Magneto-optical properties of the excited state of F centres in some alkali-halides

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Magneto-optical properties of the excited state of F centres in some alkali-halides

M. Thuau, J. Margerie

To cite this version:

M. Thuau, J. Margerie. Magneto-optical properties of the excited state of F centres in some alkali- halides. Journal de Physique, 1977, 38 (10), pp.1313-1316. �10.1051/jphys:0197700380100131300�.

�jpa-00208702�

MAGNETO-OPTICAL PROPERTIES OF THE EXCITED

STATE OF F CENTRES IN SOME ALKALI-HALIDES

M. THUAU and J. MARGERIE

Laboratoire de

Spectroscopie Atomique (*)

Université de

Caen, 14032

^Caen

Cedex,

^France

(Reçu

^le

23 fevrier 1977,

^{révisé le}

13 juin ^1977, accepté

^le

15juin 1977)

Résumé. ^- Les auteurs ont mesuré le facteur de Landé orbital et la structure spin-orbite ^du premier état excité des centres F dans NaCl, NaBr, ^{KBr et KF en} analysant par la méthode des moments les courbes d’absorption ^et de dichroïsme circulaire magnétique à diverses températures.

Ces résultats expérimentaux ^{et ceux d’autres auteurs sont} comparés ^{aux valeurs} théoriques ^calculées

par Harker.

Abstract. ^- The orbital g-factor ^{and the}

spin-orbit splittings

of the first excited state of F-centres

are measured in NaCl, NaBr, ^{KBr and KF} crystals by

observing absorption

^and

magnetic

^circular

dichroism at various temperatures ^and

using

^{the moments} method. Our

experimental

results and others are compared with Harker’s theoretical values.

Classification Physics ^Abstracts 61.70D - 78.50

1. Introduction. ^- In a recent paper, Harker

[ I ] calculates,

^{for F centres in the}

twenty alkali-halides,

various

magnetic

^and

optical properties including

the orbital

g-factor,

g, and the

spin-orbit splitting, L1,

of the first excited unrelaxed state. It is

obviously interesting

^to compare this wealth of theoretical results with the

greatest

number of available

experimental data,

^{in order to see} if Harker’s

theory

^accounts

satisfactorily

both for the

magnitudes of g

^{and L1}

and for the variations of these

parameters

^{from one} alkali-halide to the next. Of _course, for this

compari-

son, it is _necessary to discard unreliable

experimental results, especially

those obtained

by

^{the so-called}

Rigid-shift technique ; only

the results from the method of moments

[2]

may be retained.

In his _paper

(Tables

^{5 and}

6),

^Harker

[1] ]

^has

already performed

^{such a}

comparison

^between

theory

and

experiment; but, unfortunately,

^{he was not aware}

of some reliable

published experimental

^{results, and}

(of

^course

!)

^{he was}

quite

^{unaware of some unpu-}

blished data from ^our

laboratory.

The purpose of the

present

paper ^{is to} fill these _gaps, as much as we

can,

by describing

^{our own}

experimental

results in section 2 and

by comparing,

^{in section}

3,

^{our observed} data and others with Harker’s

predictions.

2.

Experiment.

^{- Our}

experiments

^{relate to}

KBr,

NaCI, NaBr and KF. We use

single crystals

^from

(*) ^{Associ6 au C.N.R.S. no 19.}

Semi-Elements

(KBr, NaCl, NaBr)

^or

Optovac (KF).

They

^are

additively

^colored

(KBr), electrolytically-

colored

(NaCI)

^or X-irradiated

(NaCl, NaBr, KF).

We observe F-band

absorption

^{and its}

magnetic

circular dichroism

(MCD)

^{with a}

previously

^described

apparatus

[3].

^The

light polarization

modulation is achieved

by

Billardon’s

photoelastic

^modulator

[4]

in the case of KBr and

by Schnatterly’s

^modulator

[5]

for the other

crystals.

^We

operate

^{in the three}

tempe-

rature ranges

(1.4

^{to 1.6}

K), (85

^{to 115}

K)

^and

(205

to 225

K).

^{For each}

crystal,

^we

experimented

^{on seve-}

ral

samples :

^{3 of}

KBr,

^{2 of} X-irradiated

NaCl,

^{1 of}

electrolytically

^colored

NaCI,

^{3 of NaBr and 1 of}

KF ;

we

generally

^{took two} observations in each tempera-

ture range and for each of the

samples.

TABLE I

Spin-orbit splittings

^L1

(in meV)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197700380100131300

1314

TABLE II Orbital

g-factors :

g

The MCD and

absorption

^{bands are}

analysed by

means of

Henry et

^{al.’s moments method}

[2].

