Calorimetric investigation of the low temperature

excitations of Pr 3+ ions in the amorphous matrix

La80Au20

P. Garoche, J.J. Veyssie, J. Durand

To cite this version:

P. Garoche, J.J. Veyssie, J. Durand. Calorimetric investigation of the low temperature excita-tions of Pr 3+ ions in the amorphous matrix La80Au20. Journal de Physique Lettres, 1980, 41(15), pp.357-360. <10.1051/jphyslet:019800041015035700>. <jpa-00231797>

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Submitted on 1 Jan 1980

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L-357

Calorimetric investigation of the low temperature excitationsof Pr3+ ions in the amorphous matrix La80Au20

P. Garoche, J. J. Veyssié (*)

Laboratoire de Physique des Solides (**), Université Paris-Sud, 91405 Orsay, France

and J. Durand

Laboratoire de Structure Electronique des Solides,Université Louis-Pasteur, 4, rue B.-Pascal, 67000 Strasbourg, France

(Re~u le 29 avril 1980, accepte le 17 juin 1980)

Résumé. 2014 Nous présentons des mesures de chaleur spécifique entre 0,3 K et 10 K, dans des champs magnétiquesatteignant 7 teslas, sur trois alliages amorphes PrxLa80-xAu20, avec x ~ 10. Les différentes contributions à lachaleur spécifique ont été séparées et analysées. On montre que l’état fondamental des ions Pr3+ est un état singulet.La séparation entre le fondamental et le premier niveau excité varie d’un site à l’autre. Dans les alliages les plusconcentrés les forces d’échange sont suffisamment fortes pour polariser les ions Pr3+ sur un certain nombre desites.

Abstract. 2014 We present specific heat measurements between 0.3 K and 10 K, in magnetic fields up to 7 teslas,on three amorphous PrxLa80-xAu20 alloys, with x ~ 10. The various component contributions to the specificheat have been separated and analysed. The crystal field ground state of the Pr3+ ions is shown to be a singlet.The separation between the ground state and the nearest level varies from site to site. In the more concentratedalloys the exchange forces are strong enough to polarize the Pr3+ ions on a number of sites.

J. Physique - LETTRES 41 (1980) L-357 - L-360 1 er AOÛT 1980,

Classification

Physics Abstracts61.40 - 75.40

The topological disorder in the amorphous stateproduces randomly distributed electric field gradientsat the atomic sites. In rare earth amorphous alloysit has been shown that the physical situation is fairlywell approximated by the random uniaxial model [1]for rare earth ions with large values of the angularmomentum J, but that substantial deviations fromthe predictions of this model can be expected whenJ is small especially for non Kramers ions [2]. In thelatter case a continuous spectrum of low energycrystal field excitations is predicted to exist as a

function of the asymmetry parameter ~ which mea-sures the departure from uniaxiality and is expectedto be rather widely distributed from site to site in thematerial. Such a situation ought to be reflectedin the low temperature specific heat by a plateauextending down to very low temperature, insteadof the typical exponential decrease of a Schottkyanomaly [3]. We have previously reported measure-ments on the amorphous Pr21Ag79 alloy between

(*) Also at Conservatoire National des Arts et Metiers, 292, rueSt-Martin, 75141 Paris Cedex 03, France.

(**) Laboratoire associe au C.N.R.S.

0.3 K and 10 K which strongly support these pre-dictions [4]. However, in order that the actual physi-cal situation may be amenable to the theoretical

picture of single ion excitations, without any appre-ciable effect arising from exchange interactions, itwas highly desirable to study more dilute systems.The present paper is devoted to an investigation ofthe low temperature specific heat of three amorphousPrxLaso-xAu2o alloys with x 10.The samples were prepared by the splat-cooling

technique and the amorphous structure was ascer-tained for each foil by X-ray scanning. The a.c.

