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Relaxed excited states determined by Jahn-Teller effect in Ti+-type centers in alkali halides
Journal of Luminescence 12/13 (1976) 139—149 © North-Holland Publishing Company
RELAXED EXCITED STATES DETERMINED BY JAHN—TELLER EFFECT IN TIP-TYPE CENTERS IN ALKALI HALIDES Atsuo FUKUDA, Akira MATSUSHIMA Nagasaki University, Faculty ofLiberalArts, Nagasaki-shi, Japan 852
and Shoji MASUNAGA Kyushu Institute of Technology, Kitakyushu-shi, Japan 804
Effects of magnetic field and hydrostatic pressure on the AT and Ax emission bands have been investigated. Results show the importance of the quadratic Jahn—Teller effect, indicating that the AT RES is related to the tetragonal minima and the Ax RES to the trigonal minima on the r~(A)and rj- adiabatic potential energy surfaces (APES). Cross sections of the APES’s along tetragonal and trigonal distortions have been calculated to explain the luminescent properties systematically.
1. Introduction There are a group of ions which have two electrons (ns)2 outside a closed shell as shown in table 1. When one of these ions exists as an impurity in an alkali halide crystal and substitutionally replaces a host ion, it forms a luminescent center (the Tittype center)~three characteristic absorption bands called A, B, and C are observed in the otherwise transparent wavelength region, and luminescence appears by excitation in these absorption bands. The center is of °h symmetry and has simple electronic states (the ground state V~and non-relaxed excited states (NRES) Fj, F~(A),F~,F~,and F~(C)).Transitions between these states result in the A, B, and Table 1 Ions with (ns)2 outmost electron configuration. These ions form luminescent centers (TiF~type centers) in alkali halides.
4 5 6
lb
lIb
Ilib
IVb
(Cu) Ag Au
(Zn0) (Cd°) (Hg0)
Ga~
(Ge2~)
Tl~
Sn2~ Pb2~
139
140
.4. Fukuda et al. / Relaxed excited states in alkali halides
C absorption bands [1] . In order to assign emission bands excitable by these absorption bands, relaxation due to the electron-lattice interaction (ELI) should be taken into account. Configuration coordinate curve introduced by Seitz [2] has been used to give a qualitative description of the relaxation processes. The ordinate is the total energy of the system for the ground and excited states of the center, i.e. adiabatic potential energy, including both electronic and lattice terms. The abscissa is a “con1~guration coordinate” which specifies the configuration of the ions around the center. An exact way to specify the configuration is to use the normal mode coordinates around the center which interact with the electronic states under consideration. The normal modes are classified according to the irreducible representations of the point group °h• When we neglect the dependence of the spin-—orbit interaction upon lattice configuration and reasonably assume that the algtlu excited states are isolated, only dig’ g~and T2g modes have the linear ELI [3] Although the number of irreducible representations is as small as three, each representation contains a great number of normal mode coordinates. Assuming the linear ELI and treating lattice vibrations classically, Toyozawa and lnoue [3] lumped a great number of these normal mode coordinates with a particular symmetry in a single interaction mode coordinate with the same symmetry. Thus the dimension of the configuration coordinates is reduced to six: ~ig(Qi)’ ~g(Q2 and Q 3), and 12g(Q4, Q5, and Q6). If we restrict our attention to an octahedral quasi-molecule composed of an impuity ion and the six nearest neighbour host ions, these interaction mode coordinates are the normal mode coordinates used by Opik and Pryce [4] and also by Kamimura and Sugano [5]. In this way the relaxation processes can be represented by the adiabatic potential energy surfaces (APES) of the algtlu excited states in the six-dimensional interaction mode coordinate space; the relaxed excited statcs (RES) can be represented by the minima on the APES’s. Opik and Pryce [4] investigated these APES’s in rather detail in connection with the Jahn—-Teller effect (JTE). They concluded that, when the spin—orbit interaction is very small, minima on the F~(Aand C) and Fj APES’s are tetragonal if and only if lb I> ~cI,while are trigonal if and only if lb 1< Id; here b and c are linear coupling constants with the and T2g modes, respectively. Lowering in symmetry from °h to D411 or D3d is caused by the ELI. Thus Tl~-typecenters are expected to provide typical examples of RES’s determined by the JTE. Corresponding to the A and C absorption bands two emission bands are expected to appear from the tetragonally or trigonally distorted RES’s. Actually, in the case of the Ag center, Kojima et al. [6] and Shimanuki [7] succeeded in constructing the APES’s by using the experimental data, which can explain all the luminescent properties of the Ag-- -center. In most of the other Tlttype centers, however, the situation is not So simple as expected because of the large ELI, i.e. the higher order JTE [8]. Complication is represented by the fact that the A-band excitation produces two emission bands, AT and Ax, in many of the Tittype centers. In most cases it is straightforward to identify the AT and Ax emission bands, because they are separated froni each other and their temperature variations are characteristic [9,10] When the AT emission band itself consists of two component bands due to the exis-
A. Fukuda et al.
/ Relaxed excited States lfl alkali halides
141
tence of the trap level or of the charge compensating vacancy, however, care must be taken not to assign one of the component bands to the Ax emission band [11,12]. In order to clarify the AT and Ax RES’s and to demonstrate the importance of the higher order (quadratic) JTE, we have investigated the effects of magnetic field [13] and hydrostatic pressure [141 on the AT and Ax emission bands.
