RESONANT RAMAN SCATTERING OF 23 cm-1 PHONONS BY Dy3+ IONS IN LaF3

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RESONANT RAMAN SCATTERING OF 23 cm-1

PHONONS BY Dy3+ IONS IN LaF3

S. Yom, R. Meltzer, J. Rives

To cite this version:

S. Yom, R. Meltzer, J. Rives.

RESONANT RAMAN SCATTERING OF 23 cm-1 PHONONS

BY Dy3+ IONS IN LaF3.

Journal de Physique Colloques, 1985, 46 (C7), pp.C7-247-C7-251.

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RESONANT

RAMAN

SCATTERING OF 23 cm-' PHONONS

BY

I)y3+ IONS

IN

LaF3

S.S. Yom, R.S. Meltzer and J . E . Rives

Department of Physics and Astronomy, University of Georgia, Athens, GA. 30602, U.S.A.

Abstract

-

The lifetime of 23 cm-l phonons in LaF3 is reduced

from 600 ns to 125 ns when the transitions within the 6~z5/2

ground manifold of Dy3+ are tuned with a magnetic field Into resonance with the 23 cm-l phonons. Our analysis suggests that the reduced lifetime results from Raman scattering of the 23 cm-1 phonons to lower energy by an amount equal to the energy difference between the two lowest Dy3+ levels.

I. EXPERIMENTAL RESULTS

The lifetime of 23 cn-I- phonons in LaF3, doubly doped with Pr 3+

(-05%) and Dy3+ (0.01%) is measured in the presence of an external

magnetic field up to 30 kG. The 23 cm'l phonons are generated by

spin-lattice relaxation within the 1 ~ 2 manifold of Pr 3+ after selec-

tive excitation of the upper crystal field level, 'D2(?1)/1/. The

phonon lifetime in zero magnetic field (600ns) is obtalned from the decay of the phonon-induced ~ D ~ ( I I ) hot luminescence. The life ime is reduced by up to a factor of 5 when the transitions within the 'H15/2

ground manifold of D ~ are tuned by the magnetic field into resonance ~ +

with the 23 cm-l phonons.

The relevant ener y levels of pr3+ and Dy3+ are shown in Fig. 1. The Zeeman levels of gX15/2(I) and (111, shown in Fig. 2, were determined from fluorescence and absorption measurements on a separate L ~ F ~ : D ~ ~ + sample. As indicated, 23 cm-l splittings occur at 15.9 and 22.7 kG. respectively.

The observed phonon decay rates, as a function of energy

splittings between level la> and Id> (see Fig. 11, are shown in Fig. 3, where the dashed line is included as an aid to the eye, and the solid curve is the best fit to the data using the model described below. The decay rates are resonantly enhanced by factors of 5 and 2.5 when the energy splittings between states

1

a> and

1

d>, and

1

a> and

I

c>, respectively, are 23 cm-l. This resonant-like behavior of the 23 cm-I phonon lifetime suggests that the additional phonon loss mechanism mav be due to resonant, or near resonant, Raman processes,whereby 23 a n d -

phonons are downshifted by an energy 6 lea ing the ionlin the state Ib>.

Since the ground state concentration of D ~ (1.6 x 10 cm-:) ~ + is much

lar er than the excited state concentration of pr3+ (max. N = 5 x l o J 7

~ r n - ~ )

