Selection rules for rare earth magnetic circular dichroism spectra

Journal of the Less-Common

Metals,

112 (1985)

115 - 191

175

SELECTION RULES FOR RARE EARTH MAGNETIC DICHROISM SPECTRA* C. GdRLLER-WALRAND University of Leuven, Heverlee (Belgium]

CIRCULAR

and L. FLUYT-ADRIAENS

Laboratory

of Inorganic

Chem~t~,

Celest~nenlaan

ZOOF, B-3030

(Received December 10,1984)

Summary Selection rules have been derived to determine the sign of the d,term with respect to the magnetic dipole and the induced electric dipole mechanisms.

In this paper we will consider the magnetic circular dichroism (MCD) of rare earths with respect to two mechanisms which mainly account for their intensities: the magnetic dipole and the induced electric dipole mechanisms. We will make reference to two papers particularly, one by Stephens on MCD [l] and recommended in recent literature (Piepho and Schatz [ 3]), and the other one by Judd [ 21 on the absorption intensities of rare earths. The main objective of the present paper is to link the so-called JuddOfelt theory with the MCD theory and to derive some simple selection rules to determine the sign of the .&-term. 1. Introduction

to MCD and sign convention:

example

of the &-term

Qualitative approach

This section is entirely based on the excellent work of Piepho and Schatz [ 3] ** Faraday discovered that all substances in a longitudinal magnetic field (H) appear to be optically active: the plane of linearly polarized light is rotated and there is a difference in the absorption coefficients for left and right circularly polarized light (1.c.p. (-) and r.c.p. (f)). This last phenomenon is known as “magnetic circular dichroism”. *Paper presented at the International Rare Earth Conference, ETH Zurich, Switzerland, March 4 - 8, 1985. **For further details see Chap. 4 in Ref. 3. @ Elsevier Sequoiaj~inted

in The Netherlands

176

'P

_+__

+a=*lgRH -a=-1gflti

/‘\

k&p.

l*l) IO)

AA=

581

A_-A.

:positive

I-1)

,.tLp.

~ JJ---IO,

‘s-

A-1 I

I

I

A*

I

/

_:_%f_ -----

a fly) ~-a ?E-Fig. 1. Definition

T-

f ~

and sign of the dl-term.

MCD can be illustrated best by considering the selection rules for left and right circularly polarized light using the example of an atom with a s2 ground state undergoing a transition to the sp state. This gives rise to the ‘S + ‘P and ‘S + 3P transitions. If the ‘S + ‘P tr~sition is considered in the presence of a magnetic field, splitting occurs in the Zeeman subcomponents ‘P-i, ‘P,, and ‘P+i and 1.c.p. and r.c.p. are permitted to the lP,i and ‘P-i components, respectively. As indicated in Fig. 1 the non-zero MCD, AA, defined as the difference in absorbance between 1.c.p. and r.c.p. (A_ -A+) is entirely explained by the fact that 1.c.p. and r.c.p. are absorbed at different energies in the presence of the field. The characteristic derivative-shaped MCD is called an d-term. The major finding of this paper is that AA is a “signed” quantity. The &term in Fig. 1 is termed positive when AA = A_ - A+ is positive to high energy.

177 Quantitative

approach

The absorption and MCD signals can be related further to molecular quantities by introducing the dipole strength (‘i3) for absorption and the d-, %- and e-terms for MCD. We now consider the quantitative treatment for the dipole strength (‘?J) and the @i-term in the electric dipole transitions. (Note that apart from the difference in the correction factor for medium effects, the expressions are the same for the electric and magnetic dipole transitions.) Absorption

The dipole strength (ii3,) is related to the zero-field absorbance of right and left circularly polarized light by AZ = yEq,f(E)Cz

(1)

where A: is the absorbance for r.c.p. and 1.c.p.; the superscript zero designates the zero-field absorbance (absence of magnetic field); and Y=

32n2log,, e 250hc

x

72, Avogadro’s number; x, effective field correction (x = a2/n for electric dipole transitions, x = n for magnetic dipole transitions); (x, electric permeability; ~1, refractive index; E, energy; f(E), bandshape function so that Jf(E) dE = 1; C, concentration in mol 1-l; z, optical pathway. For a transition A + J the dipole strength is related to the absolute square of the matrix element in the electric dipole operator by

