Time-resolved photoluminescence studies of donor-acceptor energy transfer in Cr3+:MgO

Journal of Luminescence 39 (1988) 239—246 North-Holland, Amsterdam

239

TIME-RESOLVED PHOTOLUMINESCENCE STUDIES OF DONOR-ACCEPTOR ENERGY TRANSFER IN Cr34:MgO Mary B. O’NEILL ~ and B. HENDERSON Department of Physics and Applied Physics, University of Strathclyde, Glasgow, G4 ONG, UK Received 23 October 1987 Accepted 5 January 1988

We report time-resolved measurements of non-resonant donor—acceptor energy transfer in Cr3~: MgO. Three distinct donor centres transfer excitation to the <10)(Cr~ 8V~5Cr~5) acceptor which emits light in the N1(Eu) and N1(Ev) luminescence lines. The energy transfer rates from donors to acceptors were obtained by rate equation analysis of the temporal evolution of the N1(Ev) luminescence following pulsed excitation. From the temperature dej~endencesof the transfer rate from the three donors it is deduced that the transfer mechanisms are dominated by one-phonon mission and two-phonon Raman relaxation processes. The donor—acceptor transfer is too fast to be accounted for by eitl~erelectric dipole—quadrupole or electric quadrupole—quadrupole interactions. Instead the energy transfer process is determined by antiferromagnetic superexchange between donor and acceptor.

1. Introduction the rocksalt-structured MgO substitutional 3In+ impurities are charge compensated by cation Cr vacancies. One consequence of charge compensation and the interaction between positively charged (Cr~ 5)and negatively components 3 + ionscharged occupy(V~g) several different is that the Cr crystallographic sites with octahedral, tetragonal and orthorhombic symmetry. Not surprisingly, therefore, the optical spectra of Cr3~ MgO crystals are complex and have not been cornpletely interpreted [1]. A partial tabulation of spectroscopic lines is given in table 1. Recent work [2,3] reported observation of five sharp excitation lines close to the R-line which result in N1(Eu) line emission from the <1OO)(Cr~V~Cr Mg) dimer. Subsequently the authors sho .‘edthat energy transfer occurs between (CrMS) centres m almost octahedral sites and (1OO>(Cr~V~Cr~) dimers which are close enough together that ea:h slightly perturbs the energy level structure of the other [4]. 1

In that study, high-resolution selective laser spectroscopy was used to show that these five excitation are for associate~Iwith distinct donor sites,lines labelled convenience three A, B and C, each of which transfers its excitation to a nearby (1OO)(Cr~gV~gCr~g) acceptor. These lines,

Table 1 Wavelengths of principal photoluminescence lines in Cr :MgO Defect a) Spectral Wavelength (nm) feature Eu Ev (Cr~ 4) R line 698.1 698.1 <1O0~Cr~5y,~8) N2 lines 699.2 703.8 <10O)(Cr~5V~5Cr~5) N1 lines 698.9 703.4 donor A lines a, e 697.9 698.7 donor B donor C

lines b, d lines c, d2

698.1 698.2

698.4 698.4

_______________________________________ a)

Present address: Department of Electrical and Electronic Engineering, University of Glasgow, UK.

0022-2313/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

The Kröger—Vink system df nomenclature is used, according to are which only differences from the of theA,host lattice noted. For an ion~ccrystal MXcharge an impurity on the cation site is designated A~ the superscript indicates that the impurity carries an effective charge of +1, relative to the perfect lattice. The letter V indicates a vacancy. Hence V~8indicates a catiOn vacancy with effective charge + 1(’) relative to the perfect lattice.

240

MB. O’Neill, B. Henderson

~

/ Donor—acceptor energy transfer in Cr3 +

MgO

contribute to donor—acceptor energy transfer and the magnitude of the energy transfer rate. 699nm

2. Experimental methods

N,(Eu)LINE EXCITATION LINES

e9anm

~

a b

~o~ions A

C

d

___________

B

ACCEPTOR ~(Ev)LINE

703.4nm Fig. 1. Illustrating non-resonant D—A energy transfer between three distinct donors; A, B and C, and perturbed acceptors in Cr3~: MgO.

