Nonradiative energy transfer between Cr3+ and Nd3+ multisites in Y3Al5O12 laser crystals

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Nonradiative energy transfer between Cr3+ and Nd3+

multisites in Y3Al5O12 laser crystals

J. Mareš, Z. Khás, W. Nie, G. Boulon

To cite this version:

J. Mareš, Z. Khás, W. Nie, G. Boulon. Nonradiative energy transfer between Cr3+ and Nd3+

multisites in Y3Al5O12 laser crystals. Journal de Physique I, EDP Sciences, 1991, 1 (6), pp.881-

899. �10.1051/jp1:1991174�. �jpa-00246375�

J.

Phys.

II

(1991)

881-899 _JUIN 1991, _PAGE 881

Classification Physics Abstracts 78.50 78.55

Nonradiative energy transfer between Cr~+ _and Nd~+

multisites in Y~Alsoi~ laser crystals

J. A. Mare§ (~), ^{Z. Khhs} (~), ^W. Nie (2) and G. Boulon (2)

(t)

Institute of

Physics,

Czechoslovak Academy of Sciences, Na Slovance 2, 180 40 Prague 8, Czechoslovakia

(2) Laboratoire de

Physico-Chilnie

des Matbriaux Luminescents

(*),

Universit6

Lyon

1, ^{43 Bd} du ii Novembre 1918, 69622 Villeurbanne, France

(Received13

December 1990,

accepted

in

final form

26

February 1991)

Abstract. The C~+

~Nd~+

nonradiative _energy transfer between various

C~+

_and

Ndl+

_{multisites has been studied from both} Cr~+ and

Nd~+

fluorescence

decays

in

good optical quality

solid _state laser crystals

Y3AlsO12.Nd,

Cr at low temperatures under site selective

excitation of C~+ multisites. Various Nd~+

decays (fast mono-exponential

_or double nonexpo-

nential)

have been observed. The _new

theory

of Rotman _was used to fit the Nd~+

decay

curves.

This

theory

_was derived for nonuniform correlated distribution of ions in the

crystal

and it is _an advance in comparison with the classical

Inokuti-Hirayama

theory for _a uniform and random

distribution of ions. The results show that the Nd~+ decay curves are time broadened due to the Cr~+

~

Nd~

+ nonradiative _energy transfer and that the best fits were obtained for _a nonuniform enhanced volume correlated distribution of C~+ _and Nd~+ _{ions in}

Y~Alsoj~

laser

crystals.

1. Introduction.

Progress

in _new

spectroscopic techniques

such _as

high

resolution site-selection _or time- resolved

spectroscopies

stimulates research of solid state laser materials

[1, 2].

Classical

(YAG)

_as well _{as new}

Gd~sc~Ga~oj~ (GSGG), Gd~Ga~oj~ (substituted GGG)

and

LamgAljjoj~ (LMA)

solid state laser

crystals

_{are now} studied

[3, 5].

In order to increase the

efficiency

of the

Nd~

+

-doped

laser

materials,

_a method of

codoping

with another ion

(donor)

is used

[6].

If _energy transfer from donor ions to

Nd~+ _{acceptors exists,}

_{then an}

improved pumping

of

Nd~+

_ions

can be reached. The most used

codoping

ions _are

Cr~+

_and

Ce~+

_{and the energy transfers}

Cr~+ ~Nd~+

or

Ce~+ ~Nd~+

_{contribute to}

a better

performance

of

C~+

_or

Ce~+ codoped

YAG:Nd laser rods

[7-14]. Generally,

the

Cr~

+ concentration in YAG _:

Nd,

^Cr

crystals

are low

(higher ^Cr~

⁺ concentrations result in the breakdown of

optical

and mechanical

properties

of this

crystal [14]

while the

codoping

of

GSGG with

Cr~+

_{results in}

a substantional

improvement

of GSGG laser rods

[1-3].

The modern

spectroscopic techniques

enable _a characterisation of the energy transfer between

(*)

URA 442 CNRS.

codopants

and

Nd~+

_{acceptors and also other studies of the} distributions of donors and

acceptors,

structure of

nonequivalent

centres

(multisite effect)

etc, in laser materials

[15-21].

The

quality

and

lasing efficiency

of _a solid state laser

crystal depend

_on the number of

Nd~+

or

codoping ions,

_on their

properties

and mutual interactions

[1, 2, 22].

In

codoped

YAG:Nd

crystals

there _are either

slightly perturbed

main sites

(e.g, dodecahedrally

coordinated

Y~+

_lattice

sites)

_or minor

perturbed

sites which _can be detected from their emission spectra at low temperatures

[16, 18, 23, 24].

Our last studies of

high quality

low concentrated YAG _: Cr and YAG _:

Nd,

Cr

crystals [15-17, 19]

have shown the _presence of

C~+

_and

Nd~+

_{multisites in these}

crystals (see Fig, I). Energy

transfers either between

C~+

_multisites

or from

Cr~+

_{multisites to}

Nd~+

_multisites

were observed from

high

resolution

dye

laser excitation spectroscopy at

liquid

helium

temperature

where the lines of

(al (b)

9

s~ ^{5 7} ₈

685 877 878

~Inml

Fig. I. Enfission spectra ^of YAG:Cr~+

(a) ([15])

and YAG:Nd, Cr

(b) ([16])

at 4.2 K under excitation at 532 _nm (R, Si-S~ are

Cr~+

_sites while 1, 2,.., 9 _are Ndl+ sites).

~~

~

2

~

~

^{Ii £NERGy}

j~

TRANSFER

~

~

^b

~'2

_a

~

~

~ I912

At

~

cr* Nd"

Fig.

2. Energy level schema of _one of the C~ + or Nd~+ multisites with studied transitions and energy transfer.

M 6 Cr3+

~

Nd3+ ENERGY TRANSFER IN Y3A15012 883

multisites _are well

separated [15, 16] (energy

level schema of

Cr~+

_and

Nd~+

_ions

are in

Fig. 2).

These measurements and studies _must be carried out at low temperatures ^{because due} to the

widening

and

overlapping

of the _narrow emission _or excitation lines with _an

increasing

temperature

(it

is caused

by phonon

interactions

[1, 6]),

it is not

possible

to excite

selectively

the individual

Cr~+

or

Nd~+

_{multisites at}

higher

temperatures

(e,g.

at room

temperature).