Q)=;itA FA ILkIm,,IJ~)"12 =&

,c, WLI m+llJ~,)‘l~ + l(A,Im-,IJ~>“121

dA, degeneracy of the ground state; A,, zero-field wave functions for the ground state (if A is degenerate (Y= 1 to dA); Jh, zero-field wave function for the excited state (if J is degenerate X = 1 to dJ). Note that in order to account for the MCD, it is convenient to choose unperturbed electronic wave functions which are diagonal in the Zeeman operator. mkl = Tl/@(m, f im,): electric dipole operator for r.c.p. and 1.c.p. The superscript zeros designate zero-field quantities. The subscript zero (9,) refers to zero-order moment properties (we will not discuss the “method of the moments” here). Magnetic

circular dichroism

(MCD)

Where AA is measured for MCD, the quantities appearing in the expression of the absorbance are reconsidered in the presence of a magnetic field U-0.

178

Note that in the electric is applied AAO=A:-A,O=O

dipole approximation

when no magnetic

field

{as A: = A?‘)

In other words, no natural CD exists for transitions which are only electric dipole permitted. Natural CD occurs when a transition is both electric and magnetic dipoIe permitted, so that cross terms between the matrix elements in the electric dipole operator (na, i) and the magnetic dipole operator (yk i) give rise to a difference in absorbance in zero field: AA’. The presence of a magnetic field affects the quantities appearing in A+ and A- in different ways. The example considered above (‘S --f “P) illustrates how the Zeeman splitting of an excited degenerate state (‘P) gives rise to an &-term. We now consider the derivation of the expression for that particular d-term by considering the properties of the shape function f(E) under the influence of the magnetic field. The derivation of the c- and q-terms, which take into account a population effect between the Zeeman components and a second order mixing between zero-field functions under the Zeeman operator, respectively, will not be considered. Derivation of the d-term The magnetic field perturbation xl, = -c

-

g

(Xb) is given to first order in H by

(I$, + 2Sjz)H

i

= -(u,H

= /3H(L, + ZS,)

(3)

where i sums over all electrons, p, is the z-component of the magnetic moment operator, /3 = lelh/Zmc is the electronic Bohr magneton. If the wave functions are {A,/ and I&>, as previously defined, the firstorder corrections to the energies in the presence of the magnetic field are E;,

= EA - (A,IP,IA,)~H

and E:, = EJ - GMPzlJdOH where E_.+and EJ are the zero-field energies. The consequence of the Zeeman energy shift is that the shape function f(E) becomes f&(E) which is in fact a function identical in shape to f(E) but “shifted rigidly” along the E-axis. Since the function f(E) is translated (+a) if E is replaced by E-a the “rigid shift” approximation means that (see Fig. 1) f’(E) = f(E - a) where a is due to the Zeeman splitting of the ground and excited

states:

179

a =-[CJAIP~IJA)~- (&i~u,14Jol~ = [M,lL + ~S,IJA)~- (AaIL + 2S,14J”lP~ The function order this yields:

f(E -a)

can be expanded

in a Taylor

series; to the first

WE)

f(E--a)=f(E)-u-

aE

= f(E) + [(J,xlL + 2S,lJd”-

(A,IL,

We can now express the absorbance right circularly polarized light as:

z $ IL~,Iw,IJ,)~I~ a.h A

X [(JAIL + ~S,JJA)O-(A,/L, The difference,

+ 2S,IAJ”]flH in the magnetic

field of left and

X

+ 2S,IA,)“]

AA = A- - A+, which yields the MCD signal, becomes (4)

with

dl = $

C CI(Aalm-liJd”12- I(A,~m+,~J~)0~2] x A

a.h

X K4l-L

+ 2% IJ,d”- (A,IL,

+ 2S,IA,J”l

Example of the electric dipole permitted ‘S -+ ‘P transition The zero-field wave functions which also diagonalize the operator Xb = -p zH are: (Aal = (‘SI = (Al lJ*=,> = VP+,) I&= 2) = VP,) IJ~=3 = (k,)

(5)

Zeeman

180

The Zeeman splittings correspond (‘Sl L, + 2S, i wj3H

= 0

(‘P, 1II;, + zs, I iP+ 1>OPH= +lgPH (‘P,lL,

to

(g, Land6 factor)

