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Nonequilibrium phonons in Cr3+-doped germanate glass
ELSEVIER
Physica B 219&220 (1996) 757-759
Nonequilibrium phonons in Cr3+-dopedgermanateglass P.A. van Walree a, A.F.M. Arts a, H.W. de Wijn a, *, A.A. Kaplyanskii b a Faeulty of Physics and Astronomy and Debye Research Institute, Utrecht University, P.O. Box 80.000, 3508 TA Utrecht, The Netherlands" b A.F. IQffe Physico-Technical Institute, Academy of Sciences, 194021 St. Petersbur.q, Russian Federation
Abstract
The optically induced phonon distribution in Cr3+-doped germanate glass is investigated after pulsed laser excitation. Via the anti-Stokes spectrum a nonequilibrium phonon distribution is observed, which is characterized by a marked overpopulation at higher frequencies, and persists over several milliseconds.
1. Introduction
In previous reports [1, 2], the phonon distribution in glasses was examined via the anti-Stokes spectrum following selective optical excitation within the inhomogeneously broadened 2E absorption band of Cr 3÷ dopant ions. The optically induced phonon occupation seemed to be markedly nonequilibrium at liquid helium temperatures. In particular at the high-frequency end of the phonon spectrum an overpopulation with reference to a unique equilibrium temperature was observed. The present experiments permit a more precise study of these deviations as a function of time, and point to an extreme duration of the return to equilibrium.
differ from site to site. The disorder furthermore causes the separation between the I~(2E) and 2A(2E) doublets of each Cr 3+ to differ from the next. The I~(2E) and 2A(2E) states in fact form a broad inhomogeneous electronic band. For a subset of Cr 3+ ions, therefore, optical excitation at a fixed frequency terminates in 2,g,(2E), and for another subset in I~(2E). For the former subset the excitation is followed by fast decay to I~(2E) under the emission of a phonon resonant with the local 2A(2E)-t~(2E) separation, giving rise to a Stokes emission band (Fig. 1 ). Conversely, anti-Stokes
/
"%
. 12.000
2. Electronic structure
Embedded in a crystalline host, Cr 3~ may act as a phonon detector [3]. Its properties have in particular been investigated for the case of 29 cm l phonons in ruby [4]. Recently, the implantation of Cr 3÷ in an amorphous material has led to the so-called phonon spectrometer, i.e., a system with the ability to detect a wide band of phonon frequencies [1, 2]. We consider the 4A2 ground quartet and the first excited I~(2E) and 2A(2E) Kramers doublets for a set of Cr 3+ ions in a disordered matrix. Local variations in the crystal field cause the distance from the 2E cubic parent state to 4A2 to * Corresponding author. 0921-4526/96/$15.00 @ 1996 Elsevier Science B.V. All rights reserved SSD1 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 8 7 6 - 4
13,000
U1 14,000
i
14,200
14,300
14,400
14,500
14,600
Emission frequency (crff t)
Fig. 1. The Stokes and anti-Stokes spectrum at an incident laser pulse energy of 0.8 mJ in a 200 ~tm focus. A spectrum over a wider range (inset) shows the broad 4T2 emission band. Note that the detection sensitivity drops sharply below 12 500 cm- I
758
P.A. van Walree et al./ Physica B 219&220 (1996) 75~759
luminescence out of 2,~(ZE) is observed after absorption of resonant phonons by the Cr 3+ subset that is optically excited into E(ZE). Radiative decay of the 2E levels is sufficiently slow to permit the observation of anti-Stokes processes for milliseconds after the excitation. Since the 4T2 absorption band overlaps the 2E band, excitation into 2E is accompanied by a strong 4T2 absorption [5]. Centers excited into 4T2 very rapidly relax toward equilibrium along the excited-state parabola, thereby releasing a large number of high-frequency phonons. These phonons are believed to contribute significantly to the temperature rise. The 4T2 levels experimentally show up via the associated broad emission band, stretching out over thousands of wave numbers below the ~E emission (inset in Fig. 1 ).
3.
