HIGH RESOLUTION PHONON SPECTROSCOPY AT LOW TEMPERATURES

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HIGH RESOLUTION PHONON SPECTROSCOPY AT LOW TEMPERATURES

L. Challis

To cite this version:

L. Challis. HIGH RESOLUTION PHONON SPECTROSCOPY AT LOW TEMPERATURES. Jour-

nal de Physique Colloques, 1978, 39 (C6), pp.C6-1553-C6-1558. �10.1051/jphyscol:19786599�. �jpa-

00218092�

JOURNAL DE PHYSIQUE Colloque C6, supplPment au no 8, Tome 39, aoict 1978, page C6-1553

H I G H R E S O L U T I O N PHONON SPECTROSCOPY AT LOW TEMPERATURES

L . J . C h a l l i s

Department of Physics, University o f Nottinghm, University Park, Nottingham NC7 2RD, U.K.

RLsum5.- On p r d s e n t e un expos6 s u r l e s techniques de s p e c t r o s c o p i e d e s phonons q u i s o n t capables de h a u t e r g s o l u t i o n

2

1 GHz e t s u r l e s problzmes pour l e s q u e l s i l s peuvent 8 t r e v a l a b l e s . On s ' a t t a c h e s u r t o u t ?I l a technique de croisement des frgquences.

Abstract.- A review i s given of t h e techniques of phonon spectroscopy t h a t a r e capable of high reso- l u t i o n

2

1 GHz and of problems f o r which they could be of v a l u e . P a r t i c u l a r a t t e n t i o n i s paid t o t h e frequency c r o s s i n g technique.

1 . INTRODUCTION.- Phonon spectroscopy i n t h e f r e - quency range 10 GHz t o s e v e r a l 1000 GHz c o n t i n u e s t o provide o p p o r t u n i t y f o r c o n s i d e r a b l e experimen- t a l i n g e n u i t y and t h e r e have been a number of tech- n i c a l developments s i n c e t h e review of t h i s s u b j e c t a t LT14 by Kinder / I / and t h e Nottingham Conference on Phonon S c a t t e r i n g h e l d immediately a f t e r w a r d s / 2 / . Meltzer and Rives / 3 / have developed a method of g e n e r a t i n g phonon p u l s e s a t 870 GHz with a band- width of % 500 MHz by producing p o p u l a t i o n inver- s i o n of t h e 2~ ruby l e v e l s by o p t i c a l pumping and Bron and G r i l l / 4 / have produced s t i m u l a t e d emis- s i o n phonon p u l s e s a t 720 GHz u s i n g two l a s e r s mat- ched approximately t o t h e two t r a n s i t i o n s from t h e ground s t a t e of a t h r e e l e v e l system ( v 4 + i n A1203).

These add t o t h e r e l a t e d d e t e c t i o n method developed e a r l i e r by Renk and coworkers /5/ who have r e c e n t l y been e x p l o r i n g the p o s s i b i l i t y of u s i n g o r g a n i c t r i p l e t s t a t e s / 6 / . I n p r i n c i p l e t u n i n g could be achieved w i t h a magnetic f i e l d . A second technique used r e c e n t l y by ~ r o n and G r i l l

171

which uses

E U ~ + a s a probe i o n i n SrF2 i s s i m i l a r t o t h a t of Shah e t a l . 181 with bound e x c i t o n s i n Cds. I t de- termines t h e form of a phonon f l u x d i r e c t l y from t h e s p e c t r a l d i s t r i b u t i o n of an o p t i c a l luminescen- ce sideband e x c i t e d by a l a s e r . I t i s a l s o f a s t , h a s a wide frequency range, needs no e x t e r n a l

f i e l d s b u t i n t h e system used has only modest reso- l u t i o n ^(% 100 GHz). Both t h e s e o p t i c a l techniques can be used f o r e x p l o r i n g t h e temporal and s p a t i a l decay of a phonon p u l s e . There h a s been p r o g r e s s t o o u s i n g sdperconducting d e v i c e s . Dietsche / 9 / has shown t h a t superconducting h e t e r o j u n c t i o n s can be used as t u n a b l e d e t e c t o r s . They have a s h a r p detec- t i o n t h r e s h o l d a t a frequency which is t u n a b l e s i n - ce i t i s l i n e a r l y dependent on t h e b i a s v o l t a g e .

