PHONONS IN EXCITED RUBY

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PHONONS IN EXCITED RUBY

A. Kaplyanskii, S. Basoon, V. Shekhtman

To cite this version:

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Abstract.

-

New results concerning the properties of acoustic phonons

0.87

THz in ruby are considered including (I) attenuation and anharmonic scattering of ballistic phonons and (2) kinetics of resonance phonon trapping.

Resonance interaction of the

0.87

THz (29 cm-I) phonons with

E - x

levels of CI?' ions plays an important role in many physical processes in excited ruby. Investigation of these processes provides valuable information on both the fundamental properties of the terahertz acoustic phonons proper in crystals, and phonon interaction with impurity centers. The studies have been carried out in several groups /I

-

6/. Be consider below the recent results obtained in our group.

I. Attenuation of the 29 cm-I Ballistic Phonons.

Optical detection /2/ of the

29

cm-I, TA and

LA

phonons propa-

gating ballistically in heat pulses

/3/

was used for a quanti-tiative

measurement of

29

cm-' phonon attenuation in rmby with cr3+ concen-

tration C=0.02%

/7/

and C=0.001%. Measurements were perfomed at T=

1.8 K for different directions h-d (heater-detector) lying in the

crystal symmetry plane

CV(

8

is the angle between the group veloci-

ty

f

and the a d s C 3 ) The magnitude of mean free path

i

for the

IA

and TA phonons depends essentially on the phonon propagation direc- tion in the Gv plane. Fig.1 shows a

1

vs.

8

plot. \\hen one goes over from C=0.02% to C=0.001%, the magnitude of

T

for a given 8

,

as a rule, increases strongly. In a 0.001% sample one observes weakly decaying

LA

and TA modes with

1

being far in excess of sample dimen- sions, making only a lower estimate z a 2 0 0 mm possible. At the same time for some LA modes with small

i

10 mm the magnitude of does not change significantly with C.

The results indicate an extremely large contribution to

E

from

phonon scattering; on the Cr ions and (or) accompaniing defects. The

magnitude of

7

in low concentration ruby gives the lower 1imi.t; for

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JOURNAL DE PHYSIQUE

% decay time of

LA

/8/ phonons. There exist both long lived LA mo- P

des with % 3 2 0 ps and apparently also short lived modes with T

-

P

1 ps (for the angles 8 under which the experimentally found does not depend significantly on C). The anisotropy in Z i s probably

P

associated with the elastic anisotropy of the crystal and the conser-

vation laws in the elementary events of

LA

phonon decay. Note that

theory gives for the decay time of the 29 cm-I U phonons a value of

?y -4.6 ps

/9/

assuming the crystal to be elastically isotropic.

P-

2. Decay of Ivlode-Averaged 29 cm-I Phonons.

An

attempt has been made to estimate experimentally the mode-

averaged phonon anharmonic lifetime by measuring the decay of the whole 29 cm-I nonequilibrium phonon ensemble in the crystal immersed in superfluid helium (IC=1.8 K)

.

The conditions for the

29

cm-I phonon escape from the bulk of the sample to its boundaries through which the phonons eventually lose energy to the helium bath were con- trolled. Heat pulses were injected from a heater h into cube-shaped

samples with edge lk2+10 mm. The

29

cm-I nonequilibrium phonon con-

centration was derived from R2(t) luminescence pulses esca2ing from

a test volume

-0.5

mm, pumped with cw laser at extremely low power.

Fig.2 shows R2(t) pulses in a sample with L=10 mm, C=O.5% measured with two detectors, one close to h and the other near the opposite

face. At long times the R2(t) pulses coincide thus indicating the 29

cm-I phonons to be distributed throughout the crystal. The decay of R2(t) at such times is exponential over 2+3 decades of R2 intensity.

At 5 3 3 mm the decay does not depend on the power and duration of

heating, while at L=2 mm the decay is constant only at low power in-

puts employed in the experiment.

Fig.3 shows the dependence of decay time Z on

L.

For the sample

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cxystal is determined primarily by escape, anharmonic phonon pumping being inessential.

3.