2. Magnetic field effect on the AT and Ax emission bands [13] Magnetic fields up to 42 kG were applied with a superconducting magnet in the [001] or [1111 direction of a sample. Exciting light was incident upon the (001) cleaved or (ill) polished surface of the sample and traveled along the same direction and sense as the field. Emitted light was observed head-on to the exciting light. The degree of circular polarization (DCP) of the AT and Ax emission bands was obtained as a function of the inverse of temperature 1/Tat various magnetic field strengths. Some of the results are shown in fig. I. Similar results were obtained in KBr : Ga+, KBr: Ink, and KC1: Int As stated in ref. [8] the three (nearly) tetragonal minima on the F~(A)and F 1 APES’s are responsible for the AT RES at least in the case of Ga+ and ln+. Therefore the AT RES is represented by a energy level diagram consisting of two nearly degenerate levels Eu and a trap level underneath Aid. Transition from A1~is forbidden, though vibration-induced emission from the trap level itself is observed at low enough temperatures. The depth of the trap level is determined by the spin—orbit interaction as well as the JTE. This energy level diagram can explain the characteristic features of the DCP versus 1/Tin the AT emission band at least qualitatively, though quantitative analysis has not yet been successfully performed. The apparent difference between Ga+ and In~is, for example, due to the difference in the depth of the trap level. Thus we confirm that the AT RES is correlated to the tetragonal minima on the F~~(A) and r1 APES’s. The more important conclusion we can deduce from fig. I is as follows. Since the DCP versus l/T of the Ax emission band has a remarkable resemblance to that of the AT emission band, the Ax RES is quite similar to the AT RES, consisting of two nearly degenerate levels and a trap level underneath. The existence of the trap level and the difference in its depth between Ga~and ln~suggest the possibility that, as in the case of the AT RES, the two levels are correlated to the minima on the F~(A) APES and the trap level is the corresponding minima Ofl the APES. Then two fundamental questions arise: (I) ls it possible that the two kinds of minima, one for the AT RES and the other for the Ax RES coexist on the F~~(A) and Fj APES’s? (2) What is the symmetry of the minima for the Ax RES? If we assume the linear JTE within the algtlu excited states, we could not expect other kind of minima than the kind assigned to the AT RES. Several proposals [15,16] have been made in connection with the coexistence of the two kinds of minima. Most of them, however, cannot predict that both of the A1 and Ax RES’s consist of two nearly degenerate
142
A. Fukuda et al.
0
1.0 ~
Temperature (K 5 4 3 2
/ Relaxed excited states in alkali halides
( .5
.0
KI~Ga, A
1emission
H//(0OI(
2L_
o 0
-
-
42Ok~(~~
~42O1”~~
2~8kG{
~
~
‘::±~~ 0.2
0
0.4
0.6
08
I/T (K’) Tempero~ure(K) 10 5 4 3 2 .5 I.C,[TTrT~rr-nYT-fl-T.Tn~fl~ 0.4
0
42.0~
~::
Temperature (K 5 4 3 2
1.5
KIGa, A emission o H//(00I(
25.8kG
-
00.2 ~
0
0
LO~L 0.4
0.2
10 I
0.4
0.6
I/T (K) Temperature (K( 5 4 3 2
-
KI:In,
08
1.5
£
~em~sion
L~4
_57kG~••
l/T (K~)
Fig. 1. Degree of circular polarization (DCP) versus the inverse of temperature lIT for the AT irid Ax emission bands of KI : Ga~and KI : In~at various 10011 and [1111 magnetic field strengths.
levels with its own trap level underneath and hence cannot explain the large DCP and its characteristic temperature variations observed both in the AT and Ax emission bands. An exception is our proposal [14] , made on the basis of the hydrostatic pressure experiment, that the AT RES is correlated to the three tetragonal minima and the Ax RES to the four trigonal minima. The similar proposal was made by Bacci et a!. [16] independently.
A. Fukuda et al.
/ Relaxed excited states in alkali halides
143
3. Hydrostatic pressure effect on the AT and Ax emission bands [14] The AT and Ax emission bands were measured under various hydrostatic pressures (0—10 kbar). A remarkable change as shown in fig. 2 was observed. At a temperature above 77 K the Ax emission band is stronger than the AT emission band under normal pressure (1 bar). When hydrostatic pressure is applied, however, the AT emission band becomes gradually stronger and under 10 kbar the Ax emission band almost disappears. This fact shows that the AT RES is “contracted”, while the Ax RES is “expanded” with respect to Q 1. Similar results were also obtained in KBr : ln~,NaCl : Ga~,and KBr : Ga~.In ref. [91Tlttype centers in various alkali halides are divided into three groups according to the characteristic temperatures variations of the AT and Ax emission bands. The results obtained in the present study indicate that, by applying a suitable hydrostatic pressure, the group (1) changes into
T~RT
Kiln
25
3.0 eV
Photon
Energy
4~
1:113K
/6
2.0
25
Ki: In
2kb
0,
30 eV
Photon Energy Fig. 2. Emission spectra produced by the A-band excitation in KI : In~under various hydrostatic pressures and at RT and 113 K.
144
A. Fukuda
Ct
al. / Relaxed excited states in alkali halides
the group (2) and the group (2) into the group (3); under high enough hydrostatic pressures all the centers belong to the group (3). These facts suggest the importance of the quadratic JTE; the coupling constants with the g and T2g modes depend on Q 1 in the form of b + baQi and c + c07Q1. Therefore both of the minima, tetragonal and trigonal, may coexist with different values of Q1 the AT RES is represented by the tetragonal minima and the Ax RES by the trigonal minima. Since the alkali halide crystals are almost isotropic (b c), the difference in depth between these minima is expected to be small. Hydrostatic pressure must change the difference because of the terms b~~Qi and c01Qi, making the AT RES deeper than the Ax RES and finally making the Ax RES unstable. Thus we can explain why hydrostatic pressure causes a drastic change in the population between the AT and Ax RES’s and hence in the emission spectrum. Moreover the difference among the three groups is ascribable to the difference in the coupling constants, b0~and da1~ In this way Tl+.type of the 0h centers to D4h provide and D3d typical caused examples by the EL1. AlJTE, i.e. the lowering in symmetry from though the quadratic JTE plays an important role in determining the stability of the trigonal minima, it is natural to consider that general features of the APES’s are mainly determined by the linear JTE. Therefore we calculated the cross sections of the APES’s along tetragonal and trigonal distortions without taking account of the quadratic JTE. The results help us to understand systematically the luminescent properties of the emission bands produced by the A-, B-, and C-band excitation. 4. Cross sections of the APES’s along tetragonal and trigonal distortions By diagonalizing the effective hamiltonian matrix He + HeL with the algtlu NRES’s as bases and by adding the lattice potential energy, we obtain the APES’s. If we put Q 1 = 0 (i * 3), we obtain the cross sections along tetragonal distortions as shown in fig. 3. For trigonal distortions, we can also use fig. 3 by replacing Q3 by (Q4 + + Q6)/~J3.Here He and HeL are given in tables VI and V in ref. [9] . We normalize the energy by the separation between the C and A bands, ~ = EA, and describe the algtlu excited states in terms of the parameters, ~ and x (EB — EA)/& King and Van Vieck’s X is set to be unity. We also normalize the interaction-mode coordinates as t’ollows:
q1aQ1/z~s,
q2bQ2/~,...,q6=cQ6/~.