Besides the excitation

spectra,

another _way to

study

the _energy transfer between donors and acceptors

(or

between their

multisites)

is a

study

of

selectively

excited donor _or

acceptor

fluorescence

decays [6]

and their

interpretation by using

_energy transfer theories such _as the

theory

of Inokuti and

Hyrayama [25]

_{or more} recent theories of Rotman and Hartmann

[26- 29].

The main purpose of this _paper is to present new data about

Cr~

+ and

Nd~

+ multisites and

transfer _processes between them, The _new data and results _were obtained from the

measurements of

C~+

_and

Nd~+

fluorescence

decays (for ^2E

~

~A~

or

~F~/~(a)

_~

~I~/~(l)

transitions between

Cr~+

_or

Nd~+ _levels, respectively)

at

liquid

helium

temperature.

The

decays

_were either obtained

by

selective excitation

(into absorption

lines of individual

C~+ multisites)

_or due to energy transfer from _some of the

Cr~+

_{multisites to}

Nd~

+ multisites. This _paper

belongs

to _our series of papers about

Cr~

+

doped

YAG

[15, 17]

and

C~+ codoped

YAG _: Nd

[16, 19].

2. Fluorescence

decays

^and nonradiative energy transfer mechanisms between donors and acceptors ⁱⁿ

crystals.

Various _energy transfer mechanisms between donors and

acceptors

^{have been summarized in} several

significant

books and _papers

[1, 2, 6, 25, 26, 30].

Our last results _on

YAG:Nd,

Cr

[16, 19]

show that

Cr~

+

~

Nd~

+ energy transfer is nonradiative in nature and takes

place

from the

~E

_{doublets of}

Cr~

+ ions. This is the _reason

why

_we will deal with

only

nonradiative energy transfer between donors

(D)

and acceptors

(A).

The nonradiative energy transfer between donors and

acceptors

^{arises due} to either

multipolar

or

exchange couplings [25,

3

Ii.

The classical _case where there is _no diffusion of excitation, _energy between donors and where the distribution of donors and acceptors ^is random and uniform

(see Fig. 3a)

_was treated

by

Inokuti and

Hirayama [25].

Their well-known formula for nonradiative energy transfer between donors and acceptors ^caused

by multipolar

interaction is the

following

:

ID (t)

=

ID(0)

_exp

(- t/T))

_exp ^{~ "}

_NA RI

r

(1

~ ~

l(1)