+ 28, I ‘P,)OpN = 0

(lP_,lL,

+ 2S,I’P_JJ~H=

The matrix from zero are

-1gpH

elements

in the electric

dipole operator

which are different

l(1Slm+~I’P-~)012 = I(‘Sl~-~i1P+J012 so that = 13 l~1Sllml11P~12= f l~sllmll~~12

00 = l&3/m,,I’P,,)0f2

d,

= l(‘Slm_~l’P+,~~12~~P+~IL, + 2s,11P+,)o- l(‘Slm+,I’P_,~“12~1P_,IL, + 2s,11P_,)o = +2gl{~sl~~*l~P_~ >O(2 +i = Zg+ I(41mllp)12

The ratio &,/as gives the magnetic moment in Bohr magneton. The d-term is positive. We recall that AA - ~~(-~f(~)/~~), so that a positive @&value corresponds to positive MCD (AA) on the high energy side of the band. If we label the Zeeman components by their M-values as used throughout this paper, we have for the ground state and Zeeman excited components (931 = (Ml = toi lfP+;) = IztlfV’l> = 1+1> We can formulate that: in the simple case where the ground state is labelled by M = 0 and the Land6 factor of the excited state is positive, the sign of the z#il-term is determined by the sign of M’ labelling the Zeeman component to which left circularly polarized light is absorbed. This may appear trivial in the case of the electric dipole permitted ‘S + ‘P transition, but an analogous formulation will make more sense when the induced electric dipole transitions are considered. 2. General expression By including

of MCD

the %- and C-terms the general formula

of MCD is:

(6)

181

Not considering the difference in the correction factor for medium effects and the difference in the transition operator, the expression of &, is the same for electric and magnetic dipole transitions; we will thus generalize by writing

‘c; W~IO-IJA)~~~ - I(A,10+IJ,,)012]

x

X [(JAIL+ 25,1J,~"-G4,&+ 25,1Ad"l

(7)

where for electric dipole transitions 0t=Td2 -1(

m,+im,)

and for magnetic

3, Expression notation [ 21

dipole transitions:

for the gel-term

for rare earth spectra

with respect

to Judd’s

In order to evaluate the matrix elements in the expression of the .s%,term, a detailed description of the ground and excited states is needed. Owing to the comparatively small splittings of the levels produced by the crystal field, a good approximation can be made by assuming that the quantum number, J, remains a useful quantum number. Within the fN configuration the ground and excited levels can be labelled by

and

ZN= 4fN for rare earths; N, number of electrons; J, total angular momentum; M, quantum number of the projection J, of the J vector; J/, additional quantum numbers that may be necessary to define the level uniquely; CX,(Y’, labels the degenerate components in A and A’; a,, a&, coefficients in the crystal field function written as linear combination of the complex (~~~~~1 and ~lN~‘~‘~‘) functions.

182

The di-term .d~ = -$ A

can now be written:

C [l~A,IO-lA~~)012 - I(A,10+IA~~)“121 X 01.01'

X [(A:,&

+ 2S,lA:,d”-

(AaIL, + 2S,IA,J”l

In order to simplify as much as possible the MCD formalism, we will work out this expression for the case where: (i) The ground level is non-degenerate: (Y= 1. (ii) Cubic and icosahedral groups are not considered so that the excited crystal-field levels can be at the most twofold degenerate. (iii) M and M' arestill useful quantum numbers for characterization of the crystal-field levels. With respect to the previous point, (i), this means that the ground state should be labelled by (MI = (0 I in order to be nondegenerate. Any other non-degenerate crystal-field level will indeed be written as a combination of functions labelled by different M-values. Further, if the M's areto remain useful quantum numbers for the excited levels, only the possibility of twofold degenerate crystal-field levels remains; these are labelled by I+IM’b and I-IM’I). The possibility of IM’) = IO) although it fulfils the conditions (ii) and (iii), is excluded as a transition between (MI= 0 and IM')= 0 is not permitted by right or by left circularly polarized light. In the simplified notation where (JMI stands for (ZN$JMIand IJ'M') stands for IIN$'J'M'), the crystal field ground and excited levels are given by

(Aal = (Al = (JOI for 01’= 1

IALl) = IJ'+IM'l) and:

for or = 2

IA;!) = lJ'-IM'I)

By considering points (i) - (iii), the expression of the di-term is greatly simplified as the summations over M and M' in the expressions of A, and AL> over ar and (Y’ (aM = 1 and a& = 1) reduce to one term, and the summation reduces to one term for Q, and to two terms for (II’. Thus