Then the lattice potential energies are given by 11
\
2~
A/ 2\ 2_ ~ 2
—~
~ —a~,Q1, —a~)( 1a )q~~rBq~ ,q1 q1 2 (1 —a~~)Q~/z~.=(l _a~~)(LX/b —~.
(1
—
—
2)q~ =
a 11)Q~/~=
(1
—
a11)(~/d
Cq~.
A. Fukuda et al. / Relaxed excited States in alkali halides
~ 20
-1.5
145
~ -10
-05
rr.
60’A t~
n~
-w
-i~
~
-
~ 0bQ
10
~ ~
~
°~~T ~20E~’H
Fig. 3. Cross sections of the APES’s along tetragonal distortions without taking account of the quadratic JTE. We setB = (1 — a~~)~/b2 = 0.5 and x = 0.125, 0.25, 0.5 and 0.75. If Q~is replaced by (Q4 + + Q6)f’../3 and B by C = (1 — a 2= 0.5, these are the cross sections along trigonal distortions. Solid lines show non-degeneracy 77)~/c and dotted lines double degeneracy.
Here ann, ~
and a
11 are quadratic coupling constants representing the difference in curvature between the ground and excited states. Fig. 3 is essentially the same as fig. 7 in ref. [9]. Since the assignment of the AT and Ax emission bands is different, however, let us try to improve the previous attempt to understand all the luminescent properties in terms of the APES’s. 4.1. Reason why the Ax RES is not efficiently populated optically
The similar explanation previously made in ref. [9] is plausible even in the present model. The detailed structure of the T~(A)APES near the origin prevents the Ax RES from being populated optically. Probably the gradient along Q1 is important. Note that the AT RES is contracted while the Ax RES is expanded with respect to Q1.
.4. Fukuda et al. / Relaxed excited states in alkali halides
146
4.2. Fast and slow components of decay time Since each of the AT and Ax RES’s has its own trap level, each of the AT and Ax emission bands can have the fast and slow components. The non-radiative transition from the F~(A)APES to the F 1 APES is necessary for the appearance of the slow components. When the fast and slow components show different polarization characteristics as observed by Gerhardt and Gebhardt [17], the non-radiative transi-
tion occurs before the system relaxes to the minima on the F~(A)APES. When x becomes large, there is a tendency that tetragonal or trigonal minima disappear on
the
r1
APES. When there are no tetragonal or trigonal minima on the I’j APES,
there is no region between the origin and minima where both of the F~(A)and APES’s go down parallel to each other. In such a case the non-radiative transition may hardly occur and thus we understand qualitatively why, in Kl : Tl’ and KBr: Tl+, for example, the A1 emission band does not have the slow component. Recently Niilisk et al. [18] investigated the decay time of the Ax emission band in Ga~centers in various alkali halides and found that the decay time depends strongly on the host alkali halide. This can be ascribed to the difference in x and because the calculation shows that the life time and the depth of the trap level strongly depend on these parameters. 4.3. (‘orrelation of polarization between exciting and emitted light This phenomenon has been explained qualitatively by using the three intersecting paraboloids [12,17,19—21]. The explanation is valid for the C emission band, because fig. 3 indicate that the F~(C)APES is approximated by the three intersecting paraboloids. The [7(A) APES is, however, more complicated; the contour lines in the ~g space are shown in fig. 2(b) of ref. [151 Still it has a quite simple character; it consists of three surfaces, F~~(A),F~~(A), and I7~(A),each of which has a particular symmetry, x, y, or z. Therefore we can understand the correlation of polarization. The difference in structure between the F4(A) and [7(C) APES’s causes the difference in the maximum degree of linear polarization (DLP) between the AT and C emission bands, as observed in KI : Ga+. Moreover the present model can explain the increase of the DLP below 4.2 K in
K! : Tl~etc. [20]. 4.4. Uniaxial stress effect By assuming the three intersecting paraboloids for the [‘~(C) and [7(A) APES’s, Shimada and Ishiguro [20] concluded that the C RES is elongated tetragonal while the AT RES is flattened tetragonal and hence b <0. Their conclusion concerning the
C emission band does not need any correction. Contrary to their conclusion, fig. 3 shows that the AT RES is also nearly elongated tetragonal. Since the AT RES consists of three surfaces with definite symmetry as stated above, however, we can still
A. Fukuda et al.
/ Relaxed excited states in alkali halides
147
explain the fact that .AJ/1 of the AT emission band increases while that of the C emission band decreases.
