- Email: [email protected]
Energy transfer and instantaneous spectral diffusion processes in Tb3+ compounds as probed in photon echo experiments
Journal of Luminescence 45 (1990) 387—391 North-Holland
387
Section 10. Coherence ENERGY TRANSFER AND INSTANTANEOUS SPECTRAL DIFFUSION PROCESSES IN Th3~COMPOUNDS AS PROBED IN PHOTON ECHO EXPERIMENTS G.K. LIU
‘i’,
R.L. CONE and M.F. JOUBERT
**
Physics Department, Montana State University, Bozeman, MT 59717, USA
B. JACQUIER UA 442 CNRS, Universite Lyon 1, 69622 Villeurbanne, France
J.L. SKINNER Department of Chemistry, Columbia University, New York, NY 10027, USA
Strongly-frequency-dependent. nanosecond, dephasing rates have been observed in LiTbF 4. This system was chosen since exciton phenomena had been observed earlier in stoichiometric Th~ compounds. The measured frequency-dependent dephasing rates are well described by the quasiresonant-energy-transfer dephasing theory of Root and Skinner except on the extreme-high-energy side. The measured frequency-dependent rates also exhibit the general behavior sought in searches for Anderson Localization by other groups. We have uncovered a significant ‘instantaneous spectral diffusion’ phenomenon which makes the observed dephasing rates intensity dependent and 3~echo whichions can and also contribute surroundinga frequency Tb3~ ionsdependence. occurs when A change in the dipole—dipole interaction between surrounding ionsmagnetic are excited. This causes an instantaneous shift Th in the optical frequency of the echo ion which lasts for T 1
ms. Frequency shifts caused by the first excitation pulse have no effect on echo rephasing (T1 second pulse prevent proper echo rephasing.
1. Introduction With optical coherent transient techniques having reached an advanced stage of interpretation and utilization in dilute solid systems, it has been our goal to apply such techniques to the study of energy transfer processes and collective relaxation phenomena in stoichiometric compounds where strong interactions can take place between the optically-active ions. Such cxperiments are expected to provide interesting probes of energy transfer processes, spin diffusion, and fluctuations associated with phase transitions. They are also sensitive to the nature of inhomogeneous broadening and its role in energy transfer processes. There has been general interest in finding experiments demonstrating a transition from delocalized to localized states. The extent of energy transfer and the nature of the excited states remains an open question in rare earth compounds [1]. The system LiTbF4 was chosen for these experiments since exciton or energy diffusion phenom-
*
* *
Present address: Chemistry Division, Argonne National Laboratory, Argonne, IL 60439, USA. Present address: UA 442 CNRS, Universite Lyon I, 69622 Villeurbannc, France.
0022-2313/90/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
>>
7), but those caused by the
3~ compounds ena had been[2]. observed Frequency-dependent earlier in stoichiometric dephasing is Tban obvious signature of energy transfer processes, and if the inhomogeneously-broadened optical absorption distribution (optical line shape) is thought of as a continuous ‘concentration distribution’ for weakly-perturbed sites, then changes in dephasing with site concentration can be interpreted as changes in the extent of delocalization due to quasiresonant energy transfer. Strong dependence has indeed been observed in our experiments [3,4]. We have also uncovered [3,4] a new laser-induced ‘instantaneous spectral diffusion’ process, however, which can give similar results. Even so, the data on the concentrated LiTbF 4 compound imply a significant frequency dependence which cannot be attributed to the ‘artificial’ instantaneous spectral diffusion effect. The instantaneous spectral diffusion effect, which we have reported earlier [3,4], can affect many other optical coherent transient experiments in solids. The measured dephasing rate in photon echo experiments is intensity dependent, changing by a full order of magnitude in our experiments. Such changes can dramatically alter the interpretation of experiments if not considered. The ‘true’ dephasing rate can only be measured by extrapolation to low intensity for the second laser pulse. This phenomenon is important for dilute and concentrated
388
G.K. Lw er al.
/ Spectral
neous spectral diffusion process which we mentioned above and which we describe in detail below. By contrast, no frequency dependence is expected for the tradi-
___________________________________
• : 16 kG
kG 37 kG
• : 23
o
tional low temperature dephasing processes due to phonons and fluctuating nuclear spins of ligand ions, since the weak inhomogeneous broadening has no serious
• •
• • o
•
• ~ U
• . S
•
1 + compounds
diffusion processes in Tb
•
•
o 0. I
effect on the electron—phonon coupling or an ion’s magnetic moment. For the remainder of this section, we focus our attention on the effects of quasiresonant energy transfer processes. We examine the data of fig. 1 in terms of the search for Anderson Localization and in terms of the quasiresonant transfer theory described by Root and Skinner [5]. The general shape of the data for the low energy side and central region of the line are consistent with either interpretation. The much faster dephasing or larger homogeneous linewidth on the high energy tail of the line, however, remains a problem. A possible T 1
-0.3
-0.1
0.1
WAVENUMBERS
0.3
( 1/cm )
Fig. 1. Comparison 7F 5D of experimental dephasing rates (points) for the 6F2 to 4F1 transition with the theoretical curve (solid line) for the homogeneous line width versus energy in LiThF4. The solid curve also reflects the energy dependence of the absorption coefficient and the site concentration.
systems and is largest when there are changes in the electronic magnetic moment from the ground to the excited state.
