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Phonon echoes in a dysprosium-doped glass
Solid State Communications, Printed in Great Britain.
Vol. 80, No. 11, pp. 961-963, 1991.
PHONON ECHOES IN A DYSPROSIUM-DOPED
0038-1098/91 $3.00 + .OO Pergamon Press plc
GLASS
N. Vernier and G. Bellessa Laboratoire
de Physique des solides *, Bdtiment 510, Universite Paris-Sud, 91405 Orsay, France (Received 16 July 1991; in revised form 11 September 1991 by J. Jo,frin)
Spontaneous phonon echoes in dysprosium-doped glasses have been studied. A non-exponential decay of the echo is reported. It is explained by assuming the existence of tunneling states with very short relaxation times which attenuate strongly the phonon echo generated by the standard tunneling states. This behaviour is assigned to the Kramers ions which interact strongly with some tunneling states. The results of a hole-burning experiment are reported and the effect of a magnetic field is also considered.
THE ACOUSTIC properties of glasses at low temperature are well explained by assuming an interaction of the acoustic waves with tunneling systems (TS) [l-3]. The effect of magnetic ions upon TS has been approached in two ways: glasses containing dilute magnetic ions [4], and spin glasses [S]. In the two cases, there was no evidence of the existence of some magnetic TS. Recently, an effect of the magnetic field on the sound velocity variation in a dysprosium-doped glass has been reported [6]. This effect has been ascribed to magnetic TS which are the Kramers ions whose local anisotropy axis is almost perpendicular to the local magnetic field. To explain the experimental results, it was necessary to assume the existence of TS with very short relaxation times [6]. However, the sound velocity measurements do not allow a direct determination of these ones. On the other hand, the phonon echoes are a powerful tool to study the relaxation rates of TS in glasses [7]. It is a purpose of this communication to report on a phonon echo experiment and then on the relaxation rates in a dilute Kramer+ion glass. Some results of a hole-burning experiment are also reported and the effect of the magnetic field is considered. The chemical composition of the glass was (Dy,0,),(LazG3)o.194-x(Si02)0.579(Al~G~)~.~~~. Several concentrations of Dy between 1.5 and 1Oat % were studied. At the highest concentration, there was no more non-linear effect up to 900MHz (neither phonons echoes nor saturation effect). The phonon echoes appear clearly for x < 0.06 (3 at % Dy3+) and the saturation recovery for x < 0.13 (7at % Dy3+). The sample was cooled down to 12 mK in a He3 -He4 * Associated with the Recherche Scientifique.
Centre
National
de
la 961
dilution refrigerator. The acoustic waves were generated by X-cut quartz transducers. The magnetic field was obtained from a superconducting magnet. In Fig. 1, we have plotted the amplitude of the spontaneous echo as a function of the delay r,2 between the two pulses for two magnetic field values. The pulse width is 50ns, the acoustic frequency is 650 MHz and the temperature is 12 mK. We have also plotted the results obtained in the sample without any Dy3+ (x = 0). We note first that the decay is no longer exponential, as soon as Dy is present in the sample. When the magnetic field is applied, as the two curves can be deduced from each other by translation, the only effect seems to be an increase of the amplitude of the echo. We have studied this variation more specifically. The results are shown in Fig. 2. We have chosen a short value of z,~, so that we have almost the asymptotic value corresponding to rj2 = 0. It can be seen that the amplitude rises slowly with the field up to 50 kOe. We will first explain our unusual non-exponential decay of the spontaneous phonon echo as a function of 712. Though spectral diffusion predicts an echo decay of the form exp (- mz:,) [8], previous experiments indicate that this one is rather exponential [4,7, 91. To explain our result, we assume the existence of two TS groups: the first one contains the standard TS and the second one contains the TS which are strongly coupled to the Dy3+ ions and which have very short relaxation times [6]. Hence, these ones do not give rise to a phonon echo (because the phase memory is very short) but they attenuate the phonon echo generated by the TS of the first group (due to the usual coupling between the TS and the acoustic wave). They lower its amplitude by a factor exp (- aAn) where An is the population difference between the two energy levels of
PHONON
11
0
5
ECHOES IN A DYSPROSIUM-DOPED
10
-‘.4t
I
15
20
Fig. 1. Amplitude of the spontaneous phonon echo as a function of the delay rIZ between the two pulses for two values of the magnetic field, in the sample containing 1.5at % of dysprosium. The pulse width is 50 ns, the acoustic frequency is 650 MHz and the temperature 12 mK. Circles are the experimental points in zero magnetic field and crosses are those at 50 kOe. The solid lines are the curves obtained using equation (5) with the best fit parameters. Stars are the experimental points for the sample without dysprosium. The pulse width is 50 ns, the acoustic frequency is 700 MHz and the temperature is 14mK. the TS of the second group saturated by the two exciting pulses. The equilibrium recovery of An depends on the time t elapsed since the passage of the second pulse according to: An,