Experimental
90.
o
,
,
o o
,
o Oo °
so : oOjooO~oOo0% ~
70]oOo ;2
,
,
Oo o % : ~ ° o
1.8 K
/
30
40
, o
o
,
o
--
o
,~o 020o0 ooo~oo
ooo: o,: o oo>O: oO° Oooo t
.~ 25
,
~^~c~o
60
50
70
80
Frequency
co o
~
oo ~ , ~ r ' o ~o~o
90
Oo q 0
a~o O~oo ooo o~
co oo
100
/
o o
110
120
(era 4 )
Fig. 2. The effective temperature versus the frequency as derived from a spectrum accumulated during the first 100 gs after excitation at ambient temperatures of 1.8 and 77 K. The incident laser pulse has an energy of 0.6 mJ in a 200 lam focus.
details
A GeO2 sample doped with 0.1 mol% Cr, measuring 6 × 2 × 2 mm 3 and polished to optical surface quality, was immersed in superfluid helium at 1.8 K. The Cr 3+ ions were excited at a fixed frequency of 14 400 cm-1 by use of a tunable pulsed dye laser, pumped by a frequency-doubled Q-switched Nd :YAG laser at a repetition rate of 52 Hz. The pulses had a duration of 7 ns, their bandwidth was 0 . 1 cm -~, and their energies ranged up to 1 mJ. The laser beam was directed along the longest axis of the sample and focused to a diameter of about 200 Itm. Standard photoncounting techniques following a double monochromator as frequency-selective element were employed to monitor the luminescence.
gate selecting only the first 100 Its of the luminescence. The initial "temperature" is seen to increase with increasing co. To follow the temporal dependence of Te~(~) at various co, the decay of the luminescence was measured. Apart from reduction of Teff(o) with time, /AS(CO) drops owing to the finite lifetime of 2E. The decay of 2E has been determined independently by measuring the decay of the central peak at 14400cm -~, and found to obey a stretched exponential exp[-(t/r)l*], with r = 0.35 + 0.01 ms and fl = 0,61 4- 0.01. Upon inserting z and fl as well as the initial temperatures Tefr(co,0) already arrived at in connection with Fig. 2, the development of T~fr(co)with time is deduced from
4.
IAS(~,t) __ exp[-hco/kn Teff( co, t ) ] /AS(CO,0) exp[-hco/kaTe~(co, 0)] exp[-(t/z)l~] "
Results
When an ensemble of two-level systems, such as E ( 2 E ) 2A(2E), is in thermal equilibrium, the anti-Stokes intensity scales with the upper population according to /as(CO) oc f(CO)exp(-hCO/k~T) ,
(2)
The results are presented in Fig. 3 for three values of co, viz., 30, 60, and 90cm -~. An initial decay is observed, which 25 [
,
,
.
--
(1) 9ff~ m l
in which f(CO) is the distribution of the E(2E)-2~,(~E) separations for a given energy of]~(2E) above 4A2. Spectra taken at 77 K indicate that f(CO) is faithfully represented by the intensity Is(CO) of the Stokes part of the spectrum, and that the prefactor in Eq. (1) is close to unity, more precisely 1.2. For the purpose of quantifying any nonequilibrium, it is useful to assign to each frequency co an effective temperature T~g(CO)by comparison of the anti-Stokes and Stokes intensities/As(CO) and Is(CO) according to Eq. ( 1). Confidence in this method of analysis is provided by additional spectra recorded at 77 K. Here, we indeed find Tear(co) = 77 K, independent of CO(Fig. 2). Note that in this case any heating by the laser pulse is small owing to the large specific heat at 77 K. The result at 1.8 K is shown in Fig. 2 for a time
o,,~g~o.,
o
% %o
o
I 10 0,0
' 0.5
' 1.0
1.5
2.0
T i m e (ms)
Fig. 3. The effective temperature at 30, 60, and 90 cm -~ , derived from the measured decay of the anti-Stokes intensity by use of Eq. (2).
P.A. van Walree et aL / Physica B 219&220 (1996) 757-759 is more prominent at higher frequencies. More importantly, however, the Te~(o~, t) for the selected ~o's do not converge on longer time scales, as one would expect for return to equilibrium. The initial decay observed in Fig. 3 dies out within the first few hundred microseconds. Its origin presumably is the decay of the 4T2 band, which is reasonably described by a stretched exponential with z = 20 Its and fi = 0.60 i 0.01. During this decay, the energy associated with return of the configuration coordinate to zero along the groundstate parabola is dumped into the phonon system in the form of high-frequency phonons. During their short lifetime, these high-frequency phonons presumably bring about Raman transitions between E(2E) and 2A(2E), which are more effective for higher frequencies. Before conclusions are drawn from the failure of Te~(o~, t) to converge to a single oJ-independent temperature, we investigate the effects of cooling of the illuminated cylinder at its surface. Cooling results in a radial distribution of temperatures, T(r, t), developing with t. Since the luminescence is equally collected from all parts of the illuminated cylinder, there results an apparent frequency dependence of Teer(~o,t), even in thermal equilibrium. In the spirit ofEq. ( 1 ), Te~(Oo,t) is then given by
exp[-ho)/kBT(r,t)lrdr.
