited state consequent on the mixing of S and D states. It should he noticed that in our case the interstitial which has exactly orthorhombic symmetry could be treated in the first approximation (after ~rn~~vely small displacement of the oxygen ions, see Fig. 15) as a center of symmetry L&

894

W. WARDZYI+SICI and H. SZYMCW(

a,

The crystal field of D, symmetry can be written as: V = Bo2C02+ Bo4C04+ B44(C,4+ C _ 44)

1r ,(D>)= ${I&%=2) + lDJf, = -2)) therefore the matrix element ( r ,(S)jVI r,(D))= 0 and in the first approximation one can expect an absence of any mixing between the 5D and 5S levels due to the crystal field. Therefore we can assume that although there will be mixing due to the orthorhombic symmetry and such a mixing will allow the spin lattice interaction, it will not change the energy level very much. Let us assume that the action of uniaxial stress on the ‘S state through spin-lattice interaction is given by the following spin-Hamiltonian:

where Bokl is the magnetoelastic tensor and a, is the stress tensor. Using matrix notation, for orthorhombic symmetry 4, the magnetoelastic tensor will be given by:

B13

0

0

0

821

J&2

B23

0

0

0

31

B32

B33

0

0

0 0 0

0 0 0

0 0 0

0

B4 0 0

0 B,, 0

*

=

(7)

0 0 B,

To 8nd the components of the splitting due to the removal of the orientational degeneracy one should count the centers of gravity of the splitting pattern for different stress directions as a function of stress. On the other hand the splitting pattern for a given stress direction, if not resolved, will give us the broadening of the line. The splitting around the center of gravity of the line (broadening of the line) is given by:

where B”is given by:

0

0

0

0

0 0

B33

0

0

0

0

0

0

844

0

0

0

0

0

0

85,

0

0

0

0

0

(9)

0 &

&;I

=

B,,

-

+,I

+

B2,

+

B3,)

$1

=

B21 -

+I,

+

B2,

+

B3,)

B3,

=

B3,

-

-@,I

1 3

+

B21+

B3,)

b112 =

B,2

-

+,2

+

B22 +

B32)

$2

=

822

-

$2

+

B,

+

B32)

$2

=

B32 -

+I2

+

B22 +

B32)

&3

=

B13 -

$13

+

B23 +

B33)

$3

=

B23 -

$13

+

B23 +

B33)

B33 =

B33 -

$813

+

B23 +

B33).

Because C&, = 0 the center of gravity is not shifted due to the fis, perturbation. From (6) and (8) one can 6nd: K,

B12

l53 e23

B31

where B,"are the crystal field parameters and C,” are the Racah’s irreducible tensor operators whose transformation properties are the same as those of the spherical harmonics. In the crystal field of Dzd symmetry the D state splits into 4 levels belonging to the r ,, r2, r3, r5 representations of the point group D, whereas the S state transforms according to the r, representation. The levels belonging to the same representations (in our case r,) disturb each other through the crystal field V. Since the wave function r,(D)has the form:

B,,

l&2 _ B22 _ B32

<2,

ri,,

=

@,,a,

+

B1202

+

B,3a3Wx2

+

@,,a,

+

B22~2

+

B23a3)Sy2

+

(B,P,

+

B32a2

+

B33~3)&

+

W,X

+

WP44~4

+

WV,

+

~,SJ&~,

@,,a,

+

B,2~2

+

+

Wx&

B,,~,Y%*

(Bz,a,

+

B22~2

+

B23”3)Sy2

+

@3,~1

+

B32”2

+

B33~3182

+

W,&

+

WyM,4~4

+

WxX

+

%9x$

+

VW&J,

-

WPI

+

B13u3)

-

2@3,0,

W~P, +

B32”2

W,)B,,~, (10)

+

-

+

+ +

B22~2 B33~3).

+

+

WJB,,~, +

B,2~2

B23”3) (11)

Therefore the shifting of the center of gravity will be given by:

The center of orthorhombic

& -

fis, =W11 + 4,

+ B&,

+ (42 + 42 + B33a2 + (43 + B23 + B33b31.

(12)

Since H&f$, does not depend on spin operator S, all

spin-levels of the 5S state are shifted in the same way (there is no broadening). For stress parallel to [lOO] [OlO] and [OOl] directions from (12) we will have: A, = 2(B,, + B2, + B3,b A2 = W,2

+ B22+ B32b

A3 = 2@,3 + B23 + 43)~

and the components are given by:

of piezospectroscopic

tensor (5)

A, = 2(B,, + B2, + B3,) A2 = 2(B,, + Bz + 832)

(13)

.43 = 2@,3 + B23 + B33).

For stress parallel to [l 1 l] direction from (12) we will have: A = 2(B,, + B,, + B3,+ B,, + B,

895

symmetry in chromium

Unfortunately we have no information about the spin-Hamiltonian parameters of the 5S level (or in other words we have no data on the crystal field splitting of this level). Of course crystal field with D2 symmetry can remove spin degeneracy of the ‘S level, but the values of such splitting probably are small (smaller than the half width of lines) and cannot be observed. Therefore it was not possible to determine wave-functions of levels of ‘S state which are split by the crystal field. In our further considerations we adopted the following procedure. To explain that some lines remain comparatively narrow with the increasing uniaxial stress we will assume that the appropriate Bk parameters cause the disappearence of same spin-operators in the Hamiltonian & (14). Occurrence of the spinoperators fit, has to lead to the shifting of the separate levels and as a result to the broadening of the line. The above argumentation will be applied to the different stress directions used in the experiment. For stress parallel to [lOO] [OlO] and [OOI] directions Hamiltonian g8, (14) has the following form, respectively I?A, = KB,,S,2 + B,,S,z + B3J,z) -A& HA1 = [(B,2S,Z+ B22S,2 + B32S:) - A&

(15)

I?Aj= KB,sS,z+ B23S;+ B33Sz2) - A3b

As one can see from Fig. 12 there is no broadening of A3 line and therefore

+ B32+ B13+ B23+ B33$ =(A,+A,+A3)$

1

B,3g B23s 833s ;A3.