5. Future problems In order to confirm the present model, it is important to determine the symmetry of the Ax RES more directly. Paramagnetic resonance in the relaxed excited states is useful for this purpose [22]. It is also informative to observe the decay time by applying a magnetic field in various crystalographic directions. Analysis of the anisotropy in the DCP shown in fig. I must be useful, too. The problem should be treated dynamically, though, because of the following reasons. In fig. 1 the DCP shows satu-
ration and the saturated value depends on the field strength. This fact indicates that the doubly degenerate Eu state has a zero field splitting. Since the exact symmetry of the real minima is not tetragona! or trigonal but slightly deformed, the ~ state is splitted. This splitting is, however, only potentially active [3] and hence the quantum-mechanical energy levels are still degenerate. In this way we have to treat the dynamic coupling between E~and At~in the case of the AT RES,
Ai~x Eu
=
~g’
E~x
Eu
31g + /32g’
Ettg + (&2g) + 1
and in the case of the Ax RES, A 1uXEu=~g,
Eu>ut1g+(&2g)~g
Natsume [23] considered such a coupling when no magnetic field is applied. His calculation will be extended to include the effect of a magnetic field. So far we are concerned mainly with the AT and Ax emission bands. But fig. 3 can also be used in understanding the characteristic features of the emission bands produced by the B- and C-band excitation. For example, quenching of the C emission band depends on the fact that the 17(A) APES crosses the r~ and r~APES’s. It is interesting to investigate whether or not there is an emission band from the tngonally distorted C excited state which corresponds to the Ax emission band.
Acknowledgement Numerical calculations were carried out by FACOM 230-75 at the Computer Center of Kyushu University. This work is partially supported by the Grant-in-Aid for Scientific Research from the Ministry of Education in Japan.
148
A. Fukuda et al. / Relaxed excited states in alkali halides
References [1] W.B. l’owler, in: Physics of color centers, ed. W.B. Fowler (Academic Press, New York, 1968) p. 133. [21 F. Seitz, J. Chem. Phys. 6 (1938) 150. [31 Y. Toyozawa and M. lnoue, J. Phys. Soc. Japan 21(1966)1663. 141 U. Opik and M.H.L. Pryce, Proc. Roy. Soc. 238 (1957) A425. [51 II. Kamimura and S. Sugano, J. Phys. Soc. Japan 14 (1959) 1612. 161 K. Kojima, S. Shimanuki and T. Kojima, J. Phys. Soc. Japan 33(1972)1076. [71 S. Shirnanuki, J. Phys. Soc. Japan 35 (1973) 1680. [8] A. Fukuda, K. Cho and H.J. Paus, in: Luminescence of crystals, molecules, and solutions, ed. F. Williams (Plenum Press, New York, 1973) p. 478. 191 A. Fukuda,Phys. Rev. Bi (1970)4161. [10] J.M. Donahue and K. Teegarden, J. Phys. Chem. Solids 29(1968) 2141. [1111W.Klcemann,Z.Phys. 249 (1971) 145. 1121 A. Fukuda, in: Physics of impurity centers in crystals, ed. G.S. Zavt (Tallinn, USSR, 1972) p. 505. 1131 A. Fukuda, J. Phys. Soc. Japan 40(1976), to be published. 1141 5. Masunaga, S. Emura, H. Yamamoto, A. Fukuda and A. Matsushima, Contributed paper at International Conference on Color Centers in Ionic Crystals (Sendai, 1974) Abst. Gl32. 1151 A. RanfagniandG. Viiani, J. Phys. Chem. Solids 35(1974)25. [161 M. Bacci, A. Ranfagni, M.P. Fontana and G. Viiani, Phys. Rev. Bi 1(1975) 3052. 1171 V. Gerhardt and W. Gebhardt, Phys. Stat. Solidi (b) 59 (1973) 187. [181 A. Niilisk, T. Soovik and V. Tatanly, Phys. Stat. Solidi (b) 64 (1974) K135. [191A. Fukuda, S. Makishima, T. Mabuchi, R. Onaka, J. Phys. Chem. Solids 28 (1967) 1763. [20] 1. Shimada and M. Ishiguro, Phys. Rev. 187 (1969) 1089. [211 V. Hizhnyakov, S. Zazubovich and T. Soovik. Phys. Stat. Solidi (b) 66 (1974) 727. [221 P. Edel, C. Hennies, Y. Merle d’Aubigne, R. Romestain and Y. Twarowski, Phys. Rev. Letters 28(1972)1268. [23] V. Natsume, Ph. D. Thesis, The University of Tokyo, Tokyo, 1974.
Discussion D.S. McClure: I was intrigued by the fact that the application of hydrostatic pressure sends all of the spectra into group III regardless of which group they are in to start with. There must be a correlation between the host crystal properties such as the lattice constant, and the group. llave you found such a correlation? A. Fukuda: There does not seem to be any simple correlation between the spectral group and either the experimental parameters (G, ~) or the lattice parameters (a radius ratio of impurity to host ion). G.F.J. Garlick: Can it be assumed that we do have random dispersion of Tl+ ions in all of the 4alkali halides and negligible occurrence of defects in association with Tl+ ions Tl+__Tl+ or Tl defect which might give anisotropy effects of similar size to Jahn—Teller effects even when present in small concentrations? A. Fukuda: Yes, it can, except for divalent cation centers (Sn2+ and Pb2+). If we assume anisotropy due to defects in association, we cannot explain the characteristic features of the correlation of polarizalion between exciting and emitted light. S. Radhakrishna: What do you think will be the influence of a lattice which does not have a triply degenerate vibration mode (e.g. ADP or KDP) on the emission spectra of ns2 type impurities?
A. Fukuda et at / Relaxed excited states in alkali halides
149
A. Fukuda: In that case, the symmetry is lower than °h and the splitting of energy levels due to the lower symmetry might play an important role in the emission spectra. F. Williams: In accordance with request of Professor Garhick I shall comment on his question. I agree with Professor Fukuda. The best evidence for thallium being substitutional and distributed at random cation sites in alkali halides, at least in KCI, is the work of Runciman and Steward on the lattice constant of mixed crystals. They showed that Vegard’s law was obeyed, consistent with Tl+ at random K+ sites.
