The non-luminescent and spin-dependent disexcitation process observed in F-center pairs in alkali halides at low temperature is explained by a covalent bond within the pair. Exchange effects give a negative contribution to the lattice potential energy. If the pair separataion is small, local modes become unstable and spontaneous lattice distortions bring back the pair in its ground state

Aegerter, Michel A.

Jaccard, C.

Scientific documents from the Saarland University,

Volume 44A, number 6 PHYSICS LETTERS 16 July 1973
NON-LUMINESCENT DISEXCITATION OF F-CENTER PAIRS BY
EXCHANGE-SOFTENED VIBRATIONAL MODES
C. JACCARD and M. AEGERTER
Institut de Physique de 1 ‘Université, 2000 NeuchcItel, Switzerland
Received 18 April 1973
The non-luminescent and spin-dependent disexcitation process observed in F-center pairs in alkalihalides at low
temperature is explained by a covalent bond within the pair. Exchange effects give a negative contribution to the
lattice potential energy. If the pair separation is small, local modes become unstable and spontaneous lattice distor-
tions bring back the pair in its ground state.
Alcali halide crystals with a high concentration of F- We consider a pair of F centers located at sites a
centers show at low temperature a strong variation of and b (separation R). The first one is in its relaxed cx-
the luminescent quantum yield under an applied static cited state and the second one in its ground state. A
magnetic field [1, 21 which allows optical detection of local vibrational mode (frequency w, amplitude q
electronic and nuclear magnetic resonances [3,4]. with <q2)~=~= I) mixes to the electronic state an-
These phenomena are explained by interaction of pairs other one ~ ~, having an energy higher by 6. Up to the
of neighbouring centers, in which the electronic disex- second order, the q dependent wave function and its
citation path (radiative or non-radiative) depends on energy take the form
the symmetry of the two-spin wave function. Accord-
ing to an hypothesis put forward by Markham et a!. — ~- w~q~)— wq~
1+.
[5] and resumed by Luty [5] in order to explain the
correlation observed between the F and the F’ band E =E0 — 6iv
2q2 1-
intensities, the electron of the excited member of a the ~Li~admixture being then w2. With this wave func-
pair shifts non-radiatively to the other member to tion, the total energy of the pair is calculated accord-
form an F’ center and then comes back to its ground ing to the Heitler-London scheme, while assuming that
state by a tunnel effect. The necessity for the F’ the perturbation of the second center at b is negligible
center to be in a singlet spin state sets the condition (state va). The result is a function of the pair spin (50
for this process, consistent withmost of the observa- or 1) and of q, with an exchange energy J
0 forq0.
tions. This mechanism, being spin dependent, should The term in w
2q2, including the vibrational potential
respond to EPR and if it is the only one, the relative energy, is relevant for the stability and takes the form
variation of the F’ concentration should be of the or-
der of the relative luminescence variation (> 10—2). 1 d2E = + ~ 6+(.JJlIVbI~/l) —(~/OIVbI 1,1)0)
But with well separated pairs [3], the F’ absorption 2 d(wq)2 4w2
dependence on EPR is much smaller than 10~[7]. e2 e2
~ }+(5—~~-)(J
1—J0)
This suggests another spin dependent mechanism for
non radiative disexcitation, which has nothing to do
with transient F’ centers. In this paper we develope J1 is the exchange energy for the a-center in a pure ~!e~
state and Vb is the local potential at site b. The expres-
qualitatively the following hypothesis: Provided a
sion in the parenthesis is independent of the total spin
suitable spin state, a covalent bond is formed between s and is certainlynegative because the electron clouds
the two members of the pair; the exchange “softens” screen the electrostatic interaction between the ions