3 _s

To

~~~

where

ID(t)

and

ID(0)

are donor fluorescence

intensity

at times t _or t ₌

0, respectively,

vi

is the intrinsic donor fluorescence lifetime if _no acceptors are present,

N~

the

concentration of

acceptors, Ro

^{the critical}

distance, r(1-

^~ _{the Euler function and}

s s =

6,

⁸ or 10 the coefficients of

multipolar

interactions.

The real distribution of

impurities

in

crystals

is far from

being

uniform and random. It is necessary ^to use restricted

geometries (crystals

_are

finite),

but the _most

important assumption

is the

position

correlation between donors and acceptors as was introduced

by

Rotman and Hartmann

recently [26, 28].

The correlation _means that the location of _a donor at _a

specific

site is influenced

by

the presence of

nearby acceptors

^which means that the distribution of

acceptors

^{around donors is} not uniform.

Figure

3a

presents

^{the radial}

probability

distribution

functions for _a

uniform,

excluded and enhanced volume distribution of

acceptors

^around donors.

JOURNAL DF PHYSIQUE i T ], M 6. JtJIN iQ91 35

~

r< Ro q

uniform

2

I

i

_{°O 2 3}

a

~

3

f

f excluded

J

~ ~ ~

y

^C

# _{~_}

_q

m o

$

~ °O 2 3

+ d

fl

~ enhanced

~ -3

0 10 20 40 50

)

^' t[PSI

b)

~0 _{2 3}

a)

_{radial distance} Inm)

Fig.

3.

(a)

The radial distribution for uniform, excluded and enhanced volume distribution of acceptors ^{around donors.}

(b) Sample decay

curves for excited donor concentrations for various donor- acceptor distributions

(I-H

means

Inokuti-Hirayama).

This

figure

is taken from Rotman and Hartmann

[26].

For excluded volume

(sphere

of radius

ri)

of acceptors ^{around each donor and} no diffusion between

donors,

the

intensity ID (t)

of donor fluorescence for

multipolar couplings

is

given by

ID(t)

=

ID(0) exp1-

^{~ exp}

^{(cvi Ii}

^~P+

^{(zi)lexp zil)}

,

(2)

vo

where _c is the average concentration of

acceptors (c

=

3N~/4 arr(), _Vi

=

~

arr)

is the 3

excluded volume

(sphere

of radius

rj), Zj

=

(llo/rj)~(t/T)),

_~fi~

_(Zj)

= ~fi

I, ~, _Zj

_is

s

the

degenerate hypergeometric

function and

Ro

^{the critical radius.}

For enhanced volume correlated

placement

of

acceptors

around each donor the

intensity

of donor fluorescence

ID(t)

is

given by

ID(t)

=

I~(0) xp1-

_~

A ^~

(art/T))~'~

To ^Co

cvj (B

A 4~~

(Zj )

_exp

(- Zj cV~(I B)

_~P~

(Z~) exp(- Z~)1

,

(3)

where

Vi

=

~

arr)

and V~ ₌ ^~

arr(

are the volumes of

spheres

of radii _rj and r~,

respectively,

A

3 3

and B _are constants of distribution

(see Fig. 3a),

_co

=

3/4 arR/

the critical concentration and

M 6 Cr3+

~

Nd3+ ENERGY TRANSFER IN Y~A15012 885

z~

=

(Ro/r~)~(t/Tf).

For enhanced volume correlated arrangement ^the constants A _» I in the

sphere

of radius _rj while in space between _rj and _{r~ B}

< I. For excluded volume correlated

placement

A

< I in the

sphere

of radius _rj. For uniform random distribution A

= B

= I is

valid and the classical

Inokuti-Hirayama equation (I)

is derived from

equation (3).

The radii

rj, r~ are connected with constants A and B

by

the

expression Ar)+ B(r(- r/)

=

r(.

A

detailed treatment of donor fluorescence

decays according

to

equations (1)-(3) gives

_us

(see Fig. 3b)

data about the distribution of donors and

acceptors

ⁱⁿ

crystals.

The deviations often observed between the measured and theoretical fluorescence

decay

curves can be

explained by

the correlation

theory given

above for donor and acceptor ^ions.

But there _are also

discrepancies

which cannot be

explained by

this

theory, especially

the fast energy transfer at short times

[32, 33].

A model which _can

explain

this behaviour is the

multiple

mechanism model where it is assumed that the critical distance

Ro (from multipolar couplings) changes

with

donor-acceptor separation

distance due to several mechanisms of

energy transfer which _occur

simultaneously (e.g, dipole-dipole

and

quadrupole-dipole

_or

exchange

and

dipole-dipole etc.).

Rotrnan

[32]

has derived the formula for the _case of two

multipolar

transfer mechanisms characterized

by

critical distances

Roi

^and Ro~

Roj

_< ri <

Ro2

which is

ID(t)

=

I~(0)

_exp

~-

^{~ exp}

-

~ r

(1

~ ~

+

T~ cot ^s To

+

C~'l iffi+ (Zll)/~Xp(Zll)

ffi

+

(~f12)/~XP(~f12)1), ⁽⁴⁾

where _cot

=

~ and

zj,

=

(Ro ~/rj)~(t/Tf)

and the other parameters ^{and variables} are the 4 «rot

same as those in

equations (2)

and

(3).

The most

important

result _was obtained for

Rot

_» Ro~ where fast initial transfer _occurs while for

lloi

_{< Ro~ the} initial

decay

is less than for the standard _case of _one interaction mechanism

(Rot

=

Ro~) [32, 33].

3.

Experiment

and

experimental procedure.

The YAG _: Cr or YAG _:

Nd,

Cr

crystals

measured _were

prepared by Monokrystaly Turnov,

Research Institute for

Single Crystals,

511 19

Turnov,

Czechoslovakia. The measurements of

fluorescence

decays

_were carried out _on either YAG _: Cr

crystals containing

~

0.08 at.9b Cr

or on YAG

:Nd,

Cr

crystals doped roughly by

I at.9b Nd and 0.04 at.9b Cr.

The

experimental

details for fluorescence spectra ^and

decay

measurements have been described in _our

previous

_papers

[12, 15, 19].

The measurements were carried out at

liquid

helium temperature and the

following

kinds of excitations _were used _:

(I)

Direct selective

C~

+ site excitation which _means excitation of

~E

level of

only

_one from the

Cr~+

_{multisites and record of}

Cr~+

fluorescence

decay

of the _same multisite.

(2)

Indirect selective

C~

+ site excitation which is excitation of

~E

_level of

only

_one from the

Cr~

+ multisites and record of

Cr~

+ fluorescence

decay

from another

Cr~

+ multisite

(this

excitation is due to the _energy

transfer).

(3)

Indirect selective

Nd~+

_{site excitation which}

means selective excitation of

~E

_{level of}

only

_one from the

Cr~+

_{multisites and record of}

Nd~+

fluorescence

decay

^of _one of the

Nd~+

_multisites

(this Nd~+

_{excitation is due to}

Cr~+ ~Nd~+

_{energy transfer between}

multisites,

_see

Fig. 2).

(4)

Broadband indirect

Nd~

+ site _or broadband

Cr~

+ site excitation which _mean excitation of the

Cr~

+ multisites

by

2nd harmonic of YAG _i Nd laser

(532 nm)

into

~f~ ^Cr~

⁺

absorption

band and the record of

Nd~+

_or

Cr~+

fluorescence

decays

^{of individual}

Nd~+

or

C~+

multisites.

Nd~+

_ions

are excited due to

C~+ ~Nd~+

_{energy transfer between}

multisites since _at A~~ ₌ 532 _nm there is no

Nd~+ absorption, C~+

_ions

only

_are excited.

Excited

Nd~

+

~E

_{levels and some} of

Nd~

+ levels

together

with

possible C~

⁺

~

Nd~

+ energy transfer excitation _are sketched in

figure

2.

4.

Experbnental

results.

4,1

Nd~+

FLUORESCENCE DECAYS. The detailed measurements of

Nd~+

fluorescence

decays (for

_~F~/~

(a)

- ~I~/~

(l) transition)

_were carried out either under indirect selective

Nd~+

_{site excitation}

or under broadband indirect

Nd~

+ site excitation. The results of these measurements are

displayed

in

figures

4-8. All these

figures

show the

Cr~+

~

Nd~

+ energy transfer between multisites

clearly.

A summary of

Cr~

+

~

Nd~

+ site _to site energy transfer at 4.2 K is

presented

in table1.

Table I.

Summary of C~+

~

Nd~+

energy

transfers

between various multisites in YAG _:

Nd,

Cr

crystal

_at 4.2 K obtained

from

measurements

of Nd~

⁺

fluorescence decays

and emission and excitation spectra

of selectively

excited

Nd~

+ ions

[16] ~Nd~

⁺ sites

Nd1, 2,..

,

9 _are denoted

by 1, 2,.., 9).

No energy

transfer

_was observed

from

_S~ sites to other multisites

(only

_a weak _one to R sites

).

Cr3+ site Transfers to Nd3+ sites Nd3+ fluorescence

components

R 1,

2,

...,

7 fast and slow

St

1,

2, 3, 6,

7 fast and slow

S~

1, 2,

...,

7

only

fast

S~ 1,

2,

...,

6 fast and slow

54 1, 3, 4, 5,

6

Yi

1,

2,

7

Y2

1,

4, 5,

7

Y~ 1, 4, 5,

7

Y4 1, 4, 5,

7

Generally, Nd~+

fluorescence

decays

