ULTRASONIC ATTENUATION AND SOUND VELOCITY ANOMALIES BELOW 5 K IN LaAl2

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ULTRASONIC ATTENUATION AND SOUND VELOCITY ANOMALIES BELOW 5 K IN LaAl2

S. Ewert, A. Hof, D. Lenz, H. Schmid

To cite this version:

S. Ewert, A. Hof, D. Lenz, H. Schmid. ULTRASONIC ATTENUATION AND SOUND VELOCITY

ANOMALIES BELOW 5 K IN LaAl2. Journal de Physique Colloques, 1981, 42 (C5), pp.C5-695-C5-

700. �10.1051/jphyscol:19815107�. �jpa-00220975�

JOURNAL U!i PHYSIClUE

CoZZoque C.5, suppZ6ment- au T Z ' 3 0 , I'orne 42, octobrc 1981 page C5-695

ULTRASONIC ATTENUATION AND SOUND VELOCITY ANOMALIES BELOW 5 K I N LaA12

S . Ewert, A . Hof, D. Lenz and Y H. ~ c h m i d t *

11. Phys. J n s t i t u t and*~nstil;u-1; J i i ~ IqetctZZkunde und MetaZZphy.;ik der Rhrfi kachen und Sonderforschuny:;bereich 125, Aachen

-

^JuZ-ich

-

Kd'Z??, r". 3. G.

Abstract.- Anelastic anomalies in LaA12 and (La+O.23at%Gd)Al2 be- low 10K have been studied by MHz attenuation and sound velocity in the normal- and superconducting state. Three anelastic pro- cesses involving different lattice defects have been identified.

Two of them are shown to exhibit a strong dependence on the con- centration of unpaired electrons. For one process this is due to changes in theelectronic component of the resonance damping con- stant, for the other due to changes of the relaxation rate. The third process is tentatively attributed to trapped hydrogen.

1. Introduction.- Measurements of ultrasonic attenuation (UA) and sound velocity (SV) in LaA12 /1/ and (La,Gd)A12 /2/ have revealed anomalous anelastic contributions superimposed on the normal temperature dependen- ce of UA and SV below 10K both in the superconducting ( S C ) and normal- conducting (NC) state. The origin of the underlaying atomistic processes is still unclear since detailed knowledge of the process parameters (re- laxation time, life time T , relaxation strength A d i s lacking. The ano- malies in (La,Gd)A12 were traced back to a simple relaxation process governed by the interaction of lattice defects with both conduction electrons and phonons /2/. Similarities of UA in LaA12 with UA in amor- phous superconductors and in glasses have been pointed out and the ano- malies were attributed to two-level systems with a broad distribution

in T and A R

-

^1/T / I / . The present note reports on simultaneous UA and SV measurements which are especially promising for the evaluation of

T (TI /2/.

2. Experimental.- We measured the frequency dependence of UA and SV (10 to 90 MHz), pulse echo and pulse-echo-overlap technique resp.) on a LaA12 crystal (residual resistivity ratio RRR=485) and for comparison on a (La+O. 23%Gd) A12 crystal (RRRgr155) in a ~ e ~ - c r ~ o s t a t surrounded by a LN2-cooled solenoid to suppress superconductivity. Growth and cha- racterization of the crystals has been described by Beyss et a1 /3/.

3 . Results.- We report mainly on LaA12 (figs.l,2) which exhibits low

temperature effects similar to those in (La,Gd)A12 (fig.3,/1,2/). The relative change of SV yields the modulus defect MD = AM/Mo =

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19815107

C5-696 JOURNAL DE PHYSIQUE

2 (v (8K)-v (T) ) /v (8K). We use v (8K)

,

the observed maximum velocity as refe.

rence instead of the unrelaxed velocity vo (see below). Below 8K the SV decreases (a MD is observed) in both samples at all frequencies in the NC and SC state. In the NC state MD increases monotonically with decrea- sing temperature. In the SC state MD is en-

hanced directly below Tc and becomes re- duced at lower temperatures, The NC+SC difference is pronounced in (La,Gd)A12

(fig.3) and tends towards MD=O for T+OK (c. f

.

