Evidence for energy transfer induced by superexchange in LaF 3 : Pr3+

(1)

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Evidence for energy transfer induced by superexchange

in LaF 3 : Pr3+

J.C. Vial, R. Buisson

To cite this version:

J.C. Vial, R. Buisson. Evidence for energy transfer induced by superexchange in LaF 3 : Pr3+. Journal

de Physique Lettres, Edp sciences, 1982, 43 (21), pp.745-753. �10.1051/jphyslet:019820043021074500�.

�jpa-00232120�

(2)

Evidence for energy transfer

induced

by

superexchange

in

_{LaF3 :}

Pr3+

J. C.

Vial

and R. Buisson

Laboratoire de

_{Spectrométrie Physique}

_(*),B.P. 53 X, 38041 Grenoble _Cedex,France (1~~~~c le

1.5,~ui~t

1982, r~vis~ le 2

_septembre,

acce~te le 10

_{septembre 1982)}

Résumé. 2014 Les taux d’extinction pour

plusieurs

paires

de Pr3+ dans

_LaF3

faiblement

dopé

ont été

mesurés directement.

Puisqu’ils

sont

significatifs

pour

quelques paires

seulement, le mécanisme est

à courte

_portée.

A

_partir

des valeurs mesurées, la forme du déclin de la fluorescence de cristaux

fortement

dopés

est

_prévue.

Le bon accord avec

_{l’expérience}

montre l’intérêt de relier les mesures

microscopiques

et

_{macroscopiques. Enfin,}

des _argumentssont _{avancés pour prouver que le mécanisme}

de transfert est le

superéchange.

Abstract 2014 Direct measurement of fluorescence

quenching

rates for various Pr3+

pairs

in

weakly

doped LaF3

are

_reported.

Since few

_{pairs only}

are

_quenched,

the transfer mechanism is short range.

From the rate values, the

_shape

of the fluorescence

_decay

for

_{heavily doped samples}

is

_predicted.

The

_good

agreement with the observed

_decay

proves the interest of the connection between

micros-copic

and

_macroscopic

measurements.

_Finally

_argumentsare

_developed

to prove that the transfer

mechanism is

_{superexchange.}

Classification

Physics

Abstracts 78.5020137855

Among

the

_possible

interaction mechanisms for

_optical

_{excitation, exchange}

is often discounted in rare earth

inorganic

_systems

although Birgeneau pointed

out that it could be as efficient as

the other mechanisms

_{[1]. Frequently,}

a

_multipolar

electric interaction is

_postulated,

the nature

of which is deduced from the

_shape

of the donor fluorescence

_{decay using}

the

_{Inokuti-Hirayama}

formula

_[2].

When used for

_{randomly doped}

_crystals,

that method

_implies

a statistical _average over the

possible

positions

of the

_acceptors

around the donors and is

subject

to the

_hypothesis

that a

_single

mechanism is active. It is well known that the conclusions deduced from this «

macros-copic

»

_approach

are

_{questionable,}

the fit between theoretical and

_{experimental decay}

curves never

_{being perfect Improvements}

of this

_approach

either

by

Dornauf and Heber

_[3]

and Siebold

(*)

Laboratoire associ6 au C.N.R.S.

(3)

L-746 JOURNAL DE _{PHYSIQUE -}LETTRES

and Heber

_[4]

with a « discrete model » instead of a continuous

_model,

or

_{by Hegarty et}

al.

_[5]

who deduce the

_microscopic

transfer rate between two

_nearby

ions from

_macroscopic

_results,

need nevertheless the

_hypothesis

that a

_single

mechanism is active.

It has been shown

_recently

that

_microscopic

transfer rates can be measured

directly

when a class of

_pairs

of ions can be

_selectively

excited

_{[6]. Using}

_{weakly doped crystals, pairs}

are well

« _{isolated » and their intrinsic}_behaviour_{is observed.}From these measurements, it was inferred

that the transfer mechanism could not be the same for

_weakly

and

_{strongly coupled pairs.}

The

possible

co-existence of various mechanisms has been considered

_by

Watts

_[7]

who

_showed,

by

numerical calculation of the

_{quadrupole-quadrupole}

and

_{dipole-dipole coupling strength}

between

Yb3 +

and

_{Er3 +,}

that the former dominates the latter for ions

_{separated by}

less than 9

A.

