RECENT EXPERIMENTAL STUDIES OF DYNAMICS OF SPIN GLASSES

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RECENT EXPERIMENTAL STUDIES OF DYNAMICS OF SPIN GLASSES

A. Murani

To cite this version:

A. Murani. RECENT EXPERIMENTAL STUDIES OF DYNAMICS OF SPIN GLASSES. Journal de

Physique Colloques, 1978, 39 (C6), pp.C6-1517-C6-1526. �10.1051/jphyscol:19786594�. �jpa-00218087�

JOURNAL D E PHYSIQUE

Colloque C6, supplkment au no 8, Tome 39, aofit 1978, page

C6-1517

RECENT EXPERIMENTAL STUDIES OF DYNAMICS OF S P I N GLASSES

A.P. Murani

Institut Lme-Langeuin, B.P.

156X,

38042 GrenobZe Cedex, F~rance.

Rdsum6.- On prdsente une revue des rdsultats expdrimentaux sur la dynamique de spin des verres de spin en alliages binaires, obtenus par des techniques esr, nmr, precession de muons, effet &ss- bauer et de diffusion de neutrons. Les rdsultats peuvent Etre dzcrits de facon cunsistante en ter- mes de spectre de temps de relaxation evoluant continuellement avec la temperature et s'dtendant de temps relativements courts

(T 'L

10-13s)

2 des temps trSs longs (T*) 2 des tempdratures au

voisignage du point de congdlation.

Abstract.- A review of the experimental results of the spin dynamics of binary spin glass alloys obtained with the help of esr, nmr, muon precession. Gssbauer effect and neutron scattering techniques is given. The results may be consitently described in terms of a spectrum of relaxation times evolving continuously with temperature and extending from relatively short

(T 'L

10-13s) to very long times

(T*)

at temperatures around and below the freezing temperature.

1.

INTRODUCTION.- Experimental studies of dynamics of spin glasses began about two decades ago with the first esr and

6 3

nrnr measurements on dilute

~ ~

Cu-Mn alloys by Owen et al. /I/ followed by further

-

investigations of the more concentrated alloys where the effects of freezing of spins on the dynamical properties were studied through the temperature de- pendence of the esr signal 12-41. Initially, host nrnr measurements were aimed at the magnetic proper- ties associated with the Kondo effect in very di- lute alloys 151 but more recently the nmr technique has also been applied to study the process of free- sing of spins in more concentrated alloys 16-91.

A closely similar probe is the muon precession technique 1101 which has also been sucessfully used in investigations of spin glasses 1111. A certain difference of feature from the nrnr and because of the unexplained weaker influence on the muon's free precession decay rate due to rapid solute spin fluctuations at high temperatures, the method becoies effectively comparable to the ~Essbauer effect technique which has been widely us& to study the onset of magnetic "ordering" in spin glass alloys /12-151. Neutron scattering techniques provide the most direct probes of spin dynamics and have been increasingly used in recent years to study dilute alloys as well as the more concentra-

I

ted spin glasses 116-221.

In the following we review the results of experi- mental studies of dynamics of spin glass alloys. We begin by considering the dynamics in the dilute

limit and at high temperatures and then proceed to examine its temperature dependence across the spin glass freezing temperature, in order to gain some insight into the process of freezing of spins espe- cially in relation to the question of the sharp phase transition predicted theoretically 123-251.

Finally we review the spin dynamics below the freezing temperature and examine the low temperature excitations of the spin system.

2. DILUTE LIMITIHIGH TEMPERATURE SPIN DYNAMICS.- The first esr measurements on dilute &-Mn alloys were carried out with the aim to study the s-d in- teraction between the conduction electrons and the localised

Mn

spins 111. Observation of well defined resonance signal with a relatively small g-shift and a linear Korringalaw temperature dependence of the line-width yield a coupling constant which is several orders of mangitude smaller than the Js-d obtained independently from the

3~~

nrnr line-shape and width in the same system 1261. It was soon re- cognised however 1271 that because of the strong coupling of the localised spins with the conduction electrons and the relatively long relaxation time constant of the latter with the lattice, the esr is bottlenecked so that the full effect of the s-d

interaction on the g-shift and the line-width and hence the spin dynamics cannot be observed. The longitudinal and the transverse relaxation times T1 and Tp of the host Cu-nuclei are, however, direc- tly influenced by the spin fluctuations. From the measurements of Ti in dilute

E-Mn

alloys Alloul et

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786594

c6-1518 JOURNAL DE PHYSIQUE

a l . 151 deduce Mn s p i n f l u c t u a t i o n time c o n s t a n t of The r e s u l t s show t h a t t h e s p e c t r a l f u n c t i o n becomes

T % IO-"/T. narrower i n t h e c e n t r a l r e g i o n w i t h a s h i f t of some

R e s u l t s of a r e c e n t n e u t r o n s c a t t e r i n g i n v e s t i g a t i o n of t h e i n t e n s i t y i n t o t h e h i g h energy wings. A t of t h e dynamics of s - M n a l l o y s c o n t a i n i n g between h i g h e r q ' s we observe i n c r e a s i n g broadening of t h e

1 and 7 a t XMn I281 show t h a t t h e s p e c t r a l f u n c t i o n s p e c t r a w i t h i n c r e a s i n g c o n c e n t r a t i o n . It should be i n t h e d i l u t e l i m i t i s a simple L o r e n t z i a n w i t h a mentioned, however, t h a t i n t h e a n a l y s i s of t h e d a t a r e l a t i v e l y narrow width ( h a l f w i d t h

r

^% 2 mdV a t t h e q-range h a s been e f f e c t i v e l y extended t o lower 300 K) r e s u l t i n g p r i n c i p a l l y from t h e Korringa re- v a l u e s and t h e energy range t o much h i g h e r v a l u e s l a x a t i o n of t h e s p i n s . The e f f e c t of s o l u t e - s o l u t e by a new method of a n a l y s i s of t h e TOF d a t a . I n our i n t e r a c t i o n with i n c r e a s i n g Mn c o n c e n t r a t i o n i s t o e a r l i e r measurements on a Cu-8 a t % Mn 1211 and a produce p r o g r e s s i v e l y l a r g e r d e p a r t u r e s from t h i s Au-10 a t % Fe a l l o y s 1221 a c o n s t a n t -q i n t e r p o l a - simple form which a r e p a r t i c u l a r l y n o t i c e a b l e a t t i o n t e c h n i q u e was employed which s e v e r e l y l i m i t e d

low q' s, f i g u r e 1

.

t h e lowest q-value and t h e energy range covered by

Lack of t h e o r e t i c a l models p r e v e n t a quan-

- a c o n s t a n t -q c u t through t h e q-w p l a n e , hence t h e

t i t a t i v e a n a l y s i s of t h e s p e c t r a l s h a p e s , a l t h o u g h some of t h e e a r l y measurements on Heisenberg para- magnets were analysed u s i n g semi-empirical forms of t h e s p e c t r a l f u n c t i o n s 1291. I n t h e c a s e of s p i n g l a s s a l l o y s , t h e presence of two channels of r e l a x a t i o n

-

t h e s o l u t e i n t e r a c t i o n s and t h e Korringa c o u p l i n g s

-

complicated t h e s i t u a t i o n even f u r t h e r . It should be mentioned, however, t h a t t h e

I measurements on k - F e a l l o y s by Loewenhaupt e t a1 1181 and by Scheuer e t a 1 119, 201 have been i n t e r - p r e t e d simply i n terms of a sum of two L o r e n t z i a n s p e c t r a l f u n c t i o n s of d i f f e r e n t w i d t h s which they a t t r i b u t e t o Korringa r e l a x a t i o n of s i n g l e i s o l a t e d s p i n s ( a broad L o r e n t z i a n of half-width

r

^% 10 meV a t 300 K) and of magnetic c l u s t e r s ( a narrower L o r e n t z i a n w i t h

r

%2meV a t 300 K)

.

