Evidence for intermediate temperature superconductivity as a bulk effect

Solid State Communications, Vol. 14, pp. 903—906, 1974. Pergamon Press.

Printed in Great Britain

EVIDENCE FOR INTERMEDIATE TEMPERATURE SUPERCONDUCTIVITY AS A BULK EFFECT F. Steglich and H. ArmbrUster II. Physikalisches Institut der Universitàt zu Koln, Germany

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BRD

(Received 29 November 1973 by B. Muhlschlegel)

The specific heat was measured in a highly homogenized sample of (La0 9~Ceo~oo~) Al2 between 0.35 and 1.5 K, both in the superconducting and in the normal state. The difference of the specific heats 2~C= C~ CN was observed to change its sign twice. Hence the existence of an ‘in.termediate temperature superconductor’ is suggested by means of a true volume effect. Reasonable agreement is found between the conclusions from the specific heat experiment and recent results of Winzer obtained for the upper critical magnetic field. —

FOR KONDO superconductors the pairbreaking parameter a depends strongly on temperature in contrast to the assumptions of the Abrikosov—Gor’kov (AG) theory. If the Kondo temperature TK is smaller than the superconducting transition temperature T~o of the host, a increases with decreasing temperature. According toMtiller-Hartmann and Zittartz,’ in this case a complete destruction of superconductivity, only due to the lowering of the temperature, is cxpected within a critical range of magnetic impurity concentrations.

however, do not necessarily reflect the actual bulk behavior, if the Ce impurities are distributed inbornogeneously in the LaAl2 matrix. This cannot be excluded in every case, even for annealed samples. For instance, resistivity and thermopower measurements may indicate a normal-superconducting transition which occurs above the transition temperature of the bulk whenever the first continuous superconducting path shortcircuits the sample. The2’3 transition observed diamagnetic susceptibility occurs between by these different transition temperatures when a network of superconducting paths is formed.5

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This surprising prediction has been verified by Riblet and Winzer2 and by Maple eta!.3 for the Kondo superconductor (La, Ce)A1 2 by means of standard a.c. mutual inductance technique. The required critical Ce concentrations belong to a narrow regime between 0.6 and 0.7 at.% (Ce replacing La). Since thetemperature occurrence superconductivity’) of the phenomenon is(‘intermediate subject to several restrictive conditions,4 (La, Ce)Al 2 is the only Kondo superconductor for which a reentrant superconducting-normal phase boundary has been observed so far.

In order to examine the phenomenon of intermediate temperature superconductivity by means of a true volume effect, we have studied the specific heat of (La1 _~Ce~)Al2 (x = 0.0064) between 035 and 1 .5 K. 7Preliminary results have been published In this paper we report on additional previously. measurements, particularly in the superconducting state, and we shall compare our results with the conclusions from measurements of the upper critical 8’5 magnetic field. The sample, prepared and annealed as described previously,7 was measured in a He3 cryostat by a

In the meantime this peculiar behavior of (La, Ce)Al 2 has been confirmed by measurements 4~ of transport properties,power.6 namelyAll electrical resistivity and thermoelectric these measurements,

modified ‘continuous heating method’. description, both of the calorimeter andAofdetailed the method will be given elsewhere.9 903

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TEMPERATURE SUPERCONDUCTIVITY AS A BULK EFFECT

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completely.8 Each symbol shown in Fig. 1 represents

-r 7

(La

the average of 3—10 data within a narrow temperature range of a few milhidegrees. The uncertainty of these average values, maximally of the order of 1% in the reported regime of temperatures, gives an upper limit for the scatter of the data.

09936Ce00064)A12 ______________

26-

/

sc

7?

_____ 0

0.5

,,/(~

1 ilK

Figure 1 also shows the mean dependence of the specific heat in the normal state

,/

CN

Here C’0

/

3.

3 “

=

=

~ex

+

c0~

(1)

3 (y = 3.5 rnJ/gat. K2, ‘yT+= ~3T 0.045 mJ/g at. K4),

(2)

C 0=tT.PT/

0 Oe 200 Oe

also plotted in Fig. 1 , is the specific heat of normal conducting pure LaM2, and

“I

1_

I

1 7/K 1.5 FIG. 1. Specific heat Cper gram atom vs temperature T for (LaO.~36CeO~M)Al2 in zero magnetic field and in an overcritical field of 200 Oe. The solid curve represents the mean temperature dependence CN vs T for the specific heat data in the normal state, as given in the text by equation (1). The dashed curve gives the specific heat C0 for normal conducting LaA12 This plot demonstrates the slight difference L~C CN, as compared to the large anomaly ~ex = CN C0 due to the exchange scattering. The suscep. tibiity signal x vs 7’, as recorded during the normal conducting (nc) superconducting (sc) transitions, is shown in the inset (dashed curve as described in the text). 0