The results

_reported

here,

again

based on the direct

_study

of the

_properties

of

_pairs,

show

unambiguously

that a short _rangeinteraction dominates the

dipole-dipole

interaction and is

responsible

for the

_quenching

_previously

attributed to

_{dipole-dipole coupling}

from

_macroscopic

measurements

_{[8]. They}

are then used to

_predict,

with success, the behaviour of more

_heavily

doped samples : starting

from

_microscopic

values

_{macroscopic experiments}

are

explained.

The _system

_studied,

_{LaF3 : Pr3 +,}

is a _verywell known

_system

whose _energylevels have been

tabulated in detail

_by

Carnall et al.

_[9].

Most of the energy transfer

experiments

made with it have been

_presented

and

_{analysed by}

Yen in a review _paperon _energytransfer in rare earth

ions in

_{crystals [10].}

The _present_paperis centred on the

_quenching

of the

3po

fluorescence. The first

_study

of this

quenching by

Brown et al.

_[11]

_has

shown that it results from cross relaxation between one

Pr3 +

excited and one

_nearby

unexcited

Pr3 +.

This

_quenching

has

_recently

been studied

_by

the Madison

group with modem

experimental techniques.

Lai et al.

[12], by

a

cooperative absorption,

excite

two

_neighbouring

Pr3 +

ions in

_PrF3

with a

single photon, putting

one ion into the

_{3p 0}

state,

the other into the

_{3 F2}

state. Ions excited into

_{3 Po}

have then one less

_quenching

_channel,

the

nearby

ions excited

_{into 3 F2}

_being

not able to cross relax with them.

_{By measuring}

the

change

of the lifetime of these ions with _respectto that of

_normally

excited

_ions,

the cross relaxation

rate between two

_neighbouring

ions is deduced.

_{Hegarty et}

al.

_{[8], using}

Inokuti and

_Hirayama

formula,

deduce also the value for this rate within the

_hypothesis

of

_{dipole-dipole coupling.}

To reach this

_conclusion,

_paradox

but shows the

_peculiarity

of the method.

1.

_Experimental

results. -

Figure

1 shows the

_absorption

_spectrumaround the

_{main 3H4-+ 3po}

transition. It is now well established that satellites are due to

_pairs

of ions

[6]. By monitoring

the

fluorescence induced

_by

a narrow

_{dye-laser pulse,}

it is

_possible

to record time resolved excitation

spectra

as shown in

_figure

1 or to observe the fluorescence

_decay

after a selective excitation of a

_given

satellite as

given

in

figure

2. For the

f line,

the slow

_component

associated with the central

line has been subtracted from the actual

_signal.

The

_decay

for lines a and f is

exponential

for more than two

of the main line is shorter than that of lines c and d

(this

is deduced from the

_comparison

of the two excitation _spectrashown in

(4)

Fig.

1. - The lower _curveis the

absorption

spectrum of a

_{LaF3 :}

0.1

_%

Pr3 +

_sample

around

the 3H4 -+ 3p 0

transition. The two other curves are time resolved excitation _{spectra of}

the 3 Po

fluorescence with two different

delays

after the laser

_pulse.

Note that the _gainfor the 40 us spectrum is twice that for the 5 us spectrum.

The reduction of the

_decay

time in the

_wing

of the main

_line,

_{already pointed}

out for

_heavily

doped samples [13]

as well for

1 D2

fluorescence in

weakly doped samples [14]

will be discussed

elsewhere.

As first

_{proposed by}

Brown et al.

_{[ 11 ],}

the reduction of the

_{3 Po}

lifetime results from a cross

relaxation between an excited and an unexcited ion. From the measured lifetimes r and the radiative lifetime _{To =}48 x

10- 6

_J.1sof the isolated ions

_[15]

it is _easyto calculate the cross

relaxation rate

_{w c for}

each satellite

_by

The choice of _toas the radiative lifetime for the ions of the

_pairs

is

_{justified by}

the fact that

the relative intensities of the fluorescence lines

_{corresponding}

to the transitions

_{from 3 Po}

towards the levels of the

_{sublying multiplets}

are the same whether the central line or a satellite is excited.

If the

_perturbation

created on a

Pr3 +

_by

another

_nearby

Pr3 +

_{changed significantly}

the oscillator

strengths

of the

transitions,

it would be

_surprising

that this

_change

would be the same for all

the transitions.

