Electron-phonon interactions in CsCdBr3=Yb3+

Article abstract of DOI:10.1063/1.474851

Pronounced electron-phonon coupling is observed for the ²F_7/2?²F_5/2 4f transitions of Yb³⁺ doped into CsCdBr₃. A comparison of the Raman spectrum and the luminescence excitation sideband accompanying the ²F_7/2(0)→²F_5/2(2′) crystal-field transition reveals vibrational properties of the [YbBr₆] coordination unit that differ markedly from those of the CsCdBr₃ host. In particular, the vibronic transition associated with the totally symmetric [YbBr₆] stretching mode appears as a very weak feature at 191 cm^-1 in the Raman spectrum, whereas the totally symmetric [CdBr₆] stretching mode of the CsCdBr₃ bulk, which appears as a strong feature at 162.5 cm^-1 in the Raman spectrum, is only weakly discernible in the sideband. This is direct evidence for a large contribution from [YbBr₆] local modes and a small contribution from bulk modes to the vibronic intensity. The intensity of the local mode is enhanced by approximately a factor of 2 in the Raman spectrum when the laser is tuned into resonance with the ²F_7/2(0)→²F_5/2(2′) absorption of Yb³⁺, providing direct confirmation of its assignment. The observation of the first and second members of a Franck-Condon progression for both the local and the bulk totally symmetric modes indicates that a Δ process, rather than an M process, induces the vibronic intensity. Huang-Rhys factors of S_local=0.010±0.002 and S_bulk=0.15±0.03 were determined from the data, and reflect quite different electron-phonon coupling strengths. These results suggest that multiphonon relaxation of excited electronic states proceeds by the excitation of local modes of [YbBr₆] followed by energy transfer to bulk modes of the lattice, possibly through a nonlinear coupling mechanism which is discussed briefly.

Full text of DOI:10.1063/1.474851

Electron–phonon interactions in CsCdBr 3 :Yb 3+
Markus P. Hehlen, Amos Kuditcher, Stephen C. Rand, and Michael A. Tischler
Citation: The Journal of Chemical Physics 107, 4886 (1997); doi: 10.1063/1.474851
View online: http://dx.doi.org/10.1063/1.474851
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Electron–phonon interactions in CsCdBr :Yb3؉
3
Markus P. Hehlen, Amos Kuditcher, and Stephen C. Rand
Optical Sciences, The University of Michigan, Ann Arbor, Michigan 48109-2122
Michael A. Tischler
The Harrison M. Randall Laboratory of Physics, The University of Michigan, Ann Arbor,
Michigan 48109-1120
͑
Received 11 June 1997; accepted 24 June 1997͒
Pronounced electron–phonon coupling is observed for the F7 ↔ F 4f transitions of Yb3ϩ
2
2
/2
5/2
doped into CsCdBr . A comparison of the Raman spectrum and the luminescence excitation
3
2
2
sideband accompanying the F7/2(0)→ F5/2(2Ј) crystal-field transition reveals vibrational
properties of the ͓YbBr ͔ coordination unit that differ markedly from those of the CsCdBr host. In
6
3
particular, the vibronic transition associated with the totally symmetric ͓YbBr ͔ stretching mode
6
Ϫ1
appears as a very weak feature at 191 cm in the Raman spectrum, whereas the totally symmetric
CdBr ͔ stretching mode of the CsCdBr bulk, which appears as a strong feature at 162.5 cm in
Ϫ1
͓
6
3
the Raman spectrum, is only weakly discernible in the sideband. This is direct evidence for a large
contribution from ͓YbBr ͔ local modes and a small contribution from bulk modes to the vibronic
6
intensity. The intensity of the local mode is enhanced by approximately a factor of 2 in the Raman
2
2
3ϩ
spectrum when the laser is tuned into resonance with the F (0)→ F5/2(2Ј) absorption of Yb
,
7/2
providing direct confirmation of its assignment. The observation of the first and second members of
a Franck–Condon progression for both the local and the bulk totally symmetric modes indicates that
a ⌬ process, rather than an M process, induces the vibronic intensity. Huang–Rhys factors of
Slocalϭ0.010Ϯ0.002 and Sbulkϭ0.15Ϯ0.03 were determined from the data, and reflect quite
different electron–phonon coupling strengths. These results suggest that multiphonon relaxation of
excited electronic states proceeds by the excitation of local modes of ͓YbBr ͔ followed by energy
6
transfer to bulk modes of the lattice, possibly through a nonlinear coupling mechanism which is
discussed briefly. © 1997 American Institute of Physics. ͓S0021-9606͑97͒00637-5͔
I. INTRODUCTION
as the spatial extension of the electron–phonon interaction is
therefore a prerequisite to a detailed understanding of the
energy flow in electronic dynamics involving the vibrational
system. Direct information on the spatial extension of
electron–phonon interactions in particular is difficult to ob-
tain, since in most luminescent materials such as
The optical spectra of noncentrosymmetric solids doped
with trivalent rare-earth (RE3 ) ions typically are dominated
by electric-dipole induced electronic transitions between the
states of the 4f shell. These electronic transitions can be
accompanied by vibronic sidebands which are a result of
interactions of the 4f electronic system with the various vi-
ϩ
3ϩ
RE -doped YAG, YLiF , LaCl , or Cs Lu Br , in which
4
3
3
2
9
3ϩ
the RE ion substitutes for a chemically similar ion, the
vibrational properties of the nearest surroundings of the
RE ion are almost identical to those of the host lattice. One
3ϩ
brational modes of the surroundings of the RE ion. With
the exception of Pm3 , vibronic sidebands have been ob-
ϩ
3ϩ
served for all the RE3 ions in a variety of solids.