certain localized vibrational lattice modes, up to the
and thereby soften the local mode, reducingits fre-point to make them unstable, so that even at zero
temperature the system shifts to its ground state only quency to w’ < w. The last, spin dependent term in-duces a softening only for the singlet state 50, and
by tumbling down vibrational states. this can lead to an instability of the mode, i.e. a nega-
391
Volume 44A, number 6 PHYSICS LETTERS 16 July 1973
ence of a neighbour within the critical distance, can
be depicted in a configuration diagram (fig. 1), for a
- non softening mode A and a softening mode T. The
S=Qj44A former expresses the relacation between the ground
J state F0(ls) and a relaxed excited state F*(2s), and, the latter couples F*(2s) to a higher lying state e.g.B F*(2p).- - The instability of the T mode for the spin singlet
A produces a saddle-shaped energy surface, on which
the system glides until it meets the energy surface of
Fig. 1. Configuration diagram for the energy of the triplet the ground state (ABC). For the spin triplet, the ener-
and singlet relaxed excited states and for the ground state gy surface has always a minimum, from which the
(see text). ground state is reached either by a vertical radiative
transition (A’B’C) or through a highly excited vibra-
tive frequency, provided the two following conditions tional state at high temperature (A’B”C). The effect
are satisfied: of the neighbouring centre is todecrease the curvature
I ) ,j1 > ~ this should be the case since the higher of the energy surface preferentially for the singlet spin
lying state 1i~extends farther in the lattice than the state, and this is enough to change the luminescent
lower lying state ~ yield of the pair, in agreement with the observations.
2) The local mode should couple strongly the two At short distance, the ground state might show a sec-
states, so that the admixture is large: ondary potential well corresponding to the pair “F’
w
2 > hw’/2(J
1 — J0). ±vacancy” into which the system can glide and get
These conditions are satisfied if the separation of trapped momentarily, until it reaches point C by tun-
the pair is smaller than a critical valueR~.This param- nelling through the potential wall.
eter has been estimated with properly scaled hydrogen-
like wave functions, approximating the excited states We are indebted to Professor F. Bassani for valuable
~o and ~i by 2s- and 2p-functions, respectively. They discussions and to the Swiss National Foundation for
should describe reasonably well the F center at large support of this work.
distance. For the ground state, a ls-function can be
used and the integrals can be calculated from
Roothaan’s formulae [9] ; an alternative way is to as- References
sume a delta function, and the evaluation is then
straightforward. In both cases, one finds a critical [1] F. Porret, F. Lüty, Phys. Lett. 26(1971)843.
radius of about 30—40 A provided the admixture is [2] C. Jaccard et a!., Phys. Stat. Sol. (b) 50 (1972) 187.
[3] Y. Ruedin et aI. Phys. Stat. Sol. (b) 54 (1972) 565, 55
of the order of 0.1. This agrees with the model propos- (1973) 215.
ed by Bogan and Fitchen [8]. The estimated critical [41PA. Schnegg, C. Jaccard and M. Aegerter, Phys. Lett.
radius is within a factor of 2 or 3 of the value of 80 A 42A (1973) 369.
obtained from the luminescent behaviour in a magnet- f5] J.J. Markham, R.T. Platt and l.L. Mador, Phys. Rev. 92
ic field [2]. However according to a recent work by (1953) 957.161 F. LUty Halbleiterphysik, Vol. VI, 238 (1961) (Viehweg.F.S. Ham (private communication), the considered
Braunschweig).
states are not purely electronic but vibronic, and tak- I~]P.A. Schnegg et a!., (to be published).
ing this into account would give a better description [8] L.D. Bogan and D.B. Fitchen, Phys. Rev. B, 1 (1970)
of the lattice with the electrons. 4122.
The cycle of an optically excited center, in the pres- 191 C.C.J. Roothaan, J. Chem Phys. 19(1951)1445.
392


