Effect of J-mixing on the intensities of f-f transitions of rare earth ions

228

Journal of Luminescence 33 (1985) 228-230

North-Holland, Amsterdam Replacement of Journal of Luminescence 3 1/32 (1984) 204-206

EFFECT OF 3—MIXING ON THE INTENSITIES OF f-f TRANSITIONS OF RARE EARTH IONS Shangda XIA and Ylmin CHEN Department of Physics, China University of Science and Technology, Hefei, Anhui, China A revised Judd—Ofelt formula which still includes three parameters Q~and takes conveniently 3-mixing effect into account has been 3~is derived. successful. The application of this formula to EuP 5O14 and Y2O3:Er 1. INTRODUCTION The states of rare earth ions located in crystal field circumstances are 3—mixing states. 3—mixing effect contributes the transition intensities of RE ions, especially distorts some selection rules of number 3. The 3-0 formula for the transition between the crystal-field levels may include the 3-mixing effect, but a tedious crystal—field fitting must be completed in advance to get the crystal—field eigenfunctions.

The 3—0 formula for intermultiplet transi-

tions is easy to use and has been applied extensively, but it does not include the 3—mixing effect. In this paper, a revised formula which still includes three parameters 0~and takes conveniently the 3-mixing effect into account has been derived. It is particularly suitable to RE ions in low symmetry crystal field. The application of this formula to EuP 3~’is successful. 5O14 and Y2O3:Er 2. INTENSITY FORMULA OF DIPOLE TRANSITION 2.1. The crystal field state in crystal field representation is fN[~JA]Fr>

=

/~

a(lsJA,~3A;r) f~JArr>

(1)

where ~ = [casL], A is an irreducible representation of the group chain connected group SO(3) and crystal field symmetry group. 2.2.

Following B. R. Judd, we add the contribution of the configuration

fN_l(j~)via the interaction of odd crystal field HOCE = ~ A~ Y~C~t)(i) to formula (1). tpt Then the matrix element of electric dipole transition



L

=

~

f f pi j ~

A~r~

0022-2313/85/$3.30 © Elsevier Science Publishers By. (North-Holland Physics Publishing Division)

(2)

229

S. Xia, V. Chen / Effect ofJ-Mixing

where

~

? (p,t,Ary).U~

tAry

=

q

~ V q (Xtp)’U~ tp p+q

ed 2.3.

Line strength

~

(3)

~ ~‘ 2 /~ ,~ Z (f~D(l)~j)I2 e A.r.-y. Ar q

=

(4)

111 ff Here we adapt the following two approximations:

j2

(A)

‘J’A’ rPfJffif r~. •

) a(rPfJfAf~rl~J~A’; f r f ) * a(r~.J.A.,rP~JA~r iii liii

~ V q (A,t,Ar AtAry

•<

J~A~rfY f U(X) Ar~iJiAiriTi>I

(5)

or

That is, we neglect the cross terms between different states admixed to
We must introduce certain average 3-mixing coefficient, for we are

dealing with intermultiplet transitions.

Ia(tpJA,1~’J’A’;r)I2 with / ~

We replace approximately

the following expression:

6rr’~yy’

=

a(~JA,iJ’A’;r)’2~

AFy Ar

I

Ary Ar y

,/

‘6

rr

-~

‘I’

Ary

6

AF

(6)

y’ rr’6yy’

This is a good approximation especially for Kramers’ ions located in low symmetry

circumstances (such as Clh~ C 2, C1 symetry etc.). Then, completing the summation by means of the formulae of reference 2, we get

s~=

2 e A=2,4,6

a(J~,rp.~J’)’2 _____________

23I +1 1

t~).J. t()~J~

~ 2J~,+1

(7)

2

1

where =

~ Iv (x,t,Ary).vq(A,t,Ary)*/(2x+l) tt’ AFy q q *

~ Yq(A~t~P)•Yq(X~t’~P)/(2A+1) tt’ p q 2.4.

(8)

Similarly, the line strength of magnetic dipole transition is:

= ~

~

~

23’ +1

23’ +1

•2 (9)

S. Xia. Y. C/ten / Effect off-Mixing

230

3. CALCULATION OF 3-MIXING COEFFICIENTS 3.1. We calculate the coefficients a of formula (6) in first-order

approximation: 2=

~2

~

ja(~J,~3)I

AFy AFy’

E(rpj)

-

E(~’3’) 2

=

=

E(~J) - E(~’J)

~

~

~

K=2.4.6

=

where

3.2.

(23+1) 11

-

2

(~3~ ~‘3’)

(10)

E(~J)_E(~J) ~

a(~3~~3)!2j

(11)

~2 = 21 lB 2 K 2K+1 q Kq

(12)

According to reference 3, the splitting of multiplet ~3

A(*J)2 ~

~

[E(~3n)-E(~J)J2= 23+1

K=2.4.6 <~3~[u~lN3>2

(13)

Then, when the splitting data of several multiplets are known, the parameters

are easy to get by fitting calculation and the coefficients obtained.

a(rPJ,r~’3’)J2 can be

4. EXAMPLES

4.1.

Emission spectra of EuP 3~ intermediate 5O14 coupling wavefunctions from ref. 4) to calculate We took the E~ and the crystal-field splitting data from ref. 5) to get ~. For example, the experimental branching ratio are 0.003, 0.014 and 0.00 for forbidden transition 5D

7F 7F 7F 0-. 0, 3 and 5, respectively, while the calculated ones are 0.0020, 0.0120 and 0.0018. 3~ 4.2.tookAbsorption spectra ofand Y2O3:Er We the wavefunctions the splitting data from ref. 7). The result has been improved slightly compared with ref. 8) - R.M.S. was reduced from 0.50 x106 to 0.39 x106, for the 3-mixing effect is weak here. REFERENCES

1) B. R. Judd, Phys. Rev. 127 (1962) 750. 2) Tang Au-Chin et al., Theoretical Method of the Ligand Field Theory: Sections 3.1, 4.1, 4.3, 5.4 (Beijing 1979). 3) R. P. Leavitt, J. Chem. Phys. 77 (1982) 1661. 4) G. S. Ofelt, 3. Chmm. Phys. 38 (1963) 2171. 5) C. Brecher, 3. Chem. Phys. 61 (1974) 2297. 6) B. Blanzat et al., 3. Sol. State Chem. 32 (1980) 185. 7) P. Kisliuk et al., 3. Chem. Phys. 40 (1964) 3606.

8) W. F. Krupke, Phys. Rev. A 145 (1966) 325.