labelled a—e, are linked in pairs, a with e, b with d 1 and c with d2, each pair resulting in preferential transfer of excitation to a specific subset of <10)(Cr~5V~5Cr~5) centres: the process is illustrated in fig. 1. The aim of the present work was to elucidate the dynamics of this energy transfer process using time-resolved excitation spectroscopy. When optical excitation and emission transitions occur on the same site the luminescence decays with a decay time that is characteristic of the centre. However, if the excitation energy at one site (donor) is transferred to another site (acceptor), then the acceptor luminescence signal first excitation rises to a maximum at the of the pulse and from then zero decays. In start consequence, measurement of the temporal evolution of donor and acceptor luminescence yields information about which excitation and emission centres

In this study a Lambda Physik Model FL2002 pulsed dye laser was pumped using the amplified second harmonic from a Spectron Model 2 Qswitched Nd3 ± : YAG laser pulsed at rates up to 20 Hz. The dye used for wavelengths in the range 695—704 nm was LDS685 dissolved in ethanol. The spectral width of the laser emission was typically 0.2 cm1 and the pulse length was 10—15 ns. The laser intensity on the crystal was kept low and weak beam focussing used to avoid local heating and non-linear effects in the crystal. The emitted radiation was taken from the crystal at right angles to the excitation beam and focussed onto the slits of a 1 m grating monochromator, before being detected using a GaAs photomultiplier tube and current amplifier. The temporal resolution of the system was limited by the 1 ~ts response time of the current amplifier. In general, the excitation pulse and luminescence signal were non-resonant, thus avoiding saturation of the phototube. The time profile of the luminescence was collected using a 16-bit transient recorder with a 20 ns—50 ~ss variable time gate. If 1000 channels are used per sweep then the minimum time base is 20 ms. Using this system the complete decay profile is recorded after each pulse. Once recorded the data was transferred to and stored on a PDP11 cornputer. Data averaging was achieved by computercontrolled repetitive scanning of the recorder’s time base following each laser pulse. Typically 5000 sweeps were averaged in about 7 mm, the averaged data being stored on magnetic disc for subsequent analysis. The crystals used in the present work contained 760, 1300 and 3600 ppm by weight of Cr203 added to the MgO before melting. The samples, cleaved along {100) faces andcontained polished in to adimen3, were variasionstemperature of 5 x 5 x 1 (4—300 mm ble K) cryostat which permitted control of the sample temperature to ±0.1 K. In the CW laser excitation studies reported earlier it was shown that slightly perturbed, iso-

M.B. O’Neill, B. Henderson

/ Donor—acceptor energy transfer in Cr3 +

lated (Cr~)centres were linked by energy transfer to the <100)(CrMgV~gCrMg) pair centres The measurements reported here involved exciting into each of the lines a—e associated with the donor (Cr~ 5)centres and measuring the temporal profile of the emission m the N1(Ev) hne of the (10O>(Cr~5V~5Cr~5) dimers.

MgO

2

~

18

a

~

2

18

b 2

3 Results and discussion

3

3.1. Measurements at 4.2 K

10

I—

18

C

7

2

~‘

In fig 2 is shown the temporal evolution of the N1(Ev) fluorescence line at 4.2 K following a laser pulse within the excitation lines a—d at X = 698.4 tim. On time scales longer than 1—2 ms the luminescence decay profiles follow the radiative decay of the N1(Eu) line with TR 8.4 ms: the decay is identical irrespective of which of the

241

10

18

5

.

5 4s TIME/10 Fig. 3. Evolution of acceptor luminescence in the N

—

1(Eu) line and excitation in lines a (697.91 nan), b (698.05 mn), c (698.22 nan) and d (698.40 nan) at 4.2 K.

\ Ic.

6

excitation lines is used. As fig. 3 shows, however, the initial rise and decay occurs on a different time scale for each of the lines a—d. The rise time

2 10

~

a

~

5

15

25

~

2

¶ —

stronger N1(Eu)atline of energy transfer this obscures wavelengththe (X excitation = 698.7 urn). The data in fig. 3 confirm that energy is trans-

b

10

ferred at different rates from donors A, B and C

~.

6

~ .5

.

T~-~-~

2

1

from line d has two components due to transfer from the B and C donors. Overlap of excitation line e with the short wavelength edge of the much

25

3.