jexp (-t/T,)g(T,)dT,
1 (
, >
(1)
where An, is the equilibrium value and g(T,) is the density of states of the TS of the second group. The x
50 Y
i
340
Vol. 8’0, No. 11
360
360
400
Frequency (MHz)
2712OIS)
An =
GLASS
x
Fig. 3. Attenuation variation of a probing pulse at different frequencies as a saturating pulse at 350 MHz is sent in the sample. The Dy3+ concentration is 6.7 at %. Circles are the experimental points in zero magnetic field and crosses are those at 50 kOe. The solid lines are the fits with the best parameters. In zero magnetic field, the fit has been done with a Gaussian line. At 50 kOe, the sum of a Gaussian and a Lorentzian line is used. usual distribution g(T,) obtained for the TS (see [3]) cannot be applied here: the relaxation rates are much greater than the ones found in the sample containing no Dy 3+ [IO]. So a new mechanism much more efficient than the direct one-phonon process must be involved. This mechanism is not explained yet, and we cannot evaluate the theoretical distribution g( T, ). However, it seems reasonable to have g( T, ) decreasing when T, is increasing. We have obtained a good agreement with our experimental results by taking a hyperbolic distribution similar to that used for the standard TS: g(T,)
=
l/T,
for Tj B T,min
r g(T,)
=
0
for Tl < T,.,in’
(2)
Our experiments extend from 7,? = 0.2 ps to 10 ps. To take into account the very short relaxation times, we suppose: T,,,,,in e 0.2~s.
(3)
Then, the integral in equation (I) can be evaluated analytically and An takes the form: An = o
I
0
10
20
30
40
1
60
Magnetic field (kOe)
Fig. 2. Amplitude of the spontaneous echo as a function of the magnetic field in the sample containing 1.5at % of dysprosium. The pulse width is 50ns and T,* is 200ns. The acoustic frequency is 650MHz and the temperature is 12mK.
(l/a){-
Y + D ln (r,,)},
(4)
where y and p are two constant parameters. Hence, the attenuation factor of the phonon echo is exp (- D In (7,*)) and the final form of the echo decay is: A =
Ah exp (-27,*/T;
- /? ln
(T,,)),
(5)
whereT; is the dephasing time and Ai = A, exp (y). Using equation (5), we can fit very well the experimental results (Fig. 1). The dephasing times giving the best
Vol. 80, No. 11
PHONON ECHOES IN A DYSPROSIUM-DOPED
fits are 10 and 25 ps for 0 and 50 kOe, respectively. For the sample containing no Dy3+ , T; = 6 ps (Fig. 1). The dephasing times are of the same order of magnitude as in fused silica at the same temperature [4]. Presently, we cannot explain the so short dephasing time obtained in the sample containing no dysprosium. Indeed, we have verified that Tl,minwas in this last sample larger by at least one order of magnitude than in the Dy-doped samples [lo]. Lastly, it must be pointed out that the field dependence of the echo amplitude (Fig. 2) is not due to a trivial attenuation effect. This has been established by doing a saturation recovery experiment (a strong saturation pulse is sent in the sample and the attenuation of a small probing pulse is then measured as a function of the delay between the two pulses) where it has been shown that the attenuation of the probing pulse did not depend on the magnetic field for the same saturating pulse. This effect which exists whatever the nature of the ions (Kramers or not Kramers) is not yet explained [4]. An interesting information about the TS involved is provided by a hole-burning experiment. The resulting curves are shown in Fig. 3. The saturating pulse was at a fixed frequency (350MHz). The probing pulse was emitted after one round trip of the saturating one. Its electromagnetic power was adapted for each frequency to keep constant the effective acoustic power. Its attenuation was measured with and without the saturating one. In zero magnetic field, the line is Gaussian. When the magnetic field is applied, the Gaussian background remains, and a Lorentzian line appears superimposed. These curves are not obvious to explain. The width of the Lorentzian line is probably not intrinsic because, due to the saturating pulse, the line broadening depends on JIJc, which is not small (where J is the acoustic power of the saturating pulse and Jc the critical power) [ 111.Our evaluation of Jc leads to a linewidth due solely to the power of the order of 5MHz and the width of the experimental Lorentzian line is 8 MHz. Hence, this linewidth can-
GLASS
963
not be considered as a measurement of some Tz. However, the fact that two lines appear in the presence of a magnetic field confirms the assumption that there are two species of TS, which evolve differently with respect to the magnetic field. In conclusion, we have studied the spontaneous phonon echoes in glasses doped with Dy3+ ions. Their non-exponential behaviour is well explained by assuming the existence of a species of very fast relaxing TS, in addition to the standard TS. That is a new evidence for the existence of such entities in a glass containing magnetic Kramers ions [6]. Lastly, a holeburning experiment has revealed the existence of two lines as a magnetic field is set up. Further experiments with a better sensitivity are needed to go further in the explanation of this effect and to clarify the coupling between TS and Kramers ions. Acknowledgement
- The authors are indebted J. Godard who prepared the samples.