_can be divided into two groups :

a)

The fast

Nd~+

_pure

exponential decays (see Fig. 6)

which _are observed

mainly

for indirect selective

Nd~+

_site

excitation, especially

for the excitation due _to the transfer S~ ~

Nd~

+ sites Nd 1,

2,

..,

7.

Also indirect excitation S~ _~

Nd~+

_{sites Nd}

_6,

_{7 results in almost pure}

exponential decays (see Fig. 7).

The observed

Nd~

+

decays

consist of _one

exponential

and the lifetimes _are in the range 230-250 _~Ls which agrees with the usual

Nd~+

fluorescence lifetimes in YAG _: Nd

[13].

The

only

observed small deviation from _pure

exponential shape

has been

through long

tail parts of these

decays

where the calculated local lifetimes _are between 400-480 _~Ls.

b)

The double

Nd~

+ fluorescence

decays (see Figs. 4,

5 and

8).

This _means that the

decays

consist of _two parts : the first _one is fast and almost

exponential (it

is similar to the fast

exponential decay

of

Nd~

+ while the second _one

(long

tail

part)

is

mostly nonexponential.

The

long

tail parts ^{arise due} to the slow energy transfer from the

~E

doublets of

C~+

_{multisites and}

are observed

mainly

for the

following ^{C~+ ~Nd~+}

transfers:

St

_~

Nd~

+ sites Nd

2, 3, 6, 7,

R

~

Nd~

+ sites Nd 1,

2, 3, 5, 6,

7 and S~ ~

Nd~

+ sites %4d 1,

2,

M 6 Cr3+

~

Nd3+ _{ENERGY TRANSFER IN} Y~A150j2 887

6,

7

(see again

Tab.

I).

A rate between fast short and

long

tail

parts (If~~/If~~)

for the double

decays

is

varying

between 10 and 144

according

to the

types

^of

C~

+ and

Nd~

+ multisites. For broadband indirect

Nd~

+ site excitation

(via ~r~ Cr~

⁺

band)

both types of

Nd~

+ fluorescence

decays

_are also observed, The

efficiency

of the

C~+

~

Nd~+

_energy transfer is not easy to calculate due to the

variety

of

Cr~+

_and

Nd~+ multisites[16].

The average values of

C~+ ~Nd~+

_transfer efficiencies _are

given

in table II. The

Nd~+

_multisites

can be divided into two groups

according

to the mechanism of the

Cr~+

~

Nd~+

_{energy transfer}

:

the

Nd~+

_sites

_Nd8,

_Nd9

are sites where there is _no energy transfer from any

Cr~

+ sites for indirect selective

Nd~

+ site excitation. This is

surprising, especially

for Nd 9 site because this is the

Nd~+

_{site with the}

highest

concentration. For broadband indirect

Cr~° R site excitation Cr~~ Si site excitation

-Ndl,2 ----Nd2,3 ^1°~ -Ndl,2 ----Nd2,3

---~-Nd5 -..-.-Nd6,7 -.---Nd6,7

10 10

",,

lo 15 20 25

tlrrsl

^{I,O 2,5}

~~ lo?

,

',,

io ',,

'---

~~

o o,5 1,o 1,5 o 15 25

10'

iQ3

~iQ2~ C HM

'~

lo lo ".,

'.,

'., ~"-:-.,-,-,,-,

5 lo 15 20 5 lo 15 20

tlmsl timsl

Fig. ^4.

Fig.

5.

Fig.

4.

Nd~

+ fluorescence

decays

for _some of the Nd~+ multisites in YAG _: Nd, Cr at 4.2 K excited by indirect selective

Nd~+

_{site excitation (into Cr~+ R sites).}

Fig. ^5. Ndl + fluorescence decays ^for some of the Nd~+ multisites in YAG _: Nd, Cr at 4.2 K excited by indirect selective

Nd~+

_{site excitation}

(into Cr~+ St

sites).

Cr~~

S~

site excitation

Nd1,2

----Nd2,3

Nd4 ---Nd5 Nd6,7

io'

10~

~

j

o ~

~

Z

io lo

0 5 lo 15 20 25 0 O,5 1,O 1,5 20 25

t lms t ms1

Fig.

6.

Nd~

+ fluorescence

decays

for _some of the Nd~+ multisites in YAG _: Nd, Cr at 4.2 K excited

by

indirect selective Nd~+ _{site excitation}

(into C~+S~ sites).

Cr~~ _S~ site excitation

Ndl,2 Nd6,7

10' 10~

~ ~

C

° ',

~

~

",

lo ~°

~~",~~

t

ms j t

Fig.

7. Nd~+ fluorescence

decays

for _some of the Nd~" multisites in YAG Nd, Cr at 4.2 K excited

by

indirect selective Nd~+ site excitation

(into Cr~+S~ sites).

Nd~

+ site

excitation,

the

Cr~

+

~

Nd~

+ energy transfer is observed for Nd 8 and Nd 9 sites

(see Fig. 8)

and the fluorescence

decays

_are almost fast and

purely exponential,

the other

Nd~

+ Sites Nd 1,

2,

...,

7 _are Sites for which the

Cr~

+

~

Nd~

+ energy transfer is observed under indirect selective

Nd~+

_{site excitation}

(see

Tab. I and

Figs. 4-7).

The

decay

_curves of

Nd~

+ fluorescence _were

analyzed by

the method described in

[16].

We have evaluated the local

lifetimes,

that is the lifetimes for various time spans

through

short and

long

tail parts ^of

decays.

The detailed results of these calculations _are summarized in table III. We _see that the local lifetimes _vary from 220 _~Ls to

~

7 _ms. The shortest lifetimes

are identical with

Nd~

+ fluorescence lifetimes

[13, 16, 23, 24].

The

longest

lifetimes arise due

M 6 Cr3+

~ Nd3+ ENERGY TRANSFER IN

Y3A150j2

889

Ae~

~ 532 nm

-Ndl,2 ----Nd2,3 -.-.-.Nd4 ---Nd5 -..-..-Nd6,7 Nd(9

lo' 10'

~' bd

io io

0 5 10 15 20 25 0 0.5 _1,0 1,5 lo 25

t lmsl t lms

Fig.

8. Ndl + fluorescence

decays

for _some of the

Nd~

+ multisites in YAG Nd, Cr at 4.2 K excited by broadband indirect

Nd~+

_{site excitation}

(into ~r2

^broad

Cr~+ band).

Table II.

Cr~

+

fluorescence I@letimes OfYAG

_: Cr

(Tc~)

and YAG _:

Nd, Cr(Tc~,~~)

with the average

transfer efficiency (~~~

=

l Tc~_Nd/Tc~)

for ^Cr~+

multisites at 4.2 K.

Crystal

Parameter R

St 52 53 54

YAG _: Cr Tc~

[ms]

9.2 5.2 8.8 8.6 12.8

YAG _:

Nd,

_{Tc~_~~}

[ms]

5.7 3.0 5.7 5.7 9.7

YAG

Nd,

_~~~ 0.38 0.42 0.35 0.34 0.24

~~4 ^R

S, S~

S~

~=

^532nm

~i

pq '

'

i~ ' '

' '

"

'

i

o 5 lo 15 20 25

t

lms

Fig.

9. Cr~+ fluorescence

decay

_curves for ~E

~ ~A~ transition under broadband

Cr~

+ site excitation

(into

~r~ ^broad

C~+ band).

Table III.

Nd~

+ local

fluorescence lJetimes for

YAG _:

Nd,

Cr

crystals

excited

by

either indirect selective

Nd~+

_{site excitation}

_(due

_to

transfer from Cr~+ multisites)

_or indirect broadband

Nd~+

_{site excitation at 4.2K. Local}

lJetimes

_were calculated

for

the

following

ranges 5-400 ~s

(Tj~~),

400-800 _~Ls

(T~~),

800-1 500 ~s

(T~~~),

1.5-3.0 _ms (Tj~~~) ^{and 3-25} ms

(Tcr).

site

((ml

Nd

sit~ _[nm]

^{~~~~~ ~~~~ ~~~ ~~~~ ~~~~ ~~~~ ~'°~~ ~~~~ ~~~ ~~~~}

St

686.8

1,

2 874.8 506 600 0.94

Sj

686.8

2,

3 875,1 394 940 1.81 3.2

Sj

686.8

6,

7 876.3 476 1.7 3,6

R 687.3 1, ^{2 874.8 520 2.6} 5. I

R 687.3

2,

3 875.1 498 2.3 6.5

R 687.3 5 875.9 358 2.4 6.8

R 687.3

6,

7 876.3 441 2.1 6.I

S~ ^687.75

2,

3 875.1 230.6 420 1.7

S~ ^{687.75 4 875.4 235.6 477}

S~ 687.75 5 875.9 241.3 468.7

S~ ^687.75

6,

7 876.3 250.4 556

S~ 688.25

1,

2 874.8 265 384 762 1A 2.8

S~ 688.25

6,

7 876.3 276 438

1,

2 874.8 266 389 769 5.1

2,

3 875.04 254.7 259.3 311.8

~

2,

3 875.2 396 448 0.89

~ _2,

_{3 875.0 333.6 4.5}

(

_{4 875.4 250 329 601}

~ 4 875.4 333 6.1

)

_{5 875.9 236.6 263 358}

1 5 875.9 298

u

6,

7 876.3 219 261 323 0.61

'~

6,

7 876.3 285 4.8

8 876.75 269

9 877.45 259.4

to the energy transfer between

Cr~+

_and

Nd~+

_ions

(between ^~E Cr~+

_{level and}

some of

Nd~+ _levels,

see

Fig. 2).

After the end of the excitation

pulse

all the

Nd~+

fluorescence

decay

_curves reach the

maximum of their

intensity quickly

in

comparison

with the

Nd~+

_{shortest lifetimes}

T ~

230-250 _~s, ltisetimes of

Nd~

+ fluorescence in YAG _:

Nd,

Cr _are

ranging

^between 4 and 15 ~s for all indirect

Nd~

+ site excitations. For

Nd~

+ fast

exponential decays,

the risetimes

are shorter l ~s or

below).

4.2

Cr~+

FLUORESCENCE DECAYS. The

Cr~+

fluorescence

decays

for the

~E~

_~A~

transition _were Studied for various multisites in YAG _: Cr and YAG _:

Nd,

Cr. The detailed results _are summarized in

figure

9 and table IV.

Generally,

due to

Cr~+

~

Nd~+

_energy

transfer between multisites it iS

possible

to observe

C~

+

decays through ^Nd~

⁺

decays (these

transfers widen the

Nd~

+

decays

_{aS can} be _Seen from Tabs.

III,

IV and

Figs. 4,

8 and

9).

The

M 6 Cr3+

~ Nd3+ ENERGY TRANSFER IN Y3A150j2 891

Table IV.

Cr~+

_local

fluorescence lifetimes

in

YAG:Nd,

Cr

crystals (for ^~E~ ~A~

transition

)

under direct _or indirect selective

Cr~

+ site excitation in the time range 0.1-25 _{mS at} 4.2K

(upper part).

The lower part presents

C~+ fluorescence iJetimes of

YAG:Cr and YAG _i

Nd,

Cr

crystals (T~

is the

fluorescence risetime).

site