ϩ
1–4
The
exception is the class of compounds containing well-defined
integrated intensity of the vibronic sideband relative to its
zero-phonon line is usually low, although vibronic transition
probabilities approaching or even exceeding zero-phonon
transition probabilities have been found for certain transi-
molecular species. The ternary chloride ͑NH ͒ GdCl for ex-
4
2
5
ϩ
ample contains NH molecular units in the second coordina-
4
tion sphere of Gd3 , and electron–phonon coupling beyond
ϩ
ϩ
4
tions in some compounds.5 Recently, Gd and Pr -doped
–8
3ϩ
3ϩ
the first ͓GdCl6͔ coordination sphere to NH vibrational
6
8
modes was observed in the P7/2→ S luminescence
crystals received particular attention for, besides having ad-
vantageous energy levels, they represent the extrema of the
sideband.10 In ͑NH ͒ YCl :Eu , electron–phonon coupling
3ϩ
4
3
6
ϩ
to those high frequency NH4 vibrational modes in the sec-
ond coordination sphere was suggested to account for the
unexplained minimum of the electron–phonon–coupling
strength in the middle of the lanthanide series.9
3ϩ
unusually low Eu luminescence quantum yield of this
Vibronic sidebands, although usually weak and often ig-
nored, are just one of the many manifestations of electron–
phonon coupling in rare-earth-ion doped solids. Multiphonon
relaxation of excited states and phonon-assistance in non-
resonant energy transfer are other ubiquitous phenomena of
key importance to excited-state dynamics and, ultimately, to
the role rare-earth ions play in their many applications.
Knowledge of the electron–phonon coupling strength as well
material.10 Rare-earth-ion doped compounds such as CaF ,
2
3
ϩ
CdF , CsMgCl , or CsCdBr , in which RE ions substitute
2
3
3
for divalent metal ions, constitute another class of materials
for which electron–phonon coupling beyond the first coordi-
nation sphere may be directly observed. Various defect struc-
tures are formed in these materials as a result of charge com-
pensation. These defects typically have different symmetry
4886
J. Chem. Phys. 107 (13), 1 October 1997
0021-9606/97/107(13)/4886/7/$10.00
© 1997 American Institute of Physics
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Hehlen et al.: Electron–phonon interacting in CsCdBr :Yb3
ϩ
4887
3
properties which, in addition to the different mass and charge
single monochromator and detected by a cooled InGaAs di-
ode using a lock-in amplifier. The unpolarized Raman spec-
tra were obtained using the polarization-scrambled 488.0 or
514.5 nm line of an argon-ion laser. The Raman spectrum
was independent on the choice of either one of these wave-
lengths. The scattered light was collected in a backscattering
arrangement, dispersed by a 1 m double monochromator, and
detected by a photomultiplier and a photon counter. Unpo-
larized resonant Raman spectra were recorded using an
argon-ion-laser pumped Ti:sapphire laser as excitation
source in a similar geometry and with the sample cooled to
12 K by a closed-cycle helium refrigerator. The scattered
light was dispersed by a triple monochromator and detected
by a liquid-nitrogen-cooled CCD detector.
3
ϩ
of the RE ion, may significantly alter the vibrational prop-
erties compared to the respective host lattice site. In this
context, the vibrational system may be regarded as being
composed of the local vibrational modes of the RE3 defect
embedded in the bulk modes of the host lattice.
