CONCENTRATION AND TEMPERATURE DEPENDENCE OF THE MAGNETIC HEAT CAPACITY OF DILUTE Cu Mnx

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CONCENTRATION AND TEMPERATURE DEPENDENCE OF THE MAGNETIC HEAT

CAPACITY OF DILUTE Cu Mnx

W. Fogle, J. Ho, N. Philipps

To cite this version:

W. Fogle, J. Ho, N. Philipps. CONCENTRATION AND TEMPERATURE DEPENDENCE OF

THE MAGNETIC HEAT CAPACITY OF DILUTE Cu Mnx. Journal de Physique Colloques, 1978,

39 (C6), pp.C6-901-C6-902. �10.1051/jphyscol:19786400�. �jpa-00217870�

JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-901

CONCENTRATION AND TEMPERATURE DEPENDENCE OF THE MAGNETIC HEAT CAPACITY OF DILUTE CM Mn*

W.H. Fogle, J.C. Ho and N.E. P h i l l i p s

Materials and Molecular Research Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720, U.S.A.

Résumé.- Nous avons mesuré la chaleur spécifique des échantillons de Cu_ Mn avec des concentra- tions comprises entre 102 et ÎO1* at.ppm . A. basse température, la chaleur spécifique magnétique est donnée par AC = AT+BT2 avec A indépendant de concentration.

Abstract.- We have measured the heat capacity of samples of Cu^ Mn with concentrations between 102 and 101* at.ppm. At low temperatures the magnetic heat capacity is given by AC = AT+BT2

with A independent of concentration. The entropy associated with the spin system is Rln5.

We have measured the heat capacity of seven samples of the spin glass Cu Mn with concentrations between 1 02 and lO1* at.ppm. For three of the most dilute samples the measurements extend from 60 mK to 20 K; for the other samples measurements were made only below 1 K. The results give a fairly complete picture of the concentration and temperature depen- dence of the low-temperature magnetic heat capacity, and are therefore of interest for comparison with the numerous recent theoretical treatments of spin glasses. For this purpose, Ou Mn has the disadvanta- ge that the hyperfine heat capacity dominates all other contributions at sufficiently low temperatures (this was a significant limitation for the two most

dilute samples). This is outweighed, however, by two important advantages : (1) as the classic example of a spin glass, Cu Mn has been extensively studied by other techniques, and (2) the Kondo temperature is known /l/ to be very low. The results also establish the entropy associated with the Mn spin system.

For the 572 afppm and more concentrated samples the Mn hyperfine field was determined from T_1,and T- 2 terms in the heat capacity without ma- king any assumption about the form of the magnetic heat capacity, AC. The hyperfine fields so obtained were independent of concentration to within the ac- curacy of the data, and the most reliable value, 290 kOe, was assumed valid for the 96.6 and 231 at.ppm samples. The magnetic heat capacity, obtained by subtracting the hyperfine heat capacity and that for pure copper, is shown as AC/T vs.T for the re- gion below 0.5 K in figure 1. Maxima in AC/T for the 96.6 and 231 at.ppm samples are apparent near 0.1 and 0.2 K, respectively. The maximum values of

AT/C increase and shift to higher temperatures with further increases in concentration : for the 1152 at.ppm sample the maximum is about 3.2 mJ/mole K2

and occurs near 1.1 K; for a 1 % sample, earlier measurements HI show that the maximum is greater

than 5.5 mJ/mole K2 and occurs above 4 K.

4| 1 1 1 1

3 - - • " * - * * ^

I >°*° %

,§ V CuMn ^V

1_ , o 10,700 at. ppm ^ v 1 - o 5,900 » " w -

" • 1,400 •• " * * * „

< o , , | 5 2 •• « ^ ' ^ . 572 » »

* 231 " » v 96.6 " •

o' 1 1 1 1 0 0.1 0.2 0.3 0.4 0.5

T(K)

Fig. 1 : The low temperature magnetic heat capacity of Cu Mn.