TIME/10 Fig. 2. The growth and decay of acceptor luminescence following pulsed laser excitation at X — 698.4 nan, measured at 4.2 K.

to the (10>(Cr~5V,~Cr~5) acceptors, which is physically realistic for distinct and independent donor—acceptor pairs. Conventional models of energy transfer, based upon random distributions of donors and acceptors, require complex statistical averaging of the transfer rateconfigurations over individual pairs in random [5].donor—acceptor Standard rate equation analysis then grossly simplifies dynamics of energy transfer. Nonetheless to interpret the above

M.B. O’Neil4 B. Henderson

242

/ Donor—acceptor energy transfer in Cr3 +

results we have assumed macroscopic rate equations to be appropriate, an approach that should be correct in the present case. As discussed earlier [4] the sharp line excitation and photoluminescence lines associated with the D—A transfer process imply that donor and acceptor occupy welldefined, but slightly perturbed, lattice positions. If this is the case then transfer is a one-step process; excitation does not migrate among donors and each donor transfers its excitation to one acceptor. Since the relative positions of donor and acceptor are fixed, the energy transfer rate, which depends only upon the donor—acceptor separation, is constant. In consequence, macroscopic rate equations can be used to describe collectively the dynamics of a microscopic energy transfer process from all donors to their respective acceptors. This may be confirmed by measuring the temporal evolution of the donor luminescence, since if the donor—acceptor transfer rate, WDA, is constant for a particular D—A pair, then the luminescence should be described by a single exponential function, exp( WDt), when allowance has been made for any back transfer from acceptors to donors. The donor decay profiles for emission in line e when exciting in line a at 4.2 K and 77 K are shown in fig. 4. The luminescence profile at 4.2 K is well

a

b FAST

EMISSION

~\ \

z W

MgO

described by a single exponential decay with WD = 2.11 x 10” s~, verifying that a common transfer rate is involved. Note that this value is equal, to within experimental error, that determined from measurements of the decay of the acceptor luminescence on exciting into line a, notwithstanding the overlap of the line e emission and the short-wavelength edge of the R-line. The data at 77 K show two components, a fast component associated with energy transfer and a long-lived component at the decay time of the N 1-line due to back transfer from the N1 acceptor. 3.2. Analysis of intensity-timeprofiles at 4.2 K The experimental evidence (ref. [4] and sect. 3.1) justifies the use of a constant energy transfer rate, WDA, and therefore, of macroscopic rate equations to interpret the pulsed luminescence measurements. Since at 4.2 K there is no back transfer from acceptor to donors the decay of excited donors and acceptors after pulsed excitation into the donor line is given by d N (t) = + WJ~ND(t)+ WDAND(t), (1) d an dNA( t) dt =—WDAND(t)+W,~NA(t), (2) where ND and NA are the number of excited donors and acceptors respectively, W,~and W,.~ being the radiative decay rates of the isolated donor and acceptor. Solving these linear differential equations with the initial condition that NA(t) =Oatt=’Oyields — ______

ND(t)=ND(0)exp[—(W~+WDA)t], and

LONG LIVED EMISSION

~ \ NA( t)

-

=

ND (0)

~

—

WDA

WDA

\ 2

4

6

è

10

12

14

•ACKQNOUND 0

5

10

1’S

2~O 25

30

TIME / 10

5,.

x[exp(—w,~t)

1~

Fig. 4. Decay of donor luminescence (line e) on exciting in line a at (a), T — 4.2 and (b), T — 77 K.

—exp[—(W~+ WDA)t]] Since the luminescence intensities ID(t) and IA(t) vary as ND ( t) and NA(r) respectively then ~

,~

—

k

—

i a

exp

i 55,R — ~

TIT

D + rr DA

M.B. O’Neill, B. Henderson

/ Donor—acceptor energy transfer in Cr3 +

and

$ [exp(

=

—

exp

{

—

—

MgO

243

the data points in fig. 3 for excitation in line a, and the values of x2 in table 2 for excitation in lines a, b and c show that the donor—acceptor

Wt)