RELAXED EXCITED STATES DETERMINED BY JAHN—TELLER EFFECT IN TIP-TYPE CENTERS IN ALKALI HALIDES Atsuo FUKUDA, Akira MATSUSHIMA Nagasaki University, Faculty ofLiberalArts, Nagasaki-shi, Japan 852
and Shoji MASUNAGA Kyushu Institute of Technology, Kitakyushu-shi, Japan 804
Effects of magnetic field and hydrostatic pressure on the AT and Ax emission bands have been investigated. Results show the importance of the quadratic Jahn—Teller effect, indicating that the AT RES is related to the tetragonal minima and the Ax RES to the trigonal minima on the r~(A)and rj- adiabatic potential energy surfaces (APES). Cross sections of the APES’s along tetragonal and trigonal distortions have been calculated to explain the luminescent properties systematically.
1. Introduction There are a group of ions which have two electrons (ns)2 outside a closed shell as shown in table 1. When one of these ions exists as an impurity in an alkali halide crystal and substitutionally replaces a host ion, it forms a luminescent center (the Tittype center)~three characteristic absorption bands called A, B, and C are observed in the otherwise transparent wavelength region, and luminescence appears by excitation in these absorption bands. The center is of °h symmetry and has simple electronic states (the ground state V~and non-relaxed excited states (NRES) Fj, F~(A),F~,F~,and F~(C)).Transitions between these states result in the A, B, and Table 1 Ions with (ns)2 outmost electron configuration. These ions form luminescent centers (TiF~type centers) in alkali halides.
4 5 6
lb
lIb
Ilib
IVb
(Cu) Ag Au
(Zn0) (Cd°) (Hg0)
Ga~
(Ge2~)
Tl~
Sn2~ Pb2~
139
140
.4. Fukuda et al. / Relaxed excited states in alkali halides
C absorption bands [1] . In order to assign emission bands excitable by these absorption bands, relaxation due to the electron-lattice interaction (ELI) should be taken into account. Configuration coordinate curve introduced by Seitz [2] has been used to give a qualitative description of the relaxation processes. The ordinate is the total energy of the system for the ground and excited states of the center, i.e. adiabatic potential energy, including both electronic and lattice terms. The abscissa is a “con1~guration coordinate” which specifies the configuration of the ions around the center. An exact way to specify the configuration is to use the normal mode coordinates around the center which interact with the electronic states under consideration. The normal modes are classified according to the irreducible representations of the point group °h• When we neglect the dependence of the spin-—orbit interaction upon lattice configuration and reasonably assume that the algtlu excited states are isolated, only dig’ g~and T2g modes have the linear ELI [3] Although the number of irreducible representations is as small as three, each representation contains a great number of normal mode coordinates. Assuming the linear ELI and treating lattice vibrations classically, Toyozawa and lnoue [3] lumped a great number of these normal mode coordinates with a particular symmetry in a single interaction mode coordinate with the same symmetry. Thus the dimension of the configuration coordinates is reduced to six: ~ig(Qi)’ ~g(Q2 and Q 3), and 12g(Q4, Q5, and Q6). If we restrict our attention to an octahedral quasi-molecule composed of an impuity ion and the six nearest neighbour host ions, these interaction mode coordinates are the normal mode coordinates used by Opik and Pryce [4] and also by Kamimura and Sugano [5]. In this way the relaxation processes can be represented by the adiabatic potential energy surfaces (APES) of the algtlu excited states in the six-dimensional interaction mode coordinate space; the relaxed excited statcs (RES) can be represented by the minima on the APES’s. Opik and Pryce [4] investigated these APES’s in rather detail in connection with the Jahn—-Teller effect (JTE). They concluded that, when the spin—orbit interaction is very small, minima on the F~(Aand C) and Fj APES’s are tetragonal if and only if lb I> ~cI,while are trigonal if and only if lb 1< Id; here b and c are linear coupling constants with the and T2g modes, respectively. Lowering in symmetry from °h to D411 or D3d is caused by the ELI. Thus Tl~-typecenters are expected to provide typical examples of RES’s determined by the JTE. Corresponding to the A and C absorption bands two emission bands are expected to appear from the tetragonally or trigonally distorted RES’s. Actually, in the case of the Ag center, Kojima et al. [6] and Shimanuki [7] succeeded in constructing the APES’s by using the experimental data, which can explain all the luminescent properties of the Ag-- -center. In most of the other Tlttype centers, however, the situation is not So simple as expected because of the large ELI, i.e. the higher order JTE [8]. Complication is represented by the fact that the A-band excitation produces two emission bands, AT and Ax, in many of the Tittype centers. In most cases it is straightforward to identify the AT and Ax emission bands, because they are separated froni each other and their temperature variations are characteristic [9,10] When the AT emission band itself consists of two component bands due to the exis-
A. Fukuda et al.
/ Relaxed excited States lfl alkali halides
141
tence of the trap level or of the charge compensating vacancy, however, care must be taken not to assign one of the component bands to the Ax emission band [11,12]. In order to clarify the AT and Ax RES’s and to demonstrate the importance of the higher order (quadratic) JTE, we have investigated the effects of magnetic field [13] and hydrostatic pressure [141 on the AT and Ax emission bands.