ϩ
In this paper we present a detailed study of vibronic
3
ϩ
coupling in Yb -doped CsCdBr . The comparison of the
3
Raman spectrum with the luminescence excitation spectrum
2
2
of the sideband accompanying the F7/2(0)→ F5/2(2Ј)
crystal-field transition of Yb3 reveals strong coupling to the
vibrational modes of the first Yb3 coordination sphere and
weak contributions from coupling to modes of the second
coordination sphere and beyond. In particular, resonant Ra-
man spectra are used to assign a weak feature in the Raman
spectrum to the local mode associated with the highest-
energy vibration of the first Yb3 coordination sphere. The
appearance of two-phonon replica of both the local and the
bulk mode as well as of the respective combination mode in
the vibronic sideband is direct evidence for a Franck–
Condon-type process inducing the vibronic intensity. The re-
sults provide insight into the spatial extension of vibronic
interactions and to the various steps required for the nonra-
diative relaxation of electronic excited states of rare-earth
ions in solids.
ϩ
ϩ
Except for the absorption and the resonant Raman spec-
tra, all experiments were carried out at either 78.5 or 15.5 K
with the sample mounted in a cold-finger cryostat.
ϩ
III. RESULTS AND DISCUSSION
A. 4f energy levels of Yb3 in CsCdBr3
؉
The diamagnetic salt CsCdBr is a member of the in-
3
verse perovskite family with the hexagonal CsNiCl
3
structure.12 It crystallizes in the D6h space group and consists
of linear chains of face-sharing ͓CdBr6͔4 units with the
chains being arranged along the crystallographic c-axis and
4
Ϫ
ϩ
the Cs ions occupying high-symmetry sites between the
II. EXPERIMENT
chains. It was first shown by electron paramagnetic reso-
nance ͑EPR͒ measurements that trivalent rare-earth ions
(RE3 ) preferentially are incorporated as charge compen-
Optical quality crystals of Yb3ϩ-doped CsCdBr were
3
ϩ
grown using the Bridgman technique from 99.5% cationic
purity ͑c.p.͒ CsBr ͑dried in vacuum at 250 °C͒ and CdBr2
3
ϩ
3ϩ
13,14
sated RE -vacancy-RE
ion pairs
having
a
3ϩ
3ϩ
͑obtained from 99.998% c.p. CdO and HBr, and sublimed at
RE –RE
intra ion-pair distance of approximately 6.0
Å. Several other RE minority sites have since been iden-
tified. The point symmetry for a RE ion on a Cd site is
14
3ϩ
4
40 °C͒, and YbBr . The anhydrous YbBr was obtained in a
3
3
3ϩ
2ϩ
four-step process by formation of ͑NH ͒ YbBr from evapo-
4
3
6
rating a 47% HBr solution of Yb O ͑99.999% c.p.͒ and
C
͑Refs. 15–19͒ thus, for odd 4f-electron systems, the
2
3
3v
Sϩ1
2
NH Br ͑99.8% c.p.͒, then drying of ͑NH ͒ YbBr in a nitro-
L multiplets are split into (2Jϩ1)/2 Kramers doublets.
4
4 3
6
J
13
3ϩ
gen stream at 200 °C, decomposition of ͑NH ͒ YbBr to
In its ͓Xe͔4f electron configuration, Yb only has
4
3
6
11
2
2
NH Br and YbBr at 420 °C in vacuum, and final sublima-
two multiplets, i.e., an F ground state and an F excited
4
3
7/2 5/2
tion of YbBr at 1040 °C in a boron–nitride ampoule. The
state which, in C3v symmetry, are split into 4 and 3 crystal-
field levels labeled ͑0͒, ͑1͒, ͑2͒, ͑3͒ and (0Ј), (1Ј), (2Ј),
respectively. The three prominent lines observed at 10 122,
3
3
ϩ
CsCdBr :Yb sample was obtained from cutting a crystal
3
along planes containing the crystallographic c-axis and ap-
plying an optical polish to the surfaces. The total ytterbium
concentration of the sample used for this study was 1.47
Ϯ0.04 mol% as determined by inductively coupled plasma
Ϫ1
10 138, and 10 599 cm in the 19 K absorption spectrum
͑Fig. 1͒ can consequently be assigned to the (0)→(0Ј,1Ј,2Ј)
zero-phonon transitions of Yb3 , respectively. Each of the
transitions is accompanied by a multipeak sideband which
results from electron–phonon interactions discussed in Secs.