(3)
To estimate T(r, t), we consider a cylinder of radius R and infinite length whose temperature is raised at t = 0 to a uniform value To, while the ambient temperature is kept zero. Classical diffusive heat conduction then leads to a radial temperature distribution developing with time [6] according to 2To ~-~ Jo(~,,r)
where J0 and Jl are Bessel functions of order 0 and 1, and ~, are the positive roots of J o O t R ) = 0. The rate of the heat flow is determined by the diffusivity •, which has been set to 2 x 10 7m 2 s - I so as to reproduce the slow decay of the overall temperature. We furthermore adopted the experimental R = 100btm, and To ,-~ 2 0 K in accordance with Fig. 3. The calculations show that the Tefr(o9,t) that would have been measured by luminescence in the case of thermal equilibrium indeed increase with frequency. At times of, say, 0.5ms, however, the calculated equilibrium increment in Te~(~o,t) is less than 2 K when going from 30 to 90 c m - t . This is far less than the effect of 5 K found in Fig. 3. It is noted that relaxing the strict condition that T(r,t) = 0 beyond r = R, or for that matter a somewhat nonuniform initial distribution, does not alter this conclusion.
Acknowledgements The work was supported by the Netherlands foundations FOM and NWO.
References
exp[-h~o/kB Te~(o), t )] = 2R -2
759
.
2 ..
T(r,t) = - - ~ ,~,~,J'(~" 2.., .J,~-((~-~.R) expt-K~,, t ) ,
(4)
[1] S.A. Basun, P. Deren, S.P. Feofilov, A.A. Kaplyanskii and W. Strek, J. Lumin. 45 (1990) 115. [2] A.A. Kaplyanskii, A.V. Akimov, S.A. Basun, S.P. Feofilov, E.S. Moskalenko, J. Ko6ka and J. Stuchlik, J. Lumin. 53 (1992) 7. [3] K.F. Renk and J. Deisenhofer, Phys. Rev. Lett. 26 (1971) 764. [4] M.J. van Dort, J.I. Dijkhuis and H.W. de Wijn, Phys. Rev. B 41 (1990) 8657 and references therein. [5] A. Lempicki, L. Andrews, S.J. Nettel, B.C. McCollum and E.I. Solomon, Phys. Rev. Lett. 44 (1980) 1234. [6] H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids (Oxford University Press, Oxford, 1959).
Physica B 219&220 (1996) 757-759
Nonequilibrium phonons in Cr3+-dopedgermanateglass P.A. van Walree a, A.F.M. Arts a, H.W. de Wijn a, *, A.A. Kaplyanskii b a Faeulty of Physics and Astronomy and Debye Research Institute, Utrecht University, P.O. Box 80.000, 3508 TA Utrecht, The Netherlands" b A.F. IQffe Physico-Technical Institute, Academy of Sciences, 194021 St. Petersbur.q, Russian Federation
Abstract
The optically induced phonon distribution in Cr3+-doped germanate glass is investigated after pulsed laser excitation. Via the anti-Stokes spectrum a nonequilibrium phonon distribution is observed, which is characterized by a marked overpopulation at higher frequencies, and persists over several milliseconds.
1. Introduction
In previous reports [1, 2], the phonon distribution in glasses was examined via the anti-Stokes spectrum following selective optical excitation within the inhomogeneously broadened 2E absorption band of Cr 3÷ dopant ions. The optically induced phonon occupation seemed to be markedly nonequilibrium at liquid helium temperatures. In particular at the high-frequency end of the phonon spectrum an overpopulation with reference to a unique equilibrium temperature was observed. The present experiments permit a more precise study of these deviations as a function of time, and point to an extreme duration of the return to equilibrium.