2. Magnetic field effect on the AT and Ax emission bands [13] Magnetic fields up to 42 kG were applied with a superconducting magnet in the [001] or [1111 direction of a sample. Exciting light was incident upon the (001) cleaved or (ill) polished surface of the sample and traveled along the same direction and sense as the field. Emitted light was observed head-on to the exciting light. The degree of circular polarization (DCP) of the AT and Ax emission bands was obtained as a function of the inverse of temperature 1/Tat various magnetic field strengths. Some of the results are shown in fig. I. Similar results were obtained in KBr : Ga+, KBr: Ink, and KC1: Int As stated in ref. [8] the three (nearly) tetragonal minima on the F~(A)and F 1 APES’s are responsible for the AT RES at least in the case of Ga+ and ln+. Therefore the AT RES is represented by a energy level diagram consisting of two nearly degenerate levels Eu and a trap level underneath Aid. Transition from A1~is forbidden, though vibration-induced emission from the trap level itself is observed at low enough temperatures. The depth of the trap level is determined by the spin—orbit interaction as well as the JTE. This energy level diagram can explain the characteristic features of the DCP versus 1/Tin the AT emission band at least qualitatively, though quantitative analysis has not yet been successfully performed. The apparent difference between Ga+ and In~is, for example, due to the difference in the depth of the trap level. Thus we confirm that the AT RES is correlated to the tetragonal minima on the F~~(A) and r1 APES’s. The more important conclusion we can deduce from fig. I is as follows. Since the DCP versus l/T of the Ax emission band has a remarkable resemblance to that of the AT emission band, the Ax RES is quite similar to the AT RES, consisting of two nearly degenerate levels and a trap level underneath. The existence of the trap level and the difference in its depth between Ga~and ln~suggest the possibility that, as in the case of the AT RES, the two levels are correlated to the minima on the F~(A) APES and the trap level is the corresponding minima Ofl the APES. Then two fundamental questions arise: (I) ls it possible that the two kinds of minima, one for the AT RES and the other for the Ax RES coexist on the F~~(A) and Fj APES’s? (2) What is the symmetry of the minima for the Ax RES? If we assume the linear JTE within the algtlu excited states, we could not expect other kind of minima than the kind assigned to the AT RES. Several proposals [15,16] have been made in connection with the coexistence of the two kinds of minima. Most of them, however, cannot predict that both of the A1 and Ax RES’s consist of two nearly degenerate
142
A. Fukuda et al.
0
1.0 ~
Temperature (K 5 4 3 2
/ Relaxed excited states in alkali halides
( .5
.0
KI~Ga, A
1emission
H//(0OI(
2L_
o 0
-
-
42Ok~(~~
~42O1”~~
2~8kG{
~
~
‘::±~~ 0.2
0
0.4
0.6
08
I/T (K’) Tempero~ure(K) 10 5 4 3 2 .5 I.C,[TTrT~rr-nYT-fl-T.Tn~fl~ 0.4
0
42.0~
~::
Temperature (K 5 4 3 2
1.5
KIGa, A emission o H//(00I(
25.8kG
-
00.2 ~
0
0
LO~L 0.4
0.2
10 I
0.4
0.6
I/T (K) Temperature (K( 5 4 3 2
-
KI:In,
08
1.5
£
~em~sion
L~4
_57kG~••
l/T (K~)
Fig. 1. Degree of circular polarization (DCP) versus the inverse of temperature lIT for the AT irid Ax emission bands of KI : Ga~and KI : In~at various 10011 and [1111 magnetic field strengths.
levels with its own trap level underneath and hence cannot explain the large DCP and its characteristic temperature variations observed both in the AT and Ax emission bands. An exception is our proposal [14] , made on the basis of the hydrostatic pressure experiment, that the AT RES is correlated to the three tetragonal minima and the Ax RES to the four trigonal minima. The similar proposal was made by Bacci et a!. [16] independently.
A. Fukuda et al.
/ Relaxed excited states in alkali halides
143
3. Hydrostatic pressure effect on the AT and Ax emission bands [14] The AT and Ax emission bands were measured under various hydrostatic pressures (0—10 kbar). A remarkable change as shown in fig. 2 was observed. At a temperature above 77 K the Ax emission band is stronger than the AT emission band under normal pressure (1 bar). When hydrostatic pressure is applied, however, the AT emission band becomes gradually stronger and under 10 kbar the Ax emission band almost disappears. This fact shows that the AT RES is “contracted”, while the Ax RES is “expanded” with respect to Q 1. Similar results were also obtained in KBr : ln~,NaCl : Ga~,and KBr : Ga~.In ref. [91Tlttype centers in various alkali halides are divided into three groups according to the characteristic temperatures variations of the AT and Ax emission bands. The results obtained in the present study indicate that, by applying a suitable hydrostatic pressure, the group (1) changes into
T~RT
Kiln
25
3.0 eV
Photon
Energy
4~
1:113K
/6
2.0
25
Ki: In
2kb
0,
30 eV
Photon Energy Fig. 2. Emission spectra produced by the A-band excitation in KI : In~under various hydrostatic pressures and at RT and 113 K.
144
A. Fukuda
Ct
al. / Relaxed excited states in alkali halides
the group (2) and the group (2) into the group (3); under high enough hydrostatic pressures all the centers belong to the group (3). These facts suggest the importance of the quadratic JTE; the coupling constants with the g and T2g modes depend on Q 1 in the form of b + baQi and c + c07Q1. Therefore both of the minima, tetragonal and trigonal, may coexist with different values of Q1 the AT RES is represented by the tetragonal minima and the Ax RES by the trigonal minima. Since the alkali halide crystals are almost isotropic (b c), the difference in depth between these minima is expected to be small. Hydrostatic pressure must change the difference because of the terms b~~Qi and c01Qi, making the AT RES deeper than the Ax RES and finally making the Ax RES unstable. Thus we can explain why hydrostatic pressure causes a drastic change in the population between the AT and Ax RES’s and hence in the emission spectrum. Moreover the difference among the three groups is ascribable to the difference in the coupling constants, b0~and da1~ In this way Tl+.type of the 0h centers to D4h provide and D3d typical caused examples by the EL1. AlJTE, i.e. the lowering in symmetry from though the quadratic JTE plays an important role in determining the stability of the trigonal minima, it is natural to consider that general features of the APES’s are mainly determined by the linear JTE. Therefore we calculated the cross sections of the APES’s along tetragonal and trigonal distortions without taking account of the quadratic JTE. The results help us to understand systematically the luminescent properties of the emission bands produced by the A-, B-, and C-band excitation. 4. Cross sections of the APES’s along tetragonal and trigonal distortions By diagonalizing the effective hamiltonian matrix He + HeL with the algtlu NRES’s as bases and by adding the lattice potential energy, we obtain the APES’s. If we put Q 1 = 0 (i * 3), we obtain the cross sections along tetragonal distortions as shown in fig. 3. For trigonal distortions, we can also use fig. 3 by replacing Q3 by (Q4 + + Q6)/~J3.Here He and HeL are given in tables VI and V in ref. [9] . We normalize the energy by the separation between the C and A bands, ~ = EA, and describe the algtlu excited states in terms of the parameters, ~ and x (EB — EA)/& King and Van Vieck’s X is set to be unity. We also normalize the interaction-mode coordinates as t’ollows:
q1aQ1/z~s,
q2bQ2/~,...,q6=cQ6/~.