^{In our}

results,

^we take into account the various

possible

errors or uncertainties :

light depolarization by

crys- tal

strains, depth

^of

light polarization modulation,

determination of the

absorption

^{and MCD base}

lines, sample

decoloration

during experiments,

^tem- perature ^and

magnetic

^field

determinations,

^M-centre

absorption

under the F-band. Our results for L1 and g ^are in the second columns of table I and _{II respec-}

tively.

The third columns contain other

experimental

results from several authors.

3. Discussion. ^- 3.1 SPIN-ORBIT SPLITTINGS. ^-

We have listed in the two last columns of table I the theoretical results obtained

by

^Harker

[1] :

this author

uses for the F electron an

envelope pseudo-wavefunc- tion,

u, which he

orthogonalizes

^{to the}

occupied orbitals, 4>i,

^{of the}

crystal ions;

^so that the F-wave- function is

given by

N is the normalization factor :

Si

^{is the}

overlap integral

^between

pseudo-wavefunc-

tion u and the

occupied

^orbital

øi : Si = Oi I u > ;

the summations run over all the

occupied

orbitals of

neighbouring

ions. 03A8 _may be viewed as a combination of a smooth

p-like

^wave

^function,

^{out of the}

^ions,

^and

of

wiggles,

^{centered on the}

ions, ensuring

^{the ortho-}

gonality.

^Two calculations have been

made;

^{in the}

first _one, u was obtained from a variational calcula- tion with a

point-ion lattice;

ⁱⁿ the second _one, an

approximate

correction was made for the finite size of ions. The.J’s from these two calculations are listed in columns 4 and 5

respectively

^{of table I. It is}

easily

seen that the

comparison

^between

experiment

^and

theory

^is

satisfactory :

^{the order of}

magnitude

^{of L1}

is

correctly

^accounted

for,

^{as well as its}

huge

^varia-

tions

(by

^{a factor} up ^to 20 or

so)

among the various alkali-halides. There are

comparatively

^{small diffe-}

rences between the

predictions of point-ion

^{and ion-size}

theories,

^{so that it seems difficult to} decide with cer-

tainty

^{which is best.} One may choose as a test the

quantity

which is

equel

^to 0.32 for the

point-ion theory

^and

to 0.15 for the ion-size

theory.

^{Thus the more}

sophis-

ticated ion-size

theory

^{seems to}

give

^{a better account}

of the

spin-orbit splitting

^{on the basis of}

existing experimental

^data.

3.2 ORBITAL g-FACTORS.

- Harker [1 has perform-

ed four calculations

of g :

^{he uses either a}

point-ion

^u

or an ion-size _{u ;} he

employs

^either Thuau and Mar-

gerie [10]’s

formula for _gorb

(gradient)

^{or Smith}

[11]’s

modification of this formula

(dipole) (1).

^{These four}

results are tabulated in the four last columns of table II. It appears that the

theory correctly

^accounts

for the orbital

g-factor being

of the order of

unity

and

varying comparatively

little from one alkali- halide to the next.

But,

^{at first}

sight,

^{there seems to}

be no connection between the

predicted

and observed values of the

g-shift :

We calculate

for 9

^a

quantity

^{similar to the above}

defined q

^{and we find}

respectively 0.40, 0.20,

^0.56

(’) ^{In Smith’s} formula, ^{Thuau and} Margerie’s matrix elements of _{p among} ionic orbitals ø j’ øk ^are expressed ^{in terms of the cor-} responding ^matrix elements of r through

which seems of dubious validity ^here since the available ionic orbi- tals are only approximate eigenfunctions.

and 0.27 for the

point-ion dipole, point-ion gradient,

ion-size

dipole

^{and ion-size}

gradient

calculations. Thus the

gradient

calculations are

clearly

^favoured

by

expe- riment with

respect

^{to the}

dipole

calculations. This

was

already

^noticed

by

^Harker

[1]

^{and this is}

gratifying,

since the theoretical foundation of the

gradient

^cal-

culation is sounder than that of the

dipole.

^{On the}

other

hand,

^{the more naive}

point-ion

calculations appear ^to

yield

somewhat better results than the more

sophisticated

ion-size, ^{but this} difference _may be

unsignificant

in view of the

experimental

uncertainties.

In

figures la,

^{lb and}

1 c,

^we

attempt

^{to visualize}

more

clearly

^how g

depends

^on

the

cation and the anion.

Figures

^{la and lb}

correspond respectively

to Harker’s calculations

point-ion gradient

^{and ion-}

size

gradient.

^A definite trend is visible on

figure

^la

and also

(though

^less

clearly)

^on

figure lb : g

^is pre- dicted to increase with cation size and to decrease with the anion size

(with

^the

exception

of Cl- and

Br-,

9

which are calculated to

yield comparable results).