An a c modulation v o l t a g e i s used t o l i m i t d e t e c t i o n t o a bandwidth % 10 GHz. Huet, P a n n e t i e r , Ladan and Maneval / l o / have used t h e c u t o f f i n phonon a t - t e n u a t i o n a t q > 2kF t h a t occurs i n a d e g e n e r a t e e l e c t r o n gas t o o b t a i n s p e c t r o s c o p i c i n f o r m a t i o n about a phonon beam. By working w i t h n-InSb samples of v a r y i n g dopings they were a b l e t o move t h e cut- o f f throughout the range 20 t o 500 GHz. There have a l s o been improvements i n t h e frequency c r o s s i n g technique i n which an unknown resonant frequency i s measured by t u n i n g a known Zeeman frequency un- t i l they a r e e q u a l ( c r o s s ) when a s h a r p minimum i s observed i n t h e thermal magnetoresistance. One re- c e n t development i n v o l v e s t h e use of an a c modula- t i n g f i e l d t o improve t h e s e n s i t i v i t y / 1 1 / and t h e use of a d i f f e r e n t i a l arrangement f o r measuring thermal c o n d u c t i v i t y by L o c a t e l l i 1121 a l s o looks promising f o r t h i s technique'. Our understanding of t h e s e v a r i o u s quantum techniques has been improved t o o by many u s e f u l t h e o r e t i c a l and a n a l y t i c a l con- t r i b u t i o n s /13/. We have a l s o s e e n a s i g n i f i c a n t

advance i n t h e i n t e r e s t i n g p o s s i b i l i t y of a c h i e v i n g s p e c t r o m e t r i c d e t e c t i o n u s i n g i n t e r f e r e n c e e f f e c t s . Zur Nieden and Weis /14/ have demonstrated t h e po- t e n t i a l use of F o u r i e r . t r a n s f o r m spectroscopy by observing the r e f l e c t i o n of 24 GHz phonons a t a s u r f a c e p l a t e d w i t h a f i l m of condensed g a s of s t e a d i l y i n c r e a s i n g t h i c k n e s s . We r e c a l l t h a t e a r - l i e r work ( e . g . / 1 5 / ) u s e d helium f i l m s and s o was l i m i t e d t o f r e q u e n c i e s below 300 GHz. There have been developments i n phonon echo work and i n par- t i c u l a r i n t h e i r g e n e r a t i o n i n g l a s s e s 1161. Also U l r i c h and Weis 1171 have succeeded i n producing v e r y narrow phonon beams (9 GHz) which can be d i s - placed l a t e r a l l y . U n f o r t u n a t e l y t h e r e i s no time t o review the v a r i e t y of experiments t h a t have been

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786599

c6-1554 JOURNAL DE PHYSIQUE

carried with these and other phonon techniques.

2. HIGH RESOLUTION SPECTROSCOPY.- In this talk I am going to concentrate on just one aspect of phonon spectroscopy which is the ability to carry out ex- periments at relatively high resolution 2

1

GHz.

This is appreciably higher than the 5-10 GHz that can be achieved using Fourier transform infra-red spectroscopy although this sort of resolution can readily be achieved using carcinotrons. These have however the disadvantage that each tube is only

tunable over a frequency range of

Q 10 %.

We recall too that for examining impurities in solids etc phonon spectroscopy is very often much more sensi- tive than far infra-red spectroscopy.

High resolution is of value in many investi- gations.,These include

:

(i) Precise measurements of energy levels and spin Hamiltonian parameters.