calorimetry technique was used for the measurements.The salient features of the experimental set-upand procedure have been described in a previouspaper and references therein [5]. The requirementthat the sample assembly be in thermal equilibriumon a time scale much shorter than the period ofthe temperature oscillations sets an upper limitto the appropriate frequency to be used [6]. This limithas been experimentally determined before each runand the working frequency was chosen to be wellbelow this limit. This was typically 0.2 Hz at the lowesttemperatures. The heat capacity of the substrate

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019800041015035700

L-358 JOURNAL DE PHYSIQUE - LETTRES

and its addenda was measured separately and sub-stracted from the data. The three samples used hadthe nominal compositions x = 1, 5 and 10. Hereafterthey will be labelled Prl, Prs and Prlo. They weighedrespectively 12, 9.5 and 7 mg. Additional data weretaken in magnetic fields, applied perpendicular to

the plane of the foils and ranging from 0 to 7 teslas.

Fig. 1. - The molar specific heats of two PrxLa8o_xAu2o amor-phous alloys below 10 K : Prs(x = 5) in zero field, Prl(x = 1) inzero field and in a field of 7 teslas.

Fig. 2. - The molar specific heats of three Pr,,Laso-.,AU20 amor-phous alloys below 3 K : Prlo(x = 10) in zero field, Prs(x = 5)in zero field, Prl(x = 1) in zero field and in a field of 7 teslas.

The zero field results, plotted in figures 1 and 2,show that samples Pr 1 and Prs become super-conducting at about 3.4 and 1.7 K respectively withtransition widths between 0.1 and 0.2 K. Belowthese transitions the specific heat does not exhibitthe steep decrease commonly observed in super-conducting materials. Moreover the specific heatof sample Prl 1 for instance is between three and fourtimes larger than that of La8oAu2o between 0.3 Kand 1 K. This behaviour implies that praseodymiumis responsible for some additional contribution to thespecific heat, varying rather slowly with temperatureand remaining substantial down to the lowest tem-perature of the measurements. Such a component,

hereafter designated by CE, will be imputed to crystalfield excitations of the Pr ions in the following dis-cussion. Thus, this simple qualitative observationraises doubts on the relevancy of the uniaxial modelin the system.Another striking feature of the zero field data

is the low temperature upturn which is observedin the specific heat of sample Prl o. We believe thatthis anomaly is mainly nuclear in origin for the twofollowing reasons. (i) First, the bulk magnetic mea-surements performed down to 1.8 K on a foil takenfrom the same batch as sample Pr 1 o exhibited somelow temperature departures from the Curie-Weisslaw [7]. Such departures, although not accountedfor by a pure uniaxial model in the sense of Harriset al. [1], are typical of crystal field effects. No evi-dence was found down to 1.8 K of any trend toward

magnetic clustering of the spin glass type, whereas,for the amorphous PrgoAu2o. a susceptibility maxi-mum was found to occur at 5 K, which is thoughtto be indicative of a concentrated spin-glass or

mictomagnetic regime [8]. Thus, for sample Prlo,with only 10 at. % Pr, the crystal field effects are

likely to prevail over any possible exchange contri-bution at low temperature. (ii) Second, applyinga strong magnetic field (1 teslas) merely enhancesthe anomaly in the specific heat of sample Prlo,instead of shifting it towards higher temperaturesand spreading it over a wider temperature range;moreover it makes similar upturn grow in samplePrl just in the same temperature range (Fig. 2).Consequently the main part of the zero field low

temperature upturn in Prlo is not likely to resultfrom thermal excitations of magnetic clusters, as

previously observed for instance in nearly magneticamorphous alloy Yo.22Nio.~s [9]. Instead it may be

reasonably identified with a nuclear contribution.