These results are now used to determine the nature of the

_{coupling responsible}

for the observed

cross relaxation. As it will appear

below,

this determination will result from

_strongly

_convergent

evidence. The

_{only remaining problem}

lies in the

_difficulty

of

_associating

a definite class of

_pairs

with each satellite. This

_problem

has

_already

been

_pointed

out

_[6]

and its resolution would need

(5)

L-748 JOURNAL DE PHYSIQUE - LETTRES

Fig.

2. -

3p 0

decay

of a

_{LaF3 :}

0.1 _%Pr3 + _sample

following

a selective excitation: 8 of line f, 0 of line a,

. of lines c, d, and the central line. The two other curves

_correspond

to lines b and e. Note that for f

line,

the contribution of the

_wing

of the main line has been subtracted.

Table I. - Values

of

the

_decay

time 1: and

of

the cross relaxation rate

_{W ~}

_for

the various

_pairs

associated with the satellite

_{of figure}

1.

The determination of the nature of the

_coupling

between the two

Pr3 +

ions of a

_pair

is based on three arguments now

explained

in detail.

1.1 VARIATION OF THE TRANSFER RATE WITH THE DISTANCE. -

The sequence of the transfer rates of table

_I,

after normalization is 1-0.26-0.01-0.006.

From

the

_LaF~

_structure

_[17],

the

_possible

pairs

can be characterized

_by

the

couple

_(n-R)

when n is the number of sites at a

_given

distance R

from a La site. The list of these

couples, starting

from the lowest

R,

is

Pairs in the same bracket are

_{nearly equivalent}

but those

_belonging

to classes

_{having n}

= 2

have a

_symmetry

_operatorwhich

inter-changes

the two ions. This

_operator

is a two-fold axis for

(6)

mechanism is

_supposed

for the cross

_relaxation,

the rates would _vary

_along

the R - 6

_following

normalized sequence : 1-0.81-0.75-0.64-0.10-0.089 and if a

dipole-quadrupole

transfer mechanism

is

_supposed,

the sequence would be

R ‘ 8

i.e. : 1-0.75-0.68-0.55-0.048-0.040. Even if a satellite

would

_correspond

to more than one class of

_pairs,

it is clear that these two _sequencesare

incom-patible

with the sequence of the observed rates. This is the first argument for

_{rejection of}

dipole-dipole

and

_{dipole-quadrupole}

mechanism.

’

1.2 ORDER OF MAGNITUDE. - From

the energy levels of

LaF3 :Pr3+

[9],

the more

_probable

quenching

processes for the

3p 0

fluorescence are :

the former

_being

assisted

_by

the emission of an _{energy of}265

cm-1

as

_phonons,

the latter

_needing

the

_absorption

of a

_phonon

of 71 cm - 1. At low

_temperature,

_only

the former is active. From the

_general

_{theory developed}

_by

Holstein et al

[ 18]

it is easy to show that the transfer rate takes

the form

where

and I i >

=

~0~(9), ~G~(9) ~

the

_single

intermediate state

which,

by

far,

gives

the _greatest

contribution,

£1’ EF, Ei

the energy of these electronic

_{states, ~ ~ ~}

_and

_{I VF >}

the vibronic states

associated

_with

_{I i > and}

_{F ~}

_p(EF)

the

_density

of states of the final state and

_HOL

an ion lattice

Hamiltonian. Due to the

fact

that

_{~p ~}

250

_{cm- 1,}

two

_phonons

of total _{energy of 265}

cm-

1

must be emitted

_between

_{I I > and}

F ~

Thus

_{H OL is}

an effective Hamiltonian able to induce a

two

_phonon

process. The term in brackets is of the same order of

_magnitude

as a one ion relaxation

rate

_W~~,

_between

_{flG4(9) >}

and

_{J ~0~(8) ~}

which would create two

_phonons

of a total _energy

of 265

em -- 1

instead of 336

em - 1

for a real relaxation between these states. This rate is itself

of the same order of

_magnitude

of rates

_involving

similar

_phonons

which can be deduced from

linewidth measurements

_{[19]. Equation (2)}

can thus be written as :

with

The ion-ion interaction is estimated in the case where it is

_multipolar

electric

_using

the calcu-lations of Kushida

_[20]

and the wavefunctions of Weber

_[21].

For two ions at 5

A

one from

ano-ther,

the results are :

These weak values result from the

_{spin-forbidden}

matrix elements

_{between 3pO}

and

₁₀₄

and between

_3H4

and

_1~4;

the zero value for

_{quadrupole-quadrupole}

interaction results from J selection rule between

_3pO

and

_104.