(ii) Weak ion-ion (exchange) or ion-defect in- teractions (say

0-10

GHz) . The sensitivity of phonon spectroscopy allows one to work at low concentra- tions

;

at higher concentrations distant pairs are likely to be part of larger clusters.

(iii) Hyperfine splittings (25-1000MHz). The determination of the nuclear degeneracy is helpful in identifying impurities in new host lattices.

(iv) Small splittings produced by external fields, g, E, and 2. If these are non-linear it is useful to be able to work down to small splittings.

(v) Lineshapes. These can provide information on lifetimes and strain distributions. We note the general spectroscopic problem of the increase in apparent linewidth that occurs when the resonant attenuation aRR 5

1

(R is a specimen dimension).

This can be more critical for phonons where aR can be large even at modest concentrations.

(vi) Tunnelling splittings of molecular groups, e.g. CH,. Many lie in the range

0-10

GHz. They may however be too weak to detect even in concentrated systems as the transitions are normally spin for- bidden.

3. HIGH RESOLUTION TECHNIQUES IN PHONON SPECTROSCO- PY.- Three of the present techniques have resolu- tions 2 1 GHz. In all three a particular phonon frequency

v

is selected by tuning a Zeeman fre-

0

quency of

a

probe ion in the crystal with a magne- tic field. The resolution is limited by the line- width of the Zeeman transition. A fourth technique

1181 generates coherent phonons of narrow bandwidth by piezoelectric excitation from a far infra-red laser. It is not yet suitable for spectroscopy sin- ce continuously tunable sources are not available but it clearly has considerable potential.

3.1. Spin-Phonon Spectrometer using Circular Dich- roism (Anderson and Sabisky 1511.- This technique is well established and only an outline is given here. An optical technique, circular dichroism,is used to measure the spin temperature of two ground state Zeeman levels which is determined by the in- tensity of the phonon flux at

v

. The most conve-

0

nient systems have been found to be T.m2+ in CaF2, SrF2 and BaF2 which provide resolutions of

%

75 MHz.

The experimental arrangement used to detect cohe- rent phonons at 24 GHz is shown schematically in figure

1.

The phonons are generated piezoelectrical-

RF cutoff channel

I \ ^MAGNET cry;;fa' I

Stub of reentrant cavitv

1-79

I=

Movable -Light

Beam

Fig. 1

:

The experimental arrangement (schematic) used by Anderson and Sabisky 1151.

ly by a film transducer and the RF cutoff channel prevents the microwave power passing into the crys- tal. The signal is shown in figure

2.

The linewidth is very largely due to the detector and the struc- ture is caused by nearby fluorine nuclei. The tech- nique has been used in various experiments at fre- quencies up to 300 GHz and also for detecting pul- ses. It has not so far been used in spectroscopic investigations of impurities so that its resolution has not been fully exploited.

3.2. Spin-Phonon Spectrometer Using Optical Emis- sion (Renk et al. 151, Kaplyanskii et al. 1191, Dijkhuis et al. /20/, Meltzer and Rives 131) .- ^The

phonon flux at v is again used to change the popu-

0

lations of two levels which in principle are tuna-

ble. In this technique the levels are excited (so

far the

2~

levels in ruby) and optically pumped

and the phonon flux is measured from the enhanced

FREQUENCY (MHz) -100 -50 0 50 100

I I I I I

FIELD B (mT)

F i g . 2 : The p o l a r i z a t i o n s i g n a l from S ~ F Z ( T ~ ~ + ) produced by phonons a t 24 G H z . The frequency i s gi- ven by hv = gf3B (Anderson and Sabisky / 1 5 / ) .

o p t i c a l e m i s s i o n a t t h e h i g h e r of t h e two frequen- c i e s ( t h e R 2 l i n e f o r ruby, s e e f i g u r e 3 ) . The ex-

ABSORPTION BANDS UMP

RUBY LEVELS

MOVABLE PUMP

\

RI&RZ FLUORESCENCE

F i g . 3 : The energy l e v e l s of ruby and t h e e x p e r i - mental arrangement (schematic) used by Renk and Deisenhofer 151.