(w,~+ WDA )~}}~

(4)

give the temporal evolution profiles of donor and acceptor luminescence signals. The values WDA, W~and WA”~ are determined from the measured versus time curve by computer fitting to eq. (4), using a non-linear least-squares fitting program in which the numerical parameters are varied until the best fit is obtained. A measure of the suitability of the theoretical function chosen to represent the time evolution of the acceptor luminescence is the value of IAO)

transfer is well described by eq. (4). Furthermore, since WDA differs in each case, lines a, b and c originate from different centres, in accord with the CW measurements cited earlier [4]. The time dependence of the N 1(Eu) luminescence intensity on exciting into line d is not satisfactorily described by eq. (4). Nor would it be expected to be if, as indicated by the CW measurements, line d actually consists of overlapping lines from the B and C donors. Modification of the theoretical approach to include transfer from two donors to a single acceptor leads to an equa-

N

F )2 Y~ where for each time channel, i, 1’1 is the measured intensity integrated over all scans and F its theoretical value. Using an iterative process numerical 2 parameters which determine 1~arethe varied x 2 gives ratiountil of the is miuiniised. Physically x actual spread of data points about the theoretical function to a statistical random spread. When n) 1, where N is the total number of points in a scan and n is the number of parameters, the theoretical model gives a good description of the fluorescence profile. Table 2 lists the values of WDA obtained for donor—acceptor transfer from the A, B and C donors. The solid curve through —

1=1

‘

—

lion of the form IA(t)—/3lexp(—Wlt)—$2exp(—W2t) $~exp( W3t), where —

~1

w

3

=

~

—

(4a)

w

2

=

W~(B)+

WD(B)A

and

W~(c)+

The second and third terms describe the rise in the acceptor luminescence due to transfer from two independent centres B and C. As table 2 shows eq. (4a) describes the emission profile of the N1(Eu) line on excitation into line d rather well yielding energy transfer rates equal within the estimated errors to those determined by pumping separately into lines b and c. 3.3. Measurements above 4.2 K

Table 2 Donor—acceptor transfer rates measured by pulsed excitation into lines at 4.2 K

2 a)

Excitation line

Wavelength (nan)

WDA s’) (10”

x

a b c d, d 2 et

697.9 698.1 698.2 698.4

1.80 ±0.15 4.4 ±0.3 3.4 ±0.2 4.4 ±0.3

1.19 1.70 0.85 1.08

a) b)

698.4 3.6 ±0.2 1.08 0.35 1.37 values698.7 indicate how well2.11 the± theoretical model (e~l. The fits (4)) x the measured luminescence profile using the quoted values of WDA. Measured from the decay of the donor luminescence (line e)

2

on exciting into line a.

The excited states of donors A, B and C are not degenerate with either the Eu or the Ev states of the <100>(Cr~gV~gCr~g~) acceptor, so that for energy to be conserved during energy transfer, the energy differences between donor and acceptor levels must be made up by the emission or absorption of phonons. Thege are many relaxation processes m which the ion—phonon acontributes characteristic dependence of WDA oninteraction temperato the energy transfer, each exhibiting ture. We have, therefore, measured the time dependence of the N 1-fluorescence line at temperatures ranging from 4.2 K to 77 K on excitation

MB.

244

O’Neill, B. Henderson

/

3 + MgO

Donor—acceptor energy transfer in Cr

VAN VAN,

1

NCN,

WDA.

Making the further assumption that NA(O)

0, and solving for NA(t) yields, ND(0) NA(t) = 1 + exp(—ho.,/kT) X F(t, lIT), =

4.0

(7)

where 3.0 7.0

S

~,I/

•

2.0

6.0 6.0

S

_______________________ 20 40 60

1.0 ~5.o 5.0

Is:

• 4.0

__________________________

0

20

40

60 4.0

S

•S S

____________________________________ 0

20

40

60

3.0 50

TEMPERATURE °K Fig. 5. Showing the temperature dependence of the donor—acceptor transfer rates for excitation in lines a, b and c (• cooling down, a heating cycle).

into lines a, b and c. The data shown in fig. 5 have been corrected for temperature-dependent backtransfer from the N1 acceptor to the particular donor. This is assumed to take the form WAD exp( ho,/kT), where 1k~3is the energy difference between the excited state of the donor and the Ev statetakes of theinto acceptor. an approximation which accountThis oneisphonon absorption but neglects any possible two-phonon backtransfer processes. Using the simplification that W~= W W”~ the differential equations describing the temporal evolution of excited donors and acceptors are given by —

dND

— —

—

=

—

(W’~+

WDA

) ND + WADNA,

(5)

and dNA

i

F(t, 1/T) = exp(— WRt) ho,~ —exP[—(W~+WDA(1+exP(_~JJ/tJ.