Anharmonic Scattering of the 29 cm-I Ballistic Phonons. Phonon-phonon scattering plays an important role in physical phenomena in crystals. As for the terahertz range, we are aware of only one unsuccesful attempt /11/ to observe heat pulses interaction. We have succeeded in directly observing the merging of the 29 om-' phonons with acoustic phonons of higher frequency

>

2 THz /12/.

Heat pulses 200 ns long are injected at

50

H z from the heater h, into an A1 0 :0.02% Cr crystals at 1.8

K

(Fig.4). The

29

cm-I pho-

2 3

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JOURNAL DE PHYSIQUE

h2 at the side face of the sample.

We have observed a decrease of the I(t) pulse amplitude in the presence of the heat pulse from h2 which directly indicates scatte-

ring of the 29 cm-I

FTA

phonons by the phonons injected from h2. The

relative change

DI/I

of the R2-pulse amplitude depends on the delay

kt2-tl between the current pulses through hl and

h;Z.

The A 1/1 (t)

*

dependence is shown in Fig.4 where we adopt tl=O and the moment tl of passage of the ballistic FTA phonons past h2 is specified. At de-

*

lays t > t l the effect naturally disappears. For t < 0, when the haat pulse from h2 is emitted long before the injection of 29 cm-I phonons from hl, the aI/I signal decays slowly with I t l

.

This indicates that the effective screening phonon cloud injected from h2 decays very slowly (with

'CS

3

ps)

.

The delayed kinetics and observed localization (<

0.3

mm) of

the screening cloud near h2 demonstrate that the

29

cm-I FTA phonons

are scattered by high frequency phonons, a>>

29

cm-I, which Leave the near surface region slowly because of Rayleis scattering /15/.

This conclusion agrees with the strong frequency dependence (- w4)

of the processes, TA(29)+LA(u ) -r LA( W +29), and TA(29)+TA( w )

-

LA

(L~+29) which are apparently responsible for the observed escape of

the

29

cm-I FTA phonons from the ballistic mode. Knowing the FYA pho-

non transit time 0.15 ps past h2 and the magnitude of their damping

(--5%),

one can evaluate FTA phonon merging time as - 3

PS.

Hence P

the

29

cm-I phonon anharmonic lifetime near the heat injector is de-

termined not only by decay but also by merging which may reveal it- self in experiments on

29

cm-' phonon resonance trapping /16/.

4. Resonance Trapping of the 29 cm-I Phonons.

The trapping of 29 cm-I pho:lons in excited ruby /1,2/ is due to

their multiple resonance scattering involving the levels of the

2

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in contrast to

%,

includes intervals of free phonon transit between scattering events.

In the present work, the times

TI

and TO were measured in one experiment in the same pumped volume of a ruby crystal with 0.02%

cr3+ with a given concentration N* of CJ? metastable ions.

(a) A pulsed copper-vapor laser

( A

~510.5 nm, 578.2 nm, repeti-

tion frequency f=10 kHz, energy 2xl0-~ J, pulse duration a t=20 ns)

creates in the crystal a n excited volwne ds1.5 mm. Since f"<< 2

R the concentration N is almost constant, the role of an individual

Cu-laser pulse being reduced to the injection of 29 cm-I nonequilib-

rium phonons in -* transitions. The resulting pulses exhibit an

exponential decayfrom which one could derive Z1. The time TC, was

determined from the time averaged relative intensity q =R2/R1.

Fig.5 shows the dependence of

TI

and To on the average laser power

-

P.

The curves Z1(P) and

T0(P)

approach one another with increasing

P exhibiting a clear tendency of crossing.

(b) The crossing of Z1(P) and To(P) (at large N*) was observed in experiments with two lasers in an arrangement close to that of

*

ref./5/.

A

steady-state concentration

N

was produced with cw Ar-la-

ser (P=0.1+0.8

W,

d=0.3 am).

A

nitrogen laser beam (f=100

Hz,

~ t = 1 5

ns, pulse energy IO-~J) was focussed on the same spot. The N2-laser

generates pulses of

29

cm-I probe phonons which induce R2(t) pulses.