^{also /I/)}

.

In LaA12 the MD reduc- tion around at 1K is only of order 2x1 0-' and

-

most important

-

below 1K the MD in- creases again. This indicates that in both crystals the limiting MD has not been reached at 0.5K.

In contrast to the small NC+SC effects on SC directly below Tc the rela- ted UA effects are strong since UA sensiti- vely responds to phonon-electron (PE) inter- 3

action / 4 / whereas Av/v is not influenced I . . . I , . . . I within 1

o - ~

/ 5 / . The PE contribution haNE ^{0 1 2 3 L 5 6 7 8}

Temperature T I K I

(indicated in figs.1-3 by the shaded areas)

FIG. 1 T-dependence of a and drops to zero below Tc according to the ty- NC and SC state pe of the NC+SC transition (BCS-behaviour (10 MHz)

in LaA12 /6/; AG-behaviour in (La,Gd)A12 1,. 3.27 K /7/). These PE effects only partly explain

our aN(T)-dependence in the NC state (aN monotoneously increasing down to lowest T instead of LaNE being independent of T _/4/)

f=QOMHt

-

and in the SC state (pronounced as-maximum

-I

at

-

1K (LaA12) and as-shoulder (La,Gd)A12). ¹ The further evaluation of UA (in con-

trast to MD which is directly obtained as

:

₅

1

a relative quantity) depends on the know- ' B ledge of AaNE and the background attenua-

-

^uo

tion aB (due to thermoelastic effects, Sam- u la

0

ple- and soundfield-geometry) .For (La,Cd)A12 ₁₂₀ the evaluation of LaNE, and aB has been

{

¹¹⁵

described elsewhere / 2 / . For LaA12 fig.4

shows a(T,130 MHz). We assume that ag is ^{0 1 2 3 6 5 6 7 8}

Temperature T I K I

given by the measured attenuation around

FIG.2 as fig.1 (90 MHz) 70K since AaNE (70K)zO. Fig. 4 shows that aB

-

closely approaches ag ( 0.5K) anc? is inde-

?endent of temperature between 0.5 and 10K.

Since doNE

-

f2, at 130 MHz AaNE>>AaNR. R- nally with aN being temperature independent between 3 and 6K we obtain AaNE (1 30 MHz) =

aN(5K)-aB. From this value the LaNE-contri- -4 x = QM123 f =90MHs

butions for the lower frequencies have been -5

calculated. Fig.5 shows aB(f) and AaNE (f)

-

which yields the "anomalous" UA contributhns

2

4 7 2

AaNR = aN- (AaNE + aB) (1) AaSR = as- (Aa ES + a ~ ) (2) shown in figs. 1-3. In the NC state AaNR mo- notonically increases down to the lowest T

(parallel to the MD increase). In the SC

state this contribution is strongly modified

, ,

^a

due to the pairing of electrons which caus- Temperature T

es the peaked AaSR(T) curves. Fig.2 shows FIG.^ as fig.2 (LarGd)A12 that ActSR can even be larger than AaNR

(c. f. also /8/).

4. Discussion.- For further understanding of the underlaying anelastic processes we 8

consider the frequency dependence of UA and MD. Federle et a1 / 7 / reported a linear quency dependence for the quantity aN(T)

-

aS(0.4K) shown for comparison in fig.5.How- o m Tmp.mtura T tK1

ever, according to eqs. ( I 1. ( 2 ) this quanti-

ty still contains the PE contribution. Af- a(130

evaluation of ag, AaNE ter subtraction of the corresponding

AaNE(f) contributions Federle's results exhibit a nonlinear f-dependen- ce in agreement with the present AaNR(f) results (fig.5). We note that our AaNR is more than an order of magnitude smaller (the same holds for MD). ~ h u s we conclude that the anomalies are caused by lattice defects of different concentrations in the investigated crystals.

