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Bound multiphonon complexes in NaNO2
Volume 157, number 6,7
PHYSICS LETTERS A
5 August 1991
Bound multiphonon complexes in NaNO2 R. Kato, M. Ashida Department of Physics, Faculty ofScience, Kyoto University, Kyoto 606, Japan
J. Köhler’ and D. Schmid Lehrstuh!flir Festkorperspektroskopie, IPKM, Heinrich-Heine-Universität, W-4000 Düsseldorf Germany Received 13 May 1991; accepted for publication 27 May 1991 Communicated by V.M. Agranovich
Indications ofthe two-phonon quasi-bound state and bound multiphonon complexes in NaNO2 are observed in high resolution spectra ofthe triplet and singlet luminescence and of the multiple-order Raman scattering caused by the v2 vibration of NO~.The anharmonicity constant and the width of the I v2 phonon branch are estimated to be A = 0.8 ±0.5 cm’ and 2 W= 1.7 ±0.5 cm respectively.
1. Introduction
signed to the electronic transition ‘A1—~‘B, in NO; and the near UV luminescence to the reverse 3B, in ‘A transition ‘B1 ‘A,. The weak luminescence the visible region is assigned to the transition 1. Both luminescence spectra consist of series of vibronic lines caused by the coupling of the electronic states with the v2 bending vibration of NO;. Raman scattering under excitation near the lowest singlet exciton level, which we denote as v,~exciton, gives multiple-order Raman lines due to the v2 vibration of NO; (see fig. 1, bottom). It should be noted that all these luminescence and Raman spectra are caused by different transitions to the same final states. By comparing the spectra we can get information about the final states of the transitions, that is, the phonon states associated with the internal vibration of NO;. These phonons are regarded as vibrational Frenkel excitons [21. In the following sections we describe experimental methods and the results which show the evidence for the two-phonon quasi-bound state and the bound multiphonon complexes. —+
We report in this Letter the experimental results which are ascribed to the two-phonon quasi-bound states and bound multiphonon complexes. Theories on the two-phonon and many-phonon bound states were developed by Agranovich and coworkers [1—5] and others [6,7] in recent years. Most of the experimental results were reported on internal vibrational modes of the compounds which contain small molecules such as NH.~,CO~,NO;, etc., and on those of solid gases such as CO2, N2O and so on [8—11]. Sodium nitrite is a well-known ferroelectric which contains NO; as a constituent ion. Below T~ (—~163.5°C)it has an orthorhombic structure which belongs to the space group C~ [121. In the low temperature phase all the NO; molecules are aligned along the b-axis. Low temperature optical spectra in UV and visible regions [13—20] and multiple-order Raman scattering [2 11 have been studied extensively by some of the present authors and coworkers and by others. Fig. 1 presents a survey of the optical spectra of NaNO2 at 2 K. The UV absorption is asPresent address: Huygens Laboratorium, Rijksuniversiteit Leiden, 2300 RA Leiden, The Netherlands. 0375-960l/91/$ 03.50 © 1991
—
—~
2. Experiment Polarized luminescence spectra were measured using a photon counting system and a Spex double
Elsevier Science Publishers B.V. (North-Holland)
435
Volume 157, number 6,7
5 August 1991
PHYSICS LETTERS A
3600
3800
4000
4200
4400
4800
4800 5000
~630f829—
5500
hI
p~.
Singlet Lumi.
312
H
0—2112
(A)
829~’ 112 Triplet Lumi.
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0—3112 s
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5312 8hz
1112 ‘I
I
28000
3112
2312
II 20000
I
26000
24000
7hz
22000
I
18000
18000
WAVENUMBER (cm’) Fig. 1. Survey of the optical spectra of NaNO 2 at 2 K. Top: spectra of the singlet absorption and luminescence, and that of the triplet luminescence. Bottom: spectrum of multiple-order Raman scattering caused by the u2 vibration of N07.
monochromator with a polarizer in front of the entrance slit. The spectral resolution of the system was less than 0.5 cm~.Highly purified NaNO2 crystals with polished ac faces were excited with the 365 nm line of a 500 W mercury lamp for the measurement of the luminescence spectra. Polarized Raman spectra were measured using the same monochromator dnd a boxcar integrator under excitation near the lowest singlet exciton level with light from a tunable N2/dye laser system. The spectral width of the light I from the laser was about 1.4 cm All the measurements were carried out at about 2 K. —
.
3. Results and discussion Profiles of the triplet luminescence lines at 2 K are shown in fig. 2. They are caused by transitions from the lowest triplet exciton level to the v2 phonon 1evels in the ground electronic state. The 0—0 line is very sharp reflecting the transition at the F point in the Brillouin zone. It has a Lorentzian shape and its width is 0.5 cm~,corresponding to the limit of the spectral resolution in the present experiment. The 0— I v2 line has an asymmetric shape and its width is 1.2 cm~.The 0—2i’2 and 0—3v2 lines show almost symmetric shapes with widths of 0.6 and 0.7 cm ‘, 436
Triplet Lumineacence 0—3t’z
16470 -
El/c
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16480 17295
at 2K
0H~z
17305 18125
18135
18960
WAVENUMBER (cm~}
.