The l a t t e r have a p p a r e n t l y been i d e n t i f i e d w i t h s t a t i s t i c a l near- neighbour c l u s t e r s such a s p a i r s , t r i p l e t s and h i g h e r agglomerates. T h e i r a n a l y s i s i m p l i e s t h a t t h e r e l a t i v e i n t e n s i t y o f t h e broad, h i g h energy p a r t of t h e s p e c t r a l f u n c t i o n ( a s s o c i a t e d w i t h s i n - g l e i s o l a t e d s p i n s - should d e c r e a s e w i t h i n c r e a s i n g s o l u t e c o n c e n t r a t i o n whereas t h e r e s u l t s f o r

& -

Mn a l l o y s show t h a t t h e i n t e n s i t y i n t h e h i g h energy wings i n c r e a s e s w i t h i n c r e a s i n g s o l u t e c o n c e n t r a t i o n and t h a t t h e s p e c t r a l f u n c t i o n i n t h e d i l u t e l i m i t

' i

a s s o c i a t e d w i t h t h e Korringa r e l a x a t i o n of i s o l a t e d d e v i a t i o n s from t h e simple L o r e n t z i a n form of t h e s p e c t r a l f u n c t i o n a t h i g h energy t r a n s f e r s and l o w q ' s could n o t b e observed.

Fig. 1 : S(q,w) v s w f o r q = 0.08

I-'

a t 300 K f o r s p i n s is a simple L o r e n t z i a n of r e l a t i v e l y narrow s e v e r a l E-Mna l l o y s . The continuous curves repre-

s e n t t h e b e s t f i t s t o t h e d a t a u s i n g t h e Lorentzian ( r 'L

*

^{at 300 f o r}

^{& -}

^MU

form of t h e s p e c t r a l f u n c t i o n . The i a t a p o i n t s f o r 3. THE TEMPERATURE DEPENDENCE OF THE SPIN DYNAMICS.- e l a s t i c s c a t t e r i n g a r e not shown i n t h e diagram.

R e s u l t s from r e f . 1281. ( F r e e z i n g of S p i n s ) . 3 . 1 . Neutron S c a t t e r i n g Measu- rements.- An important o b s e r v a t i o n from t h e r e s u l t s of t h e l a s t s e c t i o n i s t h a t t h e paramagnetic

s p e c t r a l f u n c t i o n h a s c o n t r i b u t i o n s from two chan- n e l s of r e l a x a t i o n , namely t h e Korringa mechanism and t h e s o l u t e - s o l u t e i n t e r a c t i o n s . The temperature dependence of t h e dynamics i s t h e r e f o r e expected t o b e r a t h e r complex and r e f l e c t t h e temperature dependence of b o t h t h e s e p r o c e s s e s .

The r e s u l t s of a r e c e n t d e t a i l e d s t u d y on a Cu-3 a t

% Mn a l l o y 1291 a r e shown i n f i g u r e 2 where t h e temperature dependence of t h e h a l f - w i d t h s of t h e s p e c t r a a r e shown f o r q = 1.0

i-'

and f o r t h e l i m i t q*

.

Fig. 2 : The half-widths a t h a l f - h e i g h t s f o r t h e broad p a r t of t h e q u a s i e l a s i i c s p e c t r a f o r a Cu-3 a t % Mn sample f o r q = 1.0 A-' and i n t h e l i m i t q+O. The i n s e t shows t h e ac s u s c e p t i b i l i t y

x

on t h e same temperature s c a l e . The dashed l i n e s show t h e high t e m p e r a t u r e s l o p e s . R e s u l t s form r e f . 1301.

The dashed l i n e g i v e s t h e h i g h temperature e x t r a p o - l a t i o n s f o r t h e two c a s e s . I n t h e same diagram, on t h e same temperature s c a l e t h e a . c s u s c e p t i b i l i t y

x

i s a l s o shown, w i t h a peak a t 17 K. The r e s u l t s i n d i c a t e t h a t t h e s p e c t r a l width b e g i n s t o narrow a t r e l a t i v e l y h i g h t e m p e r a t u r e s , reaches a c e r t a i n f i n i t e v a l u e and t h e n i n c r e a s e s a g a i n a t lower temperatures t h u s going through a shallow minimum a t a temperature w e l l above t h e " f r e e z i n g tempera- t u r e " of 17 K. S i m i l a r r e s u l t s have been o b t a i n e d f o r a Cu-8 a t % Mn and a Au-10 a t % Fe a l l o y s 121, 221. However, t h e r e s u l t s of measurements on a s e r i e s of AuFe a l l o y s by Scheuer e t a l . 119, 201 a p p a r e n t l y show l i n e a r d e c r e a s e t o z e r o a t T=O of t h e line-widths a s s o c i a t e d w i t h t h e i s o l a t e d s p i n s and t h e magnetic c l u s t e r s mentioned e a r l i e r . We r e c a l l t h a t t h e n e u t r o n s c a t t e r i n g c r o s s - s e c t i o n f o r a system of N s p i n s i s given by

where S.(q,w) i s t h e dynamic s t r u c t u r e f a c t o r r e p r e - s e n t i n g t h e i n e l a s t i c j q u a s i - e l a s t i c s c a t t e r i n g and S ( q ) r e p r e s e n t s t h e e l a s t i c s c a t t e r i n g .