differ from site to site. The disorder furthermore causes the separation between the I~(2E) and 2A(2E) doublets of each Cr 3+ to differ from the next. The I~(2E) and 2A(2E) states in fact form a broad inhomogeneous electronic band. For a subset of Cr 3+ ions, therefore, optical excitation at a fixed frequency terminates in 2,g,(2E), and for another subset in I~(2E). For the former subset the excitation is followed by fast decay to I~(2E) under the emission of a phonon resonant with the local 2A(2E)-t~(2E) separation, giving rise to a Stokes emission band (Fig. 1 ). Conversely, anti-Stokes
/
"%
. 12.000
2. Electronic structure
Embedded in a crystalline host, Cr 3~ may act as a phonon detector [3]. Its properties have in particular been investigated for the case of 29 cm l phonons in ruby [4]. Recently, the implantation of Cr 3÷ in an amorphous material has led to the so-called phonon spectrometer, i.e., a system with the ability to detect a wide band of phonon frequencies [1, 2]. We consider the 4A2 ground quartet and the first excited I~(2E) and 2A(2E) Kramers doublets for a set of Cr 3+ ions in a disordered matrix. Local variations in the crystal field cause the distance from the 2E cubic parent state to 4A2 to * Corresponding author. 0921-4526/96/$15.00 @ 1996 Elsevier Science B.V. All rights reserved SSD1 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 8 7 6 - 4
13,000
U1 14,000
i
14,200
14,300
14,400
14,500
14,600
Emission frequency (crff t)
Fig. 1. The Stokes and anti-Stokes spectrum at an incident laser pulse energy of 0.8 mJ in a 200 ~tm focus. A spectrum over a wider range (inset) shows the broad 4T2 emission band. Note that the detection sensitivity drops sharply below 12 500 cm- I
758
P.A. van Walree et al./ Physica B 219&220 (1996) 75~759
luminescence out of 2,~(ZE) is observed after absorption of resonant phonons by the Cr 3+ subset that is optically excited into E(ZE). Radiative decay of the 2E levels is sufficiently slow to permit the observation of anti-Stokes processes for milliseconds after the excitation. Since the 4T2 absorption band overlaps the 2E band, excitation into 2E is accompanied by a strong 4T2 absorption [5]. Centers excited into 4T2 very rapidly relax toward equilibrium along the excited-state parabola, thereby releasing a large number of high-frequency phonons. These phonons are believed to contribute significantly to the temperature rise. The 4T2 levels experimentally show up via the associated broad emission band, stretching out over thousands of wave numbers below the ~E emission (inset in Fig. 1 ).
3.
Experimental
90.
o
,
,
o o
,
o Oo °
so : oOjooO~oOo0% ~
70]oOo ;2
,
,
Oo o % : ~ ° o
1.8 K
/
30
40
, o
o
,
o
--
o
,~o 020o0 ooo~oo
ooo: o,: o oo>O: oO° Oooo t
.~ 25
,
~^~c~o
60
50
70
80
Frequency
co o
~
oo ~ , ~ r ' o ~o~o
90
Oo q 0
a~o O~oo ooo o~
co oo
100
/
o o
110
120
(era 4 )
Fig. 2. The effective temperature versus the frequency as derived from a spectrum accumulated during the first 100 gs after excitation at ambient temperatures of 1.8 and 77 K. The incident laser pulse has an energy of 0.6 mJ in a 200 lam focus.
details
A GeO2 sample doped with 0.1 mol% Cr, measuring 6 × 2 × 2 mm 3 and polished to optical surface quality, was immersed in superfluid helium at 1.8 K. The Cr 3+ ions were excited at a fixed frequency of 14 400 cm-1 by use of a tunable pulsed dye laser, pumped by a frequency-doubled Q-switched Nd :YAG laser at a repetition rate of 52 Hz. The pulses had a duration of 7 ns, their bandwidth was 0 . 1 cm -~, and their energies ranged up to 1 mJ. The laser beam was directed along the longest axis of the sample and focused to a diameter of about 200 Itm. Standard photoncounting techniques following a double monochromator as frequency-selective element were employed to monitor the luminescence.
gate selecting only the first 100 Its of the luminescence. The initial "temperature" is seen to increase with increasing co. To follow the temporal dependence of Te~(~) at various co, the decay of the luminescence was measured. Apart from reduction of Teff(o) with time, /AS(CO) drops owing to the finite lifetime of 2E. The decay of 2E has been determined independently by measuring the decay of the central peak at 14400cm -~, and found to obey a stretched exponential exp[-(t/r)l*], with r = 0.35 + 0.01 ms and fl = 0,61 4- 0.01. Upon inserting z and fl as well as the initial temperatures Tefr(co,0) already arrived at in connection with Fig. 2, the development of T~fr(co)with time is deduced from
4.
IAS(~,t) __ exp[-hco/kn Teff( co, t ) ] /AS(CO,0) exp[-hco/kaTe~(co, 0)] exp[-(t/z)l~] "
Results
When an ensemble of two-level systems, such as E ( 2 E ) 2A(2E), is in thermal equilibrium, the anti-Stokes intensity scales with the upper population according to /as(CO) oc f(CO)exp(-hCO/k~T) ,
(2)
The results are presented in Fig. 3 for three values of co, viz., 30, 60, and 90cm -~. An initial decay is observed, which 25 [
,
,
.
