BOTTLENECK OF 29 cm–1 PHONONS IN RUBY

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BOTTLENECK OF 29 cm–1 PHONONS IN RUBY

K. F. Renk, J. Peckenzell

To cite this version:

K. F. Renk, J. Peckenzell. BOTTLENECK OF 29 cm–1 PHONONS IN RUBY. Journal de Physique

Colloques, 1972, 33 (C4), pp.C4-103-C4-105. �10.1051/jphyscol:1972422�. �jpa-00215099�

JOURNAL DE PHYSIQUE

Colloque C4, suppKment au no 10, Octobre 1972, page C4-103

BOTTLENECK OF 29 em-I PHONONS IN RUBY

K. F RENK

and J. PECKENZELL Physik-Department, Technische Universitat Miinchen,

8046 Garching, Germany

Resum6. -

Une methode optique pour detecter des phonons A 29 cm

en rubis est appliquke pour Ctudier l'interaction des Btats Clectroniques E(~E) et 2 A(zE) du Cr3

excite, avec les phonons resonnants

29 cm

Pour 10

cm

Cr

excites les phonons

29 cm

sont emprisonnes dans le cristal par suite de la diffusion resonnante aux Cr3

excites. On a trouve que le temps de vie des phonons emprisonnes s'accroit si la concentration des Cr3

excites est augmentee. Ce resultat indique un sCvere

phonon bottleneck

Abstract. - An

optical detector for 29 cm

phonons

ruby is applied to study the interaction of the electronic states

and

APE) of the excited Cr3

with the resonant 29 cm

phonons.

For 1015 cm

excited Cr3

the 29 cm

phonons can be trapped in the crystal due to resonant scattering. We found that the (spontaneous) decay time of the trapped phonons increased with increasing concentration of excited Cr3

indicating a strong phonon bottleneck.

A bottleneck of 29 cm-' phonons in ruby has been found by Adde et al. [I] in the Orbach relaxation of the E ( 2 ~ ) state in ruby. We report the direct observation of a phonon bottleneck in the same system.

With an optical phonon detector [2], [3] we mea- sured how long 29 cm-l phonons need to escape from a crystal volume which contains different concentrations of excited Cr3

ions. Excited Cr3

were obtained by continuous optical pumping P with a mercury lamp (see insert of Fig. 1). The crystal 2

which was hold at low temperature (2 OK) contained * ^-

the excited Cr3+ mainly in the (metastable) E ( 2 ~ )

state

R,-level

which gives rise t o strong Rz- fluorescence radiation at 6 935 A.

Phonon pulses (of 100 ns duration) were generated by the heat pulse technique. The 29 cm-' phonons of a heat pulse are detected by the additional R,-

0 2 L 6

fluorescence radiation (at 6 922 A) from the

R2-

level

which is 29 cm-I above the R,-level.

Figure 1 shows the R2-signal from the detector volume after the phonon injection. The experimental curves demonstrate that the time of escape of the 29 cm- ' phonons increases with increasing optical- pump intensity. For weak optical pumping (PIP,

1) when only few Cr3+ ions are excited the 29 cm-' phonons escape very fast (see Fig. I). For larger concentrations of excited Cr3+ the phonons remain much longer in the detector volume. The experi- mental time of escape

of the 29 cm-I phonons

(*)

Present address

Fachbereich Physik, Universitat,

Re- gensburg, Germany.

FIG. 1.

- R2 intensity after phonon injection (at

0) for different optical-pump intensities

The insert shows schema- tically

arrangement

The 1

detector volume (shaded) contains a concentration of about 1014 cm-3 excited Cr3+

for

The ruby crystal is doped

1019

Cr3+.

29

cm-1 phonons are generated

current pulses

watts pulse power)

the heater

(obtained from the curves of Fig. 1) is drawn in figure 2 as a function of the optical-pump intensity.

The increase of

with increasing P is due t o the resonance scattering of the 29 cm-' phonons a t the excited Cr3+ (see Fig. 3). By measuring the distri- bution of the 29 cm-I phonons in the crystal at

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972422

C4- 104 K. F. RENK AND J. PECKENZELL

0 100 200

OPTICAL-PUMP I N T E N S I T Y PIP,

FIG. 2. - Decay time r,* of the 29 crn -1 phonons as a function of the optical-pump intensity. The straight line corresponds to eq. (1). For small optical-pump intensities r,* (dashed line) is reduced by the phonon diffusion out of the detector volume.

different times after the phonon injection [2, 41 it was found that for PIP, 2 50 the resonance scatter- ing is so strong that the phonons do not propagate, but, are imprisoned in a small volume adjacent to the heater. The trapped phonons can escape, how- ever, from the observed frequency band by spontane- ous decay.