2. Frequency-dependent dephasing in concentrated cornpounds 3~ in Dephasing LiTbF times have been measured for Tb stoichiometric 4 via the classic two pulse photon echo technique over a temperature range of 1.25 to 2.1 K and in a strong applied magnetic field. The sample was optically thin, and the laser pulses were in of fig. 5 ns 1 bandwidth. The points 1 duration 0.05frequency cm show the and strong dependence of the measured homogeneous linewidth F = 1/[IT(dephasing time)] and demonstrate that the values are independent of magnetic field over the range of 16 to 37 kG in this magnetically ordered system. On the high energy side of the line, no echo was observed for 20 ns pulse delay, so the echo decay is much faster there and the homogeneous linewidth greater than any of the values plotted in fig. 1. The solid curve is proportional to the measured optical absorption profile. A correspondence in behavior as a function of optical energy, between the homogeneous linewidth and the absorption profile, is expected for two processes. The first is dephasing due to quasiresonant energy transfer between neighboring ions. The second is the instanta-
energy relaxation process is considered below. In general, one expects the presence of energy transfer to speed up dephasing, so we can interpret the homogeneous Iinewidth data of fig. I as revealing a dramatic decrease of energy transfer or mobility on the low energy side. This apparent ‘transition’ from delocalized states near line center to localized (or more-localized) states on the low energy side would correspond to the lower concentration of ions in the low energy range reflected by the absorption profile [3]. This is just the type of ‘mobility-edge’ behavior which has been sought as a sign of Anderson Localization. Instead of requiring measurement of separate samples with a range of ion concentrations, we interpret the energy distribution as corresponding to an ion concentration distribution and obtain the necessary data versus concentration from a single sample. Using resonant Rayleigh scattering and various nonlinear techniques Hegarty and Sturge [6] have reported an observation of a mobility edge near the line center of a heavy-hole exciton transition in the very different multiquantum well structures of GaAs—AIGaAs. high energy excitons were delocalized in that caseThe as well. Brocklesby et al. [7] observed that the homogeneous linewidth in GaP: N showed a rapid increase at energies just above the B-line center, but they ruled out an interpretation involving a mobility edge. Returning to the interpretation of our data, a mobility-edge could also be expected on the high energy side. In our results, any such effect is hidden by another process. In the discussion below, a quantitative theory of enhanced energy relaxation on the high energy side of the line is considered. We must conclude at this time that there is insufficient evidence to identify these observations as Anderson Localization. The theory of photon echo decay due to quasiresonant energy transfer which was developed by Root and
3
G.K. Liu et al. / Spectral diffusion processes in Tb Skinner [5] predicts frequency dependent dephasing. With the assumption of microscopic inhomogeneous broadening and electric dipole interactions between rare
earth ions, that theory has given reasonable agreement with the experimental data for EuP 3~: Y 5 014 and Eu 203 [5,8]. We now describe its application to LiThF4. As the assumption of macroscopic inhomogeneous broadening gives no frequency dependence, we assume microscopic broadening and assume that dephasing is due to interactions between nearby ions which have the same optical frequencies. Without considering phonon broadening, an appropriate assumption at low temperature, the interaction Hamiltonian can be written in terms of a diagonal inhomogeneous distribution and off-diagonal intrinsic interactions, H=~hi)KiI+~ V.~i)(jj,
compounds
where I i) is the single-ion excited electronic state on the /th site. The excitation frequency at site i is co, = w0 + ~,, where a~is the central excitation frequency of the inhomogeneous line and i~ is the inhomogeneous devialion. The inhomogeneous line shape is characterized by a distribution function P(w1). The interaction matrix element between sites i and j is responsible for the homogeneous dephasing and the energy transfer processes. The summations are over all sites occupied by the optically active ions with i *j. The intrinsic interactions are assumed to be much smaller than the inhomogeneous broadening ~. The resulting dephasing rate is 2
(v1~)
where the distribution function P(~)The is derived fromnormalized the measured absorption coefficient. summation is a constant for a particular system; thus, the dephasing rate is proportional to the height of the inhomogeneous distribution P(~) at the excitation frequency. An ion at the center of the line has more nearly-resonant neighbors than do ions in the wings.
phonons. Such a mechanism is clearly asymmetric in its contribution to dephasing versus energy as the bulk of the line corresponds to acceptors for the high energy ions, whereas there are few suitable acceptors for low
energy ions. In addition to spontaneous phonon emission, thermal phonons could assist the energy transfer both ways. Assuming only one-phonon processes, the lifetime of an excitation as a function of frequency across the inhomogeneous line was calculated. The additional linewidth contribution 1/(217T1(w)) could not fit the data except by introducing a temperature T far below the actual value of 1.3 K. The one-phonon model thus was not successful for interpreting the asymmetry in the echo dephasing rate of this system.