HH-
0-0
18970
-
Fig. 2. Profiles of vibronic lines of the triplet luminescence at 2 .
.
.
-
K observed under exc,tat,on wtth the 365 nm line of a mercury lamp.
respectively. They have weak shoulders or humps on the low energy tails. The initial state of the triplet luminescence, the lowest vibrational level ofthe triplet exciton state, consists of three spin sublevels t~, ç and t~,the latter two of which are the initial states for the Eflc and EI~boptical transitions, respectively. Since the width of each sublevel is less than 0.1 cm~ [17], the profile of each line in fig. 2 reflects the spatial dispersion of the respective phonon branch and the population of the triplet exciton in the k-space. Fig. 3 shows the schematic energy level diagram and the transitions for the vibronic lines of the triplet luminescence.
Volume 157, number 6,7
PHYSICS LETTERS A
Triplet Exclthn
5 August 1991
the scattering geometry. For polished samples, or in the forward scattering geometry, the 1 v2 Raman line
-
sometimes shows an asymmetric and relatively broad shape. On the other hand, the profiles of the higher order lines differ only slightly for different samples
-—---~
-
r
and scattering geometries. Since the ordinary Raman scattering due to a phonon occurs near the F point in the k-space, the above behavior of the 1 v2 Raman line suggests that some defects or surface roughness of the polished samples give rise to the
~_—J
~~
~j~-
scatteringin which k-conservation is violated, the 1 v2 Raman linethe may reflect the width of the and 1 v2 phonon branch. Similar effects may occur for the
2
WAVEVECTOR 1k)
Fig. 3. Energy level diagram showing the transitions for the triplet luminescence,
Fig. 4 shows the profiles of the multiple-order Raman lines caused by the v2 vibration of NO; observed on a cleaved sample under near resonant excitation at v1= v~—19 cm—’, where v~is the frequency of the incident light and v00 is that of the lowest singlet exciton at the F point. The widths of all lines are in the range 1.6—1.8 cm—’, and are slightly larger than that of the incident laser line. It should be noted that the 2 v2, 3 v2, and 4 v2 lines are nearly symmetric but have weak shoulders or humps on the low energy tails. The profile of the 1 v2 Raman line in fig. 4 is as narrow as the other lines. However, it differs from sample to sample and also depends on
Raman Scattering
2t820 21830 22640 22650
23465 23475
higher order lines. However, since for these lines the overtone phonon branches (n v2) are involved, and since the widths of these phonon branches are much smaller (as discussed later), the influence of the crystallographic quality of the sample and of the scattering geometry is negligible in these cases. Fig. 5 shows the profiles of the singlet luminescence lines measured under narrow band monochromatic excitation slightly above v00. In this case, we observe strong and narrow luminescence lines as well as weak Raman-like lines [21]. The v00 line is very weak and is masked by the stray light of the incident laser. By narrow band excitation slightly above v~ the singlet exciton is created near the F point in the Brillouin zone accompanied by simultaneous creation of an acoustic phonon with a small wavevector. Since the spatial dispersion of the singlet exciton is small (—~5 cm~) [22] and thermalization of the
EJ..b
2K
i/~-l/c~-19car’
25120 25130
25950 25960
at
24290 243w
1)
P~AVENUMBER (cm
Fig. 4. Profiles ofthe multiple-order Raman lines observed on a cleaved sample in the backward-scattering geometry under near resonant excitation at v 1= vm— 19cm_i.
437
Volume 157, number 6,7
5 August 1991
PHYSICS LETTERS A
Singlet Luminescence
21840 21850
22860 22670
23485 23495
El/a at 2K
24310 24320 25135 25145
JJ;=i/~+17cm’
25990 26000
P4AVENUMBER (cm”) Fig. 5. Profiles ofthe singlet luminescence lines observed under narrow band excitation at v,= vca+ 17 cm
exciton is much slower than its decay time at 2 K [23,24], the excitons near the F point give rise to the narrow singlet luminescence lines. When the cxcitons are populated widely over the exciton band, for example by excitation far above v00 with light such
Table 1 Frequencies of 02 phonons (in cm’).
