IS THE CUSP OF THE SUSCEPTIBILITY OF AuFe SPIN GLASSES DUE TO CLUSTERS ?

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IS THE CUSP OF THE SUSCEPTIBILITY OF AuFe SPIN GLASSES DUE TO CLUSTERS ?

G. Zibold

To cite this version:

G. Zibold. IS THE CUSP OF THE SUSCEPTIBILITY OF AuFe SPIN GLASSES DUE TO CLUSTERS ?. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-896-C6-898.

�10.1051/jphyscol:19786398�. �jpa-00217867�

JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-896

IS THE CUSP OF THE SUSCEPTIBILITY OF AuFe SPIN GLASSES DUE TO CLUSTERS ?*

G. Zibold

Faehhereieh Physik, Univevsitat Konstam, D-7750 Konstanz, Vostfaah 7733, Germany

Résumé.- Les films de AuFe et CuFe évaporés sur substrat refroidi montrent un maximum arrondi de la susceptibilité initiale, au contraire des films recuits et des alliages compacts qui montrent un maximum plus pointu à températures élevées. L'influence des agglomérations de Fe et d'un libre par-

cours moyen fini des électrons est discutée.

Abstract.- AuFe and CuFe films, produced by quench condensation, show a round maximum of the initial susceptibility at temperatures T_ whereas annealed films and bulk alloys have a cusp at higher tem- peratures. The influence of Fe clusters and of a reduced mean free path of the conduction electrons is discussed.

Figure 1 shows the mass susceptibility of a Au+8at% Fe film as a function of temperature for the annealing stages 80 K and 295 K. For comparison, the wellknown result for bulk Au+8at% Fe /l/ is drawn at the upper right. In bulk Au+8at% Fe the susceptibility increases in magnitude with decrea- sing temperature, until a cusp is reached at 27.9 K

Au + 8 a t % F e

, , , , ,

Y »• 22 6 a c bulk (Canella 1972 - -jr- • • 2 2 G a c l l 5 G d c » and Mydosh)-

•P / \ 5 Oac / \ S Gac -. 100 Gdc

[io5«Srl / \ — ^ 125-

1 9 J 295K . / - \

( 0 - ⁰ « ⁰ / \

£ % 4/ \ ,15-

9 - o*» *• \ -

o • ^

«•• *•

8 -

••" ^{8 0} V ^

7

. . — /

K> ° $ * •

6 t « , . J ^-A

10 15 20 25 30 35 Temperature [ K ]

F i g . 1 : Magnetic s u s c e p t i b i l i t y of Au+8at% Fe f i l m s a s a f u n c t i o n of t e m p e r a t u r e

* Work s u p p o r t e d by D e u t s c h e F o r s c h u n g s g e m e i n s c h a f t.

if measured in a small ac field of 5G (full line in figure 1). After superimposing a dc field of 100G, this maximum rounds off and decreases in magnitude.

At the temperature T. of the maximum of the suscep- tibility, occurs a transition from paramagnetic behaviour to the spin glass state 111. The spin glass state is characterized by a frozen orientation of the spins of the magnetic ions. The cusp of the initial susceptibility raised the question whether a phase transition occurs at T, with a discontinu-

Jy t

ous slope -g£ 111. In figure 1 the film annealed at 80 K shows a round maximum of the susceptibility at 23 K in an ac field of 22G and 1100 Hz. The magni- tude of the susceptibility is smaller than in the bulk sample. The superposition of a dc field of

115G does not change the susceptibility (full dots in figure I). After annealing this film at room temperature the value of the susceptibility is about 30% higher in the whole temperature range.

The maximum of the susceptibility, if measured without dc field, is sharper than the maximum at the annealing stage 80 K. After superposition of a dc field of 115G, the maximum of the susceptibility rounds off and its magnitude is about 4% smaller.

For bulk Au+8at% Fe, it is known that super- paramagnetic clusters exist with ferromagnetic cou- pling between either first or second near neighbours 131. In the film annealed at 80 K, the Fe atoms are distributed at random. Due to statistics, next nea- rest Fe neighbours exist, which are coupled ferro- magnetically as can be deduced from the large magnetic moment of Fe in these films. On annealing at room temperature the number and magnetic moment of the superparamagnetic clusters increases and so

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786398

the value of the susceptibility increases. The clusters with the largest magnetic moment can be blocked in an external field at a temperature higher or lower than Tf, depending on the increase or de- crease of the local potential at the cluster site due to the external field. Hence, the cusp like maximum of the susceptibility in films annealed at