to
REFERENCES 1.
P.W. Anderson,
2. 3.
Philos. Mug. 25, 1 (1972). W.A. Phillips, J. Low Temp. Phys. 7,35 1 (1972). For a review, see W.A. Phillips, Rep. Prog. Phys.
4. 6. 7.
B. Halperin & C.M. Varma,
50, 1657 (1987). F. Lerbet & G. Bellessa, J. Phys. (France) 49, 1179 (1988). N. Vernier & G. Bellessa, Europhys. Lett. 14,349
(1991).
B. Golding & J.E. Graebner, Phys. Rev. Left. 37,
852 (1976).
8.
J.L. Black & B.I. Halperin, Phys. Rev. B16,2879
9.
L. Bernard, L. PichC, G. Schumacher & J. Joffrin, J. Low Temp. Phys. 35, 411 (1979). Saturation recovery displays relaxation times inferior to 10~s in the 1.5% Dy sample. In the sample containing no Dy, T,,,i” (E = 700 MHz) was about 100 ps at 12 mK. L. Allen & J.H. Eberly, Optical Resonance and Two-Level Atoms, Wiley, New York (1975).
10.
11.
(1977).
Vol. 80, No. 11, pp. 961-963, 1991.
PHONON ECHOES IN A DYSPROSIUM-DOPED
0038-1098/91 $3.00 + .OO Pergamon Press plc
GLASS
N. Vernier and G. Bellessa Laboratoire
de Physique des solides *, Bdtiment 510, Universite Paris-Sud, 91405 Orsay, France (Received 16 July 1991; in revised form 11 September 1991 by J. Jo,frin)
Spontaneous phonon echoes in dysprosium-doped glasses have been studied. A non-exponential decay of the echo is reported. It is explained by assuming the existence of tunneling states with very short relaxation times which attenuate strongly the phonon echo generated by the standard tunneling states. This behaviour is assigned to the Kramers ions which interact strongly with some tunneling states. The results of a hole-burning experiment are reported and the effect of a magnetic field is also considered.
THE ACOUSTIC properties of glasses at low temperature are well explained by assuming an interaction of the acoustic waves with tunneling systems (TS) [l-3]. The effect of magnetic ions upon TS has been approached in two ways: glasses containing dilute magnetic ions [4], and spin glasses [S]. In the two cases, there was no evidence of the existence of some magnetic TS. Recently, an effect of the magnetic field on the sound velocity variation in a dysprosium-doped glass has been reported [6]. This effect has been ascribed to magnetic TS which are the Kramers ions whose local anisotropy axis is almost perpendicular to the local magnetic field. To explain the experimental results, it was necessary to assume the existence of TS with very short relaxation times [6]. However, the sound velocity measurements do not allow a direct determination of these ones. On the other hand, the phonon echoes are a powerful tool to study the relaxation rates of TS in glasses [7]. It is a purpose of this communication to report on a phonon echo experiment and then on the relaxation rates in a dilute Kramer+ion glass. Some results of a hole-burning experiment are also reported and the effect of the magnetic field is considered. The chemical composition of the glass was (Dy,0,),(LazG3)o.194-x(Si02)0.579(Al~G~)~.~~~. Several concentrations of Dy between 1.5 and 1Oat % were studied. At the highest concentration, there was no more non-linear effect up to 900MHz (neither phonons echoes nor saturation effect). The phonon echoes appear clearly for x < 0.06 (3 at % Dy3+) and the saturation recovery for x < 0.13 (7at % Dy3+). The sample was cooled down to 12 mK in a He3 -He4 * Associated with the Recherche Scientifique.