as the Hg 365 nm line, we usually observe wide and asymmetric lines of the singlet luminescence [18] caused by the dispersion of the singlet exciton in the k-space and its dominant population near the zone boundaries [22]. As seen in fig. 5 weak humps or shoulders are noticeable on the low energy tails of the 0—2 v2 to 0—5 v2 lines of the singlet luminescence. Thewidthofthe0—l p2lineis ~—1.6cm’,whilethat of the 0—2 v 2 line is 1.4 cm’ and those of the other lines are about 1.2 cm ‘, Accurate values of the peak positions of the triplet luminescence and Raman lines were obtained within an accuracy of ±0.5 cm’ by simultaneous registration ofknown reference lines. From those figures we derived the fundamental and overtone frequencies of the p2 phonon. They are shown in table I. The left column presents the frequencies of the TO-mode obtamed in the c(a,a)~scattering configuration. Those of the LO-mode obtained in the b(a,a)13 configuration are compiled in the middle column. The right column gives the frequencies obtained from the triplet luminescence, The anharmonicity constant A of the p2 vibrational levels, that is, the binding energy of the p2 biphonon (BP) state is estimated from the relation E22E0—2A, where E0 is the fundamental energy of the v2 phonon and E2 is the energy of the first overtone. The obtained value ofA is 0.8 ±0.5 cm —‘. The
c(a,a)C b(a,a)b TO-mode LO-mode 102 829.3±0.5 830.5±0.5 828.8±0.5 202 1657 1657 1657.6 302 2483 2483 2483 4”2 3307 3307 50 4130 4130
438
Raman scattering configurations
‘.
. Triplet luminescence LO-mode (near zone boundary)
2±0,5cm’,0,8±0,5cm’,2~l,7±0,5cm’
2
&T,
higher order anharmonicity constant A is negligible. The LT splitting of the 1 i’2 phonon, ALT, is estimated to be 1.2 ±0.5 cm~from the frequencies of the 1 x’~ Raman lines measured in the b(a,a)b and c(a,a)~ scatteringconfigurations. The obtained value is consistent with that reported by Castelluci and Schettino [25] within the experimental error. In order to estimate the width of the I v2 phonon branch, we discuss here the difference between the frequencies of the 1 v2 phonon derived from the triplet luminescence and from the Raman scattering in the b(a,a)b configuration. The latter gives the 1 v2 frequency of the LO-mode near the F point of the Brillouin zone. On the other hand, we may take the former as the 1 p2 frequency ofthe LO-mode near the zone boundary. The reason is as follows: By the cxcitation with the Hg 365 nm line higher vibronic cxcitons of singlet nature are primarily created. They relax into the lowest singlet exciton state and are
Volume 157, number 6,7
PHYSICS LETTERS A
transformed into the triplet excitons through the vibronic spin—orbit interaction assisted by lattice phonons [20]. After further relaxation triplet cxcitons are populated widely over the lowest triplet cxciton level in the Brillouin zone. However, the population is not uniform but is dominant in the region of large k-values. This was confirmed by comparing the profiles of the phonon sidebands associated with the 0—0 lines of the triplet luminescence and absorption spectra, as in the case of the singlet exciton [22]. Since the exciton is of typical Frenkel type and is well localized on the NO; site in the crystal, the interaction of the exciton with a short wavelength acoustic phonon is stronger and will give rise to the dominant population near the zone boundary. The optical transition from the lowest triplet exciton level to the 1 i.’2 phonon branch occurs vertically following the k-conservation rule. Then the profile of the 0—1 v2 line of the triplet luminescence reflects the population of the exciton in the k-space and the coupling strength of the exciton and the phonon. The coupling strength is much larger for the LO-phonon than for the TO-phonon. Then the peak of the 0—1 p2 line is likely to correspond to the transition in the region near the zone boundary, and we may take the difference between the 1 v2 frequencies obtained from the b(a,a)b Raman scattering and from the triplet luminescence to be the full width (2W) of the 1 p2 phonon branch, more rigorously the width of the 1 ~.‘2 ( LO) branch, assuming a monotonic change of the phonon frequency with k. The obtained value of 2W is 1.7 ±0.5 cm* This value is consistent with the result reported by Chisler et al. [26] and is nearly of the same magnitude as ALT. We listed the values of A, 2W and ALT in the lowest row of table 1. The small values ofALT and W reflect the small oscillator strength ofthe bending vibration of NO;. The widths ofthe overtone branches estimated in a similar way are 0.6 cm’ for the 2 v2 branch and less for higher ones. The accuracy of the obtained values ofA, 2 Wand ALT is rather poor, since we made the measurements under relatively weak excitation conditions to avoid damage due to the UV irradiation. If we excite the samples with strong light, they are damaged and their spectra are broadened and changed significantly. It should be noted that the width of the 0—2 p2 line of the triplet luminescence is smaller than that of the ‘~