Then, in an attempt to proceed further towardsa quantitative analysis, we assume that the normalstate data, obtained with or without an appliedmagnetic field H, may be fitted to the expression :

The normal state electronic term yT and the latticeone pT3 are supposed to be field independent andidentical in the three samples, while we let the nuclearcontribution A(x, H) T -2 and the electric field contri-bution CE(x, H, T) be both concentration and fielddependent. For given values of x and H the data areanalysed in two steps : at the lowest temperatureswe get a fairly good estimate for A and a less goodone for y, at the higher temperatures the usual plotof C/T versus T2 yields informations concerning# and CE. Though we are unable to ascribe a definiteform to CE(x, H, T) it should be proportional to xwherever it may be imputed to the crystal field excita-tions of non interacting Pr ions. Thus it appearsthat, starting from the experimental curves of twosamples only, such an assumption, as far as it is

L-359LOW TEMPERATURE EXCITATIONS OF Pr3+ IN AMORPHOUS La80Au20

correct, does provide the basis for a rather accuratedetermination of y, ~i and CE/x. Then the range ofvalidity of the assumption may be assessed moreor less soundly by checking whether or not the cor-responding results are consistent with the experi-mental data obtained on the third sample. Actuallysuch a fitting procedure works fairly well for tem-peratures higher than 1 K, and a coherent pictureemerges from the whole body of our experimentalresults. In particular it is gratifying that our estimateof y, f3 and CE/x in zero fields, obtained from a fitto the normal state measurements, obey, within

experimental accuracy, the requirement that the

entropies associated with the superconducting andnormal states must be equal at the superconductingtransition points.The electronic and lattice contributions that we

derive are close to, but smaller than published valuesfor the corresponding terms in amorphousLasoAu2fO [ 10], yielding y = 5 mJ . mole -1 K - 2 andeo = 119 K, instead of y = 7 mJ . mole -1 K - 2 andeo = 96 K. The difference between the values of yis rather meaningless since the electronic contri-bution in our alloys is only a small fraction of thetotal specific heat. But the lattice term as it is givenin reference [10] for La8oAu2o is definitely too largeto fit our experimental results, especially in the hightemperature range. It should be noted however,first, that this term has been estimated from data

points on La8oAu2o spanning a temperature rangeof less than 2.5 K, second, that we have indicationsthat 9p may be slightly temperature dependent(although such a dependence cannot be taken intoaccount by the present analysis) and third, that ourestimate of the Debye temperature is in better agree-ment with the value eo = 123 K derived from Moss-bauer measurements on amorphous La7sAu22 at

18 K [11].The component CE/x is displayed on figure 3

where, for each of the samples, we have representedby error flags the effect of an uncertainty of ± 1 %in the whole heat capacity, inclusive of the addenda,in order to appreciate the limits of validity of thepresent analysis. The following features should beunderlined : CElx increases only gently with tempe-rature along a structureless perfectly smooth curve,it is not affected, within experimental accuracy,by applying an external field of a few tenths of atesla, but it is strongly depressed below 4 K by a fieldof 7 teslas (see Fig. 3). On the other hand the uniaxialanisotropy model, gives the same crystal field energylevels at each site with a doublet Jz = ± J as theground state, implying first that CE/x, in zero appliedor exchange field, should be a Schottky anomaly,increasing exponentially with temperature at low

temperature, and second, that it should be appreciablyaltered by the removal of the twofold degeneracyof the ground state when applying even a weakmagnetic field. Thus our experimental observations

Fig. 3. - The contribution CElx of the crystal field excitationsper mole of Pr to the specific heat of Prs and Prl. The dashed curverepresents the same contribution with an applied field of 7 teslas.

rule out the relevancy of the uniaxial model andrather suggest the presence of two low-lying nondegenerate levels with the separation between themdistributed from site to site around some non zero

average value. This is in qualitative agreement withthe crystal field level structure calculated by Coch-rane et al. [12] when using computer generatedclusters of randomly close-packed hard spheres totake into account the disordered structure of the

amorphous state. Finally it can be seen from figure 4that, below 1 K, the CE/x curves pertaining to the

Fig. 4. - The contribution CE/x to the specific heat of Pri o, Prsand Prl below 1 K.

different samples start to deviate from each other,the higher the Pr concentration the greater CE/xat the lowest temperature. This behaviour, takenin conjunction with the relative magnitude of thenuclear terms to be discussed now, suggests that,in this low temperature regime, exchange inter-actions interfere appreciably. However the cir-cumstances under which a magnetic moment maybe induced on the Pr3 + ions will not be examinedhere.