295 K and in bulk alloys is produced by those super- paramagnetic clusters with the largest magnetic moment. These clusters are formed because of the diffusion of the Fe atoms. If this diffusion is prevented e.g. by producing the alloy at 20 K with the method of quench condensation, a round maximum of the susceptibility is found as demonstrated by the film annealed at 80

in figure

The experimental data concerning the dependence of the temperature Tf on the Fe concentration and the annealing temperature of AuFe and CuFe films is given in the table 141. For comparison, the known

values for bulk AuFe /I/ are given too. In addition calculated values for the temperature Tf are presen- ted. These calculations /5,6/ are based on the

interaction between magnetic atoms and on the dam- ping of this interaction for a finite mean free path of the conduction electrons 171. Larsen /5/ takes into account also fluctuations in the distance of nearest neighbour spins and calculates Tf values by adjusting two parameters (K A and B) 151. Kinzel and Fischer /6/ calculate for an Ising spin glass in case.1 for correlated spins (small concentration) and case I1 for uncorrelated spins (higher concen- trations) the change of T with the mean free path

f

A. Exuerimental values for the mean free path are known from resistivity measurements /8,9,10/. Cal- culated T values are normalized for every Fe con-

f

centration to the experimental Tf values of bulk AuFe

or to the Tf value of the CuFe film annea- led at 295 K. The calculations 151 and case I /6/

are in qualitative accord with experiment only for

Table

-

Temperature Tf of the maximum of the initial susceptibility of AuFe and CuFe films.

Experiment Theory

a)

Larsen f) Kinzel

Fischer

annealed I

a1 loy at A

K Tf Tf Tf Tf

i

.- .-

bulk h) 5 6 13.9 13.9 13.9 13.9

80 18.7

13.5 16.1 16.6 18.8

bulk h) 26 20 19.6 20 20

80 11.4 d) 23 20.9 21.3 25

295

too

bulk h) 17 28 28.7 28 28

80 8 d) 29.5 2

.6 23.2 29.3

Au

l2at%Fe 295 9.3 31.5 26.

26.5 31.3

1100 33

bulk h) I4 36 36.4

a) electron mean free path

b) temperature Tf of the maximum of the initial susceptibility at 1100 ffz

c) Korn 1970, Buchmann et al. 1977

d) values extrapolated from c)

e) Korn et al. 1976

f) A/K

502, B

4 for AuFe, A/K

900, B

4 for CuFe

values normalized to experimental Tf of bulk

alloys

h) Canella and Mydosh 1972.

Au+2at% Fe and C u + l a t % Fe. Case I1 / 6 / a g r e e s q u a l i t a t i v e l y w i t h t h e measured Tf v a l u e s f o r Au+8at% Fe and Au+l2atX Fe. I n t h e l a t t e r c a s e , t h e v a l u e s f o r t h e mean f r e e p a t h X a r e e x t r a p o l a t e d v a l u e s ( i n t h e t a b l e d ) ) . F o r CuFe a l l o y s w i t h more t h a n l a t % Fe, t h e dependence o f Tf on t h e mean f r e e p a t h o f t h e c o n d u c t i o n e l e c t r o n s i s s t r o n g l y over- e s t i m a t e d by t h e c a l c u l a t i o n s /5,6/.

The d e s c r i b e d measurements i n d i c a t e t h a t t h e c u s p o f t h e s u s c e p t i b i l i t y of s p i n g l a s s e s i s d u e t o s u p e r p a r a m a g n e t i c c l u s t e r s r e s u l t i n g from d i f f u - s i o n . Quench condensed f i l m s do n o t show a c u s p a round maximum o f t h e i n i t i a l s u s c e p t i b i l i t y . The q u a l i t a t i v e agreement between measured and c a l c u l a - t e d T v a l u e s a s a f u n c t i o n of t h e mean f r e e p a t h

f

o f t h e c o n d u c t i o n e l e c t r o n s f o r s m a l l c o n c e n t r a t i o n of t h e m a g n e t i c component, s u g g e s t s t h a t t h e pro- p e r t i e s o f m e t a l l i c s p i n g l a s s e s a r e m a i n l y d e t e r - mined by t h e RKKY i n t e r a c t i o n . A second c o n t r i b u t i o n o f a n amount o f some p e r c e n t comes from s u p e r p a r a - magnetic c l u s t e r s a n d t h i s c o n t r i b u t i o n i n c r e a s e s w i t h t h e c o n c e n t r a t i o n o f t h e m a g n e t i c atoms.

R e f e r e n c e s

/ I / C a n e l l a , V. and Mydosh, .T.A., Phys. Rev.

(1972) 4220

/ 2 / Heber, G . , Appl. Phys. 10 (1976) 101

-

/3/ Duff, K . J . and C a n e l l a , V . , Amorphous Magnetism, ed : H.O. Hooper and A.M. de Graaf (Plenum N.Y.)

1973, pn. 207-214

/ 4 / Z i b o l d , G. and Korn, D., J. Magnetism and Magnetic M a t e r i a l s , t o be p u b l i s h e d

/ 5 / L a r s e n , U., S o l i d S t a t e Commun

22

7

(1977) 2163

/ 7 / De Gennes, P.G., J . Physique Radium

2

/ 8 / Korn, D . , Z. Phys.

238

/ 9 / Buchmann, R . , F a l k e , El., J a b l o n s k i , H.P. and Wassermann, E.F., P h y s i c a 86-88B (1977) 835 and

t o b e p u b l i s h e d

/ l o / Korn, D . , P f e i f l e , H. and Niebuhr, J . , Z . Phys.

B23 (1976) 23

-