0—1
5 August 1991
p
2 line. In addition, the value of A is nearly the same as that of W. Then we cannot expect the appearance of the biphonon (BP) state which splits off from the two-phonon dissociated state. Following the model calculation of Belousov [21, we therefore ascribe the narrow 0—2 p2 line to the two-phonon quasibound state which is located near the bottom of the two-phonon dissociated band. The weak shoulder on the low energy tail of the line seems to correspond to the two-phonon dissociated state. Similarly, the 2 i.’2 Raman line and the 0—2 v2 line of the singlet luminescence, both with weak shoulders on their tails, are also ascribed to the two-phonon quasi-bound state. The binding energy e of the three-phonon bound state (triphonon: TP) is estimated using the relation 8= I3Eo—E~I.The obtained value of e is 4.9±0.5 cm’ and is nearly of the same magnitude as 6A. The higher order anharmonicity constant A is nearly zero, (6Ara 0.1 cm’). The formation of the three-phonon bound states (the ground state of TP and its excited states: BET) depends on the values of A, A and W as well as on the dimensionality of the crystal as discussed by Agranovich et al. [3,4]. The obtained valuesofA,Aand Ware not sufficiently accurate to discuss the details of the three-phonon bound states. However, we may ascribe the narrow 0—3v2 lines of the triplet and singlet luminescence and the 3 i.’2 Raman line to the TP or BET, taking account of the facts that these lines are narrower than the 0—1 p2 lines and appear at an energy near 3E0—6A, and also taking account of the highly anisotropic nature of the NaNO2 crystal. The weak shoulders on the tails of the lines may be ascribed to the biphonon plus free one-phonon state (BP + P) or the free three-phonon (P + P + P) state. Concerning the bound four-phonon or five-phonon complexes, the present experiment does not provide enough quantitative data to discuss the details of the complexes. However, we just make the following comment; the relatively narrow 0—4v2 and 0—5 v2 lines of the singlet luminescence and the 4 i.’2 Raman line, all of which have weak shoulders or humps on their tails, may be ascribed to the bound multiphonon complexes, that is, nP and (n— 1 )P+P or (n—2)P+2P or (n—2)P+P+P, and so on.
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Volume l57,number6,7
PHYSICSLETTERSA
References [1] V.M. Agranovich and 1.1. Lalov, Soy. Phys. Usp. 28 (1985) 484, and references therein. [21 M.V. Belousov, in: Excitons, selected chapters, eds. El. Rashba and M.D. Sturge (North-Holland, Amsterdam, 1986) ch. 9, p 395 [3] V.M. Agranovich, O.A. Dubovsky and A.V. Orlov, Phys. Lett.A 119 (1986) 83. [4] V.M. Agranovich, O.A. Dubovsky and A.V. Orlov, Solid State Commun. 70 (1989) 675. [5] V.M. Agranovich, O.A. Dubovsky and A.V. Orlov, Solid State Commun. 72 (1989) 491. [6]J.C. Kimball, C.Y. Fong and Y.R. Shen, Phys. Rev. B 23 (1981)4946. [7]F.Bogani,J.Phys.C 11(1987)1283,1297. [8] D.A. Dows and V. Schettino, J. Chem. Phys. 58 (1973) 5009. [9] V. Schettino and P.R. Salvi, Spectrochim. Acta 31(1975) 399 [10] VS. Gorelki, G.G. Mitin and MM. Sushchinskii, Soy. Phys. Solid State 16 (1974) 1019. [II] M.V. Belousov, D.E. Pogarev and A. Shultin, Soy. Phys. Solid State IS (1974) 1701. [12] S. Sawada, S. Nomura, S. Fujii and I. Yoshida, Phys. Rev. Lett. 1(1958)320.
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[131 W. Dietrich, F. Drissler, D. Schmid and H.C. Wolf, Z. Naturforsch.28a (1973) 248. [141 M. Kamada, M. Yoshikawa and R. Kato, J. Phys. Soc. Japan 39 (1975)1004. [15) M. Kamada, T. Yoshimura and R. Kato, J. Phys. Soc. Japan 42 (1977) 1660. [16] M. Kamada and R. Kato, J. Phys. Soc. Japan 45 (1978) 169. [171W. DietrichandD.Schmid,Phys.State.Sol. (b) 74(1976) 609. [181 F. Lisse, J. Köhler, H. Pufahl and D. Schmid, Phys. Stat. Sol. (b) 140 (1987) 605. [19] T. Kobayashi and R. Kato, J. Phys. Soc. Japan 54 (1985) 424. [20] R.M. Hochstrasser and A.P. Marchetti, J. Chem. Phys. 50 (1965) 1727. [211 T. Sakaiand R. Kato, Solid State Commun. 59 (1986) 721. [22] M. Ashida, Y. Kawaguchi and R. Kato, J. Phys. Soc. Japan 58 (1989) 4620. [23] T. Sakai, H. Kawaura and R. Kato, J. Phys. Soc. Japan 56 (1987) 1943. [24] J. Kdhler, M. Ashida, R. Kato, Th. Schmidt and D. Schmid, J. Lumin. 44 (1991) 239. [25] E. Castelluci andV. Schettino, Phys. Stat. Sol. (b) 91(1979) 641. [26]1.N. Goncharuku, V.Yu. Davydov, E.A. Ivanov and E. Chisler, Soy. Phys. Solid State 20 (1978) 1676.