III B and III C. The (0)→(0Ј,1Ј,2Ј) energies are very simi-
lar to those measured in Cs Yb Br ͑10 119, 10 146,
ϩ
3ϩ
optical emission spectroscopy ͑ICP-OES͒. Since Yb is eas-
2
ϩ
2ϩ
2ϩ
ily reduced to Yb and moreover, Yb substitutes for Cd
3ϩ
when doped into CsCdBr , typically both Yb and Yb
3
will be present in a Yb-doped CsCdBr crystal grown by the
3
3
2
9
Ϫ1
20
3ϩ
method described above. The yellow color of the crystal is
10 590 cm , respectively ͒ in which Yb has a sixfold
2ϩ
indication for the presence of some Yb , and therefore the
bromide coordination geometry closely resembling the one
3ϩ
3ϩ
3ϩ
Yb concentration is likely to be smaller than the above
value.
of Yb in CsCdBr :Yb . From the luminescence spectrum
3
͑Fig. 2͒, the (0Ј)→(0,1,2,3) transitions are found at 10 122,
Ϫ1
Polarized absorption spectra were recorded on a double-
beam spectrophotometer with the sample cooled to 19 K by
a closed-cycle helium refrigerator. An argon-ion laser
pumped Ti:sapphire laser was used as excitation source for
the near-infrared luminescence and luminescence excitation
spectra. The sample luminescence was dispersed by a 1 m
10 007, 9 955, and 9 658 cm
,
along with the
(1Ј)→(0,1,2,3) transitions which are observed as a result of
thermal population of (1Ј) at 15.5 K. These energies indicate
Ϫ1
a ground-state splitting of 0, 115, 167, and 464 cm which
again is quite similar to that found in Cs Yb Br ͓0, 114,
3
2
9
Ϫ1
140, 441 cm ͑Ref. 20͒.͔ Both the ground and excited-state
J. Chem. Phys., Vol. 107, No. 13, 1 October 1997
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4888
3ϩ
Hehlen et al.: Electron–phonon interacting in CsCdBr :Yb
3
2
2
3ϩ
2
2
3ϩ
FIG. 1. Unpolarized F → F absorption spectrum of CsCdBr :Yb at
FIG. 2. Unpolarized F5/2→ F7/2 luminescence spectrum of CsCdBr3 :Yb
7
/2
5/2
3
1
9 K. The labels ͑0͒ and (0Ј,1Ј,2Ј) refer to the crystal-field levels of the
F7/2 ground state and F excited-state multiplet, respectively.
at 15.5 K. The labels ͑0,1,2,3͒ and (0Ј,1Ј) refer to the crystal-field levels of
the F7/2 ground state and F5/2 excited-state multiplet, respectively.
2
2
2
2
5/2
splittings reflect the dominance of the octahedral over the
trigonal component of the crystal field, since the ͑0͒-͑1,2͒-͑3͒
and the (0Ј,1Ј)-(2Ј) splittings are much larger than the ͑1͒-
veals quite a complex structure, with many more lines span-
ning a wider frequency range than in the Raman spectrum.
Such a pronounced qualitative difference between the Raman
spectrum and the vibronic sideband is typically not observed
2
2
͑
2͒ and (0Ј)-(1Ј) splittings. The F7/2 and F crystal-field
5/2
3
ϩ
energies determined here agree with those reported in an
for rare-earth-ion doped solids in which the RE ions sub-
stitute for chemically alike ions. We do not attempt to ana-
lyze all the features of the sideband shown in Fig. 3. Rather
we focus on the highest-energy transitions which are distinct
and well isolated. In the isostructural compounds CsCoCl3
and CsMgCl3, the A1g bulk mode was found to have the
highest frequency of all the Raman and IR-active optical
modes.27 Also, no modes with frequency higher than the A1g
bulk mode were found in an analysis of vibronic sidebands
2
1
earlier study except for ͑2͒ and (2Ј). A small, unexplained
shift of the (0)→(2Ј) transition to higher frequency with
increasing temperature was observed. Therefore, the slight
discrepancy in these energies between the two studies most
likely result from the different temperatures ͑10 K vs 15.5 K͒
at which the spectra were recorded.
3؉
B. Bulk and local modes in CsCdBr :Yb
3
2
ϩ 25
in CsCdBr :Co
.
We therefore assume that the A Ra-
3
1g
The Raman-active first-order normal modes ͑corre-
sponding to phonons near kϭ0 around the Brillouin zone
Ϫ1
man transition at 162.5 cm represents the highest-energy,
center͒ of the CsCdBr host can be derived from a nuclear
3
22,23
4
site group analysis of the unit cell.