I n f i g u r e 3 t h e observed temperature v a r i a t i o n s of t h e e l a s t i c c r o s s - s e c t i o n , t h e i n t e g r a t e d quai- e l a s t i c c r o s s - s e c t i o n a s w e l l a s t h e i r sum a r e shown f o r a Cu- 8 a t % Mn sample 1211. The e l a s t i c s c a t - t e r i n g i s approximatly c o n s t a n t a t high temperatures where i t i s due t o t h e n u c l e a r incoherent c r o s s -

s e c t i o n of t h e sample, but t h e n begins t o i n c r e a s e w i t h d e c r e a s i n g temperature around about t h e same temperature where t h e q u a s i - e l a s t i c s c a t t e r i n g s t a r t s t o d e c r e a s e , t h e s e v a r i a t i o n s b e i n g continuous a c r o s s t h e s p i n g l a s s f r e e z i n g temperature determi- ned from t h e a c s u s c e p t i b i l i t y measurements.

t

^O

^{Q-ELASTIC 1}

F i g . 3 : The temperature dependence of t h e e l a s t i c c r o s s - s e c t i o n (energy r e s o l u t i o n 230 peV), t h e in- t e g r a t e d q u a s i - e l a s t i c c r o s s - s e c t i o n and t h e i r sum, measured f o r a Cu-8 a t % Mn sample. The dashed ver- t i c a l l i n e marks t h e temperature of t h e maximum i n t h e a c s u s c e p t i b i l i t y . R e s u l t s from r e f . / 2 1 / .

It should b e remembered, however, t h a t t h e separa- t i o n of t h e e l a s t i c s c a t t e r i n g from t h e i n e l a s t i c / q u a s i - e l a s t i c s c a t t e r i n g c o n t r i b u t i o n s i s l i m i t e d by t h e f i n i t e i n s t r u m e n t a l energy r e s o l u t i o n . A s seen below t h i s h a s s p e c i a l r e l e v a n c e f o r s p i n g l a s s e s where w i t h t h e e v o l u t i o n of c o r r e l a t i o n s i n

C6-1520

JOURNAL DE PHYSIQUE

the spin system with decreasing temperature a whole spectrum of r e l a x a t i o n times T develops. I t t h e r e - fore appears meaningful to express S.(q,u>) as

S.(q,w) = EP(T,r

a

) i r p V

( 2 )

where P(T, T ) is the probability distribution at temperature T of the relaxation times T (= -fi/r ) . Hence if T is small compared to the elastic energy resolution AE of a spectrometer the scattering would be indistinguishable from that due to a truly elastic process. It is obvious therefore that if a wide spectrum of relaxation times exists in spin glasses the result of measurement of the elastic scattering cross-section will depend strongly on the instrumental energy resolution i.e. the measu- rement time constant. This is clearly borne out by the results of measurements of the elastic scatte- ring cross-section for the Cu - 8 at % Mn alloy /31/ employing energy resolutions of 1.5, 25 and 230 yev, figure A.

Fig. A : The temperature variation of the measured elastic cross-section 4S' using energy resolutions of a) 1.5 ueV, b) 25 yeV and c) 230 yeV, for several q-values. The arrows indicate the temperature where marked increase in the cross-section with decreasing

temperature begin.Results from ref. /31/.

We see that the temperatures where the marked in- crease of the elastic scattering cross sections occur depend strongly on the energy resolutions em- ployed and hence on the measurement time constant T ( = fi/AE). It should be noted that these temperatu- res vary systematically with T and are all higher than the temperature of the maximum in the ac sus- ceptibility shown by the dashed vertical line in the figure.

The elastic magnetic scattering i.e. the static structure factor S (q) has a special significance in spin glass theory, it heing directly related to the Edwards-Anderson order parameter cj. (23), for Se(q) = | F2( q ) 2 [ixp i£.(r.-r.J <Si> <S.>

ij

= 2 F2(q)Zexp f i£. r j <Si + n> <Si> (3) where r = r. - r. and the bar represents the ave-

—n —j —l

rage over-all spins.Hence, taking the inverse Four- rier transform we obtain the EA order parameter

7 1 se (<*>

* " <Si> • N \ 2 F M ^ <⁴>

Although measurements of S (q) over the whole q-range are not practicable, the results over a limited q-range can nevertheless reflect the actual behaviour of the order parameter q. As seen from the above results S (q) is peaked in the forward direction (q=0) and for the q- range over which any temperature dependence is seen, the temperature of the marked increase is roughly the same.

Hence each of the S (q) vs T curves represents the tempe- rature variation of the EA order parameter qT where the subscript T denotes the finite time constant x of the

o o measurement, a^. is defined as

^ O " ^{< S}i^{> 2}T⁰ " i X >T ^{< S}i^{> 2}X (5) a o a

where the bracket < > represents the time average over the period x.

Thus all quasi-elastic processes with time constants T longer than T (=-n7A~) contribute to the order

ct o Ziii

parameter S^. . As discussed below the Mossbauer ot

effect which is another probe for the dynamics of spins does, in effect, measure the square root of the order parameter 5^ with a time constant x ^ 10-7(for 57Fe).These results also show a si-

o

gnificantly higher temperature for the marked in- crease in the average nuclear hyperfine field (commonly referred to as the "ordering" temperature) compared with the temperature of the maximum in the ac susceptibility X /'^) 15/.

3.2. ESR measurements.- The observation of the esr of Mn solute spins in Cu-Mn alloys owes to the bot- tleneck effect in the combined resonance of the

l o c a l moment conduction e l e c t r o n s p i n systems due t o t h e r e l a t i v e l y long r e l a x a t i o n time c o n s t a n t of t h e l a t t e r t o t h e l a t t i c e 1271. The combined reso- nance of t h e coupled systems n e v e r t h e l e s s r e f l e c t s t h e dynamics of t h e Mn s p i n s which b e a r s t r o n g r e - semblence t o t h e s p i n dynamics observed i n neutron s c a t t e r i n g measurements. Following Owen e t a l . 1121 t h e e s r s p i n dynamics i n c o n c e n t r a t e d

G-k

a l l o y s were s t u d i e d i n d e t a i l by G r i f f i t h s / 3 / and l a t e r by Okuda and Date 141. I n c l o s e s i m i l a r i t y w i t h t h e temperature dependence of t h e q u a s i - e l a s t i c s p e c t r a l width i n n e u t r o n s c a t t e r i n g t h e e s r line-width d e c r e a s e s with d e c r e a s i n g temperature and t h e n goes through a s h a l l o w minimum a t a temperature w e l l above t h e s p i n g l a s s f r e e z i n g temperature, f i g u r e 5.

F i g . 5 : The e s r l i n e - w i d t h AH and t h e l i n e - s h i f t ( w / y

-

H ) a s a f u n c t i o n of temperature f o r a Cu-2 a t % Mn % l o y . The temperature of t h e maximum i n t h e s t a t i c s u s c e p t i b i l i t y f o r t h i s c o n c e n t r a t i o n of Mn i s expected t o be around 13

-

14 K. R e s u l t s from r e f . / 4 / . The i n s e t shows t h e e s r i n t e n s i t y - pro- p o r t i o n a l t o t h e s u s c e p t i b i l i t y

x -

and t h e q u a n t i - t y S.IxT ( s i g n a l i n t e n s i t y x temperature) p l o t t e d a s a f u n c t i o n of temperature f o r a Cu-4 a t % Mn a l l o y . The r e s u l t s o b t a i n e d a r e s l i g h t l y d i f f e r e n t i f a s t e a d y f i e l d of 5 kOe is a p p l i e d when c o o l i n g t h e sample t o low temperatures. R e s u l t s from r e f . 131.