--
(1) 9ff~ m l
in which f(CO) is the distribution of the E(2E)-2~,(~E) separations for a given energy of]~(2E) above 4A2. Spectra taken at 77 K indicate that f(CO) is faithfully represented by the intensity Is(CO) of the Stokes part of the spectrum, and that the prefactor in Eq. (1) is close to unity, more precisely 1.2. For the purpose of quantifying any nonequilibrium, it is useful to assign to each frequency co an effective temperature T~g(CO)by comparison of the anti-Stokes and Stokes intensities/As(CO) and Is(CO) according to Eq. ( 1). Confidence in this method of analysis is provided by additional spectra recorded at 77 K. Here, we indeed find Tear(co) = 77 K, independent of CO(Fig. 2). Note that in this case any heating by the laser pulse is small owing to the large specific heat at 77 K. The result at 1.8 K is shown in Fig. 2 for a time
o,,~g~o.,
o
% %o
o
I 10 0,0
' 0.5
' 1.0
1.5
2.0
T i m e (ms)
Fig. 3. The effective temperature at 30, 60, and 90 cm -~ , derived from the measured decay of the anti-Stokes intensity by use of Eq. (2).
P.A. van Walree et aL / Physica B 219&220 (1996) 757-759 is more prominent at higher frequencies. More importantly, however, the Te~(o~, t) for the selected ~o's do not converge on longer time scales, as one would expect for return to equilibrium. The initial decay observed in Fig. 3 dies out within the first few hundred microseconds. Its origin presumably is the decay of the 4T2 band, which is reasonably described by a stretched exponential with z = 20 Its and fi = 0.60 i 0.01. During this decay, the energy associated with return of the configuration coordinate to zero along the groundstate parabola is dumped into the phonon system in the form of high-frequency phonons. During their short lifetime, these high-frequency phonons presumably bring about Raman transitions between E(2E) and 2A(2E), which are more effective for higher frequencies. Before conclusions are drawn from the failure of Te~(o~, t) to converge to a single oJ-independent temperature, we investigate the effects of cooling of the illuminated cylinder at its surface. Cooling results in a radial distribution of temperatures, T(r, t), developing with t. Since the luminescence is equally collected from all parts of the illuminated cylinder, there results an apparent frequency dependence of Teer(~o,t), even in thermal equilibrium. In the spirit ofEq. ( 1 ), Te~(Oo,t) is then given by
exp[-ho)/kBT(r,t)lrdr.
(3)
To estimate T(r, t), we consider a cylinder of radius R and infinite length whose temperature is raised at t = 0 to a uniform value To, while the ambient temperature is kept zero. Classical diffusive heat conduction then leads to a radial temperature distribution developing with time [6] according to 2To ~-~ Jo(~,,r)
where J0 and Jl are Bessel functions of order 0 and 1, and ~, are the positive roots of J o O t R ) = 0. The rate of the heat flow is determined by the diffusivity •, which has been set to 2 x 10 7m 2 s - I so as to reproduce the slow decay of the overall temperature. We furthermore adopted the experimental R = 100btm, and To ,-~ 2 0 K in accordance with Fig. 3. The calculations show that the Tefr(o9,t) that would have been measured by luminescence in the case of thermal equilibrium indeed increase with frequency. At times of, say, 0.5ms, however, the calculated equilibrium increment in Te~(~o,t) is less than 2 K when going from 30 to 90 c m - t . This is far less than the effect of 5 K found in Fig. 3. It is noted that relaxing the strict condition that T(r,t) = 0 beyond r = R, or for that matter a somewhat nonuniform initial distribution, does not alter this conclusion.
Acknowledgements The work was supported by the Netherlands foundations FOM and NWO.
References
exp[-h~o/kB Te~(o), t )] = 2R -2
759
.
2 ..
T(r,t) = - - ~ ,~,~,J'(~" 2.., .J,~-((~-~.R) expt-K~,, t ) ,
(4)
[1] S.A. Basun, P. Deren, S.P. Feofilov, A.A. Kaplyanskii and W. Strek, J. Lumin. 45 (1990) 115. [2] A.A. Kaplyanskii, A.V. Akimov, S.A. Basun, S.P. Feofilov, E.S. Moskalenko, J. Ko6ka and J. Stuchlik, J. Lumin. 53 (1992) 7. [3] K.F. Renk and J. Deisenhofer, Phys. Rev. Lett. 26 (1971) 764. [4] M.J. van Dort, J.I. Dijkhuis and H.W. de Wijn, Phys. Rev. B 41 (1990) 8657 and references therein. [5] A. Lempicki, L. Andrews, S.J. Nettel, B.C. McCollum and E.I. Solomon, Phys. Rev. Lett. 44 (1980) 1234. [6] H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids (Oxford University Press, Oxford, 1959).