Centre
National
de
la 961
dilution refrigerator. The acoustic waves were generated by X-cut quartz transducers. The magnetic field was obtained from a superconducting magnet. In Fig. 1, we have plotted the amplitude of the spontaneous echo as a function of the delay r,2 between the two pulses for two magnetic field values. The pulse width is 50ns, the acoustic frequency is 650 MHz and the temperature is 12 mK. We have also plotted the results obtained in the sample without any Dy3+ (x = 0). We note first that the decay is no longer exponential, as soon as Dy is present in the sample. When the magnetic field is applied, as the two curves can be deduced from each other by translation, the only effect seems to be an increase of the amplitude of the echo. We have studied this variation more specifically. The results are shown in Fig. 2. We have chosen a short value of z,~, so that we have almost the asymptotic value corresponding to rj2 = 0. It can be seen that the amplitude rises slowly with the field up to 50 kOe. We will first explain our unusual non-exponential decay of the spontaneous phonon echo as a function of 712. Though spectral diffusion predicts an echo decay of the form exp (- mz:,) [8], previous experiments indicate that this one is rather exponential [4,7, 91. To explain our result, we assume the existence of two TS groups: the first one contains the standard TS and the second one contains the TS which are strongly coupled to the Dy3+ ions and which have very short relaxation times [6]. Hence, these ones do not give rise to a phonon echo (because the phase memory is very short) but they attenuate the phonon echo generated by the TS of the first group (due to the usual coupling between the TS and the acoustic wave). They lower its amplitude by a factor exp (- aAn) where An is the population difference between the two energy levels of
PHONON
11
0
5
ECHOES IN A DYSPROSIUM-DOPED
10
-‘.4t
I
15
20
Fig. 1. Amplitude of the spontaneous phonon echo as a function of the delay rIZ between the two pulses for two values of the magnetic field, in the sample containing 1.5at % of dysprosium. The pulse width is 50 ns, the acoustic frequency is 650 MHz and the temperature 12 mK. Circles are the experimental points in zero magnetic field and crosses are those at 50 kOe. The solid lines are the curves obtained using equation (5) with the best fit parameters. Stars are the experimental points for the sample without dysprosium. The pulse width is 50 ns, the acoustic frequency is 700 MHz and the temperature is 14mK. the TS of the second group saturated by the two exciting pulses. The equilibrium recovery of An depends on the time t elapsed since the passage of the second pulse according to: An,
jexp (-t/T,)g(T,)dT,
1 (
, >
(1)
where An, is the equilibrium value and g(T,) is the density of states of the TS of the second group. The x
50 Y
i
340
Vol. 8’0, No. 11
360
360
400
Frequency (MHz)
2712OIS)
An =
GLASS
x
Fig. 3. Attenuation variation of a probing pulse at different frequencies as a saturating pulse at 350 MHz is sent in the sample. The Dy3+ concentration is 6.7 at %. Circles are the experimental points in zero magnetic field and crosses are those at 50 kOe. The solid lines are the fits with the best parameters. In zero magnetic field, the fit has been done with a Gaussian line. At 50 kOe, the sum of a Gaussian and a Lorentzian line is used. usual distribution g(T,) obtained for the TS (see [3]) cannot be applied here: the relaxation rates are much greater than the ones found in the sample containing no Dy 3+ [IO]. So a new mechanism much more efficient than the direct one-phonon process must be involved. This mechanism is not explained yet, and we cannot evaluate the theoretical distribution g( T, ). However, it seems reasonable to have g( T, ) decreasing when T, is increasing. We have obtained a good agreement with our experimental results by taking a hyperbolic distribution similar to that used for the standard TS: g(T,)
=
l/T,
for Tj B T,min
r g(T,)
=
0
for Tl < T,.,in’
(2)
Our experiments extend from 7,? = 0.2 ps to 10 ps. To take into account the very short relaxation times, we suppose: T,,,,,in e 0.2~s.
(3)
Then, the integral in equation (I) can be evaluated analytically and An takes the form: An = o
I
0
10
20
30
40
1
60
Magnetic field (kOe)
Fig. 2. Amplitude of the spontaneous echo as a function of the magnetic field in the sample containing 1.5at % of dysprosium. The pulse width is 50ns and T,* is 200ns. The acoustic frequency is 650MHz and the temperature is 12mK.