Another important r e s u l t from t h e measurements i s t h a t t h e e s r l i n e p o s i t i o n b e g i n s t o s h i f t ' t o lower f i e l d s around about t h e same temperature as t h a t of t h e minimum i n t h e l i n e - w i d t h . T h i s temperature de- pendent f i e l d s h i f t was f i r s t observed by Owen e t a l . /2/ who i n t e r p r e t e d it i n terms of an a n t i f e r -

1

romagnetic resonance. Recently, Malozemoff and Jamet 1321 have i n t e r p r e t e d t h e i r measurements of t h e e s r f i e l d - s h i f t s i n t h i n f i l m s of amorphous Gdn.37Aln.67 samples i n terms of l o c a l demagnetizing f i e l d s due t o inhomogeneous m a g n e t i s a t i o n r e g i o n s

w i t h i n t h e system and suggested t h a t a s i m i l a r i n t e r p r e t a t i o n could be a p p l i e d t o t h e e s r r e s u l t s f o r Cu

-

M n a l l o y s a l s o .

-

We r e c a l l t h a t t h e resonance i n t e n s i t y of t h e e s r s i g n a l i n t h e paramagnetic phase i s p r o p o r t i o n a l t o t h e s u s c e p t i b i l i t y

X.

This s i g n a l i n t e n s i t y and t h e q u a n t i t y ' s i g n a l i n t e n s i t y x temperature' i n G r i f - f i t h s ' r e s u l t s / 3 / a r e shown i n t h e i n s e t i n f i g u r e 5. The l a t t e r q u a n t i t y , i t should b e p o i n t e d o u t , corresponds t o t h e i n t e g r a l of t h e broad q u a s i - e l a s t i c s c a t t e r i n g i n t e n s i t y i n n e u t r o n s c a t t e r i n g measurements. The s i m i l a r i t y between t h e temperatu- r e v a r i a t i o n of t h e two, p a r t i c u l a r l y t h e i r c o n t i - nuous diminuation a c r o s s t h e f r e e z i n g temperature i s t h e r e f o r e n o t s u r p r i s i n g . Assuming t h a t hhe sus- c e p t i b i l i t y obeys approximately t h e Curie-law

x

⁼ C/T, t h e broad q u a s i - e l a s t i c spectrum i n n e u t r o n s c a t t e r i n g measurements is t h e n seen t o b e propor- t i o n a l t o t h e number of s p i n s w i t h r e l a t i v e l y r a p i d r e l a x a t i o n times. S i m i l a r l y i n t h e e s r t h e q u a n t i t y

"resonance i n t e n s i t y x temperature" i s p r o p o r t i o n a l t o t h e number of Mn s p i n s which can "respond" with t h e resonance frequency. Both r e s u l t s t h e r e f o r e in- d i c a t e a p r o g r e s s i v e and continuous diminution a c r o s s t h e s p i n g l a s s f r e e z i n g temperature of t h e f r a c t i o n of Mn s p i n s with r e l a t i v e l y r a p i d f l u c t u a - t i o n t i m e s . Also, t h e i n t e g r a t e d resonance i n t e n s i t y which should s t r i c t l y b e p r o p o r t i o n a l t o t h e s t a t i c s u s c e p t i b i l i t y x ( w 0 ) i n e f f e c t measures an e f f e c t i - ve s u s c e p t i b i l i t y a t a frequency w s i n c e t h e reso- nance s i g n a l only i n c l u d e s Mn s p i n s which can "reso- n a t e l1 w i t h t h e d r i v i n g microwave f i e l d . Hence, a s w i t h t h e n e u t r o n s c a t t e r i n g r e s u l t s 1211 t h e tempe- r a t u r e of t h e maximum i n t h e resonance s i g n a l should occur a t a h i g h e r temperature t h a n t h e maximum i n t h e s u s c e p t i b i l i t y measured w i t h a slower frequency of t h e a c technique allowing, of course, f o r any f i e l d v a r i a t i o n of t h e temperature of t h e maximum.

Although t h e r e a r e i n d i c a t i o n s i n G r i f f i t h s ' r e s u l t s /3/ t h a t t h i s may b e s o , t h e s u g g e s t i o n needs f u r - t h e r v e r i f i c a t i o n .

3.3. NMR measurements .Host 3 ~ u nmr measurements on Cu-Mn s p i n g l a s s a l l o y s c o n t a i n i n g between 1000 and -

4000 ppm Mn were f i r s t r e p o r t e d by McLaughlin and A l l o u l 161. The r e s u l t s show continuous diminution w i t h d e c r e a s i n g temperature a c r o s s t h e s p i n g l a s s

t r a n s i t i o n temperature of t h e l o n g i t u d i n a l and t h e t r a n s v e r s e r e l a x a t i o n times and of t h e resonance i n t e n s i t y . I n t h e s e d i l u t e samples t h e a u t h o r s found no evidence of any s t a t i c line-broadening e f f e c t s due t o f r o z e n - i n c o n f i g u r a t i o n s of Mn s p i n s ,

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whereas i n subsequent measurements by L e v i t t and Walstedt / 7 / on a more c o n c e n t r a t e d a l l o y c o n t a i n i n g

1 a t % MrI and on a l l o y s c o n t a i n i n g 0.6 and 1 a t % M r I

/a/

t h e l i n e - w i d t h AH was found t o i n c r e a s e r a t h e r slowly w i t h f i e l d and t o have a l a r g e f i n i t e v a l u e AHo a s H + 0 , g i v i n g d e f i n i t e evidence of s t a t i c f i e l d s due t o "frozen-in" Mn s p i n s . I n t h e s e l a t t e r measurements t h e resonance i n t e n s i t y was found t o d e c r e a s e w i t h d e c r e a s i n g temperature from a tempe- r a t u r e w e l l above TF, a s i n t h e more d i l u t e a l l o y s , and t o go through a minimum a t a temperature around T 12 i n c r e a s i n g a g a i n a t low t e m p e r a t u r e s , f i g u r e 6.

F

I _0.1

I

I 10

REDUCED TEMPERATURE T/To

Fig. 6 : The temperature dependence of t h e nmr s p i n echo i n t e n s i t y f o r t h r e e Cu-Mn a l l o y s of Mn concea- t r a t i o n s 0.19, 0.62 and 1.01 a t % Mn. The tempera- t u r e s c a l e i s r e l a t i v e t o To t h e s p i n g l a s s freezing temperature observed i n t h e s t a t i c s u s c e p t i b i l i t y measurements. R e s u l t s from r e f .

/a/.

The t r a n s v e r s e r e l a x a t i o n time TI was s i m i l a r l y found t o go through a ( s h a l l o w e r ) minimum a t a tem- p e r a t u r e below TF, and i n c r e a s e by a small amount a t low t e m p e r a t u r e s , f i g u r e 7.