In electron spin echo studies of rare earth compounds Mims [9] and Klauder and Anderson [10] pointed out a power dependent phenomenon called instantaneous spectral diffusion. The analogous optical effect was observed for the first time our knowledge 3~:toLiYF [3,4] in our experiments on Tb 4. For our observations, this phenomenon has been identified as arising from the magnetic dipole—dipole interaction. Subsequent experiments by Huang et al. [11] have shown that instantaneous diffusion effects can also arise from smaller optically-induced changes in the crystal field. In the magnetic compounds of interest here, the optical transition energies are quite sensitive to fluctuating magnetic fields. Thus the magnetic dipole—dipole interaction [1] plays an important 3~ion role in has thealine 3~: LiYF verybroadlarge ening. In 1%Tb the Tb in the ground state), magnetic dipole moment4, (8.SS!.LB and the changes in local magnetic fields accompanying an optical excitation are dramatic. Due to the Zeeman effect in the ground and excited electronic states, an optical frequency is shifted by ~
~,
=
—
g 2 )/2] 9’ B
The homogeneous line width can be expressed as F’ ~ — F ~ —
0
389
3. Instantaneous spectral diffusion
i
1/T2(~a) = 2.rrP(ia)~
+
+ AP~w1,
where F0 is the frequency-independent dephasing. Fig. I shows2. the resulting with with 1’~= the 0.5 MHz and homogeA = 260 This model fit agrees observed (MHz) linewidths except on the high energy side. The neous constant F 0 presumably represents the contribution from the fluctuation of local fields of the host nuclear spins and the electronic spin flips in the ground state. The approximate value of V is 1 MHz. To explain the anomalous fast dephasing on the high energy side, spontaneous phonon emission processes were considered. An excitation on the high energy side could transfer to a lower energy site and the energy mismatch could be released in the form of a phonon or
~
H/h,
where g1 and g2 are the g-factors for the ground and excited state, respectively, and z~sH is the total change in the local field. Optical excitations caused by the echo-generating change the magnetic of the excited ions;pulses this leads to changes in themoments local fields for neighboring ions. For the dipole—dipole interaction [1], the change in local field at site i after the excitation of a neighboring ion at site j is /
=
[(g1
—
=
[(g1
—
2
\
3
g~)/2]9’~t 1 —3 cos 0. ~)/r~ where is the distance between sites i and j, and is the angle between the z-direction and the line joining i and j. The resonance frequency shift of i is then 2 ~v,j
g2)/2]
2
9’B(1
2 —
3 cos
1
3
390
G.K. Liu et al. / Spectral diffusion processes in Tb
g
and a sum must be evaluated over the sample. The frequency shifts due to the first pulse are present throughout the echo-generating sequence and are fixed since T 1 >> r where T is the pulse separation. Their effects are equivalent to those of the normal static inhomogeneous broadening and are removed by the echo sequence. In contrast, the shifts due to the second pulse are present only for part of the echo sequence, so their effects are not removed by the rephasing process, and they prevent complete rephasing of the echoes. This disruption of the rephasing makes a contribution to the measured homogeneous linewidth given by [4] F’
=
1/~T2’
0.20[(g1
—
=
1/rrT2’ 29’~rdI2{1 — exp[—a(w)L]}
— —
O.2O(g~— g2)
compounds
____________________________________
• 0
I
~
________________________________________ •
Z.
a ~
g2)29’~/h~~e’
where n e is the density of excited ions created by the second laser pulse in the echo-generating pulse sequence. The experimental parameter n,~is directly proportional to the intensity of the second pulse. The numerical factor 0.20 includes a lattice sum for the dipole—dipole interaction and is therefore somewhat crystal-structure-dependent. When n~ expressed in terms of experimental parameters, the isabove formula b 141 ecomes F’
+
.—
U
.~
=
•
:
=
11(12
7.1
io ~.o ~.o i~.o i~.o2) 18.0 EXCITATION INTENSITY (MW/cm . . Fig. 2. Excitation intensity dependence of the measured unewidth for Tb3~: LiYF 4 at 1.3 K. The solid curves are the best fit to the experimental data points. Dephasing only depends on curve with ‘2 of varied is 26 kHz/(MW/cm2), and slope the intersecthe intensity the second laser pulse ‘2• The of the 0.0
.
Lh2w 0
‘
where ‘2 is the intensity of the second pulse, a(i~) is the frequency-dependent absorption coefficient and L is the optical path length in the crystal. In our experiments, the echo decays were recorded over 2 to 3 decades of dynamic range as a function of delay time. To study the effect of excitation intensity on the dephasing rate of the photon echoes, the peak intensities of the first and second laser pulses 2were by independently from 2 tolaser overintensities 15 MW/cm controlling the varied nitrogen pump without any disturbance to the beam paths or the echo optical
tion point is 28 kl-Iz as
‘2
tends to zero.
system. Fig. 2 shows the measured homogeneous line width F as a function of the intensities of the laser pulses at H = 42 kG and T= 1.3 K. The experimental data obey the simple formula predicted by the above model F — Fo + F’ — F + a 2’
3~: LiYF For I%Tb 4, the peak absorption coefficient for this transition is 2.5 cm~, L = 0.2 cm, thus 40% of the laser power is absorbed in the inhomogeneous line center. In this group of experiments, the laser line width was 0.3 cm — and the inhomogeneous line width of the sample was 0.4 cm~. With the assumption of Gaussian line shapes, an then average neous line was 30%absorption instead ofacross 40% inthe theinhomogecenter of the line. The ground state has a linear Zeeman effect with g~= 17.7. The F 1 levels of the excited state vary quadratically at low field and asymptotically approach linear Zeeman splittings at high field with g2 = 12. At 42 kG, the effective value is 9.1. The pulse length 14 = 5 >< 10~ s, and v0 = 6.22)x 1014 The calculated is inHz. reasonable agreevalue a = 25 kHz/(MW/cm ment with determined thefrom experimental a fit to value the data of 26 points kHz/(MW/cm2) in fig. 2.