_{Using (4)}

and

_(5),

the transition

_probability

₍₂₎

is estimated

(7)

L-750 JOURNAL DE PHYSIQUE - LETTRES

to be :

These rates are _verysmall

compared

to the measured 97 000 s-1 and 25 000 s-1 values for lines f and a. The upper limit for

_{dipole-quadrupole}

interaction becomes however

_comparable

with the rates observed for the lines b and e.

Thus,

a short range interaction has to be considered

in order to

_explain

the

_experimental

measurements of the cross relaxation transfer rates.

1. 3 INTERPRETATION OF FLUORESCENCE DECAY IN HEAVILY DOPED CRYSTALS. -

Recently,

Hegarty et

al.

_[8]

have studied the

_quenching

of the

_3Po

fluorescence in

_{heavily doped samples.}

For a 20

_{% sample, they explain}

the observed

3pO

fluorescence

_{decay by}

_anyof the usual mechanisms.

_They

note however the existence of an

exponential

tail at

_long

times and

_they

attribute it to

_special

ions

_occupying

« non

_quenching

» sites.

_Subtracting

this tail from the total

signal, they

obtain the

_decay

of the « normal » ions which is in _agreementwith a

_{dipole-dipole}

interaction.

It is shown

here,

that the observed

_signal

can be

_{interpreted by taking}

into account

_only

transfer between the two ions of the

_pairs

associated with satellites f and a. For

that,

it is necessary to

recall some results on transfer in diluted

_systems.

In a

crystal doped

with a concentration _x,

the fluorescence

_decay

of the donor

_ions,

in absence of back

_transfer,

can be written as :

where

_Wr

is the radiative rate,

W,,

the non radiative cross relaxation rate induced

_by

one of the

_Na

equivalent

ions which make the class a of

pairs

with the central ion. The contribution to

_4J(t)

of the class oc is

( 1 -

jc)~

for t >

_{1 / Wa}

and

_{( 1 )Na}

for t

1/~.

Since table I

_gives

the values of the

_W,,,

for the various classes of

_pairs,

it can be seen that in the time interval 100-200 _J,1S,

_pairs

associated with satellites f and a contribute to

_{4J(t) by (1 -}

_x)Nf+N°

while

_pairs

associated with satellites

b,

e, c, d do not contribute

_{significantly.}

Thus,

in this time interval :

This behaviour

_predicted

from the results of table I is in

_qualitative

_agreementwith the

experi-mental

_{0(t) reported by Hegarty et}

al.

_[8]

for x = 0.20 _asshown in

figure

3,

since the

exponential

variation at

_long

time with a rate

_Wr

is indeed observed. The

_comparison

between this

_decay

and

_{equation (7) gives}

the value

_{of ( 1 -}

_x)Nr+Nø

from which one deduces

_{(N f}

+

_{Na) ~}

9.

_Thus,

only

cross relaxation between one ion and its

_possible

9 first

_neighbours

has to be considered.

However,

by looking

at the list of the

_{pairs given by equation (1),}

one can

hardly

find what are

the

_pairs

associated with lines f and a. In the

_following,

we _{suppose that the 6 classes}of

_pairs

of

the first bracket are associated with satellite

_{f (N f}

=

6)

and that the 4 classes of

pairs

of the second

group in the second bracket are associated with satellite a. This choice is the weakness of our

interpretation

because it appears as an ad hoc choice.

_Indeed,

if

_Nf

= 6 _canbe

justified by

the

near

equivalence

of the

pairs

of the first

bracket,

the

single peculiarity

which can be

_given

to

justify

Na

= 4 is that the other 2 classes of

pairs

of the second bracket _are

pairs

with _aninversion

centre. It must be recalled that

_peculiar

and

_{unexplained properties}

have

_already

been

_reported

for some

Pr3 +

pairs [20].

The

_{decay given by equation (6)}

can then be calculated with

_only

the two classes of

_pairs

f and a,

using N f

=

6,

Na

= 4 and the values

W f

and

W a

of table I. The

comparison

with the

(8)

Fig.

3.

_{- 3Po}

fluorescence _decayof a

_{LaF3 :}

20

%

Pr3+ _sample.Points are

_experimental

_points

as

_reported

in reference

_[8].

The curve is

_0(t)

of

_equation

₍₆₎with a = f, _a,with

_Wf

and

Wa

as

_given

in table I and with

Nf

= 6,

Na

= 4 as

_explained

in the text.