The i n t e r p r e t a t i o n of s o l u t e s p i n dynamics from t h e h o s t nmr measurements i s more complicated t h a n from t h e e s r measurements f o r example, s i n c e t h e s p i n dynamics a r e observed i n d i r e c t l y through t h e i r i n - f l u e n c e on t h e h o s t Gu-nuclei which e x p e r i e n c e a wide d i s t r i b u t i o n of RKKY h y p e r f i n e f i e l d s . Presen- c e of an e x t e r n a l f i e l d f u r t h e r complicates t h e i n t e r p r e t a t i o n . For example, i n r e c e n t measurements of t h e l o n g i t u d i n a l r e l a x a t i o n times TI on e x t r e m l y d i l u t e a l l o y s c o n t a i n i n g between 10 and 40 ppm Mn 191 t h e adopted a n a l y s i s s u g g e s t s t h a t t h e i m p u r i t y

s p i n c o r r e l a t i o n time d e c r e a s e s w i t h i n c r e a s i n g a p p l i e d f i e l d .

-

3

P

⁰ EXPONENTIAL =CAY A GAUSSIAN =CAY 0 MIXED M C A Y -

EXPONENTIAL ASYMPlUTE 0

F i g . 7 : The temperature dependence of t h e t r a n s v e r s e r e l a x a t i o n time T2 f o r a CU- 1 a t % Mn a l l o y measured a t t h e resonance frequency of 25.5 Mhz.

R e s u l t s from r e f . 171.

A n a l y s i s o f t h e s e r e s u l t s apparentlyshowwelldefined t e m p e r a t u r e s f o r t h e o n s e t o f f r e e z i n g of s o l u t e s p i n s . T h e s e t e m p e r a t u r e s , f u r t h e r - m o r e , a r e thesame a s t h o s e o b t a i n e d f r o m susceptibilitymeasurements 1331. A t t h e sametime, however, t h e r e s u l t s s u g g e s t t h a t t h e mean i m p u r i t ~ s p i n c o r r e l a t i o n t i m e i n c r e a s e s c o n t i n u o u s l y w i t h d e c r e a s i n g temperature a c r o s s t h e f r e e z i n g t e m p e - r a t u r e reaching a v a l u e of about ~ 1 0 - ~ s a t a temperature r o u g h l y a f a c t o r 2 0 lower than t h e f r e e z i n g temperature T ~ '

The i n f l u e n c e on t h e t r a n s v e r s e r e l a x a t i o n time of a nucleus from a f l u c t u a t i n g source of h y p e r f i n e f i e l d hi, such a s t h e s o l u t e s p i n , may b e d i v i d e d i n t o t h r e e r e g i o n s depending on t h e r e l a t i v e time c o n s t a n t s of t h e p r e c e s s i o n p e r i o d (yh.)-l of t h e nucleus and t h e c o r r e l a t i o n time T of t h e source ( i . e

.

t h e s p i n )

.

^Thus,

a ) when (yhi) <<l/Tc, t h e c o n t r i b u t i o n t o t h e r e l a - x a t i o n time i s g i v e n by T T I % (yhi)' T ~ .

b ) However, when t h e c o r r e l a t i o n time T~ of t h e i m p u r i t y s p i n i s comparable t o (yh.)-l t h e t r a n s - v e r s e r e l a x a t i o n time i s determined d i r e c t l y by T

c ' i . e . T2 ^Q T ~ .

c ) F i n a l l y , i f t h e c o r r e l a t i o n time i s v e r y long compared w i t h ( ~ h ~ ) - ' i . e . (yhi) >> I / T ~ , t h e hyper- f i n e f i e l d only l e a d s t o s t a t i c l i n e broadening e f f e c t s , t h e c o n t r i b u t i o n t o Ta i s t h e n mainly from g r a d i e n t s i n t h e h y p e r f i n e f i e l d .

Also i n t h e i n t e r p r e t a t i o n of t h e nmr d a t a i t i s r e c a l l e d t h a t t h e s p e c t r o m e t e r dead time due t o r f p u l s e overload i s f a i r l y l o n g , 2. 50 1-1s which p u t s a l i m i t t o t h e s h o r t e s t r e l a x a t i o n time T p which can b e measured i n t h e experiments.

We can now s e e how t h e s o l u t e s p i n dynamics obser- ved i n n e u t r o n s c a t t e r i n g measurements a r e c o n s i s - t e n t w i t h t h e nmr d a t a . A t high temperatures, t h e Mn s p i n c o r r e l a t i o n time T i s s h o r t ^% 10-13s, and t h e average RKKY f i e l d hi a t t h e Cu-nucleus (% 600 Oe f o r 1 a t % Mn) i s such t h a t (yhi) <<

11~;

s o t h a t t h e c o n t r i b u t i o n t o Tz i s T?' ^% ( y h i ) 2 ~ c . Hence w i t h d e c r e a s i n g temperature a s t h e s p i n dyna- mics slow down i . e . a s T i n c r e a s e s one observes a

r e d u c t i o n of T p . The n e u t r o n s c a t t e r i n g r e s u l t s in- d i c a t e a d i s t r i b u t i o n of s p i n c o r r e l a t i o n times -c which t o g e t h e r with a d i s t r i b u t i o n of t h e h y p e r f i n e

f i e l d s hi s u g g e s t s t h a t f o r some of t h e n u c l e i T p would become much s h o r t e r t h a n f o r o t h e r s . When t h e s e times g e t s h o r t e r t h a n t h e s p e c t r o m e t e r dead time t h e corresponding n u c l e i a r e l o s t from t h e si- g n a l . A s t h e temperature d e c r e a s e s and approaches TF t h e s p i n dynamics pass r a p i d l y from t h e f a s t f l u c t u a t i o n regime (yh.) << I

ITc

t o r h e slow f l u c - t u a t i o n regime(yhi) % I / T l e a d i n g n o t only t o t h e r e d u c t i o n of t h e average measured T2 b u t a l s o of t h e i n t e n s i t y . F i n a l l y a s t h e c o r r e l a t i o n times of t h e i m p u r i t y s p i n s b e g i n t o g e t very long (yh.) >>

l / ~ ~ , t h e h y p e r f i n e f i e l d s l e a d o n l y t o s t a t i c l i n e broadening e f f e c t s , t h e i r c o n t r i b u t i o n t o T 2 of t h e observed n u c l e i h e i n g mainly through any r e s u l t a n t f i e l d g r a d i e n t s .

Thus a t low temperatures a s T2's become l o n g e r a g a i n t h e s e n u c l e i r e t u r n t o t h e s i g n a l and we s e e n o t o n l y an i n c r e a s e of t h e i n t e n s i t y b u t a l s o of t h e average measured T2. There i s , however, a n e t l o s s of s i g n a l i n t e n s i t y a t low temperatures (compared w i t h h i g h e r t e m p e r a t u r e s ) through n u c l e i which e x p e r i e n c e very l a r g e s t a t i c h y p e r f i n e f i e l d s and a r e t h u s l o s t i n t o t h e very l a r g e wings of t h e broa- dened s i g n a l , and through t h o s e t h a t s t i l l experien- c e r a p i d Mn s p i n f l u c t u a t i o n s and have T2 below t h e s p e c t r o m e t e r dead time. Thus t h e nmr r e s u l t s a r e c o n s i s t e n t w i t h a wide- spectrum of r e l a x a t i o n times a s observed i n n e u t r o n s c a t t e r i n g measurements also.