,

this process should be competitive provided the matrix elements

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C7-248 JOURNAL DE PHYSIQUE

-

23 cm-' PHONON c o u p l i n g t h e appro- p r i a t e s t a t e s a r e s u f f i c i e n t l y l a r g e . F a r from r e s o n a n c e t h e luminescence from t h e ' ~ ~ ( 1 1 ) s t a t e d e c a y s w i t h a s i n g l e decay r a t e o v e r s e v e r a l d e c a d e s , w i t h a s m a l l background o f slow decay ( 1 . 1 ~ 1 0 ~ s-1) which i s a t t r i b - u t e d t o h e a t i n g o f t h e c r y s t a l by t h e l a s e r p u l s e . However, f o r f i e l d s n e a r 15.9 and 3 ~ G 4222 22.7 kG t h e i n i t i a l f a s t decay r a t e s , 5937 % which produce t h e i d > d a t a i n F i g . 3, a r e followed by a much slower decay ( 0 . 5 ~ 1 0 ~ 57 S-1) f o r t i m e s g r e a t e r 3 "4 t h a n 0.5 p s . 0 11. _MODEL CALCULATIONS- pr3+ Dy3+ W e p r e s e n t below a r a t e e q u a t i o n model which t a k e s i n t o a c c o u n t t h e s i n g l e F i g I. R e l e v a n t e n e r g l e v e l s o f p r 3 + and phonon p r o c e s s between DY J+ i n LaF3. 23 cm-I phonons a r e g e n e r a t e d t h e two e x c i t e d s t a t e s f o l l o w i n g p u l s e d l a s e r e x c i t a t i o n a t 5917A. o f p r 3 + , t h e Raman F l u o r e s c e n c e i s o b s e r v e d a t e i t h e r 7886 o r s h i f t i n g o f t h e 23 5837

&.

The d e t a i l s o f t h e Zeeman l e v e l s of cm-I phonons i n v o l v - t h e two l o w e s t Dy3+ s t a t e s and t h e r e l e v a n t i n g t h e ground ma i- phonons f o r t h e Raman p r o c e s s e s a r e shown i n f o l d s t a t e s of Dyqt t h e c i r c l e . and t h e s i n g l e phonon

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N _ D ~

refer to the. states in Fig. 1. &he pfihn n op~u~atiofi'b -ers 823,

p23 -6 and jY6 refer to the three pertinent phonon groups indicated In

Flg. 1. Ti.pr and

it^^

are the single phonon relaxation rates between

the appropriate levels,

~

i

is the anharmonic decay rate (1.6 x lo6

k

~

s-l) of the 23 cm-1 phonons and TZ),) are the diffusion loss rates of

the phonons out of the excited volume as determined by elastic point

defect scattering. The Raman rates WRIU and WR DN include processes

involving the transitions

1

a>+

1

c> +

1

b>

pf

us

1

a>+l d>+

1

b> and the

reverse processes.

Fig. 2. Experimental Zeeman levels

of 6~15/2 (I) and (11)~ obtained from fluorescence and absorption measurements. The solid lines represent a theoretical fit to the non- linear Zeeman effect in a magnetic field along the c-axis. The dotted

line is the 23 cm-I phonon energy

from the lowest Zeeman component.

Splittings of 23 cm-I are observed

at 15.9 and 22.7 KG.

10 l l l I ~ l l 8~t I, 8 ~r l ~

Fqg. 3. 23 cm-I phonon relaxa-

tlon rate as a function of the energ difference between the Q3*

7

a> and Id> states (see

Fig. 2). The dashed line drawn

through the data is an aid to the eye. The solid curve represents the best fit using the model discussed in the text. Peaks

(a) and (b) which correspond to fields of 15.9 and 22.7 KG, have half-widths of 1.0 and 1.4 cm-l, respectively.

9

-

According to Orbach/2/, the probability per unit time for the incident or emitted phonons at frequencies wnrlmt and wnlml respect- ively, to be shifted in frequency by 6/K through the process

1

a> -+

I

c>

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C7-250 JOURNAL DE PHYSIQUE 1

₊

1 2 i-.

1

(anlrnl

-

XI

1

-*+~r 6)3 w3 X E n'm' 1 2 H fiwnrm +A;

2rH

where A1 = Ec - E ~ , Ec -Eb,

rH

is the ~omogeneous linewidth associ-

ated with the

1

a>

+bf

c> = + Ib> process and p is the phonon occupation

number.

In the present case the inte ral is evaluated in two steps.