In the D6h space
group of CsCdBr with two formula units in the primitive
3
unit cell, the Cs, Cd, and Br atoms occupy sites of DЈ ,
3
h
24
D3d , and CЈ symmetry, respectively. These three sites
2v
give rise to the modes A ϩB ϩE ϩE , A ϩB
2
u
1g
1u
2g
2u
2u
ϩE ϩE
,
and A ϩA ϩA ϩB ϩB ϩB ϩE
1
u
2u
1g 2g 2u 1g 1u 2u
1g
ϩ2E ϩ2E ϩE , respectively, with the modes A2g
1
u
2g
2u
ϩ2B ϩB ϩ2B ϩ2E being silent and A ϩE be-
1
g
1u
2u
2u
2u
1u
23
ing the acoustic modes. From the remaining active optical
modes 2A ϩ3E ϩA ϩE ϩ3E , which we refer to
2
u
1u
1g
1g
2g
as bulk modes, A ϩE ϩ3E are Raman active. All these
1
g
1g
2g
modes are observed in the unpolarized Raman spectrum
shown in Fig. 3. Both the energies and relative intensities of
the Raman transitions are in agreement with previously re-
ported Raman spectra of undoped CsCdBr3.2
5,26
Pronounced vibronic sidebands are observed in both the
absorption spectrum ͑Fig. 1͒ and the luminescence spectrum
3ϩ
FIG. 3. Unpolarized Raman spectrum of CsCdBr :Yb with the incident
3
laser wavelength at 514.5 nm ͑top trace͒ and unpolarized luminescence ex-
citation spectra obtained by monitoring the (0Ј)→(2) transition ͑Fig. 2͒ at
͑Fig. 2͒. In the discussion below, we focus on the (0)→(2Ј)
1
004.5 nm ͑bottom traces͒. For the Raman and excitation spectra the fre-
zero-phonon line and its vibronic sideband since it is well
separated in frequency from all the other transitions. The
luminescence excitation spectrum of the vibronic sideband
accompanying this (0)→(2Ј) zero-phonon line ͑Fig. 3͒ re-
quency is normalized to the incident laser and the (0)→(2Ј) zero-phonon
line ͑Fig. 1͒, respectively. The assignments of the Raman transitions are
taken from Refs. 25, 26. The inset shows an enlargement of the
Ϫ1
180–200 cm spectral range.
J. Chem. Phys., Vol. 107, No. 13, 1 October 1997
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Hehlen et al.: Electron–phonon interacting in CsCdBr :Yb3
ϩ
4889
3
bond strength, a ratio of EYbBr /ECdBrϭ1.132 is predicted
from Eq. ͑1͒. This value is within 4% of the experimental
ratio 191/162.5ϭ1.175, providing further support for the
mode assignments.
The fact that the A1g local-mode frequency is so similar
to the respective frequency in Cs Yb Br but significantly
3
2
9
different from the A1g bulk-mode frequency indicates a high
Ϫ
3
degree of flexibility in the ͓CdBr ͔ linear chains of
n
CsCdBr . Obviously, forces exerted by the host lattice do not
3
constrain the ͓YbBr ͔ normal-mode frequencies to be the
6
3ϩ
same as CsCdBr bulk-mode frequencies. The Yb defect
3
site is apparently able to accommodate local forces by bend-
ing of adjacent metal–halogen–metal bond angles. This flex-
Ϫ
3
ibility of the ͓CdBr ͔ linear chains is reflected not only in
n
the large angular distribution of the crystallographic c-axis
3
ϩ
of 11Ϯ2° measured in CsCdBr :Pr using hole-burning
3
Stark spectroscopy29 but also in the fact that metal ions over
a wide range of charge, size, and chemical characteristics can
FIG. 4. Relative unpolarized Raman intensity of the bulk mode at
Ϫ1
Ϫ1
1
62.5 cm (I ) and the local mode at 191 cm (I ) as a function of the
B L
3
ϩ
incident laser frequency in CsCdBr :Yb at 12 K. The enhancement of the
3
be doped in significant amounts into crystals of the CsCdBr3
ratio I /IB on the (0)→(2Ј) resonance is approximately a factor of 2. Part
L
family.24
of the unpolarized absorption spectrum ͑from Fig. 1͒ is shown for compari-
son.