PHYSICS LETTERS A
5 August 1991
Bound multiphonon complexes in NaNO2 R. Kato, M. Ashida Department of Physics, Faculty ofScience, Kyoto University, Kyoto 606, Japan
J. Köhler’ and D. Schmid Lehrstuh!flir Festkorperspektroskopie, IPKM, Heinrich-Heine-Universität, W-4000 Düsseldorf Germany Received 13 May 1991; accepted for publication 27 May 1991 Communicated by V.M. Agranovich
Indications ofthe two-phonon quasi-bound state and bound multiphonon complexes in NaNO2 are observed in high resolution spectra ofthe triplet and singlet luminescence and of the multiple-order Raman scattering caused by the v2 vibration of NO~.The anharmonicity constant and the width of the I v2 phonon branch are estimated to be A = 0.8 ±0.5 cm’ and 2 W= 1.7 ±0.5 cm respectively.
1. Introduction
signed to the electronic transition ‘A1—~‘B, in NO; and the near UV luminescence to the reverse 3B, in ‘A transition ‘B1 ‘A,. The weak luminescence the visible region is assigned to the transition 1. Both luminescence spectra consist of series of vibronic lines caused by the coupling of the electronic states with the v2 bending vibration of NO;. Raman scattering under excitation near the lowest singlet exciton level, which we denote as v,~exciton, gives multiple-order Raman lines due to the v2 vibration of NO; (see fig. 1, bottom). It should be noted that all these luminescence and Raman spectra are caused by different transitions to the same final states. By comparing the spectra we can get information about the final states of the transitions, that is, the phonon states associated with the internal vibration of NO;. These phonons are regarded as vibrational Frenkel excitons [21. In the following sections we describe experimental methods and the results which show the evidence for the two-phonon quasi-bound state and the bound multiphonon complexes. —+
We report in this Letter the experimental results which are ascribed to the two-phonon quasi-bound states and bound multiphonon complexes. Theories on the two-phonon and many-phonon bound states were developed by Agranovich and coworkers [1—5] and others [6,7] in recent years. Most of the experimental results were reported on internal vibrational modes of the compounds which contain small molecules such as NH.~,CO~,NO;, etc., and on those of solid gases such as CO2, N2O and so on [8—11]. Sodium nitrite is a well-known ferroelectric which contains NO; as a constituent ion. Below T~ (—~163.5°C)it has an orthorhombic structure which belongs to the space group C~ [121. In the low temperature phase all the NO; molecules are aligned along the b-axis. Low temperature optical spectra in UV and visible regions [13—20] and multiple-order Raman scattering [2 11 have been studied extensively by some of the present authors and coworkers and by others. Fig. 1 presents a survey of the optical spectra of NaNO2 at 2 K. The UV absorption is asPresent address: Huygens Laboratorium, Rijksuniversiteit Leiden, 2300 RA Leiden, The Netherlands. 0375-960l/91/$ 03.50 © 1991
—
—~
2. Experiment Polarized luminescence spectra were measured using a photon counting system and a Spex double
Elsevier Science Publishers B.V. (North-Holland)
435
Volume 157, number 6,7
5 August 1991
PHYSICS LETTERS A
3600
3800
4000
4200
4400
4800
4800 5000
~630f829—
5500
hI
p~.
Singlet Lumi.
312
H
0—2112
(A)
829~’ 112 Triplet Lumi.
El/a
0—3112 s
6000
E//c 0—4112
0—5112
2
x10
T2°~
O~i112T2o~
Raman ‘~829 b(a,a)b 112 ~Z I
41)2
5312 8hz
1112 ‘I
I
28000
3112
2312
II 20000
I
26000
24000
7hz
22000
I
18000
18000
WAVENUMBER (cm’) Fig. 1. Survey of the optical spectra of NaNO 2 at 2 K. Top: spectra of the singlet absorption and luminescence, and that of the triplet luminescence. Bottom: spectrum of multiple-order Raman scattering caused by the u2 vibration of N07.
monochromator with a polarizer in front of the entrance slit. The spectral resolution of the system was less than 0.5 cm~.Highly purified NaNO2 crystals with polished ac faces were excited with the 365 nm line of a 500 W mercury lamp for the measurement of the luminescence spectra. Polarized Raman spectra were measured using the same monochromator dnd a boxcar integrator under excitation near the lowest singlet exciton level with light from a tunable N2/dye laser system. The spectral width of the light I from the laser was about 1.4 cm All the measurements were carried out at about 2 K. —
.
3. Results and discussion Profiles of the triplet luminescence lines at 2 K are shown in fig. 2. They are caused by transitions from the lowest triplet exciton level to the v2 phonon 1evels in the ground electronic state. The 0—0 line is very sharp reflecting the transition at the F point in the Brillouin zone. It has a Lorentzian shape and its width is 0.5 cm~,corresponding to the limit of the spectral resolution in the present experiment. The 0— I v2 line has an asymmetric shape and its width is 1.2 cm~.The 0—2i’2 and 0—3v2 lines show almost symmetric shapes with widths of 0.6 and 0.7 cm ‘, 436
Triplet Lumineacence 0—3t’z
16470 -
El/c
G—2IJz~
16480 17295
at 2K
0H~z
17305 18125
18135
18960
WAVENUMBER (cm~}
.