&I =

c

[IV010-lJ’M’)012-

I(J010+IJ'M')012] x

+IM'I,-IM'I

x [(J'M'IL, + 2S,IJ’M’)“I as c

I(J010-IJ’M’)“12

+mf'I.-WI

=

x IU010+IJ'M')"12 +IwI.-IM'I

183

and (J’iJiv’~

IL, + 2sz~J’+1M’l)o=

-_(J’-IM’I

IL, + 2~~lJ’-~~‘~}o

one obtains: ge, = 21(JOIO~IJ’M’)012(J’M’IL,

+ 2S,(J’M’)

The matrix element in the Zeeman operator Russell-Saunders coupling scheme to give (J’M’IL,

+ 2S,IJ’M’)

can be worked

out

in the

= g&f’

so that 38, = 2l~~OlO_~~‘~‘~~~~~’

0%

with g=l+

J(J+l)-JqL+l)+S(S+?) 2J(J+ The following

1)

statement

, the Landi, factor.

can be made:

For a positive g-value the sign of the &?&xrn is determined by the sign of M’ labelling the Zeeman component to which left circularly polarized light is absorbed. For a negative g-value the opposite is true.

(10)

We recall that the &,-signal, by its derivative shape function, was shown to be active in differentiating transitions that involve degenerate levels from transitions between nondegenerate levels. In the last case $5’signals will be obtained. Moreover, the &i-term by its sign provides information on the sign of the Land6 factor and the sign of the M’value. Finally the ratio &i/Q, gives the magnetic moment in Bohr magneton, which, when multiplied by the magnetic field, gives the total Zeeman splitting. We now consider the expression of the d,-term in the framework of two mechanisms which account predominantly for the intensities for rare earths: the magnetic dipole mechanism and the induced electric dipole mechanism, First, however, we will briefly discuss the formalism for a hypothetically permitted electric dipole transition using Judd’s notation and Racah’s “irreducible tensor method”. A previously discussed example of an electric dipole transition is the case of IS + ‘P, the results of which are known from the previous section. Note that for rare earths no electric dipole transitions are permitted within the 4fN-configuration and that other parity configurations (4fN- ‘d or 4fN- ‘g) are mixed in to break up the Laporte selection rule. This is the basis of the induced electric dipole transition theory. This theory, published independently by Judd and Ofelt [2] and known as the Judd-Ofelt theory, explains how the mixing occurs under the terms of odd parity in the expansion of the crystal-field Hamiltonian.

184

Through this mixing, the M’-value appearing in the intensity matrix element of the &r-term will be dependent on the crystal-field potential. The d,-term is thus related to the Land6 factor which is a free-ion property, however, it is also related by its sign and magnitude to the AI’value which provides information on the site symmetry through the induced electric dipole mechanism.

4. Electric dipole mechanism:

O- = m_, = -lelDiil

We recall that the cases where permitted electric dipole transitions can be measured in the near UV-visible region are few for rare earths because most transitions appearing in that region of the spectrum are intra 4fNconfiguration transitions. We now refer to Ce3+, Pr3+ and Tb3+ whose spectra exhibit the 4fN + 4fN- ’ 5d transitions [5, 111. With Pr3+ in a CaFz host, the first 4fN + 4fN- ’ 5d absorption is located at about 45 000 cm-’ while that of any of the other lanthanides (except Tb3+) is at least 10 000 cm-’ to higher energy. For a permitted electric dipole transition corresponding to a 4fN + 4fN- ’ 5d transition the intensity matrix element is [ 111 (4fN$dOI-lelD?1~14fN-1(n’l’)$‘J’M’)o where -_lelDi’,’ is the electric dipole operator with -_le] the electron charge and Dy’ the tensor or rank 1 with q = -1 for left circularly polarized light. 06” = xCrjC,‘(ej, pj) i with C,‘(ej, Cpi)= (4n/3)“2Y~,(ej, pj), Y14 being a spherical tical to the angular part of the p-orbitals). This expression can be reduced to

_:

&, (4fNJIJ Il-_lelD(1)I14fN-1(~‘I’)rll’J’)o

The J-dependency of the matrix element Saunders coupling may be determined by

of eqn.