For stress parallel to [llO] [Oil] and [loll directions from (12) we will have:

(16)

For stress parallel to [I 1l] direction

A, = (B,, + B2, + B3, + 42 + 42 +

+ 42k~ = (A, + A2$

W,Sz + SzS,P,

+ (SxSz + XV4, A,=(B,2+B,+B32+B,3+B23

+ C&S,+ Sy&Vhl$. (17)

+ B33k = 642 + A36 4

= (4,

As one can see from Fig. 12 there is no broadening of this line. It means that:

+ B2, + B3, + 43 + B23

+ B33b = (4

+ ~434

B,sB,,aB,rO

The broadening of the observed lines will be determined by the Hamiltonian fis, which could be rewritten in the following form:

and B,,+B,,

“B2,+B22aB3,+B34(A,+AJ.

(18)

For stress in [l lo] direction from (14) we will have:

&, = (B,,Sx2 + B,,S; + B3,S,3u, ri, = ; fiA, + f Z?A,+ (S,S,. + S,.S,)B,, p

+ (B,2Sz2+ B22Sy2 + B32Szz)~2 + (B,,S,z + B,,s,z + B33Sz2b3 + W,Sz +

+ W,)B,~,

2(S,S, + S,S,)B,a,

I& = ; I+,+ + ; I&, + (S,Sz + S&B,

+ WxSz + &W4,~,

- A,a, - A2a2- A303. (14)

& = $A, + ;HA, + (S,S, + S,S,)B,, p.

p

(19)

896

W. WMDZY&SIUand H. SZYMCZAK

The fact that line A is narrow results directly from the above given conditions (16) and (18). The above discussion indicates that it is possible to explain the observed splitting and broadening of the lines under uniaxial stress if the magnetoelastic tensor

(7) from the spin-Hamiltonian form:

(6) has the following

B 11;

;(A,

2. Wardzy&ki W., Szymczak H., Pataj K., tukasiewicz

T. J., J. Phys. Chem. Solids 43, 767 (1982). 3. Venugopalan S, and Ramdas A. K., Phys. Rev. B 5, 4065 (1972). 4. Wojdowski W., tukasiewicz T., Nazarewicz W. and &nija J., Phys. Stat. Sol. (b) 94, 649 (1979). 5. di Bartolo B., Optical Interactions in Solidr, chap. 15, pp. 341-377. Wiley, New York.

and &ija

+Az)-

B,,;

;A,;

0

0

0

;(A,

+Az)-

B22;

B22

iA3

0

0

0

;(A,

+Az)-

Bx;

B32

+A3

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

It should be noticed that the given above explanation of the splitting and broadening of the line under influence of the uniaxial stress, through the spin lattice interaction given by spin-Hamiltonian (6) will apply equally well for SE state, if the interstitial chromium atoms will have d6 configuration. Therefore at present the distinction between d5s’ and d” is not possible. Although we are not able to present the ultimate arguments that the chromium involved in the center is in a neutral atomic state (such arguments could be gained for example from magneto-optical measurements), the above discussion indicates that such an interpretation is very probable. Acknowledgmenrs-The authors are grateful to Prof. J. L?mijaand Dr. T. Lukasiewicz for supplying crystals used in this work and to Mgr. K. Pataj for excellent technical assistance. REFERFACES

1. Wardzyhski W., tukasiewicz Commun. 30, 203 (1975).

T. and imija J., Optics

6. Wardzyhski W., J. Phys. C 3, 1251 (1970). 7. Powell R. C.. di Bartolo B.. Birana B. and Naiman C. S., J. Appl. ihys. 37, 4973 il966).8. Yen W. M., Scott W. C. and Schawlow A. L., Phys. Rev. E 6, A27 I ( 1964). 9. Kaplyanskii A. A., Oprika Spektrosk. 16, 602 (1974); Opii& Speclroscop. 16,329 (1964). 10. Huebes A. E. and Runciman W. A.. Proc. Phvs. Sot. 86,215 (1965). 11. Abrahams S. C., Jam&on P. B. and Bernstein J. L., J. Chem. Phys. 47, 4034 (1967). 12. Svensson C., Abrabams S. C. and Bernstein J. L., Acta Cryst. B35, 2687 (1979). 13. Iniernational rabies .for X-Ray Crystallography(Edited bv K. Lo&ale). Kvnoch Press, Birminaham (1952). 14. Gilhams P. J., I&& L., Simmo&s P. E.: Henry M..O. and Uiblein Cb., J. Phys. C. Solid St. Phys. 15, 1337 (1982). 15. Komura H. and Sekinobu M., J. Phys. Sot. Japan 29, 1100 (1970). 16. Pappalardo R. and Dietz R. E., Phys. Rev. 123, 1188 (1961). 17. kuniman W. A., Proc. Phys. Sot. 86, 629 (1965). 18. Gillen R. D. and Salomon R. E.. J. Phvs. _ Chem. 74, 4252 (1970). 19. Koide S. and Pryce M. H. L., Phil. Msg. 3,607 (1958).