The experiment (Fig. 2) shows that for PIP, > 50 this phonon decay time still increases with increasing optical-pump intensity. We interprete this result by a phonon bottleneck effect : For large concentra- tions of excited Cr3+ the 29 cm-' phonons are absorbed very frequently and their energy is stored for some time as electronic excitation energy. During the lifetime of the electronic excitation, TI, phonon

FIG. 3. ^- Resonant scattering of the 29 cm -1 phonons at the R-levels of the excited Cr3

+.

decay is not possible. Therefore, we expect for the apparent decay time

for the phonons (compare Fig. 3)

2," = 7,

+

zres (1)

where z, is the

true

decay time of the 29 cm-' phonons and z,,, the time of flight between emission and re-absorption of a 29 cm-I phonon.

z,,, can be estimated for the region of small optical- pump intensities by diffusion measurements, we

obtain for the rate of resonant scattering z,,,

6 x 106(~/P,) s-I [4]. By extrapolation to the larger optical-pump intensities we obtain the upper scale of figure 2. From the straight line o f figure 2 we can now determine z,

1.4 ps for (PIP,)

0 and T I x 0.7 x lo-' s which follows from the slope of the curve.

The phonon decay time

of the 29 cm-' phonons is about ten times larger than expected from a simple theoretical estimate [5] for the spontaneous decay of acoustical phonons in A1203.

The experimental relaxation time is in good agree- ment with a theoretical estimate (0.3 x s) by Blume

values (4 x lo-' s) obtained from a photon echo experiment 171.

Eq. (1) can be derived from the rate equations for our system (Fig. 3), the apparent decay time corres- ponds to the relaxation time Tb of a bottlenecked spin system known from microwave investigations 181

where

is the

bottleneck factor

While in micro- wave systems z, < TI is in our system TI <

The bottleneck factor in our system is for the largest optical-pump intensity (PIP,

200)

which indicates an extremely strong phonon bottle- neck

The 29 cm-' phonons are absorbed and re- emitted about lo3 times before they decay.

For the determination of TI and of

the concen- trations N* of the excited Cr3+ must not be known.

We can, however, estimate N* from the theoretical relation between z,,, and TI

where D(v) is the density of states of the phonons in A1203 at 29 cm-'. Assuming that the R,-level is lifetime-broadened by the emission of 29 cm-' pho- nons, dv

l/nTl, we obtain for the strongest optical pumping, PIPo

200, N*

2 x loi6 cm-3 which is in reasonable agreement with a value estimated from the fluorescence intensity.

Our result demonstrates that the interaction with resonant phonon radiation can influence strongly the direct relaxation of electronic states, even if the concentration of the electronic states is only 1016 ~ m - ~ . We guess that for systems with higher concentrations of electronic levels the described phonon bottleneck effect plays an important role in the spin lattice relaxa- tion at 1012 Hz.

We thank S. Geschwind for discussions.

BOTTLENECK OF 29 CM-1 PHONONS IN RUBY

References

[I]

ADDE

GESCHWIND

and WALKER

KLEMENS

Colloque Ampkre

North-Holland, Amster-

dam,

p.

BLUME

ORBACH (R.), KIEL

and GESCHWIND

RENK

and DEISENHOFER

(S.),

A

- -

1971, 26, 764. [7]

KURNIT

A.), ABELLA

and HARTMANN (S. R.),

RENK

F.), in Festkorperprobleme

Vieweg, Quantum Electronics Conf., Puerto Rico,

Braunschweig

to be published. p.

[4]

RENK

F.), Light Scattering in Solids, Flammarion,

Paris,

p.

WOOLDRIDGE

DISCUSSION

H. J. MARIS.

In this experiment the phonons K. F. RENK.

Due to the polarizations mixing we spend part of their time in each of the 3 possible think to measure the lifetime of these 29 cm-I phonons polarizations. However, under the conditions of high which have the shortest lifetime. From theoretical phonon frequency and low temperature the lifetime of estimations by Klemens and Orbach and Vredevoe these 3 modes should be very different. In particular one expects that longitudinal phonons at 10'' Hz the low transverse mode should have a very long life- have a lifetime in the order of s.

time compared to the others. Have you made any

theoretical estimates of the phonon lifetimes