Two-photon spectroscopy of Ag+ ions in alkali chlorides

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Two-photon spectroscopy of Ag+ ions in alkali chlorides

B. Moine, C. Pedrini

To cite this version:

B. Moine, C. Pedrini. Two-photon spectroscopy of Ag+ ions in alkali chlorides. Journal de Physique, 1984, 45 (9), pp.1491-1496. �10.1051/jphys:019840045090149100�. �jpa-00209888�

Two-photon spectroscopy ^of Ag+ ^ions

in alkali chlorides

B. Moine and C. Pedrini

E.R.A. 1003-C.N.R.S., Université Claude Bernard-Lyon I, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne, ^France

(Reçu ^{le 3} fivrier ^1984, accepté ^{le 9 mai} 1984)

Résumé. 2014 La variation azimutale de la probabilité d’absorption simultanée de deux photons polarisés ^linéaire-

ment permet de déterminer de façon directe la symétrie des états excités de l’ion impureté Ag+ dans les cristaux NaCl et KCl. Les résultats expérimentaux ^{sont en} parfait ^{accord avec ceux des calculs} théoriques. ^En particulier,

ils confirment l’existence d’un effet Jahn-Teller sur le niveau 1Eg.

Abstract. ²⁰¹⁴ By polarization dependence ^of two-photon absorption, ^{one can} straightforwardly determine the symmetry ^of absorbing ^{levels of the} Ag+ ^{ion embedded in NaCl and KCl} crystals. Experimental ^{results are in}

very good agreement ^with theoretical calculations. The existence of the Jahn-Teller effect on 1Eg ^{state is experimen-}

tally proved.

Classification Physics ^Abstracts

78.20 ^- 78.55F

1. Introduction.

During ^recent years the absorption ^bands of Ag+ [1, 2] impurity ion in the alkali halide crystals ^{have been ’} carefully studied These bands are ascribed to the

parity forbidden electronic transitions (4d)10 -+ (4d)’

(5s) ^allowed by ^an interaction with odd phonons.

Many theoretical approaches ^{have been made :} semi-empirical crystal ^field [3] and molecular orbital calculations [4-5] ^{have been} applied ^{to the d9s and} d9p configurations ^of Ag+ ^{and Cu+. Most} recently,

the multiple scattering ^{Xa method} has been used to describe the Ag+ impurity ^{centre in NaCl.}

Up ^to now, experimental ^{results were} essentially dealing ^with one-photon absorption spectra. ^{In this}

case, the symmetry of the various absorption ^bands

of an impurity ^{ion in a} cubic site cannot be investigat-

ed In this work, ^we present experimental ^{results of} two-photon absorption ^{of NaCl :} Ag+ ^{and KCl :} Ag+.

This technique presents ^two fields of interest : first, ⁱⁿ

a centrosymmetric system g - g transitions are allow- ed by two-photon absorption ^and second, by polari-

zation dependence ^{of two} photon absorption, ^one

can straightforwardly determine the symmetry ^of

absorbing ^levels.

2. Theory ^of two-photon absorption.

When we study ^{the ion} photon interaction we usually expand ^the perturbation theory only ^{to first order.}

It is the ^« one-photon ^» spectroscopy. ^{If we} expand

the calculations to higher orders, ^{we find a term of}

nth order which shows the possibility ^{of « n »} pho-

ton processes. ^{Here we} limit our study ^{to n = 2.}

The transition rate corrected to second order is thus :

Where JCI is the Hamiltonian of ion-photon ^inter- action,

i > is the initial state of ion-photon system ^and f> ^{is the final state of} ion-photon system.

The second-order term represents ^a transition where the system changes indirectly ^from state i > ^{to state} f > ^{via one} intermediate state. The only ^energy-

conservation requirement ^{is that} Wi ^must equal (Up In general, the intermediate states do not have the

same energy ^as the initial state, and for each inter- mediate state there is an energy denominator 1i(Wi - WI) ^{which reduces the} corresponding contribution

by ^{an amount} inversely proportional ^{to the energy}

mismatch. In other words, ^the two-photon absorp-

tion .will be large if there is an intermediate state whose energy is close ^to 1iWi.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019840045090149100

1492

We make the electric-dipole approximation ^and

we consider two beams incident on the crystal, ^one

of energy ficol ^with polarization 81 ⁼ (11, ml, nl)

and the other of _energy nro2 ^with polarization 82 ⁼ (I2, m2, n2). ^{In this case the} two-photon absorp-

tion operator ^is proportional ^{to :}

In this matrix element the first term represents ^an absorption process where the w2 photon ^{is first}

absorbed and then the w1 photon ^is absorbed, ^and

the second term represents the process in the ^reverse order. In contrast to single-photon electric-dipole absorption where the final atomic state must have

opposite parity ^{to the} ground ^{state, we see that in} two-photon absorption ^the accessible statues f >

must have the same parity ^as the initial ground ^state.