(l/a){-
Y + D ln (r,,)},
(4)
where y and p are two constant parameters. Hence, the attenuation factor of the phonon echo is exp (- D In (7,*)) and the final form of the echo decay is: A =
Ah exp (-27,*/T;
- /? ln
(T,,)),
(5)
whereT; is the dephasing time and Ai = A, exp (y). Using equation (5), we can fit very well the experimental results (Fig. 1). The dephasing times giving the best
Vol. 80, No. 11
PHONON ECHOES IN A DYSPROSIUM-DOPED
fits are 10 and 25 ps for 0 and 50 kOe, respectively. For the sample containing no Dy3+ , T; = 6 ps (Fig. 1). The dephasing times are of the same order of magnitude as in fused silica at the same temperature [4]. Presently, we cannot explain the so short dephasing time obtained in the sample containing no dysprosium. Indeed, we have verified that Tl,minwas in this last sample larger by at least one order of magnitude than in the Dy-doped samples [lo]. Lastly, it must be pointed out that the field dependence of the echo amplitude (Fig. 2) is not due to a trivial attenuation effect. This has been established by doing a saturation recovery experiment (a strong saturation pulse is sent in the sample and the attenuation of a small probing pulse is then measured as a function of the delay between the two pulses) where it has been shown that the attenuation of the probing pulse did not depend on the magnetic field for the same saturating pulse. This effect which exists whatever the nature of the ions (Kramers or not Kramers) is not yet explained [4]. An interesting information about the TS involved is provided by a hole-burning experiment. The resulting curves are shown in Fig. 3. The saturating pulse was at a fixed frequency (350MHz). The probing pulse was emitted after one round trip of the saturating one. Its electromagnetic power was adapted for each frequency to keep constant the effective acoustic power. Its attenuation was measured with and without the saturating one. In zero magnetic field, the line is Gaussian. When the magnetic field is applied, the Gaussian background remains, and a Lorentzian line appears superimposed. These curves are not obvious to explain. The width of the Lorentzian line is probably not intrinsic because, due to the saturating pulse, the line broadening depends on JIJc, which is not small (where J is the acoustic power of the saturating pulse and Jc the critical power) [ 111.Our evaluation of Jc leads to a linewidth due solely to the power of the order of 5MHz and the width of the experimental Lorentzian line is 8 MHz. Hence, this linewidth can-
GLASS
963
not be considered as a measurement of some Tz. However, the fact that two lines appear in the presence of a magnetic field confirms the assumption that there are two species of TS, which evolve differently with respect to the magnetic field. In conclusion, we have studied the spontaneous phonon echoes in glasses doped with Dy3+ ions. Their non-exponential behaviour is well explained by assuming the existence of a species of very fast relaxing TS, in addition to the standard TS. That is a new evidence for the existence of such entities in a glass containing magnetic Kramers ions [6]. Lastly, a holeburning experiment has revealed the existence of two lines as a magnetic field is set up. Further experiments with a better sensitivity are needed to go further in the explanation of this effect and to clarify the coupling between TS and Kramers ions. Acknowledgement
- The authors are indebted J. Godard who prepared the samples.
to
REFERENCES 1.
P.W. Anderson,
2. 3.
Philos. Mug. 25, 1 (1972). W.A. Phillips, J. Low Temp. Phys. 7,35 1 (1972). For a review, see W.A. Phillips, Rep. Prog. Phys.
4. 6. 7.
B. Halperin & C.M. Varma,
50, 1657 (1987). F. Lerbet & G. Bellessa, J. Phys. (France) 49, 1179 (1988). N. Vernier & G. Bellessa, Europhys. Lett. 14,349
(1991).
B. Golding & J.E. Graebner, Phys. Rev. Left. 37,
852 (1976).
8.
J.L. Black & B.I. Halperin, Phys. Rev. B16,2879
9.
L. Bernard, L. PichC, G. Schumacher & J. Joffrin, J. Low Temp. Phys. 35, 411 (1979). Saturation recovery displays relaxation times inferior to 10~s in the 1.5% Dy sample. In the sample containing no Dy, T,,,i” (E = 700 MHz) was about 100 ps at 12 mK. L. Allen & J.H. Eberly, Optical Resonance and Two-Level Atoms, Wiley, New York (1975).
10.
11.
(1977).