where ‘2 is the peak intensity of the second laser pulse on the crystal, a = 26 kHz/(MW/cm2) is the slope for best fitting the data, and L~= 28 kHz is the true homogeneous line width including the contribution from the remaining local field fluctuations due primarily to the nuclear spin diffusion in the applied magnetic field. At high magnetic field and low temperature, the instantaneous diffusion contribution F’ dominates the echo decay rate. The intensity-dependence coefficient a is analytically determined by the formulas given above,
Potential uncertainty is due to the approximation of a continuous medium which was used in the calculation and the uncertainty of various experimental conditions such as the effective diameter of the focused laser beam, laser power loss due to the windows and prisms in the cryostat, and both spatial and frequency overlap of the two laser pulses. The observed intensity dependence is directly proportional to the excitation density created by the second laser pulse. At constant intensity, this excitation-density
3
G.K. Liu et a!. / Spectral diffusion processes in Tb dependence also leads to a frequency dependence which is directly proportional to the absorption coefficient, The predicted frequency dependence has been observed in the same crystal with the lasers adjusted for narrower bandwidth. The frequency dependence of the echo decay rate due to instantaneous diffusion arises from the excitation of more ions at line center than in the wings when the sample is optically thin. The observation of this instantaneous diffusion phenomenon in the dilute crystal obviously raised questions about its possible role in the concentrated crystal. Those experiments were carried out at reduced intensity levels after the early observation of this effect in both the concentrated and dilute crystals, and we can confidently state that the instantaneous diffusion mechanism alone is not responsible for the dramatic variation seen in fig. 1. An increase in laser intensity sufficient to give an order of magnitude change for the dilute crystal gave only a factor of two change for the concentrated sample under our operating conditions. Moreover, it is clear that the extra-fast dephasing on the high energy side of the line would not be consistent with instantaneous diffusion either.
4. Concluding remarks These results and analysis indicate that studies of stoichiometric rare earth systems can provide interesting new perspectives on the energy transfer process and on the localized versus delocalized state question. They also show that the instantaneous diffusion process is important in interpreting measurements of homogeneous line widths via coherent transients or other techniques of nonlinear spectroscopy such as spectral hole burning. We recently have observed photon echoes for Tb(OH)3 where energy transfer processes have been studied earlier [2]. The Tb(OH)3 echoes decay more rapidly than those for LiTbF4. This would be consistent with faster energy transfer, expected from the generally stronger ion—ion coupling in that compound; however, that system is also far more sensitive to instantaneous diffusion. Separate studies of echo modulation due to transferred hyperfine interactions with fluorine ligands and
±
compounds
391
of magnetic field dependence of the dephasing have been carried out on the dilute compound 1%Tb34 LjYF 4 and will be reported elsewhere. The modulation, which we have studied in detail, has no effect on the results reported here.
Acknowledgements This research was carried out at Montana State University and supported by NSF/MONTS, Research Corporation, CNRS, and NATO/OTAN Grant 84/ 0505.
References [1] R.L. Cone and R.S. Meltzer, in: Spectroscopy of Crystals Containing Rare-Earth Ions, eds. A.A. Kaplyanskii and R.M. Macfarlane (North-Holland. Amsterdam, 1987) ch. 8. p. 481. [2] R.L. Cone and R.S. Meltzer. J. Chem. Phys. 62 (1975) 3573; H.T. Chen and R.S. Meltzer, Phys. Rev. Lett. 44 (1980) 599; M.F. Joubert. B. Jacquier and R.L. Cone, Phys. Rev. B35 (1987) 8322. [3] G.K. Liu, M.F. Joubert, R.L. Cone and B. Jacquier. J. Lumin. 38 (1987) 34. [4] R.L. Cone and G.K. Liu, Bull. Am. Phys. Soc. 33 (1988) 676, N22—8. N22—7; G.K. Liu, PhD Thesis, Montana State University, 1988. [5] L. Root and J.L. Skinner. J. Chem. Phys. 81(1984) 5310; Phys. Rev. B32 (1985) 4111. [6] J. Hegarty and M.D. Sturge. J. Opt. Soc. Am. B2 (1985) 1143. [71 W.S. Brocklesby, R.T. Harley and A.S. Plaut, Phys. Rev B36 (1987) 7941. [8] R.M. Macfarlane and R.M. Shelby. in: Spectroscopy of Crystals Containing Rare-Earth Ions. eds., A.A. Kaplyanskii and R.M. Macfarlane (North-Holland, 1987) ch. 3. p. 51. [9] W B. Mims, in: Electron Paramagnetic Resonance. ed. S. Geschwind (Plenum, New York, 1972) p. 263. [10] J.R. Klauder and P.W. Anderson, Phys. Rev. 125 (1962) 912. [11] Jin Huang. J.M. Zhang, A. Lezama and T.W. Mossberg. Phys. Rev. Lett. 63 (1989) 78.