Non-luminescent disexcitation of F-center pairs by exchange-softened vibrational modes

Acronym

Volume 44A, number 6 PHYSICS LETTERS 16 July 1973NON-LUMINESCENT DISEXCITATION OF F-CENTER PAIRS BYEXCHANGE-SOFTENED VIBRATIONAL MODESC. JACCARD and M. AEGERTERInstitut de Physique de 1 ‘Université, 2000 NeuchcItel, SwitzerlandReceived 18 April 1973The non-luminescent and spin-dependent disexcitation process observed in F-center pairs in alkalihalides at lowtemperature is explained by a covalent bond within the pair. Exchange effects give a negative contribution to thelattice potential energy. If the pair separation is small, local modes become unstable and spontaneous lattice distor-tions bring back the pair in its ground state.Alcali halide crystals with a high concentration of F- We consider a pair of F centers located at sites acenters show at low temperature a strong variation of and b (separation R). The first one is in its relaxed cx-the luminescent quantum yield under an applied static cited state and the second one in its ground state. Amagnetic field [1, 21 which allows optical detection of local vibrational mode (frequency w, amplitude qelectronic and nuclear magnetic resonances [3,4]. with <q2)~=~= I) mixes to the electronic state an-These phenomena are explained by interaction of pairs other one ~ ~, having an energy higher by 6. Up to theof neighbouring centers, in which the electronic disex- second order, the q dependent wave function and itscitation path (radiative or non-radiative) depends on energy take the formthe symmetry of the two-spin wave function. Accord-ing to an hypothesis put forward by Markham et a!. — ~- w~q~)— wq~1+.[5] and resumed by Luty [5] in order to explain thecorrelation observed between the F and the F’ band E =E0 — 6iv2q2 1-intensities, the electron of the excited member of a the ~Li~admixture being then w2. With this wave func-pair shifts non-radiatively to the other member to tion, the total energy of the pair is calculated accord-form an F’ center and then comes back to its ground ing to the Heitler-London scheme, while assuming thatstate by a tunnel effect. The necessity for the F’ the perturbation of the second center at b is negligiblecenter to be in a singlet spin state sets the condition (state va). The result is a function of the pair spin (50for this process, consistent withmost of the observa- or 1) and of q, with an exchange energy J0 forq0.tions. This mechanism, being spin dependent, should The term in w2q2, including the vibrational potentialrespond to EPR and if it is the only one, the relative energy, is relevant for the stability and takes the formvariation of the F’ concentration should be of the or-der of the relative luminescence variation (> 10—2). 1 d2E = + ~ 6+(.JJlIVbI~/l) —(~/OIVbI 1,1)0)But with well separated pairs [3], the F’ absorption 2 d(wq)2 4w2dependence on EPR is much smaller than 10~[7]. e2 e2~ }+(5—~~-)(J1—J0)This suggests another spin dependent mechanism fornon radiative disexcitation, which has nothing to dowith transient F’ centers. In this paper we develope J1 is the exchange energy for the a-center in a pure ~!e~state and Vb is the local potential at site b. The expres-qualitatively the following hypothesis: Provided asion in the parenthesis is independent of the total spinsuitable spin state, a covalent bond is formed between s and is certainlynegative because the electron cloudsthe two members of the pair; the exchange “softens” screen the electrostatic interaction between the ionscertain localized vibrational lattice modes, up to theand thereby soften the local mode, reducingits fre-point to make them unstable, so that even at zerotemperature the system shifts to its ground state only quency to w’ < w. The last, spin dependent term in-duces a softening only for the singlet state 50, andby tumbling down vibrational states. this can lead to an instability of the mode, i.e. a nega-391Volume 44A, number 6 PHYSICS LETTERS 16 July 1973ence of a neighbour within the critical distance, canbe depicted in a configuration diagram (fig. 1), for a- non softening mode A and a softening mode T. TheS=Qj44A former expresses the relacation between the groundJ state F0(ls) and a relaxed excited state F*(2s), and, the latter couples F*(2s) to a higher lying state e.g.B F*(2p).- - The instability of the T mode for the spin singletA produces a saddle-shaped energy surface, on whichthe system glides until it meets the energy surface ofFig. 1. Configuration diagram for the energy of the triplet the ground state (ABC). For the spin triplet, the ener-and singlet relaxed excited states and for the ground state gy surface has always a minimum, from which the(see text). ground state is reached either by a vertical radiativetransition (A’B’C) or through a highly excited vibra-tive frequency, provided the two following conditions tional state at high temperature (A’B”C). The effectare satisfied: of the neighbouring centre is todecrease the curvatureI ) ,j1 > ~ this should be the case since the higher of the energy surface preferentially for the singlet spinlying state 1i~extends farther in the lattice than the state, and this is enough to change the luminescentlower lying state ~ yield of the pair, in agreement with the observations.2) The local mode should couple strongly the two At short distance, the ground state might show a sec-states, so that the admixture is large: ondary potential well corresponding to the pair “F’w2 > hw’/2(J1 — J0). ±vacancy” into which the system can glide and getThese conditions are satisfied if the separation of trapped momentarily, until it reaches point C by tun-the pair is smaller than a critical valueR~.This param- nelling through the potential wall.eter has been estimated with properly scaled hydrogen-like wave functions, approximating the excited states We are indebted to Professor F. Bassani for valuable~o and ~i by 2s- and 2p-functions, respectively. They discussions and to the Swiss National Foundation forshould describe reasonably well the F center at large support of this work.distance. For the ground state, a ls-function can beused and the integrals can be calculated fromRoothaan’s formulae [9] ; an alternative way is to as- Referencessume a delta function, and the evaluation is thenstraightforward. In both cases, one finds a critical [1] F. Porret, F. Lüty, Phys. Lett. 26(1971)843.radius of about 30—40 A provided the admixture is [2] C. Jaccard et a!., Phys. Stat. Sol. (b) 50 (1972) 187.[3] Y. Ruedin et aI. Phys. Stat. Sol. (b) 54 (1972) 565, 55of the order of 0.1. This agrees with the model propos- (1973) 215.ed by Bogan and Fitchen [8]. The estimated critical [41PA. Schnegg, C. Jaccard and M. Aegerter, Phys. Lett.radius is within a factor of 2 or 3 of the value of 80 A 42A (1973) 369.obtained from the luminescent behaviour in a magnet- f5] J.J. Markham, R.T. Platt and l.L. Mador, Phys. Rev. 92ic field [2]. However according to a recent work by (1953) 957.161 F. LUty Halbleiterphysik, Vol. VI, 238 (1961) (Viehweg.F.S. Ham (private communication), the consideredBraunschweig).states are not purely electronic but vibronic, and tak- I~]P.A. Schnegg et a!., (to be published).ing this into account would give a better description [8] L.D. Bogan and D.B. Fitchen, Phys. Rev. B, 1 (1970)of the lattice with the electrons. 4122.The cycle of an optically excited center, in the pres- 191 C.C.J. Roothaan, J. Chem Phys. 19(1951)1445.392