(w’~ + WAD) NA +

WDAND.

This assumption is reasonable since WR

(6) 102

In this equation hw is known to be of order 90—100 cm~’, WR is take to be the mean of W~ and W~,i.e. ca 102 ~1 and WDA is obtained by fitting the experimental lA(t) versus time curve to a relationship of the form of eq. (7). The scatter in the data points shown in fig. 5 indicates that the experimental errors in the measured values of WDA are significant. Two sources of error are inherent in least-squares fitting of the luminescence time profile to the assumed theoretical expression. First, the data from the first microsecond after excitation is discarded because it has to compete against the background luminescence of the laser, which could not be completely eliminated. The effect becomes especially important above ca 60 K where the energy transfer rate becomes ver3r fast (Wj~ 12 ~.ts). Second, when fitting the luminescence to eqs. (4) and (7) W~and WDA are interdependent; a small error in one can be2 compensated by an error in the almost unchanged. In fact, x2 other mdito leave cates howx well the calculated function describes the acceptor luminescence rather than the exactness of the different rates. Below ca 50 K this effect is small because W~ and W2~ are not strongly temperature-dependent and are in any case much slower than WDA. Although at higher temperatures the radiative decay rates are known to decay rapidly the precise temperature dependence has not been accurately determined. Finally, as the temperature rises, the zero-phonon lines broaden, hence effects due to overlap of lines become more important. These effects could only be minimised by restricting measurements to the region 4—77 K.

MB. O’Neill, B. Henderson

/ Donor—acceptor energy transfer in Cr3÷MgO

3.4. Vibrational processes inducing energy transfer The energy transfer processes discussed here are non-resonant, i.e. they involve the absorption or emission of one or more phonons. There are numerous possible lattice relaxation processes in solids and each will introduce a characteristic temperature dependence to the energy transfer rate. We have taken the temperature-dependent rate WDA(T) to be a linear sum of the various processes involved. For example, in the case of transfer from donor A, the experimental data are uniquely described by WD(A)A(T)=a{

expx exp x1 1 1 j

[expexpx2 X2 1]1

—

—

(8) where W~A)A(T) is the transfer rate from donor D to acceptor A at temperature, T. The first term in eq. (8) represents emission of a single phonon of energy energy, between hw1( = x1kT), equalstates to theof difference in the excited donor A and the Ev state of the acceptor. Since hW~ 100 cm~ this one-phonon process is almost constant at temperatures below 77 K. Equation (8) also contains a second one-phonon relaxation process in which the energy, lt~2(=x 2kT) is the energy difference between the N1(Eu) line of the acceptor and the e line of the donor, i.e. 5 cm ‘.When ~ < O~,the Debye temperature) the Raman process is independent of temperature. At low temperature W~1 7. The appearance of the T increases linearly as T term in eq. (8) is indicative of a Raman process in the energy transfer from donor A to the acceptor centre. Table 3 gives values for the transfer rates, —

WD(I)A, and the parameters a, /3~, required to reproduce the experimental temperature dependences shown in fig. 4 for the A, B and C donors. It is clear that in each case there are strong ...

245

Table 3 Relative magnitudes of various ion—phonon interactions and appropriate phonon energies in non-resonant D — A energy transfer in Cr3~ MgO Centre

A B C _______________________________________ a (s~) /k, (cm1) ~ ~ ~~ (cm~) y (s1 T7)

1.59X104 107 1.40 x i03 5 2.93x10’3

4.42x iO~ 109 0

3.23X103 105 6 xio~

—

—

3.96X1013

1.31X1013

contributions from terms one (1kg 100 cm~) and three in eq. (8). For donor B there is no contribution from the low-energy one-phonon —

emission process (term in the case transfer from donor C 2). to However, the N1 acceptor, such of a component may be present although the sparseness of data in the temperature range 40—60 K leads to some uncertainty. Given the small density of low-energy phonon states in MgO [6] it is surprising that the value of the is low-energy phonon 3s1) so large. It seems interactionthat term (/3 a term i~3 originates from a resoprobable such nant local mode of the donor—acceptor system. —

4. Comparison of theory and experiment Table 3 shows that the fastest transfer process is that from donor B to the acceptor (W~B)A 4 X 10” at 4.2 K). In consequence we anticipate that donor B is closer to the acceptor than either of donors A or C. At 4.2. K the major ion—lattice relaxation involves the emission of a single phonon of energy hw 100 cm According to Orbach [5] for one-phonon emission the transfer rate is given by ~.