harmonic

(iden-

(11) (11) in Russell-

(4fN~JII-lelD’1’114fN-‘(n’1’)~‘J’>o 6(ss’)(-l)J+L’+s+‘(2J

+ 1)“2(2J’

+ 1)

(4fNySLIl-_lelD(1)I14fN-1(n’l’)y’S’L’)o where y and y’ are additional uniquely.

quantum

numbers

which define the SL levels

185

Further reduction can be performed by introducing the coefficients of fractional parentage and the radial integrals (nil- let rl n’l’). This reduction will not be carried out here because the concept of fractional parentage is not necessary to derive the selection rules. From the previous equations, and the 3j and 6j symbols which they include, the selection rules are familiar AS=0

AL = 0, kl

AJ=O,kl

and from the 3j symbol including

(notJ=O-+J’=O)

4 for left circularly

polarized

light

M’=+l

(12)

The selection rule for M ’ is the relevant one for MCD as it points on the fact that left circularly polarized light is absorbed to the M’ = +l component, yielding a positive d,-term if the Lande factor (g) is positive for a permitted electric dipole transition. Addendum

By using this formalism on the example intensity matrix element becomes

of the ‘S -+ ‘P transition,

the

1 (sll-lelrllp> +l i =-

A_

43 The matrix element I(‘SI-lelD~1~11P+,)12

=i

@II-lelrllp)

squared gives the familiar result: I(~ll-14rll~)12

5. Magnetic dipole mechanism: O- = J.-~ =-J&L+%)“,

A list of the magnetic dipole transitions has been published [ 71. The intensity matrix element for a magnetic dipole transition

-2

by Carnal1 is:

(I_ + 24J’M’) 0

i(

J”-2

(L + 2S)IIJ’

The reduced matrix element can be calculated further; the Russell-Saunders coupling scheme, one obtains [S]

(13) in the limits of

186

forJ=

J’

(fN@LJIL

+ 2SI fNy’S’L’J’)

= 6(y, y’)6(S, S’)6(L,

L’)[(2J+

1)/4J(J+

X [S(S + 1) - L(L + 1) + 3J(J+ forJ’=

l)]

J-l


1)]“2 X

+ 2SlfN$S’L’J’)

6(Y, Y’vw, S’)W, L’)

[(S+L+1)2-J2][J2-(L-S)2]

1’2 I

4J

for J’= J+ 1
+ 2SIfNy’S’L’J’) #(S,

S’)6(L,

L’) x

[(S+L+1)2-(J+1)2][(J+1)2-(L-S)2] 4(J + 1)

1 The selection Ay = 0

1’2 I

rules correspond

Al=0

AS=0

to AL=0

AJ=

0, +l

(not 0 tf 0)

and from the 3j-symbol M’=+l

(14)

With respect to MCD, the absorption of left circularly polarized light occurs to M’ = +l leading to a positive &i-term if g is also positive. It is interesting to note that using the assumptions made previously (ground state (MI = (01 and twofold degenerate excited state IM ‘>= I+ IM’(j) the magnetic dipole transitions always appear as positive &,-terms if g is positive. These can be used as a reference to which other MCD signals can be compared and characterized with respect to their sign. An example is the 7F, + ‘Di transition for Eu3+ which shows a positive s4i-term for several complexes studied experimentally, independent of the coordination symmetry of the Eu3+ ion in these complexes. However, to apply the expressions derived above, an intermediate coupling scheme has to be considered to breakdown the selection rules based on AS and AL. This means that 7F,, and ‘D, are written as linear combinations of functions with the same J-value (see Fig. 2).

6. Induced

the

electric dipole mechanism:

O_ = m_ = -1 e IDli,

We will not reproduce here the Judd-Ofelt observation of spectra of strictly parity

theory which explains how forbidden transitions must

187

7Fo -“D2 D2d -

‘3h ,*1+1, E"

=:I, I-1)

E

d', -

-

a

=:',.

ICP

C4"

l+l) E

=:

I-1)

(01

dl

T ~

-

I+') I-1)

ICP.

ICP ii

.' a '.

(01

II

Al-

(01

A A@

A@ VE

VE

-

‘3h

E

C4"

-l+l)

=‘(

E

=::y 71-1,

‘7

~

I-1)

l-2)

I.cp

I.CP.