In addition, it is clear that the magnitude of the matrix element depends ^{on the} directions of the polariza-

tion vectors E1 and E2.

The polarization dependence ^{of the rate of two-} photon absorption has been calculated for all 32

crystallographic point groups by Bader and Gold [6]

with the method used by ^{Inoue and} Toyozawa [7].

For Oh symmetry ^{site and two identical} photons pro-

pagating along ^the [001] axis ^the angular dependence

functions for an A1g -+ Eg transition and for an

A1g -+ T2g transition are respectively :

where 0 represents ^the angle between the electric vector and the [100] ^axis.

It should be noted that the theory ^of two-photon

transitions has not been extended to include vibronic-

coupling ^{effects which are} effective with phonons ^of

even (Jahn-Teller effect) ^{and odd} symmetries. Taking

these effects into account should lead to quite ^com- plex expressions ^of two-photon transition probabili- ties, ^{but should not} modify ^the angular dependence

functions.

3. Experimental

Figure ¹ displays ^the experimental set-up ^{for the two-} photon absorption study. ^The Quantel ^{TDL YAG}

laser pumped dye ^laser system produces the visible

beam, ^{which is} frequency ^doubled by appropriate crystals (D.C.) ^{or mixed with} fundamental (1.06 ppm)

beam of the YAG laser by ^other crystals (M.C.). ^In

the case of mixing ^or doubling, ^{there is residual}

YAG fundamental and some of fundamental and

Fig. ^{1. -} Experimental set-up : ^{D.C. =} Doubling Crystal;

M.C. ⁼ Mixing Crystal; ^{O.T. =} Optical Trigger; ^{P.B. =}

Pellin-Broca prism ; ^{I. = Iris ; B.S. = Beam} Splitter ;

T. ⁼ Thermopile; ^{B.C. = Babinet} compensator; ^{L. =} Lens; ^{S. =} Sample; ^{C. =} Liquid ^helium Cryostat; ^{F. =} Filter; ^{P.M.T. =} Photomultiplier ^{Tube; P.S. = Power} Supply; ^{B.T. = Boxcar} Integrator; ^{0. =} Oscilloscope;

R. = Recorder.

doubled dye ^{in addition to the desired} wavelength

in the output beam. Isolation of this wavelength ^can

be accomplished by ^{means of a} Pellin-Broca prism

which spatially separates ^the beams of different

wavelengths. ^{A screen} (not ^{shown on} figure 1) ^then

blocks off all unwanted beams.

A small percentage ^{of the laser} photons is reflected

by ^a quartz ^made plate ^{used as a beam} splitter (B.S.)

and directed into a thermopile (T.) ^{detector. This}

beam splitter ^{is turned close to the} perpendicular

direction of the beam in order to reduce its depolarizing

effect to the minimum. Babinet compensator (B.C.)

is inserted after (B.S.) ^{and used as a} A/2 plate ^{for the}

selected wavelength ^{to rotate the} plane ^of polarization

of the laser beam. A lens (L1) ^{is used to focus the} light ^The sample (S.) ^is placed ^{in a} cryostat allowing

to work in the temperature range 1.5-300 K. The lens (L2) collects the fluorescence from the crystal

and a solar-blind filter is used to select against ^the exciting light An EMI 6256 blue sensitive photo- multiplier ^tube (P.M.T.) detects the fluorescence.

The signal is fed into a PAR Model 160 boxcar

integrator (B.I.) and visualized by ^a Tektronix 7603

oscilloscope. ^The optical trigger (O.T.) ^{utilizes a}

small amount of YAG laser light ^to produce ^an

electrical pulse ^{from a} photodiode. ^The signals

from (B.I.) ^and (T.) ^are simultaneously plugged ^into

a strip-chart ^recorder.