~~~

jnmj

site

~

~~

jnmj

^~r

lmsl

_Tr

(iocai) jmsj

Rj

687.3

St

686.8 4

9.5,

9.I

R~

686.7

Ri

687,3 immediate 9.7

R~

686.7 S~ 688.3 0.8-1.7

2.5, 3.5, 7A, 9.3, 10.7,

11.5

R~

686.7

54

689.0 3.3

1.7, 2.3, 4.9,

12.5

Sj

686.8

Si

686.8 immediate 4.9

St

686.8

Rj

687.3 1.5

3.3, 5.7,

6.3

St

686.8 S~ ^{687.7 0.5 8.9}

St

686.8 54 ^{689. I 1.6 fast}

components

_< ^I mS and

>

ex

>

em ~f

llllsj

_Tf

jlllsj

_Tr

llllsj

Site

[nm]

^Site

[nm]

YAG _: Cr YAG _:

Nd,

Cr YAG _: Cr

Rj

687.3

Ri

687.3 9.2 5.7 6

St

686.8

St

686.8 5.2 3.0 immediate

S~ ^687.7 S~ ^{687.7 8.8 5.7 0.2}

S~ ^688.3

53

688.3 8.6 5.7

54

689.0

54

^{689.0 12.8} 9,7 1.5

long

tail parts ^Of

Nd~+ decays

_appear

mainly

for indirect selective

Nd~+

_{excitation from}

Cr~+

_multisites

R, St

and _S~ and also

probably

for S~ Site. The detailed Studies of

Cr~+ decays

show that the

Cr~+

_{local lifetimes}

are

ranging

between 1.7 and 12.5 _ms. The

Cr~

+ local lifetimes and also

Nd~

+ local lifetimes increase with _an increase of

position

of time range

(after

the end of the excitation

pulse)

_on

decay

_curves

through

which the lifetimes _are

evaluated.