Since only the high temperature tails of the nuclearcontributions are observed, the data have been fitted

L-360 JOURNAL DE PHYSIQUE - LETTRES

Table I. - The experimental values of the nuclearspecific heat coefficient A in PrxLaso-xAu2o as

compared to the corresponding theoretical valuesAmax when complete polarization of the Pr3 + ions isassumed. f is the fraction of Pr3+ electronic momentswhich should have to be fully developed in order totake proper account of the experimental values of A.

to the first term AT -2 in the expansion of the nuclearspecific heat as a power series of T - 1. The resultsobtained for the coefficient A are summarized intable I. Both the magnetic and quadrupole hyperfineinteractions may contribute to A. But, on the basisof available data for crystalline samples, the lattercontribution is likely to be unimportant in our tem-perature range, though Au and Pr nuclei both carryquadrupolar moments. Now the occurrence of a

magnetic hyperfine contribution concerns the Prnuclei only, and requires that the 4f electronic shellsare partially polarized even in zero external field.As already mentioned there is actually some indicationthat the Pr. Pr exchange interactions are sufficientto cause a spontaneous moment to appear on at leasta few sites in the most concentrated alloys. In table Ithe experimental values of A have been comparedto the theoretical values Amax which should be obtainedassuming complete electronic magnetization. Sincethe magnitude of A is proportional to the averagevalue of the square of the electronic moment overthe rare earth sites, we have also noted the fraction for Pr electronic moments which should have to be

fully developed in order to take proper account ofthe experimental results. It appears that, in zero

field, the nuclear term is large in sample Prlo only,while it becomes substantial in sample Pr 1 as wellwhen a field of 7 teslas is applied. It is noteworthythat our estimate of the average value of the electro-

nic moment in sample Pr, 0 is in fairly good agree-ment with the magnetization data according to

which the moment reaches about 30 % of the ionicvalue when applying a field of 5 teslas at 1.8 K.

Finally the following picture emerges from ourresults. Nearly all the Pr3+ ions have singlet groundstate and display essentially Van Vleck paramagne-tism. But the magnitude of the gap between the

ground state and the nearest level is distributedfrom site to site. Consequently spontaneous admixingof the higher state into the ground state may occur,with a resulting magnetic polarization of the ions,on the sites where the ratio of the exchange energyto the crystal field gap exceeds a critical value. Simi-larly the magnetic polarization of the ions is increasedby an external magnetic field, leading to an enhance-ment of the nuclear contribution to the specificheat.

’

In conclusion, our measurements show evidenceof substantial departures from the uniaxial model ofHarris et al. [ 1] for rare earth amorphous alloys.According to this model the ground state of the rareearth ions should be JZ = ± J, a situation whichis definitely ruled out by our data. Fert and Camp-bell [2] have shown that important deviations fromthe uniaxial predictions have to be expected in thecase of non-Kramers ions with small values of J.Fert and Spanjaard [3] calculations, assuming valuesof the asymmetry parameter r~ equally distributedbetween - 1 and + 1, yield a better approach thanthe Harris model. But the fact that the majority ofPr3+ ions are found to lie in a singlet ground statewhen diluted in the amorphous La8oAu2o matrixsuggests a narrower distribution of q than assumedby Fert and Spanjaard. It has been shown by Coch-rane et al. [12] that the distribution of the crystalfield splitting is a quasi-Gaussian one when thedisordered structure of the amorphous state is of thetype given by the random close packing of atomicspheres. Calculations by Bhattacharjee and Coq-blin [13] are now in progress to test if assuming sucha distribution provides the basis for a more realisticmodel.

Acknowledgments. - We are grateful to A. Bhatta-charjee, I. A. Campbell, B. Coqblin and A. Fertfor fruitful discussions at various stages of this work.

References

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[4] GAROCHE, P., FERT, A., VEYSSIÉ, J. J. and BOUCHER, B., Int.Conf. on Magnetism (Munich 3-7 Sept. 1979) to bepublished.

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