WDA

=

2!,rhl

___________

—~

I~Ui

+

1 }(nq+1) vi (9)

—~

in which flq is the occupation number of phonons of wave vector q, v 1 and v~are the longitudinal and transverse sound velocities respectively, hw is the energy of the emitted phonon, p is the crystal density and I is the strength of the electrostatic interaction between the donor and acceptor. MD

246

M.B. O’Neill, B. Henderson

/ Donor—acceptor energy transfer in Cr3 ± MgO

and MA are the differences in the ion—phonon coupling strengths in ground (f) and excited states (g) i.e. MD = g(D) —f(D) for the donor with a similar term for the acceptor. Taking values of the parameters in eq. (9) from the literature [7] and using !u~ = 100 cm~ we find that the electrostatic donor—acceptor interaction strength must be at least 2.7 X ~ 2 cm~to yield an energy transfer rate of 4 )< i04 s’. There are three possible interactions which might lead to energy transfer between Cr3 + ions, viz, electric quadrupole—quadrupole (EQ—Q), electric dipole—quadrupole (ED—Q) and exchange (EX) interactions. Recent calculations [8] show that when donor and acceptor are separated by 0.84 mn the exchange interaction gives a value for 1 1.2 x ~o 2 cm1, approximately half of that estimated above. To obtain a similarly large value for I using the EQ—Q and ED—Q interactions requires that the D—A separation be not greater than 0.46 nm. This is quite unrealistic since the Eu—Ev splitting in the donor is qnly, say, 10 cm~,whereas that of the <100)(Cr~gV~gCr~g) dimer is 100 cm Such a small splitting implies that the D—A separation must be much larger. This result implies that anisotropic exchange is the predominant mechanism in the donor—acceptor energy transfer process in Cr3 + : MgO [81. This will be discussed at greater length in a subsequent publication, as will the significance that the results have for possible structural models of the D—A pairs and the distribution of Cr3 + ions and vacancies in the MgO lattice

Acknowledgements The authors are indebted to the Science and Engineering Research council for support of the experimental programme. One of us (MBO’N) is grateful to the University of Strathclyde for the award of a John Anderson research studentship. Drs. D.J.S. Birch and R.E. Imhof deserve special thanks for graciously making available to us the pulsed laser and computerized data acquisition system, without which this work could not have been completed.

References

—

—

~.

[1]There are many references in the literature to the spectroscopic complexity of the system Cr3~: MgO. A partial review is given by B. Henderson and J.E. Wertz, Defects in the Alkaline Earth Oxides (Taylor and Francis, London, 1978), but see also B. Henderson and G.F. Imbusch, Optical Spectroscopy of Inorganic Solids (Oxford Univ. Press, 1988, in press). (2] C.M. McDonagh and B. Henderson, J. Phys. C. 18 (1985) 6419. (3] A. Boyrivent, M. Ferrari, E. Duval and M. Monteil, J. Phys. C. 18 (1986) 3253. [41M.B. O’Neill and B. Henderson, J. Lumin, 39 (1988) 161. [5]See e.g. R. Orbach, in: Optical Properties of Ions in Crystals, eds. H.M. Crosswhite and H.W. Moos (Interscience, New York, 1967) p. 445; T. Holstein, S.K. Lyo and K. Orbach, in: Laser Spectroscopy of Solids, eds. W. Yen and P.M. Seizer (Springer, Berlin, 1981) p. 39. [6]G.E. Peckham, Proc. Phys. Soc. B 90 (1967) 657. (7] L.L. Chase, Ph.D. Thesis, Cornell University (1967) (Unpublished). [8] M.B. O’Neill, Ph.D. Thesis, University of Strathclyde (1987) (unpublished).