5. Discussion.

S-I CONDITION _{FOR THE} INTERPRETATION OF NONRADIATIVE

Cr~~ ~Nd~~

_ENERGY

TRANSFER BETWEEN MULTISITES.

Firstly,

_we have tried to

apply

^the standard Inokuti-

Hirayama equation (I)

for _some Of

Cr~+

Or

Nd~+ decays

at 4.2 K _as indicated in the introduction

(this experiment

had to be carried out at low

temperatures)

but _{we were} unsuccessful

(this equation

_may be used if temperatures are

higher,

_e.g. for T

= 77 K

[19]

_{as a}

first

approximation

for

decay curves).

If _{we see} the

Nd~

_{+ and}

Cr~+ decays (Figs. 4-9)

it is clear that there is

(in

most

cases)

_a fast _energy transfer

Cr~

+

~

Nd~

+ at short times which is

probably

due to another short _range interaction which results in _an increase of transfer rate

[31, 33].

To

explain

this behaviour _we have used the

recently developed

theories such _as the

modeling

of nonradiative _energy transfer either

by positional

correlation between donors and acceptors

[26]

_or

by multiple

transfer mechanism

[32].

Also the

migration

of energy between

some of

Cr~+

_donors

was taken into _account

(it

is known from _{our papers}

[15, 16]).

Our measurements have shown that there is _no

C~

+

~

Nd~

+ energy transfer to the main

Nd~

+ site Nd 9

(for

indirect selective

Nd~+

_site

excitation).

The fact that the

Cr~

+

~

Nd~

+

energy transfer takes

place mainly

between the

C~+

multisites

(R, Sj-54)

and the nfinor

Nd~

+ multisites Nd 1,

2,...,

7 is _an evidence that the distribution of

Cr~

+ and

Nd~

+ ions is not uniform in YAG

:Nd,

Cr

(transfer

takes

place

between

variously

distant

couples

of

C~+-Nd~+ _ions).

_{Another evidence of}

a nonuniform distribution follows from the

discrepancy

between

Nd~

+ and

Cr~

+ ionic radii and the radii of

Y~

+ and

Al~+

_which

they replace

_(r~

(Nd~

⁺

)

=

1.12

h

»

r;(Y~

+

= 1.01

1

_and

r,(Cr~

+

)

= 0.61

1

»

r;(Al~

⁺

) 0.531 _{[11, 19,} 27]).

These differences will result in stresses in the YAG lattice and there _are=

probably

_no

C~+, Nd~+

or

C~+-Nd~+ pairs

in at the low concentrations used. The differences in ionic radii and _stresses in the YAG lattice result in _a nonuniform distribution of the

Cr~

+ and

Nd~

+ ions in this

crystal

and

newly developed

theories must be used for

fittings

the

decays. Furthermore,

if _we have both

C~+

_and

Nd~+

_{ions in}

_YAG,

_{the other four}

C~+

_multisites

(Yi-Y~)

will arise in this

crystal [16].

One of _our main results confirms the last result that the

Cr~

+

~

Nd~

+ energy transfer takes

place

from

~E

level of

C~+

ions

[34, 35]. Here,

_we excited ~E levels of various multisites

selectively

and observed _energy transfer to

Nd~+

_multisites

(mainly

to

Nd~+

_sites

Nd,

1,

2,..., 7,

_see Tab.

I).

The

C~+

~

Nd~+

energy transfer between multisites is either _very fast

(see Fig. 6)

_or slow and double

(see

_e-g-

Fig. 4) but,

in both _cases, is nonradiative in

nature at low temperatures

(see

Tab.

II).

There _{are no} conditions for radiative

Cr~

+

~

Nd~

+

energy transfer in

YAG:Nd,

Cr at low temperatures ^{because there is} no

overlapping

between

Cr~

+ emission and

Nd~

+

absorption,

but this transfer could be observed at

higher temperatures [19].

Our recent paper

[13]

^{and the results}

presented

in table 3 show that

Nd~

+ local lifetimes _are

ranging

from 200 to 500 _~Ls. Also

Cr~+

_local fluorescence lifetimes _are in the _range 1.7- l2.5 _ms

(see

Tab.

IV).

No substantial

shortening

of

Nd~+

or

C~+

fluorescence lifetimes is observed _{as was} for

YAIO~

_: Cr

crystal (from

60 _ms to I _ms

[19])

this

clearly

indicates the presence of

Cr~

+

pairs

in

YAIO~

_: Cr. In YAG _i

Nd,

Cr the

Cr~ +, Nd~

⁺ _or

C~

+

-Nd~

+

pairs

are

probably

not

present

^{but the various}

C~

+ or

Nd~

+ local lifetimes show that there arise

complexes

or

couples (or pairs) consisting

of these ions

(e.g. Cr~+

and

Nd~+

_{ions can be} bound via

O~- ions).

5.2 FAST

Nd~

~ PURE EXPONENTIAL DECAYS. The fast

Nd~

+ pure

exponential decays (Or

fast

mono-exponential decays)

have been

mainly

observed for indirect selective

Nd~+

_site excitation via

C~+

_S~

~

Nd~

+ sites energy

transfer,

_see

Fig. 6).

If other

C~+

_multisites

are

selectively

excited the fast

Nd~

+

decays

_were almost not observed. The

C~

+ S~ enfission line

overlaps partly

with the main

C~+

_{R emission line}

(see Fig. I)

and also the energy transfer

from S~ ^to R site _was observed

[15,16] (no

_energy transfer _was observed from

S~ sites _to other

C~

₊

sites).

If _we excited the

Nd~+

_sites

indirectly

from R sites _we did not

observe the fast and

mono-exponential Nd~+ decay.

We _{can assume} that the fast

Nd~+ decays

are

only

excited via

Cr~+S~

~

Nd~+

_{sites energy transfer.}

The fluorescence lifetimes of fast

Nd~

+

decays

lie in the _range 230-250 _~Ls. This _agrees with the

Nd~

+ fluorescence lifetimes observed

[13, 23, 24].