Measurements of luminescence excitation spectra

were made at LURE (University ^of Orsay) using

ACO synchrotron ^{radiation as a} light source, and a

homemade monochromator.

The Ag+ doped ^{NaCl and KCI} crystals ^were

grown in our laboratory by ^{a standard} Bridgman technique. The concentration of silver in the crystals

used in this study ^{is about 100} ppm for NaCl and about 40 _ppm for KCI.

4. Results and discussion.

The excitation spectra for the U.V. emission bands

are shown in figures ² and 3 for NaCI : Ag+ ^and

KCI : Ag+ respectively ^{at room and} liquid ^helium temperature. ^{It is} clearly ^seen that in the two cases

the overlapping of different bands is too much impor-

tant at room temperature ^{in order to} separate ^and identify them. On the other hand, all the results of observation at liquid ^helium temperature ^{of the}

« A _», « B _», « D _», « F » and ^« G » bands _{agree very} well with those previously reported [2]. Considering

Fig. ^{2. -} Excitation spectra ^of NaCI : Ag+ (100 ppm).

Two-photon polarization studies of figure ^{5 done at wave-} lengths ^indicated by ^arrows.

Fig. ^{3. -} Excitation spectra ^{of KCI :} Ag+ (40 ppm). ^Two- photon polarization ^{studies of} Fig. ^{6 done at} wavelengths

indicated by ^arrows.

this fact, ^{we have done all the} two-photon experiments

at low temperature (T ~ ¹⁰ K) except for the « A » and ^« B » bands of NaCI : Ag+. ^{Indeed in this case}

the resolution of the two bands is not better at liquid

helium temperature ^{than at room} temperature ^and the absorption intensities ^are much weaker at low temperature. ^{To work at T = 10} K, ^{we were} obliged

to focuse the full laser _power which tended to badly pit ^the surface of the crystal. This caused defocusing

of the light ^{and a loss of} signal intensity ^{in a few}

seconds. So, for these two bands ^we have studied the two-photon polarization characteristics only ^at

room temperature.

In order to characterize two-photon absorption

processes, ^we have recorded the laser power depen-

dence of fluorescence intensity. ^The quadratic ^varia-

tion characteristic of two photon absorption ^is

shown on figure ^{4. This} experiment ^{has been done for}

several wavelengths, ^{but we} present only ^{one case.}

In each _case, we worked with two identical photons

and we fixed the laser at five wavelengths, ^{while we}

rotated the electric vector 180°. For the ^« G » bands, respectively ^{at À. = 1700 A in NaCI :} Ag+ ^{and at}

À. ⁼ 1775 A in KCl : Ag+ ^{we did not detect two-} photon absorption. The fact that these absorption

bands are two-photon ^forbidden transitions confirms the assumption ^of single-photon ^allowed transitions,

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Fig. ^{4. -} Quadratic laser power dependence ^{of fluores-}

cence intensity.

according ^{to the} high ^{value and the} temperature dependence of the oscillator strengths ( N 0.5) ^obtained

from absorption spectra [2]. ^{It should be remarked}

that the strong intensity of the G band relative to those of the other bands does not appear in the excitation spectra. ^The decrease in excitation effi-

ciency ^at high energy is ^a well-known phenomenon

in solids and the generally accepted explanation ^is

that non-radiative surface recombination becomes dominant as the absorption coefficient increases and the exciting light ^{is absorbed} closer in the sample

surface.

For KCI : Ag+ ^we fixed the laser wavelength respec-

tively ^{at 3 850} A (2 ^x 1 925) ^{for the « F »} band, 4140 A (2 ^x 2 070) ^{for the « D »} band, 4 400 A (2 ^{x 2} 200) ^{for the« B » band and 4 540} A (2 ^{x 2} 270)

for the « A » band The results are shown on figure ^6.

For NaCI : Ag+ ^{the laser} wavelengths ^{were 3 550} A,

3 850 A, ^{4 200 A and 4 360 A for the bands « F »,}

« D _», « B _», ^« A _», respectively. The results are shown

on figure ^5.