periments t o d a t e have been concerned w i t h phonon l i f e t i m e s , b o t t l e n e c k e f f e c t s e t c . a n d a g a i n no s p e c t r o s c o p i c measurements have been made. The re- s o l u t i o n i n ruby i s q u i t e good, % 500 MHz, and b e t - t e r r e s o l u t i o n might be a c h i e v a b l e s i n c e t h e in- t r i n s i c width i s only % 50 MHz and t h e l a r g e r va- l u e i s t h e r e s u l t of s t r a i n .

3 . 3 . Frequency Crossing'Spectroscopy.- This t e c h n i - que which we a r e u s i n g . i s n o t new 1211 b u t i t i s only very r e c e n t l y t h a t i t s p o t e n t i a l i n terms of s e n s i t i v i t y and r e s o l u t i o n has been r e a l i s e d through s t u d i e s of s m a l l s p l i t t i n g s and of impuri- t i e s i n low c o n c e n t r a t i o n s . The phonon s o u r c e i s a h e a t e r and i n a DC experiment t h e t o t a l a t t e n u a t i o n

-

thermal r e s i s t a n c e

-

i s measured by two bolome-

t e r s . The Zeeman frequency

v

of t h e probe i o n i s 0

v a r i e d a s b e f o r e and a s h a r p r e s i s t a n c e minimum i s recorded each time

v

c r o s s e s a r e s o n a n t frequency

0

of t h e o t h e r i o n s p r e s e n t . The method depends on t h e f a c t t h a t t h e thermal r e s i s t a n c e of a system i s a non-linear f u n c t i o n of t h e phonon s c a t t e r i n g r a - t e . So t h e r e s i s t a n c e changes r a p i d l y when two re- sonant p r o c e s s e s o v e r l a p and a t low c o n c e n t r a t i o n s (a II < 1) t h e width of t h e minimum i s governed by

R

t h e widths of t h e two p r o c e s s e s /22/.

An example i s shown i n f i g u r e 4 where a reso- nant frequency of

v3+

c r o s s e s one of Fe2+ 1231.

F i g . 4 : A v3+/l?e2+ frequency c r o s s i n g s i g n a l i n A1203 1231.

The h o s t l a t t i c e i s and t h e i o n i c concentra- t i o n s , a r e % 70 and I ppm r e s p e c t i v e l y . S i n c e t h e li- nes can b e q u i t e s h a r p , t h e i r p o s i t i o n s can be mea- sured q u i t e a c c u r a t e l y . F i g u r e 5 shows f o r example t h e a n g u l a r dependence of a

v3+/v3+

c r o s s i n g i n

F i g . 5 : ( a ) The a n g u l a r dependence B(8) of t h e

v3+/v3+

c r o s s i n g i n A1203; and (b) ~ - ~ ( 8 ) p l o t t e d a g a i n s t c o s 2 8 1241.

c6-1556 JOURNAL DE PHYSIQUE

A1203 / 2 4 / . From t h i s we d e t e r m i n e d g / g t o 2 %

1 I I

and, knowing g l l

,

t h e z e r o f i e l d s p l i t t i n g o f t h e

v3+

ground s t a t e t o 0 . 4 %, and from t h e s i z e o f t h e s i g n a l s we have a l s o d e t e r m i n e d a p p r o x i m a t e va- l u e s f o r t h e m a g n e t o e l a s t i c c o u p l i n g c o n s t a n t s f o r

v3+

/ 2 2 / . The e x p e r i m e n t a l t e c h n i q u e i s b a s i c a l l y s t a n d a r d a l t h o u g h t h e thermometers a r e mounted o u t o f t h e main f i e l d on c o p p e r w i r e s h e l d a t v a r i o u s p o i n t s w i t h n y l o n f i b r e s t o minimize v i b r a t i o n which i s a n i m p o r t a n t s o u r c e of n o i s e . Good tempe- r a t u r e s t a b i l i s a t i o n i s a l s o v e r y n e c e s s a r y . We c a n p r e s e n t l y d e t e c t changes i n t h e r m a l r e s i s t a n c e o f s h o r t (% 10 mm) A1203 samples of 1/10' and t h i s c a n b e improved by making s e v e r a l sweeps o v e r t h e l i n e and u s i n g a s i g n a l a v e r a g e r / 2 5 / .