For this _{case we can use} the

qualitative

results from the newest theories for nonradiative energy transfer

[26, 31].

^A

quantitative interpretation

has _no sense since the fast

Nd~

+

decays

_are

mono-exponential.

The correlation

(or pairing)

_or

multiple

interaction theories show that the fast initial transfer is due _to either enhanced

positional

correlation _or additional

short-range

interaction

(either multipolar

_or

exchange).

The

C~

+ S~ sites

belong

to

Cr~

+ sites with low concentrations

(~

l.9 9b from the whole

Cr~

+ concentration

[15])

and the indirect

Nd~

+ excitation via

C~

+ S~ ~

Nd~

+ sites

M 6 Cr3+

~ Nd3+ ENERGY TRANSFER IN

Y3A150j2

893

transfer is the fastest from the observed _ones. We _{can assume} that this

shortening

arises due to an

exchange

interaction if the

C~

+

S~ ions and

Nd~

+ ions _are close

together

_e.g. if

they

_are

coupled

via oxygen

O~

_{ions. Here} the

Cr~

+ and

Nd~

+ ions _are close

together (their

distance

is below

0.42nm)

^and the

probability

for _an

exchange

interaction between

Cr~+

_and

Nd~

+ is

increasing (or ^O~ neighbours

_can take

part

^{in this}

exchange interaction). Generally,

we can say that

Cr~

+ S~ ^and

Nd~

+ Nd 1,

2,

...,

7 ions which _{are near} S~ ^{ions create}

pairs

ⁱⁿ the YAG _:

Nd,

Cr

crystal (their

concentration is low 2 9b of the whole

Cr~

+

concentration)

and that _an

exchange

interaction

probably

shortens the

Nd~

+ fluorescence lifetime.

5.3 DOUBLE

Nd~+

FLUORESCENCE DECAYS. A

majority

of

Nd~+

fluorescence

decays

excited

indirectly by

_energy transfer via

Cr~+ ~Nd~+

_{sites exhibits}

a

nonexponential

character and the fast _» and _« slow _» components are observed

(both

these

components

are

mostly nonexponential).

For these

decays

_we decided to use the _new

theory

of Rotman and

Hartmann

(Eqs.(2)

and

(3))

to

analyze

them. We have outcome from the

following

assumptions

_:

(I)

the distribution of

Cr~+

_{donors and}

Nd~

+ acceptors is not uniform in YAG _:

Nd,

Cr

(this

is also

supported by

the fast

mono-exponential Nd~

+ transfer discussed in parts ^{5. I} and

5.2).

The first observation that the

impurity

distribution in

doubly doped

YAG

(by

Ce and

Nd)

is not uniform _was done

by

Rotman's

analysis

of _our data and it has shown _a certain

improvement

when this

theory

_was used

[28].

In YAG _:

Nd,

Cr

Nd~

+ and

Cr~

+ ions

replace

lattice ions

(are

in well defined

crystallographic positions)

and both excluded and enhanced correlated arrangement ^{of ions}

arise, especially

between _some

Cr~+

_and

Nd~

+ ions. Due to the

variety

of

Cr~+

_and

Nd~+

_{multisites it is not}

possible

to determine their concentrations

precisely

but for _our calculations the concentrations _were

changed (they

_are

parameters).

(2)

The

Cr~+ ~Nd~+

_energy transfer is nonradiative and takes

place

from the

~E

_{levels of}

Cr~

+ multisites _{to some} of the

Nd~

+ energy levels

(see Fig. 2)

from which there is fast radiationless relaxation _to

~F~j~

(a)

level

(at

low

temperatures).

The fluorescence transitions _among

Nd~+ 4f~

_electronic levels _are either electric

quadrupole

or

magnetic quadrupole

but also electric

dipole

transitions arise _{as a} result of the interaction between

electronic and vibrational states

[19].

This is _{a reason}

why

_we do not exclude any type ^of

multipolar

interactions

(e.g.

s ₌

6,

8 and

10),

The results of the fits for _some of the

Nd~

+ fluorescence

decays

_are

presented

in

figures 10,

11. We decided to fit the

Nd~

+

decays (Nd~

⁺ ions _are

acceptors)

for _{two reasons :}

(I)

the slow

(or long tail)

parts of

decays

ascribe the

Cr~+

_donor

decays (see

the

Nd~+

_{local lifetimes}

observed in Tab.

III) (it)

the energy transfer _was also observed between

Nd~+

_ions

[13, 23, 24]

and _{we can} say that _some of the

Nd~+

_{ions behave}

as donors and _{some as}

acceptors. ^{For instance}

figure10

_presents the results of

fittings (for

excluded volume arrangement ^of

acceptors)

for

decay

of Nd 5 site

(excitation ^Cr~

⁺

(R)

~ Nd 5

transfer).

We fitted the short and slow part

independently according

to

equation (2).

The

fitting parameters

are

given

in table V. For short range

(0-1.3 ms)

_{we see a}

roughly good

agreement between

theory

and

epxeriment

but the lifetime

Ti

= 450 _~Ls used in this fit does not

belong

to

C~

+

lifetimes,

this lifetime

belongs

to the

Nd~

+ lifetimes

(Nd~

⁺ local lifetimes _are between 250-500 ~Ls). Our conclusion is that the short part ^{of Nd 5}

decay

is influenced

by

the energy transfer between Nd 5 sites and _some of other

Nd~

+ multisites and that this conclusion is valid for the other

Nd~+

_{sites of low} concentrations

(Nd

1,

2,..., 7).

The results obtained for the

long

tail

parts

^of

Nd~

+

decays

_are somewhat different. We fitted the

long

tail part of Nd 5

decay (excitation Cr~

+ R

~ Nd 5

transfer)

but there is _no

good

agreement

^between

theory

and

experiment (see Fig.10).

The fitted lifetime

T)=

4.sms

EXPERIMENT

I

_THEORY

j~ ^O

~ u~

~

~

'

l

° llmsl ^~

~~4

EXPERIMENT THEORY

~

b

~

~ z lo

' ,

o 5 io 15

~~4

EXPERIMENT

p THEORY

~

w

~ i

'

0 lo 20 25 30

tlmsl

Fig.