387
Section 10. Coherence ENERGY TRANSFER AND INSTANTANEOUS SPECTRAL DIFFUSION PROCESSES IN Th3~COMPOUNDS AS PROBED IN PHOTON ECHO EXPERIMENTS G.K. LIU
‘i’,
R.L. CONE and M.F. JOUBERT
**
Physics Department, Montana State University, Bozeman, MT 59717, USA
B. JACQUIER UA 442 CNRS, Universite Lyon 1, 69622 Villeurbanne, France
J.L. SKINNER Department of Chemistry, Columbia University, New York, NY 10027, USA
Strongly-frequency-dependent. nanosecond, dephasing rates have been observed in LiTbF 4. This system was chosen since exciton phenomena had been observed earlier in stoichiometric Th~ compounds. The measured frequency-dependent dephasing rates are well described by the quasiresonant-energy-transfer dephasing theory of Root and Skinner except on the extreme-high-energy side. The measured frequency-dependent rates also exhibit the general behavior sought in searches for Anderson Localization by other groups. We have uncovered a significant ‘instantaneous spectral diffusion’ phenomenon which makes the observed dephasing rates intensity dependent and 3~echo whichions can and also contribute surroundinga frequency Tb3~ ionsdependence. occurs when A change in the dipole—dipole interaction between surrounding ionsmagnetic are excited. This causes an instantaneous shift Th in the optical frequency of the echo ion which lasts for T 1
ms. Frequency shifts caused by the first excitation pulse have no effect on echo rephasing (T1 second pulse prevent proper echo rephasing.
1. Introduction With optical coherent transient techniques having reached an advanced stage of interpretation and utilization in dilute solid systems, it has been our goal to apply such techniques to the study of energy transfer processes and collective relaxation phenomena in stoichiometric compounds where strong interactions can take place between the optically-active ions. Such cxperiments are expected to provide interesting probes of energy transfer processes, spin diffusion, and fluctuations associated with phase transitions. They are also sensitive to the nature of inhomogeneous broadening and its role in energy transfer processes. There has been general interest in finding experiments demonstrating a transition from delocalized to localized states. The extent of energy transfer and the nature of the excited states remains an open question in rare earth compounds [1]. The system LiTbF4 was chosen for these experiments since exciton or energy diffusion phenom-
*
* *
Present address: Chemistry Division, Argonne National Laboratory, Argonne, IL 60439, USA. Present address: UA 442 CNRS, Universite Lyon I, 69622 Villeurbannc, France.
0022-2313/90/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
>>
7), but those caused by the
3~ compounds ena had been[2]. observed Frequency-dependent earlier in stoichiometric dephasing is Tban obvious signature of energy transfer processes, and if the inhomogeneously-broadened optical absorption distribution (optical line shape) is thought of as a continuous ‘concentration distribution’ for weakly-perturbed sites, then changes in dephasing with site concentration can be interpreted as changes in the extent of delocalization due to quasiresonant energy transfer. Strong dependence has indeed been observed in our experiments [3,4]. We have also uncovered [3,4] a new laser-induced ‘instantaneous spectral diffusion’ process, however, which can give similar results. Even so, the data on the concentrated LiTbF 4 compound imply a significant frequency dependence which cannot be attributed to the ‘artificial’ instantaneous spectral diffusion effect. The instantaneous spectral diffusion effect, which we have reported earlier [3,4], can affect many other optical coherent transient experiments in solids. The measured dephasing rate in photon echo experiments is intensity dependent, changing by a full order of magnitude in our experiments. Such changes can dramatically alter the interpretation of experiments if not considered. The ‘true’ dephasing rate can only be measured by extrapolation to low intensity for the second laser pulse. This phenomenon is important for dilute and concentrated
388
G.K. Lw er al.
/ Spectral
neous spectral diffusion process which we mentioned above and which we describe in detail below. By contrast, no frequency dependence is expected for the tradi-
___________________________________
• : 16 kG
kG 37 kG
• : 23
o
tional low temperature dephasing processes due to phonons and fluctuating nuclear spins of ligand ions, since the weak inhomogeneous broadening has no serious
• •
• • o
•
• ~ U
• . S
•
1 + compounds
diffusion processes in Tb
•
•
o 0. I
effect on the electron—phonon coupling or an ion’s magnetic moment. For the remainder of this section, we focus our attention on the effects of quasiresonant energy transfer processes. We examine the data of fig. 1 in terms of the search for Anderson Localization and in terms of the quasiresonant transfer theory described by Root and Skinner [5]. The general shape of the data for the low energy side and central region of the line are consistent with either interpretation. The much faster dephasing or larger homogeneous linewidth on the high energy tail of the line, however, remains a problem. A possible T 1
-0.3
-0.1
0.1
WAVENUMBERS
0.3
( 1/cm )
Fig. 1. Comparison 7F 5D of experimental dephasing rates (points) for the 6F2 to 4F1 transition with the theoretical curve (solid line) for the homogeneous line width versus energy in LiThF4. The solid curve also reflects the energy dependence of the absorption coefficient and the site concentration.
systems and is largest when there are changes in the electronic magnetic moment from the ground to the excited state.