3 . 4 . Muon P r e c e s s i o n Technique.- I n t h i s techniqueof measurement t h e muons a r e implanted i n t o t h e sample t o be i n v e s t i g a t e d where t h e y occupy i n t e r s t i t i a l s i t e s , t h e i r s p i n s p r e c e s s i n g about a n a p p l i e d pola- r i s i n g f i e l d . Themuon h a l f - l i f e i s %2 x 10'~s. It decays through p o s i t r o n (B+) emission p r e f e r e n t i a l l y a l o n g i t s s p i n d i r e c t i o n , s o t h a t o s c i l l a t i o n s i n 6'-detection

r a t e a r e observed i n a d e t e c t o r p o s i t i o n e d a t an a n g l e t o t h e a p p l i e d f i e l d . This technique of pro- b i n g t h e dynamics of s o l u t e s p i n s i s s i m i l a r t o t h e h o s t nmr measurements i n t h a t i n b o t h c a s e s t h e s p i n dynamics i n f l u e n c e t h e t r a n s v e r s e r e l a x a t i o n times T2 of t h e probes. However, t h e dominant h y p e r f i n e f i e l d a t t h e muon s i t e i s through t h e d i p o l a r cou- p l i n g w i t h t h e s o l u t e s p i n s which i s an o r d e r of magnitude s m a l l e r t h a n t h e RKKY f i e l d a t t h e 6 3 ~ ~

n u c l e i . The gyromagnetic r a t i o y of t h e muon i s , Fi

however, an o r d e r of mangitude s m a l l e r t h a n t h a t f o r t h e Cu-nuclei, ( I thank D . McLauglin f o r b r i n g i n g t h i s t o my a t t e n t i o n ) s o t h a t t h e average ( y h . ) a t

1-1 1 t h e muon s i t e s i s of t h e same o r d e r of magnitude a s t h a t f o r t h e Cu-nuclei. However, i n t h e f a s t f l u c - t u a t i o n regime, T~ << ( y h .)-' t h e i n f l u e n c e of t h e

?J 1

s o l u t e s p i n dynamics on t h e muon f r e e p r e c e s s i o n decay time T: i s much weaker t h a n would be expected from a s t r a i g h t comparison w i t h t h e nmr r e s u l t s where t h e s p i n echo decay time ^{T p} begins t o decrea-

s e markedly from a r e l a t i v e l y h i g h temperature. It appears t h a t a s t h e temperature approaches t h e f r e e z i n g temperature TF t h e s p i n dynamics a r e slowing down t o t h e v a l u e T % (yphi)-' when t h e i n f l u e n c e on muon's d e p o l a r i s a t i o n r a t e becomes n o t i c e a b l e (T: % T ~ ) . As t h e s o l u t e s p i n dynamics slow down even f u r t h e r i . e . a s T << ( y h.)-' t h e

IJ

1

s t a t i c f i e l d s which a r e produced with random d i r e c - t i o n s and magnitudes, a l s o cause t h e same e f f e c t i v e d e p o l a r i s a t i o n of t h e muons. I n t h i s r e s p e c t t h e muon d e p o l a r i s a t i o n technique i s d i f f e r e n t from t h e h o s t nmr measurements where t h e s t a t i c f i e l d s mainly produce inhomogeneous l i n e broadening (with some of t h e n u c l e i l o s t i n t o t h e wings), i . e . t h e t r a n s v e r s e r e l a x a t i o n time Tp of t h e n u c l e i which a r e observed i n nmr i s n o t d i r e c t l y r e l a t e d t o t h e line-broade- n i n g , whereas i n t h e muon p r e c e s s i o n method T: and l i n e broadening a r e r e l a t e d .

I n f i g u r e 8 we reproduce t h e r e s u l t s of F i o r y 1111 on t h e v a r i a t i o n of t h e muon d e p o l a r i s a t i o n r a t e A i n a Au-0.7% Fe a l l o y ( A = ( y T: )- ), a s a func-

1-1

t i o n of t h e reduced temperature TIT where T ^E TF.

0'

I n t h e diagram t h e v e r t i c a l l i n e through t h e freezing t e m p e r a t u r e (TITo= 1) i s added f o r emphasis. The r e s u l t s i n d i c a t e a r e l a t i v e l y narrow t e m p e r a t u r e range over which t h e d e p o l a r i s i n g f i e l d s develop and t h e i r r a p i d continuous i n c r e a s e a c r o s s t h e temperature TF ( t h e f r e e z i n g temperature i n t h e s t a t i c s u s c e p t i b i l i t y ) and t h e approach t o s a t u r a - t i o n a s T + 0 K.

The r e l a t i v e l y weak i n f l u e n c e of t h e s o l u t e s p i n s

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on t h e T* of muons i n t h e f a s t f l u c t u a t i o n regime only s p l i t t i n g s comparable t o o r l a r g e r t h a n t h i s ( T ~ << (yhi)-') means t h a t e x c e p t over a very small

temperature range t h e muon d e p o l a r i s a t i o n p r i n c i p a l - l y o c c u r s w i t h t h e o n s e t of s t a t i c f i e l d s ( i . e . T~ > ( y h . ) - I ) . Thus t h e method becomes comparable t o t h e MEssbauer e f f e c t technique where t h e n u c l e a r h y p e r f i n e f i e l d due t o t h e s o l u t e s p i n i s " f e l t "

only when -r 2 (yhi)-l.

Fig. 8 : The muon d e p o l a r i s a t i o n r a t e A f o r a Au- 0.7 a t % Fe a l l o y a s a f u n c t i o n of t h e reduced tem- p e r a t u r e TIT of t h e maximum i n t h e s t a t i c s u s c e p t i - b i l i t y , whicg i s emphasised by t h e added v e r t i c a l

l i n e through TITo = 1. R e s u l t s from r e f . / I l l .