First for the given subset of Dy3' ions within the inhomogeneous line-

width at w 1 (width r,) an integral over the 23 cm-l phonon width, I'23r

sroduces

Then an integral over the Dy3+ inhomogeneous linewidth produces

A number of the parameters in this model are unknown, particu-

larly, ~ i l

rH

~ and rINH for the ~ , D ~ transitions, and the matrix ~ +

elements tor the Raman processes. Schultz and Jeff ries/3/ determined

TilD and the Orbach relaxation rates at low magnetic field. We

extrgpolated T - ~ to the fields of interest in this experiment

assuming isola$&8YKramer's states. From the low field Orbach relaxation rate we calculated the matrix elements for the Raman processes,

assuming no field dependence. An approximate value of

rH

is also

obtained from these matrix elements. r23 was determined experimentally using fluorescence line-narrowing techniques to be 1.5 cm-I in this

sample. The inhomogeneous Dy3+ linewidth,

rINHl

was assumed to be or

the order of 1.0 cm-l.

The calculated heights of the phonon loss rate peaks were primariLy

determined by the Raman rate constant (matrix elements) and

rH.

These

were independently varied to produce the best fit to the data. The resulting values were consistent with the values calculated from

Schultz and Jeffries/3/. The calculated widths shown in Fig. 3 were

primarily dependent on the values of

r23

and TINH. We used our experi-

mental value of i?z3 and varied

rINa

to produce the best fit to the

resonant widths.

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dependence. Fig. 4 . Time dependence of

t h e pr3+ 'D2 (11) lumines- 111.

-

DISCUSSION

cence when t h e Dy3+

1

a > +

1

d > Although some o f t h e p a r a m e t e r s o f 1

e n e r g y s p l i t t i n g i s 23 c m

.

t h e model a r e n o t w e l l known, t h e The long-time slow decay q u a l i t y of t h e f i t t o t h e d a t a , w i t h d i s a p p e a r s o f f resonance. r e a s o n a b l e v a l u e s o f t h e s e p a r a m e t e r s , _{s u g g e s t s t h a t phonon-induced Raman}

p r o c e s s e s w i t h i n t h e ground m a n i f o l d o f t h e Dy3+ i o n s a r e indeed r e s p o n s i - b l e f o r t h e o b s e r v e d b e h a v i o r o f t h e 23 cm-l phonon l i f e t i m e . E x p e r i - ments a r e c u r r e n t l y underway t o measure t h e t i m e dependence o f t h e p o p u l a t i o n o f t h e Dy3+ ] b > s t a t e t o f u r t h e r t e s t o u r u n d e r s t a n d i n g of t h e r o l e o f t h e r e s o n a n t Raman p r o c e s s e s .

?-Research s u p p o r t e d i n p a r t by t h e U . S . Army Research O f f i c e , c o n t r a c t NO. DAAG29-84-G-0021.

phonons w i l l enhance t h e r e s o n a n t Raman p r o c e s s e s Ib> l c > l a > o r Ib> + Id> +

1

a > . T h i s w i l l i n t u r n add t o t h e 23 cm-I phonon p o ~ u l a t i o n

and t h u s t h e p o p u l a t i o n of t h e (11) s t a t e . Decreasing t h e d i f f u s i o n l o s s

-1

- r a t e i n t h e r a t e equatjrons had l i t t l e . e f f e c t on t h e i n i t i a l f a s t decay, b u t had a d r a m a t i c e f f e c t on t h e decay - r a t e o f n2 f o r t i m e s g r e a t e r t h a n - a b o u t 0.51~s. The long-time t a i l o f . . t h e d a t a a t t h e r e s o n a n t f i e l d o f

5

REFERENCES ,*::

-

' ,, . . ... ..; .. . . . . . . ... a

/ I / Godfrey, L., Rives, J . E . and M e l t z e r , R. S . , J . Lumines. 18/19,

929 ( 1 3 7 9 ) .

/2/ Orbach, R . , Proc. Roy. Soc. (London) A=, 458 (19611.

/3/ S c h u l t z , M. B . and J e f f r i e s , C. D . , Phys. Rev.

149,

270 ( 1 9 6 6 ) . 15.9 kG, F i g . 4 , was reproduced s a t i s f a c t o r i l y w i t h T d ( 6 ) = 2 . 3ps. The d i f f u s i v e t i m e s f o r o t h e r f i e l d s

0 I 2 3 and phonon e n e r g i e s were s c a e d