2. Frequency-dependent dephasing in concentrated cornpounds 3~ in Dephasing LiTbF times have been measured for Tb stoichiometric 4 via the classic two pulse photon echo technique over a temperature range of 1.25 to 2.1 K and in a strong applied magnetic field. The sample was optically thin, and the laser pulses were in of fig. 5 ns 1 bandwidth. The points 1 duration 0.05frequency cm show the and strong dependence of the measured homogeneous linewidth F = 1/[IT(dephasing time)] and demonstrate that the values are independent of magnetic field over the range of 16 to 37 kG in this magnetically ordered system. On the high energy side of the line, no echo was observed for 20 ns pulse delay, so the echo decay is much faster there and the homogeneous linewidth greater than any of the values plotted in fig. 1. The solid curve is proportional to the measured optical absorption profile. A correspondence in behavior as a function of optical energy, between the homogeneous linewidth and the absorption profile, is expected for two processes. The first is dephasing due to quasiresonant energy transfer between neighboring ions. The second is the instanta-
energy relaxation process is considered below. In general, one expects the presence of energy transfer to speed up dephasing, so we can interpret the homogeneous Iinewidth data of fig. I as revealing a dramatic decrease of energy transfer or mobility on the low energy side. This apparent ‘transition’ from delocalized states near line center to localized (or more-localized) states on the low energy side would correspond to the lower concentration of ions in the low energy range reflected by the absorption profile [3]. This is just the type of ‘mobility-edge’ behavior which has been sought as a sign of Anderson Localization. Instead of requiring measurement of separate samples with a range of ion concentrations, we interpret the energy distribution as corresponding to an ion concentration distribution and obtain the necessary data versus concentration from a single sample. Using resonant Rayleigh scattering and various nonlinear techniques Hegarty and Sturge [6] have reported an observation of a mobility edge near the line center of a heavy-hole exciton transition in the very different multiquantum well structures of GaAs—AIGaAs. high energy excitons were delocalized in that caseThe as well. Brocklesby et al. [7] observed that the homogeneous linewidth in GaP: N showed a rapid increase at energies just above the B-line center, but they ruled out an interpretation involving a mobility edge. Returning to the interpretation of our data, a mobility-edge could also be expected on the high energy side. In our results, any such effect is hidden by another process. In the discussion below, a quantitative theory of enhanced energy relaxation on the high energy side of the line is considered. We must conclude at this time that there is insufficient evidence to identify these observations as Anderson Localization. The theory of photon echo decay due to quasiresonant energy transfer which was developed by Root and
3
G.K. Liu et al. / Spectral diffusion processes in Tb Skinner [5] predicts frequency dependent dephasing. With the assumption of microscopic inhomogeneous broadening and electric dipole interactions between rare
earth ions, that theory has given reasonable agreement with the experimental data for EuP 3~: Y 5 014 and Eu 203 [5,8]. We now describe its application to LiThF4. As the assumption of macroscopic inhomogeneous broadening gives no frequency dependence, we assume microscopic broadening and assume that dephasing is due to interactions between nearby ions which have the same optical frequencies. Without considering phonon broadening, an appropriate assumption at low temperature, the interaction Hamiltonian can be written in terms of a diagonal inhomogeneous distribution and off-diagonal intrinsic interactions, H=~hi)KiI+~ V.~i)(jj,
compounds
where I i) is the single-ion excited electronic state on the /th site. The excitation frequency at site i is co, = w0 + ~,, where a~is the central excitation frequency of the inhomogeneous line and i~ is the inhomogeneous devialion. The inhomogeneous line shape is characterized by a distribution function P(w1). The interaction matrix element between sites i and j is responsible for the homogeneous dephasing and the energy transfer processes. The summations are over all sites occupied by the optically active ions with i *j. The intrinsic interactions are assumed to be much smaller than the inhomogeneous broadening ~. The resulting dephasing rate is 2
(v1~)
where the distribution function P(~)The is derived fromnormalized the measured absorption coefficient. summation is a constant for a particular system; thus, the dephasing rate is proportional to the height of the inhomogeneous distribution P(~) at the excitation frequency. An ion at the center of the line has more nearly-resonant neighbors than do ions in the wings.
phonons. Such a mechanism is clearly asymmetric in its contribution to dephasing versus energy as the bulk of the line corresponds to acceptors for the high energy ions, whereas there are few suitable acceptors for low
energy ions. In addition to spontaneous phonon emission, thermal phonons could assist the energy transfer both ways. Assuming only one-phonon processes, the lifetime of an excitation as a function of frequency across the inhomogeneous line was calculated. The additional linewidth contribution 1/(217T1(w)) could not fit the data except by introducing a temperature T far below the actual value of 1.3 K. The one-phonon model thus was not successful for interpreting the asymmetry in the echo dephasing rate of this system.