In Fig. 3, a weak transition in the excitation sideband at
Ϫ1
1
64 cm coincides with the strong A1g bulk mode observed
Ϫ1
at 162.5 cm in the Raman spectrum. This weak transition
may be either of a vibronic or an electronic nature. Coopera-
tive electronic transitions on the Yb ion pairs in this ma-
terial are likely and, for example, two excited Yb ions
cooperatively relaxing from their F excited state in a ra-
first-order bulk mode in CsCdBr . The highest-energy, first-
3
order feature in the vibronic sideband on the other hand is
3ϩ
Ϫ1
observed at 191 cm , a frequency close to the value
3ϩ
Ϫ1
(
190 cm ) which was observed for the highest-energy
2
5/2
mode in both Cs Yb Br and Cs Er Br crystals with sixfold
2
2
2
2
3
2
9
3
2
9
diative ͓ F5 (iЈ), F (jЈ)͔→͓ F (m), F7/2(n)͔ transi-
/2
5/2
7/2
2
0,28
bromide coordination.
As shown in the inset of Fig. 3,
tion can give rise to intense green cooperative lumine-
Ϫ1
the 191 cm mode in the vibronic sideband is also discern-
ible as a very weak feature in the Raman spectrum. Since
there are no second-order Raman transitions which could
give rise to a transition at this frequency, we assign this weak
Raman transition to the A1g local mode associated with the
3ϩ 21
scence in CsCdBr :Yb
tronic transitions of the type ͓ F (i), F7/2(j)͔
.
In analogy, cooperative elec-
3
2
2
7/2
2
2
→
͓ F (mЈ), F7/2(n)͔ can occur in the near infrared spec-
5/2
20
tral region. From the energy levels calculated in Sec. II A,
2
2
2
2
the transition ͓ F7 (0), F (0)͔→͓ F (2Ј), F (2)͔ is
/2
7/2
5/2
7/2
͓
YbBr ͔ coordination unit. This assignment is directly con-
Ϫ1
Ϫ1
6
expected at 10 766 cm , i.e., at a frequency 167 cm
firmed by resonant Raman experiments. Figure 4 shows the
above the (0)→(2Ј) zero-phonon line. We do not have
enough experimental information to assess the contribution
of this electronic process to the transition intensity around
Ϫ1
Raman intensity of the 191 cm local mode (I ) relative to
L
Ϫ1
that of the 162.5 cm bulk mode (I ) as a function of ex-
B
citation frequency and compares I /I with the unpolarized
Ϫ1
L
B
164 cm . However, it is likely to be small, since the obser-
(
0)→(2Ј) absorption spectrum. The increase of I /I by
L
B
vation of a progression in a vibrational mode of approxi-
approximately a factor of 2 on the (0)→(2Ј) resonance is
Ϫ1
mately 164 cm ͑see Sec. III C͒ indicates significant vi-
Ϫ1
direct evidence that the 191 cm mode in the Raman spec-
Ϫ1
bronic character of the 164 cm transition. Moreover, a
trum is due to a local mode associated with Yb3
ϩ
.
Ϫ1
3ϩ
transition at 162 cm was also observed in CsCdBr :Pr
,
3
The relative frequencies of the A1g local and the A1g
bulk modes can be explained on the basis of a simple model.
These modes represent totally-symmetric stretching vibra-
tions of the M–Br bond (MϭCd,Yb), with frequencies pro-
30
which has a different ground-state splitting. Therefore, this
transition arises mainly from coupling of the (0)→(2Ј) elec-
tronic transition either to the A1g bulk mode in the second
coordination sphere or to an odd-parity local mode of the
portional in a first approximation to
force constant and ␮ is the reduced mass. Their relative fre-
ͱ
k/␮, where k is the
͓
YbBr ͔ coordination unit with a frequency similar to the
6
A1g bulk mode.
quencies should therefore be given by
3
In the vibronic sideband accompanying the H (0)
P (0) zero-phonon line in CsCdBr :Pr , the A1g local
0
4
3
3ϩ
→
3
EYbBr
ECdBr
kYbBr␮CdBr
Ϫ1
ϭ
ͱk
.
͑1͒
mode of the ͓PrBr ͔ coordination unit appears at 194 cm ,
6
CdBr␮YbBr
and another, fairly broad vibronic transition appears at
Ϫ1 30
Assuming the six M–Br bonds to be equivalent, each of the
Br ions shares 1/6 of the charge of the metal ion in the
MBr ͔ coordination unit, i.e., and of an elementary
162 cm
.