The t e c h n i q u e h a s been used t o i n v e s t i g a t e

v3+

p a i r s i n A1203 / 2 5 / . F i g u r e 5 shows t h a t , f o r f i e l d s a l o n g t h e c - a x i s (8 = 0 ) t h e

v3+

i o n s g i v e r i s e t o a c r o s s i n g a t B = 3.1 T. The l e v e l scheme i s

0

shown i n f i g u r e 6 a and Bo i s g i v e n by 2g BB=D-g BB.

I I II

Ffg. 6 : The e n e r g y l e v e l s of

v3+

i n A1203 f o r f l e l d s a l o n g t h e c - a x i s ( a ) i o n s ( b ) p a i r s w i t h

I J I

^{<< D .} The c r o s s i n g o f t h e b and c f r e q u e n c i e s

shown l e a d s t o a 7 l i n e s i g n a l c e n t r e d a t 3.1 T/25/.

Exchange p a i r i n g J S l . S 2 s p l i t s t h e

--

D l e v e l i n t o D

+

J ( f i g u r e 6 b) which g i v e s e a c h o f t h e f r e q u e n - c i e s two s i d e b a n d s . (We n e g l e c t h i g h e r l e v e l s a t

% 2D). As a r e s u l t t h e r e a r e s i x e q u a l l y s p a c e d s a - t e l l i t e l i n e s a t B f BJ, B f 2B and B i 3BJ

0 J

w i t h BJ = J / 3 g

B

a s shown i n f i g u r e 7 . I n t h i s c a v e t h e l i n e s a r e w e l l r e s o l v e d s i n c e J

I I

= 8.7 GHz. T h i s work a l s o i l l u s t r a t e d t h e s e n s i t i v i t y of t h e t e c h - n i q u e s i n c e t h e p a i r s which a r e o n l y m o d e r a t e l y c o u p l e d t o t h e l a t t i c e (G ^% 400 cm-') c o u l d r e a -

i j

d i l y b e d e t e c t e d a t a c o n c e n t r a t i o n of 2 x 10-~ppm.

The same s y s t e m h a s a l s o been u s e d t o exami- ne t h e h y p e r f i n e i n t e r a c t i o n i n

v3+

/ 2 6 / . T h i s s p l i t s b o t h f r e q u e n c i e s i n t o 8 components o f s e p a - r a t i o n s 2%(2glpB) and s ( D

-

glf3B) w i t h %=288 MHz

FREQUENCY (GHzl

-20 0 20 -20 -10 0 10 20

r n l I I I I I I I I I / I

F i g . 7 : The s e p t e t s i g n a l due t o

v 3 +

p a i r s ( a ) a 1170 ppm V sample, / 2 5 / , ( b ) p a r t o f t h e s i g n a l a t h i g h e r r e s o l u t i o n f o r a 650 ppm sample / 2 3 / .

and i f t h e s e were a l l r e s o l v e d t h e f r e q u e n c y c r o s - s i n g s h o u l d c o n t a i n 21 l i n e s e a c h s e p a r a t e d by A

H ' I n f a c t o n l y t h e 2g BB s p l i t t i n g s a r e r e s o l v e d ,

I I

t h e o t h e r s b e i n g smeared o u t by s t r a i n , and a sim- p l e model p r e d i c t s t h a t t h e c r o s s i n g s h o u l d now b e one l i n e modulated a t a f r e q u e n c y 2% ( f i g u r e 8 ) .