We know that, ⁱⁿ Oh symmetry, d10 configuration corresponds ^to A1g ^{symmetry state, and eight states}

are associated ^{with the excited} configuration ^d9 s : lEg, iT2g, 3Eg(T1g, T2g) ^and 3T2g(A2g, Eg, Tig, T2g). ^So,

we are essentially concerned with A1g -+ Eg ^and A1g -+ T2g transitions. By fitting ^{the data to a linear}

combination of Eqs. (1) ^and (2), ^{we can} determine the fraction of Eg ^or T2g ^{character at the} given wavelength.

Indeed, ^{we can} write the polarization dependence ^of

the transition probability ^{as :}

and define

The results are gathered ^{in table I.}

As table I shows, ^the similarity of results for NaCl and KCI crystals ^is especially striking. ^{We also}

note that they ^{are in} very good agreement ^with those of S. A. Payne [8]. ^{Let us focus our attention}

first on the A + B bands. In an early effort, ^Froh-

lich [9] ^and coworkers used a ruby ^{laser to show the} Eg ^symmetry of the A band of KCl : Ag+, ^{but their} investigation ^{was limited to a} single wavelength.

Here, ^{we have the} experimental proof ^{of the} assignment

of A + B bands to the 1 A1g -+ ’Eg transition. In a

recent paper [10] ^we have discussed the existence of

Fig. ^{5. -} Polarization dependence ^of two-photon signal ^{of NaCI :} Ag+ : ^ooo experiment; ^- calculated. Propagation

vector [001] ; 0 ^{measured from} [100] (in degrees).

Fig. ^{6. -} Polarization dependence ^of two-photon signal ^{of KCI :} Ag+ : ^ooo experiment ; ^- calculated. Propagation

vector [001] ; 8 ^{measured from} [100] (in degrees).

Table I. ^- Energy ^state symmetries of ^{NaCl :} Ag+

and KCI : Ag+

(*) ^Room temperature.

the Jahn-Teller effect of the 1 A1g -+ 1 Eg ^absorption

of NaCl : Ag+ ^{as was done} by ^{S. A.} Payne ^{in the}

case of NaF : Cu+ [11]. ^{The case to treat was the} simplest ^{one of an} octahedrally coordinated Cu+ ion with a doubly degenerate Eg ^{excited state. Among the}

15 normal modes of the octahedron, only ^the doubly degenerate _eg distortion can split ^the Eg ^{term in first}

order, ^so that the Jahn-Teller interaction to study ^was

that of an Eg electronic level with ^an eg vibrational mode. Evidence for the Jahn-Teller effect was revealed

by ^a study ^{of the} temperature dependence ^{of the} magnitude ^{of the observed} splitting, AE, ^{of the} 1 Eg

excited state. Therefore, ^{A and B bands are} transitions to the two components of the Jahn-Teller distorted excited state.

The spectra ^{of Cu+ in alkali halides are much} simpler than those of Ag+ ^{in the same} systems. ^For example, ^{NaCl : Cu + exhibits two bands at helium} temperature while NaCl : Ag+ shows five. We know that this difference is due. to the large spin-orbit coupling ^of Ag+ causing considerable mixing ^{of the} singlet ^{states with the} triplet ^states. Spin ^forbidden

transitions are made partially allowed and experi- mentally observable in the Ag+ systems. ^{It is the}

case of D band which is more than 80 % T2g. ^This

result confirms the assignment ^{of D band to the} absorption ^{of the} triplet ^state 3T2g(T2g) ^{for which}

the calculations have shown this triplet ^{state to}

have 30 % singlet character in NaCl. It is also gratifying

to find near 90 % T2g character for the F bands which are assigned ^{to the} singlet IT 2g absorption.

In conclusion, ^{we used} two-photon spectroscopy ^as

a powerful ^{tool to} clarify ^{the U.V.} spectra of Ag+

impurity ⁱⁿ alkali halide host crystals. ^The polari-

zation dependence ^of two-photon transition allowed

us to identify Eg ^and T2g ^state symmetries ^{in NaCl}

and KCI. The comparison ^of theory ^and experiment

has enabled us to clearly assign ^{the bands observed}

in the absorption spectra ^to the transition between the 4d1° ground ^{state and the} multiplets ^{of the} spin

orbit split ^{4d9 5s excited state.} The presence of ^a Jahn-Teller effect on then lA1g -+ lEg ^{bands was}

experimentally proved

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References

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