3.5. ~ g s s b a u e r E f f e c t . - A s a probe of s p i n dynamics t h e Mgssbauer e f f e c t i s somewhat d i f f e r e n t from t h e h o s t nmr t e c h n i q u e i n t h a t it does n o t measure t h e i n f l u e n c e of s o l u t e s p i n f l u c t u a t i o n s on t h e l o n g i - t u d i n a l o r t h e t r a n s v e r s e r e l a x a t i o n times of t h e probe n u c l e i i n a resonance mode. I n t h e Mijssbauer e f f e c t , t h e probe n u c l e u s e i t h e r e m i t s o r a b s o r b s a y-ray i n a r e c o i l e s s p r o c e s s and t h u s undergoes t r a n s i t i o n between a ground and an e x c i t e d s t a t e . The e f f e c t of a magnetic f i e l d a t t h e nucleus i s t o produce s p l i t t i n g of t h e n u c l e a r energy l e v e l s s o t h a t a h y p e r f i n e s p l i t t i n g of t h e energy spectrum r e s u l t s . I n o r d e r t h a t a f i e l d h . can cause obser- v a b l e s p l i t t i n g , however; it must remain s t a b l e a t l e a s t over t h e p e r i o d T~ of t h e n u c l e a r Larmor pre- c e s s i o n ( T ~ = (yh.)-I). The MEssbauer t r a n s i t i o n , however, h a s an i n t r i n s i c l i n e - w i d t h a / . r o s o t h a t

width can b e observed. Thus 'ro d e f i n e s t h e time cons- t a n t of t h e probe (% IO-'s f o r 5 7 ~ e ) . Hence, i n a s p i n g l a s s a t h i g h temperatures when t h e s p i n s a r e f l u c t u a t i n g r a p i d l y i . e . T % 10-13s t h e time average l o c a l m a g n e t i s a t i o n < S . > o v e r t h e ~ E s s b a u e r t r a n -

1 To

s i t i o n p e r i o d i s zero. A s t h e temperature i s reduced and t h e s p i n s b e g i n t o slow down t h e <S.>To become f i n i t e t h e ~ E s s b a u e r spectrum begins t o broaden and f i n a l l y t h e c h a r a c t e r i s t i c s i x l i n e h y p e r f i n e spec- trum i s observed a t low temperatures.

F i g u r e 9 shows t y p i c a l MEssbauer s p e c t r a f o r a

&I -

6.7 a t % Fe a l l o y observed by V i o l e t and Borg 1131.

Fig. 9 : ~ Z s s b a u e r s p e c t r a f o r a Au- 6 . 7 % Fe a l l o y observed a t s e v e r a l t e m p e r a t u r e s , i n c l u d i n g t h e c a l c u l a t e d spectrum a t low temperatures. The "free- z i n g temperature" To f o r t h i s a l l o y o b t a i n e d from a n a l y s i s of t h e s p e c t r a i s 27.6 K which i s c l o s e t o t h e temperature f o r t h e spectrum d. The i n s e t shows t h e temperature v a r i a t i o n of t h e average h y p e r f i n e f i e l d f o r a s e r i e s of

& -

Fe a l l o y p l o t t e d on t h e reduced temperature s c a l e r e l a t i v e t o To t h e "orde- r i n g " o r t h e " f r e e z i n g temperature" o b t a i n e d from a n a l y s i s of t h e s p e c t r a . R e s u l t s from r e f . /13/.

It i s i n t e r e s t i n g t o n o t e t h a t t h e average h y p e r f i n e f i e l d h measured i n a M k s b a u e r experiment i s pro- p o r t i o n a l t o t h e square r o o t of t h e E-A o r d e r para- meter 9ro d e f i n e d by e q u a t i o n ( 5 ) .

F o r ,

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where a l l s p i n s f l u c t u a t i n g w i t h t i m e c o n s t a n t s T a l o n g e r t h a n

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c o n t r i b u t e t o h .

The t e m p e r a t u r e v a r i a t i o n o f t h e a v e r a g e h y p e r f i n e f i e l d s f o r a s e r i e s o f &-Fe a l l o y s s t u d i e d by Vio- l e t and Borg 1131 a r e shown i n t h e i n s e t i n f i g u r e 9. The r e s u l t s a p p a r e n t l y i n d i c a t e w e l l d e f i n e d

" o r d e r i n g " t e m p e r a t u r e s To. It was s e e n i n t h e neu- t r o n e l a s t i c s c a t t e r i n g measurements w i t h f i n i t e e n e r g y r e s o l u t i o n s t h a t t h e " f r e e z i n g t e m p e r a t u r e s "

o b t a i n e d a r e s y s t e m a t i c a l l y h i g h e r t h e s h o r t e r t h e time c o n s t a n t o f measurement. Although d e t a i l e d c o m p a r i s i o n s o f t h e f r e e z i n g t e m p e r a t u r e s from t h e l k s s b a u e r and t h e s t a t i c s u s c e p t i b i l i t y measure- ments a r e n o t a v a i l a b l e f o r t h e &-Fe system, r e - s u l t s f o r t h e E - F e / 1 5 / and t h e

&-&

a l l o y s y s t e n s I 1 4 1 ( t h e l a t t e r w i t h s m a l l amounts of Fe and Sn a s p r o b e s ) show s y s t e m a t i c a l l y h i g h e r " f r e e z i n g t e m p e r a t u r e s " compared w i t h t h e t e m p e r a t u r e s o f t h e maxima i n s t a t i c s u s c e p t i b i l i t y . Also, t h e r e - s u l t s p r e s e n t e d i n f i g u r e 9 g i v e a somewhat f a l s e i m p r e s s i o n o f t h e a b r u p t n e s s of t h e i n c r e a s e o f t h e a v e r a g e h y p e r f i n e f i e l d a t To. For example, V i o l e t and B o r g l s a n a l y s i s o f t h e G s s b a u e r s p e c t r a f o r t h e Au-6.7 % Fe a l l o y shown i n f i g u r e 9 s u g g e s t t h a t t h e o r d e r i n g t e m p e r a t u r e To i s 27.6 K, s p e c - trum d , whereas t h e s p e c t r u m e measured a t 3 1 . 8 K s t i l l shows an a p p r e c i a b l e b r o a d e n i n g which c a n b e t r a n s l a t e d i n t o a m e a s u r a b l e h y p e r f i n e f i e l d . Thus t h e measurements i n r e a l i t y i n d i c a t e a g r a d u a l i n i - t i a l i n c r e a s e o f t h e mean h y p e r f i n e f i e l d o c c u r i n g w e l l above t h e " f r e e z i n g t e m p e r a t u r e " , i n agreement w i t h t h e o b s e r v a t i o n s o f muon p r e c e s s i o n and n e u t r o n s c a t t e r i n g t e c h n i q u e s .