HH-
0-0
18970
-
Fig. 2. Profiles of vibronic lines of the triplet luminescence at 2 .
.
.
-
K observed under exc,tat,on wtth the 365 nm line of a mercury lamp.
respectively. They have weak shoulders or humps on the low energy tails. The initial state of the triplet luminescence, the lowest vibrational level ofthe triplet exciton state, consists of three spin sublevels t~, ç and t~,the latter two of which are the initial states for the Eflc and EI~boptical transitions, respectively. Since the width of each sublevel is less than 0.1 cm~ [17], the profile of each line in fig. 2 reflects the spatial dispersion of the respective phonon branch and the population of the triplet exciton in the k-space. Fig. 3 shows the schematic energy level diagram and the transitions for the vibronic lines of the triplet luminescence.
Volume 157, number 6,7
PHYSICS LETTERS A
Triplet Exclthn
5 August 1991
the scattering geometry. For polished samples, or in the forward scattering geometry, the 1 v2 Raman line
-
sometimes shows an asymmetric and relatively broad shape. On the other hand, the profiles of the higher order lines differ only slightly for different samples
-—---~
-
r
and scattering geometries. Since the ordinary Raman scattering due to a phonon occurs near the F point in the k-space, the above behavior of the 1 v2 Raman line suggests that some defects or surface roughness of the polished samples give rise to the
~_—J
~~
~j~-
scatteringin which k-conservation is violated, the 1 v2 Raman linethe may reflect the width of the and 1 v2 phonon branch. Similar effects may occur for the
2
WAVEVECTOR 1k)
Fig. 3. Energy level diagram showing the transitions for the triplet luminescence,
Fig. 4 shows the profiles of the multiple-order Raman lines caused by the v2 vibration of NO; observed on a cleaved sample under near resonant excitation at v1= v~—19 cm—’, where v~is the frequency of the incident light and v00 is that of the lowest singlet exciton at the F point. The widths of all lines are in the range 1.6—1.8 cm—’, and are slightly larger than that of the incident laser line. It should be noted that the 2 v2, 3 v2, and 4 v2 lines are nearly symmetric but have weak shoulders or humps on the low energy tails. The profile of the 1 v2 Raman line in fig. 4 is as narrow as the other lines. However, it differs from sample to sample and also depends on
Raman Scattering
2t820 21830 22640 22650
23465 23475
higher order lines. However, since for these lines the overtone phonon branches (n v2) are involved, and since the widths of these phonon branches are much smaller (as discussed later), the influence of the crystallographic quality of the sample and of the scattering geometry is negligible in these cases. Fig. 5 shows the profiles of the singlet luminescence lines measured under narrow band monochromatic excitation slightly above v00. In this case, we observe strong and narrow luminescence lines as well as weak Raman-like lines [21]. The v00 line is very weak and is masked by the stray light of the incident laser. By narrow band excitation slightly above v~ the singlet exciton is created near the F point in the Brillouin zone accompanied by simultaneous creation of an acoustic phonon with a small wavevector. Since the spatial dispersion of the singlet exciton is small (—~5 cm~) [22] and thermalization of the
EJ..b
2K
i/~-l/c~-19car’
25120 25130
25950 25960
at
24290 243w
1)
P~AVENUMBER (cm
Fig. 4. Profiles ofthe multiple-order Raman lines observed on a cleaved sample in the backward-scattering geometry under near resonant excitation at v 1= vm— 19cm_i.
437
Volume 157, number 6,7
5 August 1991
PHYSICS LETTERS A
Singlet Luminescence
21840 21850
22860 22670
23485 23495
El/a at 2K
24310 24320 25135 25145
JJ;=i/~+17cm’
25990 26000
P4AVENUMBER (cm”) Fig. 5. Profiles ofthe singlet luminescence lines observed under narrow band excitation at v,= vca+ 17 cm
exciton is much slower than its decay time at 2 K [23,24], the excitons near the F point give rise to the narrow singlet luminescence lines. When the cxcitons are populated widely over the exciton band, for example by excitation far above v00 with light such
Table 1 Frequencies of 02 phonons (in cm’).