In electron spin echo studies of rare earth compounds Mims [9] and Klauder and Anderson [10] pointed out a power dependent phenomenon called instantaneous spectral diffusion. The analogous optical effect was observed for the first time our knowledge 3~:toLiYF [3,4] in our experiments on Tb 4. For our observations, this phenomenon has been identified as arising from the magnetic dipole—dipole interaction. Subsequent experiments by Huang et al. [11] have shown that instantaneous diffusion effects can also arise from smaller optically-induced changes in the crystal field. In the magnetic compounds of interest here, the optical transition energies are quite sensitive to fluctuating magnetic fields. Thus the magnetic dipole—dipole interaction [1] plays an important 3~ion role in has thealine 3~: LiYF verybroadlarge ening. In 1%Tb the Tb in the ground state), magnetic dipole moment4, (8.SS!.LB and the changes in local magnetic fields accompanying an optical excitation are dramatic. Due to the Zeeman effect in the ground and excited electronic states, an optical frequency is shifted by ~
~,
=
—
g 2 )/2] 9’ B
The homogeneous line width can be expressed as F’ ~ — F ~ —
0
389
3. Instantaneous spectral diffusion
i
1/T2(~a) = 2.rrP(ia)~
+
+ AP~w1,
where F0 is the frequency-independent dephasing. Fig. I shows2. the resulting with with 1’~= the 0.5 MHz and homogeA = 260 This model fit agrees observed (MHz) linewidths except on the high energy side. The neous constant F 0 presumably represents the contribution from the fluctuation of local fields of the host nuclear spins and the electronic spin flips in the ground state. The approximate value of V is 1 MHz. To explain the anomalous fast dephasing on the high energy side, spontaneous phonon emission processes were considered. An excitation on the high energy side could transfer to a lower energy site and the energy mismatch could be released in the form of a phonon or
~
H/h,
where g1 and g2 are the g-factors for the ground and excited state, respectively, and z~sH is the total change in the local field. Optical excitations caused by the echo-generating change the magnetic of the excited ions;pulses this leads to changes in themoments local fields for neighboring ions. For the dipole—dipole interaction [1], the change in local field at site i after the excitation of a neighboring ion at site j is /
=
[(g1
—
=
[(g1
—
2
\
3
g~)/2]9’~t 1 —3 cos 0. ~)/r~ where is the distance between sites i and j, and is the angle between the z-direction and the line joining i and j. The resonance frequency shift of i is then 2 ~v,j
g2)/2]
2
9’B(1
2 —
3 cos
1
3
390
G.K. Liu et al. / Spectral diffusion processes in Tb
g
and a sum must be evaluated over the sample. The frequency shifts due to the first pulse are present throughout the echo-generating sequence and are fixed since T 1 >> r where T is the pulse separation. Their effects are equivalent to those of the normal static inhomogeneous broadening and are removed by the echo sequence. In contrast, the shifts due to the second pulse are present only for part of the echo sequence, so their effects are not removed by the rephasing process, and they prevent complete rephasing of the echoes. This disruption of the rephasing makes a contribution to the measured homogeneous linewidth given by [4] F’
=
1/~T2’
0.20[(g1
—
=
1/rrT2’ 29’~rdI2{1 — exp[—a(w)L]}
— —
O.2O(g~— g2)
compounds
____________________________________
• 0
I
~
________________________________________ •
Z.
a ~
g2)29’~/h~~e’
where n e is the density of excited ions created by the second laser pulse in the echo-generating pulse sequence. The experimental parameter n,~is directly proportional to the intensity of the second pulse. The numerical factor 0.20 includes a lattice sum for the dipole—dipole interaction and is therefore somewhat crystal-structure-dependent. When n~ expressed in terms of experimental parameters, the isabove formula b 141 ecomes F’
+
.—
U
.~
=
•
:
=
11(12
7.1
io ~.o ~.o i~.o i~.o2) 18.0 EXCITATION INTENSITY (MW/cm . . Fig. 2. Excitation intensity dependence of the measured unewidth for Tb3~: LiYF 4 at 1.3 K. The solid curves are the best fit to the experimental data points. Dephasing only depends on curve with ‘2 of varied is 26 kHz/(MW/cm2), and slope the intersecthe intensity the second laser pulse ‘2• The of the 0.0
.
Lh2w 0
‘
where ‘2 is the intensity of the second pulse, a(i~) is the frequency-dependent absorption coefficient and L is the optical path length in the crystal. In our experiments, the echo decays were recorded over 2 to 3 decades of dynamic range as a function of delay time. To study the effect of excitation intensity on the dephasing rate of the photon echoes, the peak intensities of the first and second laser pulses 2were by independently from 2 tolaser overintensities 15 MW/cm controlling the varied nitrogen pump without any disturbance to the beam paths or the echo optical
tion point is 28 kl-Iz as
‘2
tends to zero.
system. Fig. 2 shows the measured homogeneous line width F as a function of the intensities of the laser pulses at H = 42 kG and T= 1.3 K. The experimental data obey the simple formula predicted by the above model F — Fo + F’ — F + a 2’
3~: LiYF For I%Tb 4, the peak absorption coefficient for this transition is 2.5 cm~, L = 0.2 cm, thus 40% of the laser power is absorbed in the inhomogeneous line center. In this group of experiments, the laser line width was 0.3 cm — and the inhomogeneous line width of the sample was 0.4 cm~. With the assumption of Gaussian line shapes, an then average neous line was 30%absorption instead ofacross 40% inthe theinhomogecenter of the line. The ground state has a linear Zeeman effect with g~= 17.7. The F 1 levels of the excited state vary quadratically at low field and asymptotically approach linear Zeeman splittings at high field with g2 = 12. At 42 kG, the effective value is 9.1. The pulse length 14 = 5 >< 10~ s, and v0 = 6.22)x 1014 The calculated is inHz. reasonable agreevalue a = 25 kHz/(MW/cm ment with determined thefrom experimental a fit to value the data of 26 points kHz/(MW/cm2) in fig. 2.