Fig.6 compares the frequency dependence of MD and AaNRr

"SR

(plotted as decrement G = 0.115 a[dB/~lsl/f[MHzl) at selected temperatu- res. In the NC state (fig. 6a) the 6 (f)

-

and MD (f) -curves are shifted towards higher values with decreasing T without significant shape change.

This indicates that the shift is due to the temperature influence onAR and not on r . The same has been found in (La,Gd)A12/2/. Furthermore, it can be derived from fig.6a that both G andMD nearly follow a 1/T-tempe- rature dependence.These findings suggest that one and the same process determines 6 and MD. However, quantitative analysis of our data reveals

JOURNAL DE PHYSIQUE

a more complex situation. As an example we compare the b(f)- and MD(f)-profiles at 1K

with the Debye function ( W T ~ ) = I T A ~ ~ - W T ~ - D(w.rl); MDl ( U T , ) = A ~ , D ( ~ U T ~ ) with D ( u T ~ ) =

I l +2 T . We fit 6 1 ( ~ ~ 1 ) with its max- imum ( w ~ ~ = l ) to the measured d(1OMHz) value

(for the moment we neglect the misfit at higher frequencies which can be removed by a distribution in T ~ ) . However, comparing MDl(wrl) with the measured MD(f)-profile a serious discrepancy results: the measu- red MD is much larger than the expected MD at all frequencies (e.g. by the factor

1

6 at 10 MHz). This discrepancy cannot be removed by any continuous distribution in

T ~ . The dashed-dotted line in fig.6a de- 50 100 200

picts the surplus modulus defect MD-MD, Frequency f IMHzl

which is nearly independent of f. This in- FIG.5 Frequency dependence dicates that the related damping takes of ctB, AuNE and AuNR.

place at frequencies well above our f- range. It remains open whether the obser-

ved increase in 6 at higher f (fig. 6a) is

, ^{--- ap}

caused by the low frequency side of this

$

additional damping process (or due to a

T l-distribution). This process has not been -'o' ->-.,

-

^{':M), LaA12 r}

reported on before (however, evaluation of Federle's data /I/ reveals the same 6/MD- discrepancy). It is known that coexistence of more than one anelastic process impedes their quantitative evaluation from 6 ( £ 1 - E 1

and MD (f ) -measurements in a narrow f-range ^{- 4}

0

and yields misleading results from simul-

taneous G/MD-measurements at a single £re- 10 100 10 loo Frequency f I MHz) quency

.

FIG. 6a FIG. 6b In order to explain the general feat-

I n f - m e

of

ures of our measurements we discuss a mod- dependence of 6 and ZAv/v=MD el based on three anelastic processes PI, in NC (a) and SC (b) state P2,P3. Fig.7 shows schematical 6(f)- and MD(f)-profiles for Tc and for three lower T in the SC state. The 6 and MD values are multiplied by T/Tc to eliminate the AR

-

1/T dependence; the three MD contributions are plotted on top of each other. In the NC state (fig.7a, valid also for all T < 5 K ) PI determines the observed 6(f) and the sum of PI+P2+P3

d e t e r m i n e s MD(f) i n t h e p r e s e n t f - r a n g e

v.-i-=G 227q

Tzl.6 K

(between d a s h e d v e r t i c a l l i n e s ) .

--1

We a t t r i b u t e t o a n overdamped re-

( e . g . d i s l o c a t i o n k i n k ) . The damping f a c - s o n a n c e p r o c e s s c a u s e d by

t o r B r e s u l t s from i n t e r a c t i o n w i t h c o n d u c t i o n e l e c t r o n s ( B ) and phonons (Bp)

E

and a p o i n t d e f e c t (BD) which i s d r a g g e d

-

by t h e l a t t i c e d e f e c t / 9 / . W e a t t r i b u t e P2 t o a p a r e l a s t i c p r o c e s s ( e . g .