Then the lattice potential energies are given by 11
\
2~
A/ 2\ 2_ ~ 2
—~
~ —a~,Q1, —a~)( 1a )q~~rBq~ ,q1 q1 2 (1 —a~~)Q~/z~.=(l _a~~)(LX/b —~.
(1
—
—
2)q~ =
a 11)Q~/~=
(1
—
a11)(~/d
Cq~.
A. Fukuda et al. / Relaxed excited States in alkali halides
~ 20
-1.5
145
~ -10
-05
rr.
60’A t~
n~
-w
-i~
~
-
~ 0bQ
10
~ ~
~
°~~T ~20E~’H
Fig. 3. Cross sections of the APES’s along tetragonal distortions without taking account of the quadratic JTE. We setB = (1 — a~~)~/b2 = 0.5 and x = 0.125, 0.25, 0.5 and 0.75. If Q~is replaced by (Q4 + + Q6)f’../3 and B by C = (1 — a 2= 0.5, these are the cross sections along trigonal distortions. Solid lines show non-degeneracy 77)~/c and dotted lines double degeneracy.
Here ann, ~
and a
11 are quadratic coupling constants representing the difference in curvature between the ground and excited states. Fig. 3 is essentially the same as fig. 7 in ref. [9]. Since the assignment of the AT and Ax emission bands is different, however, let us try to improve the previous attempt to understand all the luminescent properties in terms of the APES’s. 4.1. Reason why the Ax RES is not efficiently populated optically
The similar explanation previously made in ref. [9] is plausible even in the present model. The detailed structure of the T~(A)APES near the origin prevents the Ax RES from being populated optically. Probably the gradient along Q1 is important. Note that the AT RES is contracted while the Ax RES is expanded with respect to Q1.
.4. Fukuda et al. / Relaxed excited states in alkali halides
146
4.2. Fast and slow components of decay time Since each of the AT and Ax RES’s has its own trap level, each of the AT and Ax emission bands can have the fast and slow components. The non-radiative transition from the F~(A)APES to the F 1 APES is necessary for the appearance of the slow components. When the fast and slow components show different polarization characteristics as observed by Gerhardt and Gebhardt [17], the non-radiative transi-
tion occurs before the system relaxes to the minima on the F~(A)APES. When x becomes large, there is a tendency that tetragonal or trigonal minima disappear on
the
r1
APES. When there are no tetragonal or trigonal minima on the I’j APES,
there is no region between the origin and minima where both of the F~(A)and APES’s go down parallel to each other. In such a case the non-radiative transition may hardly occur and thus we understand qualitatively why, in Kl : Tl’ and KBr: Tl+, for example, the A1 emission band does not have the slow component. Recently Niilisk et al. [18] investigated the decay time of the Ax emission band in Ga~centers in various alkali halides and found that the decay time depends strongly on the host alkali halide. This can be ascribed to the difference in x and because the calculation shows that the life time and the depth of the trap level strongly depend on these parameters. 4.3. (‘orrelation of polarization between exciting and emitted light This phenomenon has been explained qualitatively by using the three intersecting paraboloids [12,17,19—21]. The explanation is valid for the C emission band, because fig. 3 indicate that the F~(C)APES is approximated by the three intersecting paraboloids. The [7(A) APES is, however, more complicated; the contour lines in the ~g space are shown in fig. 2(b) of ref. [151 Still it has a quite simple character; it consists of three surfaces, F~~(A),F~~(A), and I7~(A),each of which has a particular symmetry, x, y, or z. Therefore we can understand the correlation of polarization. The difference in structure between the F4(A) and [7(C) APES’s causes the difference in the maximum degree of linear polarization (DLP) between the AT and C emission bands, as observed in KI : Ga+. Moreover the present model can explain the increase of the DLP below 4.2 K in
K! : Tl~etc. [20]. 4.4. Uniaxial stress effect By assuming the three intersecting paraboloids for the [‘~(C) and [7(A) APES’s, Shimada and Ishiguro [20] concluded that the C RES is elongated tetragonal while the AT RES is flattened tetragonal and hence b <0. Their conclusion concerning the
C emission band does not need any correction. Contrary to their conclusion, fig. 3 shows that the AT RES is also nearly elongated tetragonal. Since the AT RES consists of three surfaces with definite symmetry as stated above, however, we can still
A. Fukuda et al.
/ Relaxed excited states in alkali halides
147
explain the fact that .AJ/1 of the AT emission band increases while that of the C emission band decreases.