FIELD B

-

F i g . 8 : P r e d i c t e d form o f t h e f r e q u e n c y c r o s s i n g s i g n a l f o r

v3+

i n A1203 when t h e AM = 2 e i g h t hy- p e r f i n e l i n e m u l t i p l e t ( s e p a r a t i o n 2AH) c r o s s e s t h e AM = 1 m u l t i p l e t ( s e p a r a t i o n AH). I t i s supposed

t h a t t h e AM = 2 l i n e s a r e s h a r p and r e c t a n g u l a r and t h e AM = 1 l i n e s a r e broadened i n t o a s i n g l e r e c t a n g u l a r l i n e of w i d t h 7% / 2 2 / .

The e x p e r i m e n t a l d a t a a r e shown i n f i g u r e . 9 and t h e h y p e r f i n e s p l i t t i n g i s c l e a r l y s e e n . The r e s o l u t i o n i s % 100 W z . F i g u r e 10 shows d a t a f o r t h e same c r o s s i n g o b t a i n e d u s i n g t h e a c f i e l d m o d u l a t i o n t e c h n i q u e / 2 6 , 1 1 / . A s m a l l o s c i l l a t i n g f i e l d i s ap- p l i e d and t h e a c component of t h e t e m p e r a t u r e d i f - f e r e n c e i s d e t e c t e d u s i n g a second p s d . T h i s o f c o u r s e p r o v i d e s t h e d i f f e r e n t i a l of t h e f r e q u e n c y c r o s s i n g s i g n a l .

The d i f f e r e n t i a l s i g n a l i s o f p a r t i c u l a r va- l u e . The s i z e o f t h e c r o s s i n g s i g n a l AW/Wo a t a p a r t i c u l a r v a l u e o f f i e l d i s a p p r o x i m a t e l y e q u a l t o t h e a r e a of o v e r l a p o f t h e two l i n e s . T h e r e f o r e s i n c e t h e edge o f t h e (D

-

g BB) l i n e , V i , i s v e r y

I I

we measure the width of the

VI

line to be

%

9% -

FREQUENCY KHz)

somewhat larger than the span 7% of the 8 ~ 1 lines as expected. We see too that the change in dW/dB

n occurs in the same relative place on the high field side as expected.

4. CONCLUSION.- These three techniques have high resolution but for spectroscopic work they have the limitation that there needs to be a probe ion inside the system being investigated. It will be of considerable interest to see if this limitation can be overcome in the future as

i t

has for exam- ple in work using superconducting junctions of somewhat lower resolution

(%

5-10 GHz) where the generation and detection takes place in films bon- ded to the sample.

I am most grateful to my colleagues, A.A.

-40 -30 -20 -10 0 10 20 30 40 Ghazi, D.J. Jefferies and M.N. Wybourne for allo-

FIELD 0 (mT) wing me to quote unpublished work.

Fig. 9

:

The frequency crossing signal from v3+ ⁱⁿ

A1203. The crossing occurs at 3.1 T and at a fre- quency of 166

GHz

1261.

Fig.

10 :

The first differential of figure 9 obtai- ned by ac field modulation at 3 Hz 1261.

roughly vertical dW/dB gives directly the approxi- mate form of the 2g BB line, vz. However this is only true for the first half of the line. As the II

field increases the vn. hyperfine lines "disappear"

one by one into the vl line but eventually the tail of the first vs hyperfine line emerges from the far side of vl. At this point dW/dB should change abrup- tly and in figure

10

it can be seen that this occurs just after the point midway between the fourth and

fifth hyperfine lines. Using this hyperfine "ruler"

References

/I/ Kinder,H., Proc.14th 1nt.Conf.Low Temperature Physics, edited by M. Krusius and M. Vuorio, (North-Holland, Amsterdam) Vol 5

(

1975) p.287 121 Phonon Scattering in Solids, edited by L.J.

Challis, V.W. Rampton, A.F.G. Wyatt, (Plenum, New York) 1976

/3/ Meltzer,R.S. and Rives,J.E., Phys. Rev. Lett.

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