The decay of R2(t) yields TI, the time-averaged value being q=R2/R1

-

Zoo The

rl(P)

and Co(P) curves cross at P=0.3 W,

To

exceeding

TI

at

P=0.8

W by a factor of three. Note that the behavior of the Z1(P)

and CO(P) curves in experiments (a) and (b) is similar to the one

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C6-444 JOURNAL DE PHYSIQUE

Fig.6 Fia.7

Fig.6 shows that at concentrations N * < 1018 om-3,

TI

>

To

in

full agreement with above. This interval of N* includes: (1) a regi-

*2 2

on of weak trapping where To-TN d /16,18/ and the phonons escape

from the volume by spatial diffusion typical for the "resonance flu-

orescencet1 trapping in purely elastic phonon scattering /19,20/; and

(2) a region of moderate trapping where a combined mechanism invol-

ving spatial and spectral diffusion sets in /20/, for which

Zou(Df

T)-'/*N*~ b /21/, where Df is the spectral diffusion coefficient of electronic excitations, 6 % IO"'~ cm2 is the resonance scattering cross section (Df does not depend on

N*).

In the strong trapping region one observes an anomalous ratio,

rl~ro.

The "kinetic" time

r,,

exhibits a tendency to saturation at a level of 1+3 ps, the "steady-state" time To continuing to grow ra- pidly (in ref ./I81 one observed q > 1 ~ - 2 which corresponds t~ T o >

100 ps). This inconsistency (pointed out earlier /22/) poses the question of which of the times,

TI

or

To

is the "truet1 trapping time corresponding to real number of scattering events, M. Generally

speaking, the large value of 'TO may be attributed to the feeding

of the

29

cm-I mode by the heating accompaniing optical excitation.

But this suggestion would imply that up to

5%

of the energy in

Stokes losses (-

5000

cm-I) in each optical excitation event can con-

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chopped mechanically for a time ~ t = l ms at a frequency of 200 Hz. Since at<TR, at the times when optical excitation is interrupted N

decreases insignificantly (by -2%) whereas the generation of the

-

2A-E phonons stops completely. The time profile of R2(t) for samples with C=0.0270 and C=0.5% shown in Fig.7 for P=2W reveals sections of rise and decay, each being characterized by a fast (microsecond-scale) kinetics in the beginning with a subsequent slow (milliseoond- scale) variation. The time of the slow exponential decay does not depend markedly on C, p ~ ~ 0 . 4 ms, its initial amplitude constiwing 35% of the plateau level at C=0.5% and --I% at C=0.02%. The RZ(t)

profile does not change over a wide range of N*

(P)

variation, the

magnitude of being practically independent of

N*.

The short time

of rise and decay is close in magnitude to TI observed in pulsed ex-

periments /2,5,16,22/ and exhibits a similar dependence on N* and C

*

(when going over from C=0.02% to C=O.5% it decreases for large N

from

3

ps to <

0.5

ps).

*

In the interpretation of the results obtained, account should be taken of the fact that under conditions of efficient phonon trapping scattering processes of relatively low probability may come in- to play in the pumped volume. In particular, the scattering processes which, while not leading to an irreversible disappearance of the 29 cm-I phonons, result in their being maintained for a long time in an optically inactive state, are responsible for the specific dyna- mics in the onset of equilibrium between the "ordinary" and "tailing"

*9he observed two-component decay of R (t) after the removal of pum-

ping i dicates the insignificant role gf nonresonance feeding of the

2.9 crn-q mode by wax of optical heating (or, for instance, coopera-

tive processes of E-excitation accumulation

/23/

which have in prin-

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C6-446 JOURNAL DE PHYSIQUE

resonance phonons, which is what brings about the essentially nonex-

ponential kinetics of R2(t). Among probable are the following mecha-

nisms :

(a) Inelastic 29 cm-I phonon scattering involving transfer of elect- ronic ( 2 ~ ) excitation between the cr3+ ions /22,24/ which produces, as a result of repeated scattering, spectral redistribution of the

29

om-' phonons within the inhomogeneous width of the R,,-line. The delay is connected here with the mean free path of the off-resonance phonons being much larger than that at resonance (but less, at high

*

N

,

than beam size d, which makes possible rescattering).

(b) Coherent resonance transfer of electronic excita.t;ion to several

ions thus creating a collective 2~-state /25/ is in principle con-

ceivable, provided no phase relaxation of the electronic states oc- cur. Phonon scattering accompanied by such an energy transfer in in- termediate collective state could, generally speaking, exhibit a sufficientl~. large "electronic" tailing.

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