5. Future problems In order to confirm the present model, it is important to determine the symmetry of the Ax RES more directly. Paramagnetic resonance in the relaxed excited states is useful for this purpose [22]. It is also informative to observe the decay time by applying a magnetic field in various crystalographic directions. Analysis of the anisotropy in the DCP shown in fig. I must be useful, too. The problem should be treated dynamically, though, because of the following reasons. In fig. 1 the DCP shows satu-
ration and the saturated value depends on the field strength. This fact indicates that the doubly degenerate Eu state has a zero field splitting. Since the exact symmetry of the real minima is not tetragona! or trigonal but slightly deformed, the ~ state is splitted. This splitting is, however, only potentially active [3] and hence the quantum-mechanical energy levels are still degenerate. In this way we have to treat the dynamic coupling between E~and At~in the case of the AT RES,
Ai~x Eu
=
~g’
E~x
Eu
31g + /32g’
Ettg + (&2g) + 1
and in the case of the Ax RES, A 1uXEu=~g,
Eu>ut1g+(&2g)~g
Natsume [23] considered such a coupling when no magnetic field is applied. His calculation will be extended to include the effect of a magnetic field. So far we are concerned mainly with the AT and Ax emission bands. But fig. 3 can also be used in understanding the characteristic features of the emission bands produced by the B- and C-band excitation. For example, quenching of the C emission band depends on the fact that the 17(A) APES crosses the r~ and r~APES’s. It is interesting to investigate whether or not there is an emission band from the tngonally distorted C excited state which corresponds to the Ax emission band.
Acknowledgement Numerical calculations were carried out by FACOM 230-75 at the Computer Center of Kyushu University. This work is partially supported by the Grant-in-Aid for Scientific Research from the Ministry of Education in Japan.
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A. Fukuda et al. / Relaxed excited states in alkali halides
References [1] W.B. l’owler, in: Physics of color centers, ed. W.B. Fowler (Academic Press, New York, 1968) p. 133. [21 F. Seitz, J. Chem. Phys. 6 (1938) 150. [31 Y. Toyozawa and M. lnoue, J. Phys. Soc. Japan 21(1966)1663. 141 U. Opik and M.H.L. Pryce, Proc. Roy. Soc. 238 (1957) A425. [51 II. Kamimura and S. Sugano, J. Phys. Soc. Japan 14 (1959) 1612. 161 K. Kojima, S. Shimanuki and T. Kojima, J. Phys. Soc. Japan 33(1972)1076. [71 S. Shirnanuki, J. Phys. Soc. Japan 35 (1973) 1680. [8] A. Fukuda, K. Cho and H.J. Paus, in: Luminescence of crystals, molecules, and solutions, ed. F. Williams (Plenum Press, New York, 1973) p. 478. 191 A. Fukuda,Phys. Rev. Bi (1970)4161. [10] J.M. Donahue and K. Teegarden, J. Phys. Chem. Solids 29(1968) 2141. [1111W.Klcemann,Z.Phys. 249 (1971) 145. 1121 A. Fukuda, in: Physics of impurity centers in crystals, ed. G.S. Zavt (Tallinn, USSR, 1972) p. 505. 1131 A. Fukuda, J. Phys. Soc. Japan 40(1976), to be published. 1141 5. Masunaga, S. Emura, H. Yamamoto, A. Fukuda and A. Matsushima, Contributed paper at International Conference on Color Centers in Ionic Crystals (Sendai, 1974) Abst. Gl32. 1151 A. RanfagniandG. Viiani, J. Phys. Chem. Solids 35(1974)25. [161 M. Bacci, A. Ranfagni, M.P. Fontana and G. Viiani, Phys. Rev. Bi 1(1975) 3052. 1171 V. Gerhardt and W. Gebhardt, Phys. Stat. Solidi (b) 59 (1973) 187. [181 A. Niilisk, T. Soovik and V. Tatanly, Phys. Stat. Solidi (b) 64 (1974) K135. [191A. Fukuda, S. Makishima, T. Mabuchi, R. Onaka, J. Phys. Chem. Solids 28 (1967) 1763. [20] 1. Shimada and M. Ishiguro, Phys. Rev. 187 (1969) 1089. [211 V. Hizhnyakov, S. Zazubovich and T. Soovik. Phys. Stat. Solidi (b) 66 (1974) 727. [221 P. Edel, C. Hennies, Y. Merle d’Aubigne, R. Romestain and Y. Twarowski, Phys. Rev. Letters 28(1972)1268. [23] V. Natsume, Ph. D. Thesis, The University of Tokyo, Tokyo, 1974.
Discussion D.S. McClure: I was intrigued by the fact that the application of hydrostatic pressure sends all of the spectra into group III regardless of which group they are in to start with. There must be a correlation between the host crystal properties such as the lattice constant, and the group. llave you found such a correlation? A. Fukuda: There does not seem to be any simple correlation between the spectral group and either the experimental parameters (G, ~) or the lattice parameters (a radius ratio of impurity to host ion). G.F.J. Garlick: Can it be assumed that we do have random dispersion of Tl+ ions in all of the 4alkali halides and negligible occurrence of defects in association with Tl+ ions Tl+__Tl+ or Tl defect which might give anisotropy effects of similar size to Jahn—Teller effects even when present in small concentrations? A. Fukuda: Yes, it can, except for divalent cation centers (Sn2+ and Pb2+). If we assume anisotropy due to defects in association, we cannot explain the characteristic features of the correlation of polarizalion between exciting and emitted light. S. Radhakrishna: What do you think will be the influence of a lattice which does not have a triply degenerate vibration mode (e.g. ADP or KDP) on the emission spectra of ns2 type impurities?
A. Fukuda et at / Relaxed excited states in alkali halides
149
A. Fukuda: In that case, the symmetry is lower than °h and the splitting of energy levels due to the lower symmetry might play an important role in the emission spectra. F. Williams: In accordance with request of Professor Garhick I shall comment on his question. I agree with Professor Fukuda. The best evidence for thallium being substitutional and distributed at random cation sites in alkali halides, at least in KCI, is the work of Runciman and Steward on the lattice constant of mixed crystals. They showed that Vegard’s law was obeyed, consistent with Tl+ at random K+ sites.