This work was supported by the Division of Mate- rials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786400

For the five most concentrated samples the lowest temperatures data conform to AC = AT + B T ~ , and the straight lines in figure 1 represent fits of that form. For four of these samples A is in the range 1.75 2 0.08 mJ/mole K ~ , and for the 1400 at.

ppm sample A = 2.05 mJ/mole K ~ . For the two most dilute samples A and B are not well-determined, but the straight lines in figure 1 show that the data are not inconsistent with A = 1.75 mJ/mole K ~ . We conclude that, to within the experimental error, the leading term in the low temperature heat capacity is a concentration independent linear tern AT, with A = 1.8 mJ/mole K ~ . This value of A is less than half of that ustially deduced from measurements at higher temperatures /2,3,4/. The discrepancy is not so much in the experimental data themselves, however as in the fact that the existence of the T' term and other higher order terms has not generally been recognised.

In recent years, there has been considera- ble controversy over the origin of the finite densi- ty of excitations with energy near zero in spin glasses. Recent numerical calculations by Walker and Walstedt/5/ give a zero density of local exchange fields of zero modulus, but a finite density of col- lective excitations at zero energy. Furthermore, since the density of excitations increases with in- creasing energy for low energies, their calculated heat capacity at very low temperatures is qualitati- vely similar to the AT + BT' reported here. We also note that their comparison with data /3/ obtained above 1.5 K (an extrapolation to low temperatures of a plot of C vs.T) leads to an underestimate of the low teaperature heat capacity and an exagerated im- pression of the dip in the excitation spectrum at zero energy. The agreement between their calculation and experiment at low temperatures may therefore be better than they suggest.

Data for the three sauiples that were studied to 20 K are shown in figure 2 as ACIT vs. log(T/con- centration). With certain simple assumtions, the da- ta for sufficiently dilute samples of an RKKY-coupled spin system can be expected to superpose on such a plot /6/. The deviations from an universal curve in figure 2, the steady increases in the maximum of AC/T at higher concentrations, and the concentration dependance of B (weaker than l/concentration) are closely related manifestations of deviations from this universal behavior. The high temperature limi- ting form of AC is AC = DT-'with D proportional to the square of the concentration as required /6/ in

the same model.

3-5

1 1 . -

Log (TIC I (K/at. %)

Fig. 2 : The magnetic heat capacity of three dilute Cu Mn alloys, plotted as AC/T vs. log (Tlconcentra-

-

This type of behavior has been observed in several dilute alloy systems /7/. The entropies obtained by integrating the data shown in figure 2 are within a few percent of Rln5, corresponding to a spin of 2. These results, and the results of measurements in magnetic fields, will be described in more de- tail elsewhere.

References

/I/ Hirschkoff,E.C., Symko,O.G.,and Wheatley,J.C., J.Low Temp. Phys.5 (1971) 155.

/2/ Z+mmerman,J.E. and Hoare,F.E., J.Phys.Chem.So- l ~ d s

17

/3/ Wenger,L.E.and Keesom,P.H., Phys.Rev.9 (1976) 4053.

/4/ The only other measurements below I K that are directly relevant to a discussion of AC, by Du Chatenier,F.J. and Miedema,A.R., Physica 32

(1966) 403, have been reported as showingTCh'=

2.34 mJ/mole K~ for 0.06<T<0.3 K and for 0.15 and 1.15 % samples. The relation to the results reported here, however, is clouded by the fact that near 0.1 K the actual measured heat capa- cities were approximately twice as great, but were interpreted in terms of a hyperfine field of 430 kOe. That value of the hyperfine field is also in serious disagreement with other very-low-temperature heat capacity measurements by Costa-Ribieiro, P., Picot,B., Souletie,J.

and Thoulouze,D., Revue de Physique Appliquge 9 (1974), 749, and with nuclear orientation mea-- surements by Cameron,J.A., et al.,Phys.Letters 20 (1966) 569, which give a value of 278 f

-.,.

/5/ Walker,L.R. and Walstedt,R.E.,Phys.Rev.Letters 38 (1977) 514.

/6/ Souletie,J. and Tournier,R., J.Low Temp.Phys.i

-

(1969) 95.

12, Conference Kyoto (1970);

Chouteau,G., Thesis, 1'UniversitL Scientifique et MLdicale de Grenoble (1973).