I c.p -

-

l+Z)

‘\

dl

C'

-

*2d

,-

E’

Cl

3

(01

dl

-

-

I

(01

1 -(01

d1#@

/?v"

E

-

(rlI DJ +l )

(+llci~'l-1 ) ,.J

p=+2

E

ML-2+1

,cj

P.0

M:O+l

Fig. 2. Sign of the &!,-terms for the 7Fo+ 5D1 and 7FO+ SD2 transition of Eu3+ in different symmetries ( 7Fo -+ 5D, is a magnetic dipole transition and 7Fo+ 5D2 is an induced electric dipole transition).

concern itself with non centro-symmetric interactions that lead to a mixing of states of opposite parity. One of the most obvious mechanisms is simply the coupling of states of opposite parity by way of the odd terms in the crystal-field expansion v=

CA,,DF’ t. P

where DF’ is a tensor of rank t.

where Cr'(ej9

Cpj)

=

i&

l/2

1

yt,(ej9

Yt,, being a spherical harmonic

Cpj)

and At,) a crystal-field

parameter.

188

The derivation 13 in ref. 2)

=

c (2h+ P, t. h even

[2] for the intensity

1)(-l)“+“A,,

matrix element,

-p---4

yields (see formula

t z(t, h) x

P

x (JOIlJf& IJ’M’P

(15)

where BJ e and &lM’ stand for the (JO/ and JJ’M’} states in which opposite parity configurations are mixed in. h = 2,4,6 results from the closure procedure over the perturbing opposite parity states. In fact in the procedure the electric dipole operator C$ f in Dil) and the crystal field operator Cr’ in V are combined to an operator with rank h, (C$‘Cl;“),“+ *. z(t, X) = 2X(21 + 1)(21’ + 1)(--l)“”

x

X (allr~n’l’)(ntir’1n’l’)/A(n’E’) where A(n’r’) is the average energy between the 4f states and the ~‘1’ states. The matrix element in ui + 4 can further be reduced to obtain:

In a Russell-Saunders (Jl] U’~‘IIJ’)O= (PySLJII

coupling

W’IIPy’S’L’J’)

= s(&S’)(-1)S”L’+J+h X

L

h

L’

J’

S

J

I

scheme

(2J + 1)“2(2J’ (r*ysLltU’“‘IIINy’S’L’)

where y stands for additional quantum numbers. From these expressions the following selection X = 2, 4, 6 for h = 2

t=land3

for X = 4

t = 3 and 5

for X = 6

t = 5 and 7

when t = 1,3,5 when t = 7

I’ = 2,4 1’=4

+ 1)“2 x

rules may be obtained

189

AS=0 /AJIG

and

IALl<

6 when Jor J’ = 0

AJ=2,4or6

i J = 0 * J’ = 0: forbidden

and from the 3jsymbol: M’=-(p+q)

(16)

Note that the sign of the Al-term is for induced electric dipole transitions determined by the sign of the M’-value which satisfies this last equality for left circularly polarized light (q = -l), thus: M’=-p+l

(17)

The sign of M’ is clearly related sphere around the rare earth through crystal-field terms.

7. Application

of the selection

to the symmetry of the coordination the p-value which appears in the odd

rules (see Fig. 2)

Here we briefly outline some results for the 7F0 + ‘D2 transitions in the Eu3+ spectra, which are described in detail in other papers [6,10, 13 - 151 in D3h: p = ?3 [ 91, M’ = -3

+ 1 = -2

leading to SQ, negative,

in C 4v : p = 0 [ 91, M ’ = 0 + 1 = +l leading to SQ, positive, in DZd: p = *2 [9], M’ = -2

+ 1 = -1

leading to &, negative.

With respect to the 7F, + 5D, magnetic dipole permitted transition from which the positive di-signal may be taken as a reference, the 7F, + 5D, induced electric dipole transition will exhibit a negative &i-term in the D3!* and Dzd symmetries while the di-term is positive in CQu. These examples can be understood best if one bears in mind the significance of the odd terms in the crystal-field expansion. The admixing of configurations of opposite parity comes about by the presence of odd crystal-field terms, in Judd’s notation this means that: (ZN-l(n’l’)$“J”M”IDjj)IIN$J’M’)

f 0

In other words the odd-parity where IN- ‘(n’l’) stands e.g. for 4f N-’ (e.g.: for Eu3+ ‘D, will be labeled by odd terms (e.g. t = 3 for D3h and Dzd and 3 with p = 0 for CQL,[ 91).

