MAGNETIC FIELD DEPENDENCE OF THE SUSCEPTIBILITY AND SPECIFIC HEAT IN A (La, Gd) Al2 SPIN GLASS

(1)

HAL Id: jpa-00217882

https://hal.archives-ouvertes.fr/jpa-00217882

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.

MAGNETIC FIELD DEPENDENCE OF THE

SUSCEPTIBILITY AND SPECIFIC HEAT IN A (La,

Gd) Al2 SPIN GLASS

C. Bredl, F. Steglich, H. Löhneysen, K. Matho

To cite this version:

(2)

JOURNAL DE PHYSIQUE

Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-925

MAGNETIC FIELD DEPENDENCE OF THE SUSCEPTIBILITY AND SPECIFIC HEAT IN A ( L a , G d ) A l2 SPIN GLASSX

C D . Bredl, F. S t e g l i c h , H.V. Lohneysen and K. Matho

II. Physikalisches Institut der Univers-tt&t Win, Ziilpicher Str. 77, D-5000 Win, W. Germany

xx Centre de Reeherehes sur les Tr§s Basses Temperatures, CNBS, B.P. 166 X, 38042 Grenoble, France

Résumé.- La chaleur spécifique magnétioue linéaire, Cm = yT, de <Laog2Gd008)Al2est réduite par un

champ magnétique H. Pour H £ 1 tesla, y(H) est expliqué à l'aide dû* modèle RKKÏ. La forte diminution de Y observée dans des champs faibles (H ^ 0,1 tesla) est comparée à la forte réduction de la

suscep-tibilité et attribuée au blocage de nuages superparamagnétiques.

Abstract.- The linear magnetic specific heat, C^ = yT, of (Lao.92Gdo.b8)A12 is reduced in a magnetic

field H. For H £ 1 tesla, y(H) is explained within the RKKY model. The steep decrease of y already in small fields (H < 0.1 tesla) is compared to the strong depression of the susceptibility and in-terpreted as being due to the blocking of superparamagnetic clouds.

The predominant features of spin glasses, the "cusp" in the low field susceptibility x a n d

onset of remanence below a temperature T, show up in magnetic measurements. A phenomenological des-cription l\l invokes the existence of superparama-gnetic clouds which are blocked below T- : the bloc-king of a few clouds with large moments can account for the magnetic effects. Calorimetric investiga-tions have not revealed any 'incident' in the tem-perature variation of the zero field magnetic spe-cific heat C . They show a rather large contribu-tion already well above T_ as well as a characte-ristic law C = Y T near T,_ and down to lowest

tem-m f

peratures. This suggests that only a few degrees of freedom can be connected with the blocking me-chanism, the majority being related to the internal formation of clouds.

The (La, Gd )Alg system has been shown to be a spin glass through previous investigations of x>

111 and C , /3/. Here we present a comparative stu-m

dy for a c = 8 % single crystal in fields up to 5 tesla with particular emphasis on the low field region.

The main results on x a re reported in figure 1 : (i) the susceptibility maximum x is

decrea-max sed by 85 % in a field of 0.1 tesla and (ii) Tf

is displaced from 2.3 K to 1 K. In the model of su-X work performed within the research program of

Sonderforschungsbereich 125 Aachen-Jillich-Koln

perparamagnetic clouds /!/, we interpret this as the clouds being progressively locked in as H is increased, most of the clouds are blocked in a field of 0.1 tesla, i.e. their relaxation times be-come larger than the measuring time of x (^10 1s ) .

5 |\ (La0.92Gd0.08)A,2 |

2 V * x 9

Vv *

Q\ 1 1 1 1—lo

0 0 0 5 H (Tesla) 0J

Fig. 1 : Susceptibility maximum x a an<i

temperatu-re Tf of Xmax v s- H- Lines are intended as

visual guide

The magnetic specific heat C per impurity spin, obtained by subtraction of the matrix contri-bution, varies linearly with T, as found previously for this system /3/. This holds from the lowest accessible temperature 0.4 K up to ^ 4 K, well above T, = 2.3 K. The two important results we wish to report are : (i) in the presence of a ma-gnetic field, the linear C dependence on T is not altered up to H = 5 T (ii) y decreases with H, hence all data can be described by the equation

(3)

Cm(H,T) = y(H) . T ~ where a = 1 .OO

+

0.05 as determined from log-log plots. The experimental y(H) values divided by k are shown in figure 2. In a

B

field of 5 tesla, y is reduced by 50 %. However, a strong initial decrease in as low as 9.1 tesla affects approximately 10% of y.