10. Nd~ + fluorescence decay curves of Nd 5 site

(solid lines)

excited by Cr~+ R

~ Nd 5 energy transfer at 4.2K and the fits

(dashed lines) according

to

equation (2)

for excluded volume of Ndl + acceptors around

Cr~

+ donors for short time part

(a), long

time part

(b)

and both parts

together (c).

Table V. Radius

of

excluded volume

(rj),

critical

radius,

_{parameter s}

of muhipolar

interaction and

fluorescence I)eiime T) _{for fittings of} Nd~+ decays of

Nd5 site in

YAG

:Nd,

Cr

crystal

excited due _to R ~Nd 5 energy

transfer.

a 1.2 1.4 450 _~Ls 6

M 6 Cr3+

~ Nd3+ ENERGY TRANSFER IN

Y3A150j2

895

belongs

to

C~+

_{lifetimes. This} is

again

_an evidence that the

long

^tail

parts

of

Nd~+ decays

arise due to the

C~+

~

Nd~+

_{energy transfer between} multisites.

Detailed studies of

long

tail parts ^{of double}

decays

have also been carried _out

according

to

equation (3)

for enhanced correlated

arrangement

of donors and

acceptors.

^{The results of} these

fittings

for

decays

of Nd

2,

3 sites

(excitation C~

+ R

~ Nd

2,

3

transfer)

_are

presented

in

figure11

and in table VI. We _{see a}

roughly good

_agreement between

theory

and

THEORY

xxx EXFERIMENT s=6

=

d~

~

~ _x

~ x

x

w z

~

z ,x

x x

~ ,

z

-THEORY

,x. EXPERIMENT s=8

j

«

x x

«

,z ,

x

x x

transfer and fits _according to equation (3) for hanced correlated arrangement

of

C~+ and _Nd~+ ions

for coupling

upper part, s = 6) and

(lower part,

s

_{= 8).}

Fitting

parameters

are

given _{intable VI.}

Table VI.

Average fitting

_parameters

of Nd~

⁺

fluorescence decays of

Nd 2 and Nd 3 sites in

YAG:Nd,

Cr

crystal (excited by

R

~Nd2,

3

transfer) for

enhanced volume correlated arrangement

of

ions

(description of

_{parameters see}

Eq. (3)).

Parameters

of jilted decays presented

in

figure11

_are

given

in the lowest _{two rows,}

respectively.

S ~l

[ill) R0 [nm)

_r2

[nm)

A B

Ti

_{[JIIS) C/£b}

_{~D (°)}

6 1.0 1.22 4.14 2.66 0.98 9.2 _or 25-39 1.71 1872.5

8 0.92 1.23 2.95 2.6 0.8 from 9.2 to 50 1.79 1758

6 1.0 1.09 3.93 3.0 0.97 9.2 1.ll

8 0.59 0,69 1.01 2.8 0.56 27.6 2.12 2 435

experiment

for the fitted time

part

I.1-5.5 _ms both for

dipole-dipole

and

quadrupole-dipole

interaction

(the

critical radii _are different

Ro(d-d)

= 1.09 _nm

»

Ro(q-d)

= 0.69 _nm which is

expected).

The fitted lifetimes

vi

= 9.2 _{ms or} 27.6 _{ms are} the

C~

+ lifetimes _{or are}

longer.

The

good agreement

between

theory

and

experiment

_was obtained for the slow

parts

^of

Nd~

+

decays (for

times _t

»

I;I ms)

but for the short parts of

decays

_no agreement between

theory

and

experiment

_was obtained

(for

times _t

< I.I

ms).

The average critical distances

llo

=

1.22 _or 1.23 _nm

(obtained

from several

fits)

_{are a} bit greater ^{than those from}

figure

I I but the fitted lifetimes

vi _{always belong}

_to

Cr~+

lifetimes. The radius _rj where the concentration of ions should be enhanced is rj = 0.97 _nm and inside _a

sphere

of radius rj,

couples

of

Cr~

+ and

Nd~+

_{could arise.}

5,4

Nd~

+ AND

Cr~

+ DISTRIBUTION IN YAG _: Nd~ Cr. Our

Nd~

+ and

Cr~

+ fluorescence

decay

studies of YAG _:

Nd,

Cr

crystal

at low

temperatures

^{have enabled} us to

improve

_our

knowledge

of

Cr~

+ and

Nd~

+ distribution and energy transfer _processes between them. The YAG garnet structure is cubic and _can be

expressed by (Y~ ~) [Y~Al~

~]

(Al~ )Oj~ [36, 37],

where

(Y~_~)

represents

Y~+ dodecahedrally coordinated, [Y~] (x= 0.01-0.02)

octa-

hedrally

coordinated

Y~+ (antisite defect), [Al~_~] octahedrally

coordinated

Al~+

and

(Al~) tetrahedrally

coordinated

Al~+ by

_oxygen

O~~ [12]. Cr~+

ions

prefer

to

replace Al~

+ in octahedral

positions.

In YAG lattice this octahedral site

undergoes

to weak

trigonal

distortion

along

the

(lll )

direction

[36]

and it has inversion

symmetry. Nd~+

_ions

replace mainly dodecahedrally

coordinated

Y~+

_{ions but their small}

_part

can also _occupy the

octahedrally

coordinated

Al~+

_sites

(antisite defects) [17, 24].

The antisite defects arise due to stoichiometric deviations.

Generally,

for YAG _: Nd

crystal nonequivalent crystal

field effects _were observed either _on

large

scale

(~5-6cm~~

_are differences between

spectral lines)

_{or on} small scale

(for

differences below I

cm~~).

This _was observed

mainly

for YAG:Nd Czochralski _grown

crystals [21,24]. Lupei

et al.

[24]

^have observed four

nonequivalent ^Nd~+

sites in YAG :Nd while Devor _et al.

[21]

have observed five

nonequivalent Nd~+

_{sites. We have}

4,o

I%1

88.6

Concent~ations ^~.7

~

C

r"

m -sites

smaller

cations

O~~ Vacancy

lar9er

#

~ cations

w

~

~

CRYSTAL FIELD

Fig.

12. Models of Cr~+ multisites in YAG Nd, Cr crystal.