The

_agreement

is _very

_good

for the whole time domain studied.

_Thus,

our

_{description gives}

an

alternative

_{interpretation}

of the

_{Hegarty et}

al. results which does not need to _{suppose the existence}

of

_special

ions. Our

_description

can also be used to

_predict

the

_{slopes s}

at t = 0 of _a

semi-log

plot

of

_0(t).

From

_{equation (6) :}

s can be calculated with

_{W r}

= 0.021

ps-

and

the values of

W f

and

W a

of table I and

compared

with

_experiment

Table II

_gives

the results of this calculation and the

_experimental

values for

various concentrations. The

_experimental

value for x = 0.05 is taken from _aresult observed

at T = 40 K when the

decay

is

exponential

due to the diffusion

among the

Pr3 +

ions

[13];

as shown

_by

Huber

[22]

the

slope

is also

given by (8)

in that case.

Table II shows that the

_agreement

is _very

_good

for moderate concentrations and

_gives

the

proof

that cross relaxation with the 10 near

_neighbours

_(at

a distance of less than 4.42

A)

domi-nates the

_quenching

of the fluorescence. It is

_thought

that the

_disagreement

for

_higher

concen-trations results from the fact that the essential

_hypothesis

made to establish

_{equation (6), namely}

that all transfers occur between two _ions,is no

_longer

valid and that three

_(or

_more)

ion

_quenching

processes have then to be considered.

We

_conclude,

from these three

_arguments,

that indeed a short _rangeinteraction dominates

(9)

L-752 JOURNAL DE

PHYSIQUE -

LETTRES from the

_experimental

rates

_{using equation}

₍₃₎

and the estimation

_{(4) :}

Table II. - Calculated and observed values

of

the

_slope

s

_(in

J.ls - I)

at t = 0

of

the 3Po

fluorescence

decay for

various concentrations x

of Pr3+

in

_LaF3

_(see

_Eq.

_(8)).

These values compare well with those obtained

_by

a direct measurement

_using

a two _laser

spec-troscopy

technique

[23]

which are of the order of 0.2 to 0.5 cm-1. All these values are

_compatible

with some estimations

_{by Birgeneau [1] of}

the

_{superexchange coupling.}

The structure of

_LaF3

is also in favour of this

_coupling

since for the first four classes of

_pairs

of the list

₍₁₎

_(i.e.

in the first

two

_brackets,

the two ions have in common

_{respectively :}

_polyhedron

of

_{11 ligands}

_(maximum

La-F distance 3.08

_A)).

The above values are also of the same order of

_magnitude

as those deduced

_by

Meltzer and

Moos

_[24]

from the

_lineshape

and

_position

of the

_{magnon-exciton}

transitions in

_GdCl3

and

Gd(OH)3

and attributed to

_exchange

interaction between

Gd3 +

ions. The more recent results

of Cone and Meltzer on

_Tb(OH)3

_[25]

also indicate the

predominance

of

exchange

interaction

for some exciton

_dispersion.

To

_summarize,

the direct measurement of cross relaxation rates between ions associated in

pairs

has been used to show that the

_quenching

of

_{3p 0}

fluorescence results

_essentially

from the interaction between one

Pr3+

and its

_possible

10

Pr3+

nearest

_neighbours.

This interaction is thus of short _rangeand

_arguments

are

_given

to show that it is

_{superexchange. Although}

the

efficiency

of this mechanism was

_already

observed for

_{GdCI3, Gd(OH)3,}

_Tb(OH)3

from measured exciton

_{dispersion [24,}

_25],

a

proof

based on direct measurement of transfer rates has not

_yet

been

_presented.

The values of the cross relaxation rates measured on the well isolated

_pairs

present

in

_{weakly doped crystals}

are also used to calculate the behaviour of

_{heavily doped crystals,}

making

thus the first connection between

_directly

measured

_microscopic

and

_macroscopic

quantities.

The

_comparison

of this calculated behaviour with

_experiments

is very

good

and indicates the

_{probable efficiency}

of processes

involving

more than two ions when the

concen-tration exceeds 50

_%.

It is

_hoped

that the connection between

_{microscopic properties}

and the collective behaviour in stoichiometric

crystals

will also be

_possible.

Acknowledgments.

- It is a

pleasure

for the authors to thank F. Madéore for his technical

assistance and R. Romestain for a critical

reading

of the

manuscript. They

also wish to thank

(10)

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