Fig. 2 : Coefficient y of the linear magnetic specific heat in units of kg

E.

magnetic field H. In- sert shows low field date on expanded vertical scale (horizontal scale unchanged !). Solid and dotted lines are fits to data as explained in the text

We can compare the experimental y(H) curve with the coefficient yRKKy of Cm at low temperatures which was calculated from the contribution of small clusters to the free energy in the scaling limit of the dilute R K model /4/ : ~

Here J, is the digamma function, S the spin value 4

and W1 =

-

V /v an energy proportional to the RKKY 3 0

amplitude Vo divided by the atomic volume v. We first note that from eq. (I) the area under the y(H) curve should depend only on S and g :

a, r2kB2s

tesla K-$2)

jo

yRm(H) dH =

-

= 2.46

-

'

6 % ~ ~ g

-

The area under the measured Y(H)/kg curve, inclu- ding a long tail as suggested by the upward curva- ture of the last points, cf. figure 2, is estima- ted roughly as 2.4 tesla K - ~ against 4.3 obtained from eq.(2) with S = 7 1 2 and g = 2. The order of magnitude agreement supports that the magnetic specific heat is indeed dominated by the freezing of degrees of freedom within small RKKY clusters.

We can now try a fit to our data simply by scaling yRKKY(H), eq.(l), with a reduction factor 0.55 to account for the numerical discrepancy in the aeras. The solid curve in figure 2 represents yb(H) = 0.55 y-(H) for Wl/kB = 13.4 K. For H 0.5 tesla, Y (H) describes the experimental

b

points quite well. At high fields, i.e.

gl.iBH ?, r(2S + I) c W1, yb(H) shows a long tail with a H - ~ decay. This tail is due to the Lorent- zian wings in the RKKY energy spectrum. The quan- titative disagreement in the areas as well as the values for W1 determined from different experiments

(Vo as obtained by high field magnetization /2/ yields Wl/kB = 3.5 K) is probably due to three fac- tors : (i) the Gd concentration is rather high (8%) (ii) for the calculation of V from M only the second virial approximation was used 151 (iii) high energy cutroffsare present in the spectrum 161. We estimate H

*

0.5 tesla and Hlf* 12 tesla for the

1 a

antiferromagnetic and ferromagnetic cut-offs, res- pectively. The asyumetry is caused by a ferromagnetic first and second neighbor RKKY interaction in this system 121. Qualitatively, the presence of cut-offs leads to a rapid decay of y(H) in the ran- ge of corresponding external fields.

At low fields, H

4

0.5 tesla, yb varies s m o o t h l y s ~ ~ and cannot account for the strong initial variation of the experimental y(H) curve. One can empirically describe the "excess" above the RKKY "background" by Ay (H) /k = (Y (H)

-

yb (H) ) /kg

S~

= 0.033 KK1(l

-

(HI1 tesla) ) for H

2

1 tesla (see dotted line in figure 2). This anomalous field dependence with a half width of 0.1 tesla suggests that Ay(H) is related to the same irreversible properties of spin glasses which also govern the

x

(H) behavior discussed above.

(4)

the remanent magnetization of spin glasses /I/. Multiplying the density of these "superparamagnetic

excitations", n(E) = ~ A ~ ( O ) / I T ~ ~ ~ ~ , by the half width of 0.1 tesla, we estimate a corresponding

fraction of ~ l o - ~ d e ~ r e e s of freedom of the total magnetic entropy. Since each Gd spin has 8 degrees of freedom this corresponds to

*lo2

spins in a superparamagnetic cloud.

In conclusion, our estimate of the small fraction of degrees of freedom associated with the blocking of superparamagnetic clouds is based on the observation of two distinct characteristic field scales in the coefficient y(H). This estimate should be valid quite independently of the de- tailed physical picture for the blocking.

References

/I/ Tholence, J.L., and Tournier, R., J. Physique 5 (1974) C4-229

-

/2/ v. ~Ehneysen, H., Tholence, J.L. and Steglich, F., 2. Physik B. in print

/3/ Trainor, R.J. and Mc Collum, D.C., Phys. Rev. B9. (1 974) 2145 ; ( 1 975) 3581

-

/4/ Matho, K., these conference Proceedings /5/ Larkin, A.I. and KmeltNitskii, D.E., Soviet

Physics JETP

31

(1 970) 958