as the Hg 365 nm line, we usually observe wide and asymmetric lines of the singlet luminescence [18] caused by the dispersion of the singlet exciton in the k-space and its dominant population near the zone boundaries [22]. As seen in fig. 5 weak humps or shoulders are noticeable on the low energy tails of the 0—2 v2 to 0—5 v2 lines of the singlet luminescence. Thewidthofthe0—l p2lineis ~—1.6cm’,whilethat of the 0—2 v 2 line is 1.4 cm’ and those of the other lines are about 1.2 cm ‘, Accurate values of the peak positions of the triplet luminescence and Raman lines were obtained within an accuracy of ±0.5 cm’ by simultaneous registration ofknown reference lines. From those figures we derived the fundamental and overtone frequencies of the p2 phonon. They are shown in table I. The left column presents the frequencies of the TO-mode obtamed in the c(a,a)~scattering configuration. Those of the LO-mode obtained in the b(a,a)13 configuration are compiled in the middle column. The right column gives the frequencies obtained from the triplet luminescence, The anharmonicity constant A of the p2 vibrational levels, that is, the binding energy of the p2 biphonon (BP) state is estimated from the relation E22E0—2A, where E0 is the fundamental energy of the v2 phonon and E2 is the energy of the first overtone. The obtained value ofA is 0.8 ±0.5 cm —‘. The
c(a,a)C b(a,a)b TO-mode LO-mode 102 829.3±0.5 830.5±0.5 828.8±0.5 202 1657 1657 1657.6 302 2483 2483 2483 4”2 3307 3307 50 4130 4130
438
Raman scattering configurations
‘.
. Triplet luminescence LO-mode (near zone boundary)
2±0,5cm’,0,8±0,5cm’,2~l,7±0,5cm’
2
&T,
higher order anharmonicity constant A is negligible. The LT splitting of the 1 i’2 phonon, ALT, is estimated to be 1.2 ±0.5 cm~from the frequencies of the 1 x’~ Raman lines measured in the b(a,a)b and c(a,a)~ scatteringconfigurations. The obtained value is consistent with that reported by Castelluci and Schettino [25] within the experimental error. In order to estimate the width of the I v2 phonon branch, we discuss here the difference between the frequencies of the 1 v2 phonon derived from the triplet luminescence and from the Raman scattering in the b(a,a)b configuration. The latter gives the 1 v2 frequency of the LO-mode near the F point of the Brillouin zone. On the other hand, we may take the former as the 1 p2 frequency ofthe LO-mode near the zone boundary. The reason is as follows: By the cxcitation with the Hg 365 nm line higher vibronic cxcitons of singlet nature are primarily created. They relax into the lowest singlet exciton state and are
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PHYSICS LETTERS A
transformed into the triplet excitons through the vibronic spin—orbit interaction assisted by lattice phonons [20]. After further relaxation triplet cxcitons are populated widely over the lowest triplet cxciton level in the Brillouin zone. However, the population is not uniform but is dominant in the region of large k-values. This was confirmed by comparing the profiles of the phonon sidebands associated with the 0—0 lines of the triplet luminescence and absorption spectra, as in the case of the singlet exciton [22]. Since the exciton is of typical Frenkel type and is well localized on the NO; site in the crystal, the interaction of the exciton with a short wavelength acoustic phonon is stronger and will give rise to the dominant population near the zone boundary. The optical transition from the lowest triplet exciton level to the 1 i.’2 phonon branch occurs vertically following the k-conservation rule. Then the profile of the 0—1 v2 line of the triplet luminescence reflects the population of the exciton in the k-space and the coupling strength of the exciton and the phonon. The coupling strength is much larger for the LO-phonon than for the TO-phonon. Then the peak of the 0—1 p2 line is likely to correspond to the transition in the region near the zone boundary, and we may take the difference between the 1 v2 frequencies obtained from the b(a,a)b Raman scattering and from the triplet luminescence to be the full width (2W) of the 1 p2 phonon branch, more rigorously the width of the 1 ~.‘2 ( LO) branch, assuming a monotonic change of the phonon frequency with k. The obtained value of 2W is 1.7 ±0.5 cm* This value is consistent with the result reported by Chisler et al. [26] and is nearly of the same magnitude as ALT. We listed the values of A, 2W and ALT in the lowest row of table 1. The small values ofALT and W reflect the small oscillator strength ofthe bending vibration of NO;. The widths ofthe overtone branches estimated in a similar way are 0.6 cm’ for the 2 v2 branch and less for higher ones. The accuracy of the obtained values ofA, 2 Wand ALT is rather poor, since we made the measurements under relatively weak excitation conditions to avoid damage due to the UV irradiation. If we excite the samples with strong light, they are damaged and their spectra are broadened and changed significantly. It should be noted that the width of the 0—2 p2 line of the triplet luminescence is smaller than that of the ‘~