A similar smooth

dependence of g

^{both on the cation}

size and the anion size was found in

analogous,

^but

less

extensive,

calculations we

performed

^{a few} years ago

[10].

It seems

interesting

^{to look for a}

physical

^inter-

pretation

^{of these}

predicted

smooth ion size

depen-

dences.

Using

^Smith’s

picture,

^the

g-shift

^{is decom-}

posed

into three contributions

(see

eq.

(16)

^{of ref.}

[11]).

The first describes the

quenching

^{of the}

envelope

function

angular

^momentum

by

^the orthonormali- zation process. The second arises from the orbital

angular

^{momentum of the centre of mass of the}

wiggle’s charge

distribution about the vacancy. The third is the contribution of the

angular

^momentum

of the

wiggles

about their own centres of mass. These three terms are

expected

^to increase both with the size of the cation and with the size of the anion. From

our

previous

calculations

[10],

^we have been able to evaluate these three terms for several alkali-halides and to show that the first and third are

negative,

^the

second

positive

and that there is a considerable amount of cancellation _among them : the

algebraic

sum of three

large

^terms

yields

^a

comparatively

small calculated

g-shift. Therefore,

^{it seems rather}

hazardous to try ^to deduce from Smith’s

picture something

^{about the}

physical origin

^{of the}

predicted

ion size

dependence

^of

Ag.

Let us now turn to the

comparison

of these calcu- lated

Ag

variations with the

experimental

^ones.

Figure

^{1 c fails to show a} behaviour similar to the

predictions :

^for

instance,

the fluorides are found to have small

g-factors,

^the

g-factors

of chlorides and iodides do not increase with the cation

size,

^{the bro-} mide and chloride

g-factors

^{seem rather} different from

one another. Therefore it appears :

- either that some

experimental g-factors

^are

wrong and

spoil figure Ic ;

- or that more refined calculations than those of

FIG. l. ^- g-orbital values, g, ^versus ionic radii of alkali-cations, a, with halides as parameters : a) point-ion gradient calculations [1];

b) ^ion-size gradient calculations [1] ; c) experimental.

1316

Thuau and

Margefie [10]

^{or Harker}

[1]

^are necessary to account

correctly

for the variations

of g

among the alkali-halides.

This encourages ^our

laboratory

^{in a double}

attempt :

on the one hand to measure the

g-factors

^{of other}

halides and to remeasure some of those which ^seem most

deviating

^on

picture

^{1 c. And on the other}

hand,

to start calculations with a

quite

^different

approach : remarking

^that

Chaney [13]’s

^recent L.C.A.O. calcu- lations

give

very

good

results for transition _energy, oscillator

strength,

^orbital

g-factor

^and

spin-orbit coupling

^{constant in the case of}

LiF,

^{we are}

trying

^to

extend L.C.A.O. calculations of

magneto-optical

parameters ^to other alkali-halides.

References

[1] HARKER, A. H., ^J. Phys. C, Solid State Phys. ⁹ (1976) ^2273.

[2] HENRY, C. H., SCHNATTERLY, ^{S. E. and} SLICHTER, ^C. P., Phys. ^{Rev. 137A} (1965) ^583.

[3] THUAU, ^M. and MARGERIE, J., C.R. Hebd. Séan. Acad. Sci.

268B (1969) ^1586.

[4] BILLARDON, ^{M. and} BADOZ, J., C.R. Hebd. Séan. Acad. Sci.

262B (1966) ^1672.

[5] JASPERSON, ^{S. N.} and SCHNATTERLY, ^S. E., ^{Rev. Sci.} Instrum.

40 (1969) ^761.

[6] OSBORNE, ^{G. A. and} STEPHENS, P. J., ^J. Chem. Phys. ⁵⁶ (1972)

609.

[7] ROMESTAIN, R., thèse de 3e cycle, Paris-Orsay (1965).

[8] BUISSON, ^J. P., LEFRANT, S., SADOC, A., TAUREL, ^{L. and} BILLARDON, M., Phys. Stat. Sol. (b) ⁷⁸ (1976) ^779.

[9] BROWN, ^F. C., CAVENETT, ^{B. C. and} HAYES, W., ^Proc. Roy.

Soc. A 300 (1967) ^78.

[10] THUAU, ^{M. and} MARGERIE, J., Phys. ^{Stat. Sol.} (b) ⁴⁷ (1971)

271.

[11] SMITH, ^D. Y., Phys. ^{Rev. B8} (1973) ^3939. (In ^this paper, Smith quotes ^the experimental gorb values of RbCl and RbI from a private communication of F. C. Brown.) [12] FONTANA, ^M. P., Phys. ^{Rev. B 2} (1970) ^{1107 and} private

communication of the uncertainty.

[13] CHANEY, R. C., Phys. ^{Rev. B 14} (1976) ^4578.