FREQUENCY DEPENDENCE OF THE SUSCEPTIBILITY MAXIMUM IN A SPIN GLASS

(1)

HAL Id: jpa-00217881

https://hal.archives-ouvertes.fr/jpa-00217881

Submitted on 1 Jan 1978

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

FREQUENCY DEPENDENCE OF THE

SUSCEPTIBILITY MAXIMUM IN A SPIN GLASS

H. Löhneysen, J. Tholence, R. Tournier

To cite this version:

H. Löhneysen, J. Tholence, R. Tournier. FREQUENCY DEPENDENCE OF THE SUSCEPTIBIL-

ITY MAXIMUM IN A SPIN GLASS. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-922-C6-

924. �10.1051/jphyscol:19786410�. �jpa-00217881�

(2)

JOURNAL DE PHYSIQUE Colloque C6, supplément au n" 8, Tome 39, août 1978, page C6-922

FREQUENCY DEPENDENCE OF THE SUSCEPTIBILITY MAXIMUM IN A SPIN GLASS H.V. Lohneysen , J . L . Tholence and R. Tournier

t

Centre de Recherohes sur les Trds Basses Temperatures, C.N.R.S., B.P. 166 X, 38042 Grenoble Cedex - F.

Résumé.- La température de gel du verre de spins dilué de (La Gd )A1 avec 0,6 et 1 at,%Gd, défi- nie par le maximum de la susceptibilité a.c. augmente avec la fréquence (6 Hz < v < 2 000 Hz).

Abstract.- The freezing temperature of the dilute rare earth spin glass (La Gd )A1 with 0.6 and 1 at.%Gd, as measured by the maximum of the ac susceptibility increases with frequency

(6 Hz < v < 2 000 Hz) .

According to the Neel model of superparamagnetic clouds /1,8/ with a distribution of their relaxation times T. a cloud with T is blocked when

c

the measuring frequency exceeds 1 /x . Since T de- pends on temperature, this would result in a (roun- ded) maximum of the susceptibility X at the temperature T . On the other hand, the experimentally observed rather sharp X maximum makes the idea of a (frequency independent ?) phase transition appealing 111. Recent neutron scattering experiments on rather concentrated spin glasses 13/ were interpreted as showing a "nonunique" freezing temperature depending on the momentum of incident neutrons. However, this interpretation has been seriously questioned /4/.

Measurements of the susceptibility X of concentrated CuMn 151 revealed a strong depression of X but no displacement with increasing frequency. Hence it seems desirable to look for the frequency dependence of X in a dilute spin glass with low T . For this investigation the rare earth spin glass system (La, Gd)Al 16,71 was chosen.

AC

X was measured in a mutual inductance bridge with a lock-in amplifier as null detector. The frequency range (6 to 2 000 Hz) was so chosen that even at the highest frequency the (classical) skin depth was larger than the radius of the samples. The samples and mutual inductance coils were placed in the dilute phase within the mixing chamber of a di- lution refrigerator to ensure good thermal contact.

The temperature was measured by a speer resistor placed next to the sample.

Figure 1 shows the ac susceptibility x of a AC (La, Gd)Al2 alloy (x = 0.604 at.% Gd) measured at 4

Present address : 2. Physikalisches Institut der R W T H Aachen, Templergraben 55, D-5100 Aachen, R.F.A

r 1 1

2.4 - A 0.02 Hz ("DC")- [ \ * 7.2 Hz I \ o 17.2 Hz

75> I \ o 237 Hz

3 T \ D 1142 Hz

V-°- / [A

X / / / <A

1.6- «tr \*

• <

La

1-x

Gd

x>

Al

2 \ -

x= 0.604 at % \ 1.2 I . , i A _

0 0.1 0.2 0.3 T(K)

Fig. 1 : Susceptibility vs. temperature of a (La,Gd)Al alloy at different frequencies

frequencies. The continuous X curves of which a AC few points (open symbols) are drawn to distinguish the different frequencies, have been shifted verti- cally to lie on top of each other at 0.3 K. This was necessary because the zero of the mutual induc-

tance bridge depended on frequency. Also shown in figure 1 is the " dc" susceptibility X as measured DC by extraction after the magnetic field had been switched on for % 40 s, this corresponding to a

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786410

(3)

frequency of ?. 0.02 Hz.

xDC

also served to calibrate the mutual inductance signal at 0.3 K.

The salient features of X(V,T) which can be drawn from figure 1 are the depression of the susceptibility maximum X and its displacement to

max

higher temperatures with increasing frequency. These effects are straightforward for the ac measurements (in particular, a possible overheating of the sample due to eddy currents would shift the apparentT

f to lower temperatures). However, a direct compari-

7

son of ac and dc measurements is hampered by the fact that

xAC

and

xDC

are measured in different magnetic fields,

*

0.1 Oe and 16 Oe respectively. It has been shown previously /7/ that even small magne- tic fields displace the

x

maximum to lower temperatures. Hence, some of the Xmax displacement between

xAC

^and

xDC

should be attributed to the different measuring fields employed.