-

t y p e ) c a u s e d by an i m p u r i t y w i t h

a t i o n r a t e g i v e n by t h e sum o f e l e c t r o n i c vE and p h o n o n i c vF r a t e s / 2 / . S i n c e v E + v p > > f t h e P2 d o e s n o t

loa ( tinHz )

i n t h e NC s t a t e . F o r PI w e assume t h a t i n t h e p r e s e n t T-range i n t h e NC s t a t e BE =

F I G - 7 Model f o r discussion c o n s t a n d l a r g e compared w i t h Bp / l o / + o f p r e s e n t a n o m a l i e s BD ( - e x p ( H , / k T ) , / 9 / , H I = a c t i v a t i o n

e n e r g y f o r jump o r r o t a t i o n o f t h e d r a g g e d d e f e c t ) .

I n t h e SC s t a t e d i r e c t l y below Tc ( f i g . 7 b , l . 6 K ) t h e damping f a c t o r o f PI becomes d r a s t i c a l l y r e d u c e d ( s i n c e BE

-

number o f u n p a i r e d e l e c - t r o n s / l o / ) c a u s i n g a s h i f t o f PI t o h i g h e r f . T h i s l o w e r s 6 (10MHz)

,

^{i n -}

creases 6 ( 5 0 and 90 MHz) a s s e e n i n f i g . 6 b and i n c r e a s e s t h e MD m a i n l y a t low f ( f i g . l r 3 ) . The f u r t h e r T-dependence o f PI i s d e t e r m i n e d by Bp+BD. We e x p e c t t h a t i f BD>>Bp a t low T P I moves b a c k t o l o w e r f . A d d i t i o n a l l y we assume t h a t l o c k i n g o f t h e f o r c e d k i n k m o t i o n o c c u r s a t a T where t h e jump r a t e vD--l/BD becomes c o m p a r a b l e w i t h t h e u l t r a - s o n i c f r e q u e n c y £. Thus w i t h d e c r e a s i n g T l o c k i n g r e d u c e s PI ( f i g . 7 ~ ~ 1K). S i n c e a t 1K p r o c e s s P2 h a s e n t e r e d o u r f - r a n g e we s u p p o s e t h a t t h e d r a g g e d d e f e c t ( i n v o l v e d i n P I ) i s t h e same which ( i s o l a t e d i n t h e l a t t i c e ) c a u s e s P2. A t s t i l l l o w e r T ( f i g . 7 d r 0 . 6 K ) P I r e m a i n s p i n n e d and P2 h a s moved a c r o s s o u r f - r a n g e . I t i s t h i s p a s s a g e o f P2 which c a u s e s t h e o b s e r v e d &-peak and MD-reduction i n t h e SC s t a t e a r o u n d 1K.

From peak-shape ( f i g . 1 ) and £-dependence o f p e a k - t e m p e r a t u r e ( e . g . f i g . l , 2 ) w e o b t a i n a n a c t i v a t i o n e n e r g y o f 0.45 2 0.10 m e V ( T =2.10 -1 1

0

s e c ) f o r t h e p r o c e s s P2. S i n c e d u e t o wr3<<1 shows up o n l y i n MD i t s dynamic p r o p e r t i e s remain unknown. S t r i k i n g s i m i l a r i t i e s w i t h u l t r a s o n i c e f f e c t s c a u s e d by hydrogen i n SC Nb / 1 1 / s u g g e s t t o a t t r i - b u t e P3 t o a t r a p p e d hydrogen r e l a x a t i o n p r o c e s s .

The p r e s e n t work was s u p p o r t e d by t h e DFG (SFB 1 2 5 ) . R e f e r e n c e s .

/ I / G. F e d e r l e , K. D r a n s f e l d , H.E. Bdmmel, P. Rodhammer: S o l i d S t a t e

JOURNAL DE PHYSIQITE

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