0—1
5 August 1991
p
2 line. In addition, the value of A is nearly the same as that of W. Then we cannot expect the appearance of the biphonon (BP) state which splits off from the two-phonon dissociated state. Following the model calculation of Belousov [21, we therefore ascribe the narrow 0—2 p2 line to the two-phonon quasibound state which is located near the bottom of the two-phonon dissociated band. The weak shoulder on the low energy tail of the line seems to correspond to the two-phonon dissociated state. Similarly, the 2 i.’2 Raman line and the 0—2 v2 line of the singlet luminescence, both with weak shoulders on their tails, are also ascribed to the two-phonon quasi-bound state. The binding energy e of the three-phonon bound state (triphonon: TP) is estimated using the relation 8= I3Eo—E~I.The obtained value of e is 4.9±0.5 cm’ and is nearly of the same magnitude as 6A. The higher order anharmonicity constant A is nearly zero, (6Ara 0.1 cm’). The formation of the three-phonon bound states (the ground state of TP and its excited states: BET) depends on the values of A, A and W as well as on the dimensionality of the crystal as discussed by Agranovich et al. [3,4]. The obtained valuesofA,Aand Ware not sufficiently accurate to discuss the details of the three-phonon bound states. However, we may ascribe the narrow 0—3v2 lines of the triplet and singlet luminescence and the 3 i.’2 Raman line to the TP or BET, taking account of the facts that these lines are narrower than the 0—1 p2 lines and appear at an energy near 3E0—6A, and also taking account of the highly anisotropic nature of the NaNO2 crystal. The weak shoulders on the tails of the lines may be ascribed to the biphonon plus free one-phonon state (BP + P) or the free three-phonon (P + P + P) state. Concerning the bound four-phonon or five-phonon complexes, the present experiment does not provide enough quantitative data to discuss the details of the complexes. However, we just make the following comment; the relatively narrow 0—4v2 and 0—5 v2 lines of the singlet luminescence and the 4 i.’2 Raman line, all of which have weak shoulders or humps on their tails, may be ascribed to the bound multiphonon complexes, that is, nP and (n— 1 )P+P or (n—2)P+2P or (n—2)P+P+P, and so on.
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References [1] V.M. Agranovich and 1.1. Lalov, Soy. Phys. Usp. 28 (1985) 484, and references therein. [21 M.V. Belousov, in: Excitons, selected chapters, eds. El. Rashba and M.D. Sturge (North-Holland, Amsterdam, 1986) ch. 9, p 395 [3] V.M. Agranovich, O.A. Dubovsky and A.V. Orlov, Phys. Lett.A 119 (1986) 83. [4] V.M. Agranovich, O.A. Dubovsky and A.V. Orlov, Solid State Commun. 70 (1989) 675. [5] V.M. Agranovich, O.A. Dubovsky and A.V. Orlov, Solid State Commun. 72 (1989) 491. [6]J.C. Kimball, C.Y. Fong and Y.R. Shen, Phys. Rev. B 23 (1981)4946. [7]F.Bogani,J.Phys.C 11(1987)1283,1297. [8] D.A. Dows and V. Schettino, J. Chem. Phys. 58 (1973) 5009. [9] V. Schettino and P.R. Salvi, Spectrochim. Acta 31(1975) 399 [10] VS. Gorelki, G.G. Mitin and MM. Sushchinskii, Soy. Phys. Solid State 16 (1974) 1019. [II] M.V. Belousov, D.E. Pogarev and A. Shultin, Soy. Phys. Solid State IS (1974) 1701. [12] S. Sawada, S. Nomura, S. Fujii and I. Yoshida, Phys. Rev. Lett. 1(1958)320.
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[131 W. Dietrich, F. Drissler, D. Schmid and H.C. Wolf, Z. Naturforsch.28a (1973) 248. [141 M. Kamada, M. Yoshikawa and R. Kato, J. Phys. Soc. Japan 39 (1975)1004. [15) M. Kamada, T. Yoshimura and R. Kato, J. Phys. Soc. Japan 42 (1977) 1660. [16] M. Kamada and R. Kato, J. Phys. Soc. Japan 45 (1978) 169. [171W. DietrichandD.Schmid,Phys.State.Sol. (b) 74(1976) 609. [181 F. Lisse, J. Köhler, H. Pufahl and D. Schmid, Phys. Stat. Sol. (b) 140 (1987) 605. [19] T. Kobayashi and R. Kato, J. Phys. Soc. Japan 54 (1985) 424. [20] R.M. Hochstrasser and A.P. Marchetti, J. Chem. Phys. 50 (1965) 1727. [211 T. Sakaiand R. Kato, Solid State Commun. 59 (1986) 721. [22] M. Ashida, Y. Kawaguchi and R. Kato, J. Phys. Soc. Japan 58 (1989) 4620. [23] T. Sakai, H. Kawaura and R. Kato, J. Phys. Soc. Japan 56 (1987) 1943. [24] J. Kdhler, M. Ashida, R. Kato, Th. Schmidt and D. Schmid, J. Lumin. 44 (1991) 239. [25] E. Castelluci andV. Schettino, Phys. Stat. Sol. (b) 91(1979) 641. [26]1.N. Goncharuku, V.Yu. Davydov, E.A. Ivanov and E. Chisler, Soy. Phys. Solid State 20 (1978) 1676.