The slight increase of the A1 local mode fre-
g
Ϫ
Ϫ1
3ϩ
Ϫ1
quency from 191 cm in CsCdBr :Yb to 194 cm in
3
1
2
1
3
3ϩ
3ϩ
͓
CsCdBr :Pr is expected, due to the smaller mass of Pr
3
6
3ϩ
Ϫ1
charge for ͓YbBr ͔ and ͓CdBr ͔, respectively. Further as-
relative to Yb . However the fact that the 164 cm mode
frequency in CsCdBr :Yb does not increase by going to
6
6
3ϩ
suming the force constant to be a linear function of the ionic
3
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4890
3ϩ
Hehlen et al.: Electron–phonon interacting in CsCdBr :Yb
3
3
ϩ
CsCdBr :Pr is indication for this transition not being a
3
result of vibronic coupling to a local mode but arising from
vibronic coupling of the (0)→(2Ј) electronic transition be-
yond the first ͓YbBr ͔ coordination sphere to the A bulk
6
1g
mode.
These results clearly show that vibronic coupling occurs
almost exclusively to the local modes of the first coordina-
tion sphere with minor contributions from the second or
higher coordination spheres, i.e., a characteristic vibronic in-
teraction radius of Ϸ3 Å. In terms of electron–phonon in-
teractions enabling non-radiative relaxation processes such
as multiphonon relaxation or phonon-assisted energy trans-
fer, this conclusion implies that most of the energy released
by these processes is first transferred to the local modes of
the first coordination sphere. The subsequent distribution of
this vibrational energy among the various bulk modes re-
quires resonances of those bulk modes with the local modes,
a condition which may not be well satisfied for defect mate-
rials such as RE3 -doped CaF , CdF , CsMgCl , or
3
ϩ
FIG. 5. Unpolarized luminescence excitation spectra of CsCdBr :Yb . ␯B
3
and ␯L denote the bulk-mode and local-mode frequency respectively, and
the left and right insets show the one-phonon and two-phonon replica of
both these modes, respectively.
ϩ
2
2
3
CsCdBr . Time-resolved Raman studies, such as those car-
3
4
ϩ
31
ried out for Cr -doped forsterite, could provide further
insight into the details of the nonradiative relaxation dynam-
ics in these materials. They might also answer the question
as to whether or not the lack of any strong resonances be-
tween local and bulk modes contributes, together with the
phonon coupling strength.36 At zero Kelvin, the relative tran-
sition probability for the ith phonon replica, given by
2
37
P
͗ ͘
ϭPab͉ ␹b(i)͉␹a(0) ͉ , is
a0→bi
P
a0→bi SieϪS
overall low frequencies of phonons in CsCdBr , to suppres-
3
sion of nonradiative relaxation of RE3 excited states in this
ϩ
ϭ
.
͑3͒
Pab
i!
material.
Numerous studies in recent years have found that earlier as-
sumptions that the Huang–Rhys factor is zero, implying that
the M process dominates the RE3 -ion vibronic intensities,
were often not justified. The observation of vibronic transi-
ϩ
C. Electron–phonon interaction
3ϩ
Two mechanisms, usually referred to as M and ⌬
tions in the two-photon spectra of SrMoO :Pr ͑Ref. 38͒
4
3
2
3ϩ
process, can mediate the interaction of the electronic and
the vibrational system. The M process induces vibronic in-
tensity through admixture of even-parity wave functions
and of two-phonon replica in Na La͑MO ͒ :Pr
5
4 4
(MϭMo,W) ͑Ref. 39͒ provides direct evidence for the im-
portant role that the ⌬ process can play.
͑
e.g., from the 4fNϪ15d configuration͒ to the odd-parity 4fN
As shown in Fig. 5, the bulk and local modes ␯ and ␯
B
L
Ϫ1
wave functions by coupling to an odd-parity ͑IR-active͒
observed at 164 and 191 cm in the vibronic sideband of
the luminescence excitation spectrum appear as very weak
3
,33–35
vibration.
Such vibrationally-induced, forced electric-
Ϫ1
dipole transitions lead, for example, to vibronic transitions
with a frequency differing by exactly one vibrational quan-
tum from the zero-phonon line. The ⌬ or Franck–Condon
process on the other hand induces vibronic intensity through
slightly different equilibrium structures of electronic ground
and excited states.36 In contrast to the M process, the shift of
the excited-state relative to the ground-state potential surface
along one of the configurational coordinates, measured in
terms of the Huang–Rhys factor S, gives rise to phonon
replica in the respective mode. In the harmonic approxima-
tion, the probability of a Franck–Condon-type vibronic tran-
sition from an electronic state a and vibrational state n to an
electronic state b and vibrational state m is given by
two-phonon replicas at 323 and 383 cm , respectively. That
is, they appear at approximately twice their respective fun-
damental frequencies. This is direct evidence for a ⌬ process
inducing the vibronic intensity. This result is consistent with
selection rule considerations since both the modes ␯ and ␯L
B
were assigned to A1g modes, which as even-parity modes
cannot enable M processes. The two-phonon frequencies are
at Ϸ1.96 and Ϸ2.01 times the one-phonon frequencies for
the modes ␯B and ␯ , respectively, indicating the highly
L
harmonic nature of the excited-state potential surface. Note
that the combination mode ␯ ϩ␯ is also observed.
