TIME AND TEMPERATURE EVOLUTION OF THE SATURATED THERMOREMANENT MAGNETIZATION OF A SPIN GLASS

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TIME AND TEMPERATURE EVOLUTION OF THE

SATURATED THERMOREMANENT

MAGNETIZATION OF A SPIN GLASS

J. Prejean

To cite this version:

JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-907

TIME AND TEMPERATURE EVOLUTION OF THE SATURATED THERMOREMANENT MAGNETIZATION OF A SPIN

GLASS

J.J. Prejean,

Centre de Reaherahes sur les Tree Basses Temperatures, C.N.R.S., BP 166 X, 38042 Grenoble Cidex, France.

Résumé.- Nous avons étudié la variation avec la température T et le temps î* de l'aimantation thermo-rémanente saturée a d'un verre de spin pour 3 concentrations de Mn dans Cu. La relation entre les dépendances en température et en temps est semblable à celle résultant d'une distribution de systèmes à deux niveaux thermiquement activés (loi d'Arrhénius).

Abstract.- We have studied the dependence of the saturated thermoremanent magnetization O of a spin glass on the temperature T and the time V, for 3 concentrations of Mn in Cu. The temperature and time dependences are linked by the type of relation which the assumption of a distribution of thermally activated two level systems implies (Arrhenius law).

We have studied the saturated thermoremanent magnetization,-for 3 concentrations (C = 0.5 %, 2 % 8 %) for the spin glass system £u Mn.

The thermoremanent magnetization a is obtai-ned by cooling the sample from T > T (T is the

temperature of the cusp in the reversible a.c. sus-ceptibility /l/) down to a final temperature T < T with a magnetic field H applied. Then the magnetic

field is withdrawn and the remanent magnetization o (T, H ) is measured as a function of time T : the origin of time is taken at the moment when H be-comes null.

For a given measuring time x , and a given temperature T, a (T, x ) depends on H as shown on the insert of figure 1 : it increases, goes through a maximum and reaches a saturation value a (T,x )

The figure 1 shows the dependence of a , at x = 60 s, with the external temperature T. On this diagram, one observes that for more than 90 % of its variation, O follows closely an exponential behaviour :

ar s = aQ exp(- aT) (1)

On figure 2, the dependence on time at T = 6.15 K of a of a Cu Mn 2 % is observed to show

rs —

sizable deviations to an initially logarithmic behaviour.

DISCUSSION.-^ The remanent properties of spin glas-ses have been interpreted with models /2/ derived from the Neel's theory of fine magnetic particles /3/. This theory relies on two main assumptions :

r 1 1

r-^ \ 8 7o Cu-Mn

N _ x

=60s

"5 .01A \

-.001 r- \

^ 5 £y-

8%

Fig. 1 : Temperature dependence of O at time T = 60 s for the 3 studied concentrations of Mn. Insert : dependence of 0 (at T = 4.2 K, T = 60 s) on the cooling field H for the C u M o B 2 sample. a) Potential barriers of energy W separate two easy orientations for the magnetization of some small do-mains or regions of the system. The average time ne-cessary for the magnetization to jump over the bar-rier, due to thermal fluctuations, is thus given by the Arrehenius law :

T = TQ exp(W/kT) (2)

b) To first order, it is assumed that the distribu-tion P(W) of the energy W is a constant over a wide range of temperature.

15 - T.2

Thus expression (1) should be generalized as T T

urs = a. exp (- ?;- Ln 7 ) (3)

0 0

Fig. 2 : Dependence on time at 6.15 K of Qrs of the Cu Mn 2 % sample. 2 diagrams are presented : 0 vs

-

LO^

LO^ or,

LO^

This model is able to account, for example, for the logarithmic dependence of the magnetization with time which is very generally observed on a li- mited extension of time.

For 1arge.variations of the remanent magne- tization (as shown on figure 1 when Urs varies over two orders of magnitude), assumption (b) is not suf- ficient as pointed out by Tholence and Tournier / 2 /

who accounted for the exponential dependence of u

r s on the temperature in the frame of a slightly more sophistical model : independent "antiferromagnetic clouds", each containing n spins, having an aniso- tropy energy W % n, and contributing with its un- cbmpensated moment M

=

g

king temperature TB = W/k In

.

bution of the moments M is negded : P(M ) % exp

g g

(- ~ ' 1 2 ~ ~ ).

g go

It is the purpose of the present paper to show that, although assumption (b) thus fails to be valid when the temperature is varied over a very wi- de range, assumption (a), namely the relevance of the Arrhenius law, seems to remain established all the same.

The main feature associated with eq. (2) is that it associates the time and the temperature in the same unique variable which is actualy : kT Ln

which implies :

Ln

urs

-

,L

'

It is observed (figure 2) that Ln Urs remains a linear function of Ln T over 3 decades in time. The values of the parameters To and ro by checking, at each temperature T, the validity of eq. (3) in describing the evolution of Urs with time, have been found to be nearly constant for each concentration, and the typical values are reported on table I. It is thus seen that the temperature and the time de- pendences of the thermoremanent magnetization are indeed closely correlated in agreement with the pre dictions of eq. (2). The theoretical justification of the experimentally determined values of To re- mains, so far, a weak and difficult point in these

types of approach, even when they are applied to sys- tems of fine particles which are more accurately de- fined.

Besides eq. (2) is a simplification even in Neel's approach where it is shown that To should de- pend on the external field as well as on temperature.

Mn 1

Concentration aO(emu/g) To(K) Ln

-

0.5 % 0.028 3 2 3 9

2 % 0.105 84 30

8 % 1.25 273 30

Table I

CONCLUSION.- It is confirmed that the memory effects observed in spin glasses below T are connected with

g an activated process.

The exponential behaviournoticed previously in the Ors versus T dependence is confirmed through the time dependence of the saturated thermoremanent magnetization. Notice that this feature was also pre- sent in the data of computation experiments 141, with a Monte-Carlo method and samples elaborated ac- cording to the requirement of the Edwards and Ander- son model.

References

/I/ Cannela, V., Mydosh, J.A., Phys. Rev. (1972) 4220.

/ 2 / Tholence, J.L., Tournier, R., Physica 86-88B (1977) 873-874, and Holtzberg, F., Tholence, J.L. and Tournier, R., Amorphous Magnetism II,(Plenum Press, New-York and London) 1977, 155.

131 Neel, L., Annales de Sophysique 5 (1949) 99, and J. Phys. Soc. Japan

11,