configuration state lN- ‘(n’l’)$“J”M”, 5d, mixes in the excited state EN$J’M’ 4f6$2M’ = ?2, *l or 0) under the DF’ while p is respectively +3 and ?2; t = 1

190

Specifically for DJh : (M”ID$t)(M’)= (+l ID!“3 1T2) for Cev: (M”(D(t)(M’) = (TllD~)a”d(3)(T1) P for DZd: (M”(D~)IM’) = (+l lD$:‘lTl) Thus the odd crystal-field terms mix in the IM’) excited states 172), respectively, the odd parity states characITl), IT1) for Dsh, C,> D2c3, terized by (M”I = (-+I[, (Tl(, (_+I/. In fact these small amounts of mixing in odd parity states are responsible for the intensities induced in the lit!‘) states. If one bears in mind that left circularly polarized light will be absorbed to i+l), while right circularly polarized light is absorbed to I-l), it is easy to understand that in Dsh left circularly polarized light will be absorbed to the (-2) Zeeman component because of the presence in that wave function of a small amount of 1+1> belonging to the 4fNP1 5d configuration. In the same way it becomes clear that right circularly polarized light will be absorbed to the ) +2) components that mixes in with I-1). As the g-factor for the ‘D, state is positive, 1+2) will be the higher Zeeman component and the absorption of right circularly polarized light to that component results in a negative MCD &,-signal (where, as we recall AA = A_ -A+ is measured). We hope it is now easy for the reader to understand why for the ‘F, + 5D2 transition the CGv symmetry gives a positive d,-signal while DZd and D3h give a negative &,-signal by applying to these symmetries the same “brain exercise”.

Conclusion We have investigated the sign changes of the &i-term with respect to the electric dipole, the magnetic dipole and the induced electric dipole mechanisms. In the case of a transition from a (M I = (0 I non-degenerate ground state to a twofold I + IM’I) excited state, the sign of the Ai-term is determined by the sign of the I&!‘)-value which labels the Zeeman component to which left circularly polarized light is absorbed, as long as g for the excited IfN$‘J’> level is positive. The opposite statement holds true for a negative g-value. This can be summarized as follows Electric dipole: M’=+l

leading to a positive .&i-term if g is positive

Magnetic dipole : M’=+l

leading to a positive sQ1-term if g is positive

191

Induced

electric dipole:

M’=--p+l

leading to a z8,-term

whose sign is the same as M ’ if g is

positive with

the odd crystal-field component. The electric dipole mechanism which has been studied extensively in most publications on MCD has been used here as a guide for introducing two further mechanisms: the magnetic dipole and the induced electric dipole mechanisms. The electric dipole mechanism is rarely active in providing intensity in the near UV-visible spectra of rare earth complexes because most of the transitions in that region are intra 4fN transitions which are strictly parity forbidden. On the other hand the magnetic dipole and induced electric dipole mechanisms account predominantly for the intensity in the spectra; they provide signals of practically the same order of magnitude. In this paper it is shown that while the magnetic dipole MCD signals are only dependent on the free ion properties, the induced electric dipole MCD signals are intrinsically site symmetry dependent (through the M’-value). We propose that magnetic dipole transitions (e.g. 7F0-+ ‘Di in Eu3+) transitions, whilst the induced should be considered as “sign reference” electric dipole transitions could be used as a “site symmetry MCD probe” (e.g. 7F, + ‘D, in Eu3+). p

Acknowledgments This work was supported through grants from the IWONL and FKFO Belgium. The authors are indebted to the Belgian Government (Programmatie van het Wetenschapsbeleid). References 1 P. J. Stephens,Adu.

Chem. Phys., 25 (1976) 197. 2 B. R. Judd, Phys. Rev., 127 (1962) 750. 3 S. B. Piepho and P. N. Schatz, Group Theory in Spectroscopy. With Applications to Magnetic Circular Dichroism, Wiley, New York, 1983. 4 G. S. Ofelt,J. Chem. Phys., 37 (1962) 511. 5 K. Okada, Y. Kaizu and H. Kobayashi, J. Chem. Phys., 75 (1981) 1577. 6 C. Gorller-Walrand, M. Behets, P. Porcher and I. Laursen, Inorg. Chim. Acta, 109 (1985) 83.

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76 (1982)

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77