Universaar

The non-luminescent and spin-dependent disexcitation process observed in F-center pairs in alkalihalides at low temperature is explained by a covalent bond within the pair. Exchange effects give a negative contribution to the lattice potential energy. If the pair separation is small, local modes become unstable and spontaneous lattice distor-tions bring back the pair in its ground state. Alcali halide crystals with a high concentration of F- We consider a pair of F centers located at sites a centers show at low temperature a strong variation of and b (separation R). The first one is in its relaxed cx-the luminescent quantum yield under an applied static cited state and the second one in its ground state. A magnetic field [1, 21 which allows optical detection of local vibrational mode (frequency w, amplitude q electronic and nuclear magnetic resonances [3,4]. with &lt;q2)~=~ = I) mixes to the electronic state an-These phenomena are explained by interaction of pairs other one ~ ~, having an energy higher by 6. Up to the of neighbouring centers, in which the electronic disex- second order, the q dependent wave function and its citation path (radiative or non-radiative) depends on energy take the form the symmetry of the two-spin wave function. Accord-ing to an hypothesis put forward by Markham et a!. — ~- w~q~) — wq~ 1+

C. Jaccard

M. Aegerter

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NON-LUMINESCENT DISEXCITATION OF F-CENTER PAIRS BY EXCHANGE-SOFTENED VIBRATIONAL MODES

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Non-luminescent disexcitation of F-center pairs by exchange-softened vibrational modes

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