4 . SPIN DYNAMICS BELOW TF.- I n t h e r e s u l t s r e v i e w e d above we h a v e s e e n t h a t t h e b r o a d q u a s i e l a s t i c s p e c t r a l i n t e n s i t y l y i n g o u t s i d e t h e e l a s t i c e n e r g y r e s o l u t i o n o f t h e n e u t r o n ' s p e c t r o m e t e r and t h e q u a n t i t y "resonance i n t e n s i t y x t e m p e r a t u r e " i n t h e e s r measurements show v e r y s i m i l a r t e m p e r a t u r e de- pendence and i n d i c a t e t h e p e r s i s t a n c e o f a f i n i t e , a l t h o u g h c o n t i n u o u s l y d i m i n i s h i n g , component of r a p i d l y f l u c t u a t i n g s p i n s o r s p i n s which c a n r e s - pond t o t h e microwave s i g n a l , down t o t h e l o w e s t t e m p e r a t u r e s of t h e measurements. Can t h e s e b e r e g a r d e d a s f r e e p a r a m a g n e t i c s p i n s ? We have s e e n t h a t t h e s p e c t r a l w i d t h i n t h e n e u t r o n s p e c t r a and t h e l i n e - w i d t h i n t h e esr measurements go t h r o u g h s h a l l o w minima a t t e m p e r a t u r e s above t h e " f r e e z i n g

t e m p e r a t u r e s TFn. Also

,

t h e r e s o n a n c e f i e l d i n t h e e s r b e g i n s t o s h i f t t o l o w e r v a l u e s below a b o u t t h e same h i g h t e m p e r a t u r e . Another i m p o r t a n t o b s e r v a t i o n i s f u r n i s h e d by t h e G s s b a u e r s p e c t r a on s p i n g l a s - s e s . For example, t h e s p e c t r a f o r t h e Au-6.7 a t % Fe a l l o y , f i g u r e 9 , show no d e t e c t a b l e u n s p l i t p a r a - m a g n e t i c component a t f i n i t e t e m p e r a t u r e s some way below t h e " f r e e z i n g t e m p e r a t u r e " , c . f . s p e c t r u m c a t 2 3 . 3 K, ( f i g u r e 9 ) . A l l t h e s e o b s e r v a t i o n s sup- p o r t t h e c o n c l u s i o n t h a t t h e r a p i d s p i n d y n a ~ i c s a t low t e m p e r a t u r e s a r e n o t due t o f r e e s p i n s i n t h e i r p a r a m a g n e t i c s t a t e , b u t may be t h o u g h t o f a s due t o s p i n s which become c o r r e l a t e d t o c e r t a i n time-avera- ge s p a t i a l d i r e c t i o n s o v e r time s c a l e s l o n g e r t h a n t h e t y p i c a l measurement time c o n s t a n t s o f t h e s e p r o b e s and " o s c i l l a t e " i n d i v i d u a l l y and c o l l e c t i v e l y about t h e s e e q u i l i b r i u m mean p o s i t i o n s . Thus t h e broad q u a s i - e l a s t i c s p e c t r u m o b s e r v e d i n n e u t r o n s c a t t e r i n g rraeasurements below t h e f r e e z i n g tempera- t u r e must be r e g a r d e d a s a r i s i n g from s u c h d i f f u s i v e

"spin-wave" modes. The f a c t t h a t t h e w i d t h o f t h e s p e c t r u m i n c r e a s e s w i t h d e c r e a s i n g t e m p e r a t u r e below TF i n d i c a t e s t h a t t h e s e d i f f u s i v e "spin-waves" g e t s t i f f e r w i t h d e c r e a s i n g t e m p e r a t u r e . I t s h o u l d b e remembered, however, t h a t t h e i n t e g r a t e d i n t e n s i t y of t h e s e e x c i t a t i o n s s t e a d i l y d e c r e a s e s w i t h de- c r e a s i n g t e m p e r a t u r e , f i g u r e 3 , a s does t h e q u a n t i t y

" s i g n a l i n t e n s i t y x t e m p e r a t u r e 1 ' i n t h e e s r r e s u l t s , f i g u r e 6 .

Recent n e u t r o n s c a t t e r i n g measurements on &-%

a l l o y s a t low t e m p e r a t u r e s by Scheuer e t a l . /34/

show a n a d d i t i o n a l f e a t u r e

-

a b r o a d i n e l a s t i c peak due t o s p i n wave-like e x c i t a t i o n s around a n e n e r g y t r a n s f e r w of 4 . 2 meV which t h e y c l a i m a p p e a r s d i s p e r s i o n l e s s i n t h e i r q-range o f measurement 0 . 5 < q < 1.5

I-'.

R e c e n t l y Ching and Huber 1351 have e x t e n d e d t h e i r e a r l i e r computer s i m u l a t i o n c a l c u l a t i o n s o f z e r o t e m p e r a t u r e s p i n dynamics 1361 and show t h a t t h i s peak c o r r e s p o n d s t o t h e s m a l l maximum around a f i n i t e e n e r g y i n t h e d e n s i t y of e x c i t a t i o n s t a t e s i n t h e i r c a l c u l a t i o n s .

5. CONCLUSIONS.- I n t h e f o r e g o i n g we have reviewed t h e s p i n dynamics o f b i n a r y a l l o y s o b s e r v e d w i t h a r a n g e of measurement t e c h n i q u e s . The r e s u l t s show t h e s t r o n g i n f l u e n c e o f t h e K o r r i n g a r e l a x a t i o n mechanism o n t h e dynamics o f t h e s p i n s . A d d i t i o n a l l y t h e s p i n - s p i n exchange l e a d s t o i m p o r t a n t m o d i f i c a - t i o n s o f t h e dynamics which e v e n t u a l l y r e s u l t i n s p i n g l a s s f r e e z i n g phenomena o b s e r v e d a t l o w tem- p e r a t u r e s . We h a v e s e e n t h a t t h e r e s u l t s s u g g e s t a c o n t i n u o u s e v o l u t i o n o f c o r r e l a t i o n s i n t h e s p i n

C6-1526 JOURNAL DE PHYSIQUE

s y s t e m w i t h d e c r e a s i n g t e m p e r a t u r e which may b e u n d e r s t o o d a l s o i n t e r m s o f a n e v o l v i n g s p e c t r u m of q u a s i - f r e e r e l a x a t i o n t i m e s N(T) o f t h e s p i n s y s t e m . I n a s p i n g l a s s a l l o y w i t h a m o d e r a t e c o n c e n t r a t i o n o f m a g n e t i c atoms t h e K o r r i n g a mechanism i s domi- n a n t a t h i g h t e m p e r a t u r e s s o t h a t t h e s p e c t r u m o f r e l a x a t i o n t i m e s is n a r r o w

-

o f t h e form o f a d e l t a f u n c t i o n peak which i s b r o a d e n e d b y t h e a d d i t i o n a l c h a n n e l s o f r e l a x a t i o n p r o v i d e d by t h e s o l u t e - s o l u t e i n t e r a c t i o n s . With d e c r e a s i n g t e m p e r a t u r e n o t o n l y d o e s t h e K o r r i n g a r e l a x a t i o n r a t e g e t s m a l l e r ( T a T-') b u t t h e s p e c t r u m N ( T ) becomes w i d e r a l s o .

At t e m p e r a t u r e s below t h e " f r e e z i n g t e m p e r a t u r e "

T i t a p p e a r s t h a t t h e s p e c t r u m becomes v e r y wide F e x t e n d i n g from v e r y s h o r t t i m e s ( T ^2. 1 0 - 1 3 s ) t o v e r y l o n g times ( T ^{+ a).} I t i s p l a u s i b l e t h a t many o f t h e complex s p i n g l a s s p r o p e r t i e s r e s u l t from t h i s wide s p e c t r u m o f r e l a x a t i o n t i m e s .

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