where ‘2 is the peak intensity of the second laser pulse on the crystal, a = 26 kHz/(MW/cm2) is the slope for best fitting the data, and L~= 28 kHz is the true homogeneous line width including the contribution from the remaining local field fluctuations due primarily to the nuclear spin diffusion in the applied magnetic field. At high magnetic field and low temperature, the instantaneous diffusion contribution F’ dominates the echo decay rate. The intensity-dependence coefficient a is analytically determined by the formulas given above,
Potential uncertainty is due to the approximation of a continuous medium which was used in the calculation and the uncertainty of various experimental conditions such as the effective diameter of the focused laser beam, laser power loss due to the windows and prisms in the cryostat, and both spatial and frequency overlap of the two laser pulses. The observed intensity dependence is directly proportional to the excitation density created by the second laser pulse. At constant intensity, this excitation-density
3
G.K. Liu et a!. / Spectral diffusion processes in Tb dependence also leads to a frequency dependence which is directly proportional to the absorption coefficient, The predicted frequency dependence has been observed in the same crystal with the lasers adjusted for narrower bandwidth. The frequency dependence of the echo decay rate due to instantaneous diffusion arises from the excitation of more ions at line center than in the wings when the sample is optically thin. The observation of this instantaneous diffusion phenomenon in the dilute crystal obviously raised questions about its possible role in the concentrated crystal. Those experiments were carried out at reduced intensity levels after the early observation of this effect in both the concentrated and dilute crystals, and we can confidently state that the instantaneous diffusion mechanism alone is not responsible for the dramatic variation seen in fig. 1. An increase in laser intensity sufficient to give an order of magnitude change for the dilute crystal gave only a factor of two change for the concentrated sample under our operating conditions. Moreover, it is clear that the extra-fast dephasing on the high energy side of the line would not be consistent with instantaneous diffusion either.
4. Concluding remarks These results and analysis indicate that studies of stoichiometric rare earth systems can provide interesting new perspectives on the energy transfer process and on the localized versus delocalized state question. They also show that the instantaneous diffusion process is important in interpreting measurements of homogeneous line widths via coherent transients or other techniques of nonlinear spectroscopy such as spectral hole burning. We recently have observed photon echoes for Tb(OH)3 where energy transfer processes have been studied earlier [2]. The Tb(OH)3 echoes decay more rapidly than those for LiTbF4. This would be consistent with faster energy transfer, expected from the generally stronger ion—ion coupling in that compound; however, that system is also far more sensitive to instantaneous diffusion. Separate studies of echo modulation due to transferred hyperfine interactions with fluorine ligands and
±
compounds
391
of magnetic field dependence of the dephasing have been carried out on the dilute compound 1%Tb34 LjYF 4 and will be reported elsewhere. The modulation, which we have studied in detail, has no effect on the results reported here.
Acknowledgements This research was carried out at Montana State University and supported by NSF/MONTS, Research Corporation, CNRS, and NATO/OTAN Grant 84/ 0505.
References [1] R.L. Cone and R.S. Meltzer, in: Spectroscopy of Crystals Containing Rare-Earth Ions, eds. A.A. Kaplyanskii and R.M. Macfarlane (North-Holland. Amsterdam, 1987) ch. 8. p. 481. [2] R.L. Cone and R.S. Meltzer. J. Chem. Phys. 62 (1975) 3573; H.T. Chen and R.S. Meltzer, Phys. Rev. Lett. 44 (1980) 599; M.F. Joubert. B. Jacquier and R.L. Cone, Phys. Rev. B35 (1987) 8322. [3] G.K. Liu, M.F. Joubert, R.L. Cone and B. Jacquier. J. Lumin. 38 (1987) 34. [4] R.L. Cone and G.K. Liu, Bull. Am. Phys. Soc. 33 (1988) 676, N22—8. N22—7; G.K. Liu, PhD Thesis, Montana State University, 1988. [5] L. Root and J.L. Skinner. J. Chem. Phys. 81(1984) 5310; Phys. Rev. B32 (1985) 4111. [6] J. Hegarty and M.D. Sturge. J. Opt. Soc. Am. B2 (1985) 1143. [71 W.S. Brocklesby, R.T. Harley and A.S. Plaut, Phys. Rev B36 (1987) 7941. [8] R.M. Macfarlane and R.M. Shelby. in: Spectroscopy of Crystals Containing Rare-Earth Ions. eds., A.A. Kaplyanskii and R.M. Macfarlane (North-Holland, 1987) ch. 3. p. 51. [9] W B. Mims, in: Electron Paramagnetic Resonance. ed. S. Geschwind (Plenum, New York, 1972) p. 263. [10] J.R. Klauder and P.W. Anderson, Phys. Rev. 125 (1962) 912. [11] Jin Huang. J.M. Zhang, A. Lezama and T.W. Mossberg. Phys. Rev. Lett. 63 (1989) 78.