B
L
By using Eq. ͑3͒ it is possible, in principle, to calculate
the Huang–Rhys factors S from the ratios of transition prob-
abilities Pa0→b1 /Pab and Pa0→b2 /Pab derived from experi-
mental transition intensities I in the luminescence excitation
spectrum ͑Fig. 5͒. Under the experimental conditions used
for measuring the luminescence excitation spectra, however,
it is likely that the strongly absorbing zero-phonon line is
partially saturated, i.e., its intensity is not proportional to
P
ϭPab
͉
͗
␹ ͑m͒
b
͉
␹ ͑n͒
a
͘
͉
2,
͑2͒
an→bm
where Pab is the purely electronic transition probability,
which is identical for all the vibrational states m and n, and
2
͉
͗
␹b(m)
͉
␹a(n)
͘
͉
is the vibrational overlap integral or
Franck–Condon factor, which is a measure of the electron–
J. Chem. Phys., Vol. 107, No. 13, 1 October 1997
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Hehlen et al.: Electron–phonon interacting in CsCdBr :Yb3
ϩ
4891
3
Pab . Consequently, the above two ratios would be overesti-
mated, a complication in numerous past studies.4
spatial extent of electron–phonon interactions is estimated to
be approximately 3 Å. These results all have important con-
sequences for phonon-assisted energy transfer and mul-
tiphonon relaxation of RE3 excited states. The present re-
search has shown that vibrational energy release during
relaxation of the electronic excited state of Yb3 occurs
through excitation first of local modes, and subsequently via
energy transfer through resonances with bulk modes which
complete the nonradiative relaxation process. For materials
Instead, we assume that the weakly absorbing vibronic
ϩ
transitions are unaffected by saturation ͑i.e., IϰP͒, and we
1
2
only calculate the ratio I
/I
ϭ S using Eq. ͑3͒ and
a0→b2 a0→b1
ϩ
the spectra of Fig. 5. For the modes ␯B and ␯L we then
obtain Sbulkϭ0.15Ϯ0.03 and Slocalϭ0.010Ϯ0.002, respec-
tively. Note that SbulkϾSlocal . This result reflects the fact that
the relative intensity of the modes ␯B and ␯L in the one-
phonon and two-phonon replica ͑Fig. 5͒ is reversed. Al-
though both Huang–Rhys factors found here are within the
such as RE3 -doped CsCdBr , where local and bulk mode
ϩ
3
frequencies differ markedly, the significant detuning of many
such potential resonances undoubtedly suppresses some re-
laxation pathways.
3ϩ
typical range of values reported for other RE -doped
7
,39
solids,
they indicate quite different electron–phonon cou-
pling strengths of the two modes.
Whereas the configurational coordinate for the A1g local
mode is most likely the ͑average͒ Yb–Br bond length, the
configurational coordinate describing the coupling to the
bulk mode in the second coordination sphere or beyond is
not directly obvious. The relatively large value of Sbulk indi-
cates the occurrence of local structural changes upon excita-
tion of the respective vibronic transitions and, on the basis of
ACKNOWLEDGMENTS
M.P.H. gratefully acknowledges support through a Swiss
National Science Foundation fellowship. We thank Naomi
Furer, Karl Kr a¨ mer, and Hans U. G u¨ del, University of Bern,
Switzerland, for growing and preparing the crystal, and
Geoffrey F. Strouse, Los Alamos National Laboratory, for
assistance in the resonant Raman experiments.
both the one-dimensional nature of CsCdBr and the struc-
3
ture of the dominant Yb3 pair center in CsCdBr , we can
ϩ
3
1
speculate on the nature of this structural rearrangement.
From our results on the spatial extension of electron–phonon
interactions ͑Sec. III B͒ we conclude that vibronic coupling
is not only confined to within the linear chains in CsCdBr3
but more specifically does not extend beyond the vibrational
modes of the nearest-neighbor coordination units in the
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10
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ϩ
12
͑
1980͒.
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14
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ϩ
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͑
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16
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3ϩ
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4
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6
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