The strong influence of the measuring frequency on X shown in figure 1 seems to support a model of a temperature dependent relaxation time for superparamagnetic clouds. For each cloud we assume an ~rrhenius law T = .r exp(Ea/kBT) where Ea is the

c 0

anisotropy energy which might have its origin in the dipolar coupling /I/ and T some "intrinsic" time

0

constant. In the case of a distribution of T, i.e.

Ea, the clouds with the largest anisotropy energy, Ea max ' are blocked at the highest temperatures, this giving rise to the susceptibility maximum which "defines" T for a given measuring frequence V.

f

Therefore, a plot l/Tf ys-. Rnv should give a straight line with slope kB/Eamax. Figure 2 shows such a plot for three different samples of

(La, Gd)Al, (0.584, 0.604 and 1 at.% Gd) suggesting that an Arrhenius type blocking is indeed responsi- ble for the spin glass susceptibility maximum. It is not surprising that the "dc" values of 1/T are too

f

high

-

this is probably due to the additional effect of the magnetic field which lowers Tf as mentioned above. Evaluating the slope of 1/T vs. V, we find

f

-

that Eamax/kB.x = 10 K/at.% and 12 K/at.% for the x 2 0.6 and x = 1 at.% samples, respectively. Hence Earnxis roughly proportional to x. This is in agreement which

E

x

(F

being the mean anisotropy energy of the frozen clouds at Tf for a given frequency) as found from the temperature dependence of the remanent magnetization a of spin glasses /8/.

Moreover, we find an order of magnitude agreement between E

a max and as evaluated from time and temperature dependence of ar 181 which yields

Fig. 2 : Inverse temperature of the susceptibility maximum, I / T ~ , as function of measuring frequency V

E /k x

-

^{20 Tf}

-

5.2 K/at.% with Tf = 0.26 K/at.%

a B

for ( 3 , Gd)Al, 171.

We want to caution that the assumption of a single Arrhenius law for the frequency dependenceof T is probably too simple because it implies a cons-

f

tant value of E _{a max}as v increases, i.e. the

same

(large) clouds are blocked at higher temperatures.

However, as clearly seen from figure 1 the (rever- sible) susceptibility at a fixed temperature is substantially suppressed with increasing frequency, suggesting that progressively

more

clouds are blocked whose anisotropy energy is then smaller than E

amax' This results in a positive deviation from the 1/T

f vs. Rnv straight line yielding a smaller slope and

-

an apparently higher value of E (a direct a max

observation of an upward curvature of 1/T vs RnV f -'

could be hindered by the limited frequency range available). Hence this could account for the observed difference between and E

.

On the other

a a max hand a possible diminution of E

a max itself with increasing T = Tf could have the same effect.

In conclusion we state that the first observation of the frequency dependence of the ac susceptibility maximum in a spin glass permits a rather straightforward interpretation in terms of the ani- sotropyenergyof superparamagneticcloudswhichfreeze

when T decreases and whose existence up to now was only inferred f r m remanent magnetization measurements. In addition the frequency dependence of T

f

(4)

follows a scaling law x/Tf % Rnv as a consequenceof the anisotropy interaction varying as I /r3.

ACKNOWLEDGEMENTS.- It is a pleasure to thank R. Maynard, P. Monod, R. Rammal and F. Steglich for many discussions. One of the authors (H.v.L.) thanks the C.R.T.B.T. Grenoble for the hospitality extented to him. This work was supported by the Service Na- tional des Champs Intenses.

References

/ I / Tholence, J.L. and Tournier, R., J . Physique

21,

C4-229 (1 974)

/2/ See : Anderson, P.W., in Amorphous Magnetism 11, Plenum Press New York and London, 1977, p. 1 131 Murani, A.P., Phys. Rev. Lett.

21,

450 (1976) 141 Soukoulis, C.M., Grest, G.S., and Levin, K.,

Preprint

/5/ Mukhopadhyay, A.K., Shull, R.D., and Beck, P.A., J . Less Common Met.

43,

(1975) 69

/ 6 / Bennett, M.H. and Coles, B.R., Physica

fi-E

^B

(1977) 844

/7/ v. Lshneysen, H., Tholence, J.L., and Steglich, F., Z. Physik B

9

(1978) 319

/8/ Holtzberg, F., Tholence, J.L., and Tournier, R., in Amorphous Magnetism 11, Plenum Press New York and London (1977) p. 155