40.84

0.5

C’ex =

(in T + 6.92)2

—

17.04 (0.35 K ~ T~ 1.5 K) (3)

is obtained by a least squares fit of the excess specific heat data Cex(fl = CN(l’) Co(T) due in the Ce impurities. —

.~

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The effect of the annealing process can be illustrated by comparing the susceptibility signal (see inset, Fig. 1), which was recorded simultaneously during the specific heat measurement, with the pre6 which were carried out before vious experiments annealing on a piece cut from the same sample. In the latter case a resistance ratio r~R (300 K)/R(12 K)

Experiments on dilute (La, Ce)A1 2 alloys have shown, that the jump of the specific heat at T~is depressed rapidly, and that c~(T~ becomes comparable with CN(T)107 if the Ce concentration In order to warrant a reaches clear the critical regime distinction between Cs and CN in the case of an intermediate temperature superconductor, the two phase transitions have to be separated as well as possible. This requires not only the choice of a possibly small Ce concentration, but also an extensive homogenisation of the sample by means of an appropriate annealing procedure.7 Since only temperatures of T> 0.3 K are available, the Ce substitution is restricted to ~ 0.OO64.~’~

7.2 and only partial superconductivity between the transition temperatures of about 0.4 and 0.9 K were observed. After annealing the sample was complete/v superconducting between .1 K (Fig. I), showing a resistance ratio r0.4 = and 56.6 1 From the susceptibiity signal the transition temperatures 1 .15 and 0.27 K were determined. The lower transition was measured on a part of the sample in an adiabatic demagnetisation cryostat (dashed curve in the inset, Fig. 1).

In Fig. I the specific heat ~ is shown in an expanded scale as a function of ternperature up to 1.5 K. The data in the normal state were taken in an external magnetic field of 200 Oe, which is large enough to suppress superconductivity

from our previous results. For instance, at 0.35 K we obtain ~C= 0.03 mJ/g at. K, which is almost two orders of magnitude smaller than Ce,, = 2.35 mJ/g at K. Both,the small specific heat difference ~C and the large excess specific heat C,~,in the normal state, arise

=

By taking the precautions of small Ce concentration and careful annealing, the specific heats Cs(T) and CN(r) have been separated as widely as possible. Nevertheless, they differ only slightly as expected —

Vol. 14, No. 10

TEMPERATURE SUPERCONDUCTIVITY AS A BULK EFFECT

905

in the specific heat, as was found earlier in the trans(La

port properties and the T~2and susceptibility. In order determine the po~tion the height of thetojump ~2 of this transition, the experiments have to be extended to lower temperatures.

0~~6 Ce0 ~4)At2

I .~

o.i.

‘

~ I

I I

I _________

The specific heat CN in the normal state is found to be almost totally independent of the external magnetic field up to several hundred Oe (see also reference 10). Therefore, the difference of the total entropy .~ASin zero magnetic field can be estimated from the T

data of Fig. 2: L~S(7)E S5(T~ SN(T) ~ ~ (&~/T’)dT’. As a peculiarity of the Kondo superconductor, ~.S is superconductors, for which ~ is negative in the whole seen to be positive up to about 0.7 K. This is in contrast to the well known behavior of BCS and AG —

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0

~5 1 T/K 1.5 FIG. 2. ~/T vs 7’ for the difference between the measured specific heat data C~of superconducting (La0 ~6Ce0 orJM)Al2 and the mean values CN for the data in the normal state (see equation (1) in the text). The dotted curve gives an extrapolation of the experimental data in order to determine the values, both the specific heat jump and of the transition tempera. ture, as described in reference 7. The dashed curve represents the ‘model of corresponding states’,as introduced in the text. from the same origin: the quasifree excitations, built up inside the energy gap due to spin flip processes, are evidently governed by a low temperature resonance in the non-spin amplitude the s—fexchange scattering veryflip similar to theofbehavior of the conduction electrons in the normal state. —

range of finite temperatures below 7’~.The positive difference ~.S means that the Kondo normal state is of a higher order than the Kondo superconducting state. Nevertheless, the system remains superconducting above T~2,as the difference of the free enthalpy (in zero magnetic field) T

i~~G(7)Gs(7)

—

GN(T) =

—

f ~.S dT’ 0

is negative for 7’> T~2.It is important to note that the free enthalpy, and not the entropy, determines thermodynamic stability. The results of Fig. 2 can be compared qualitatively with measurements of the upper magnetic field 8’5which corresponds to thecritical thermodynamical H~2, critical field H~by H~ 2(r,x, 7)

Figure 2 shows ~?/T= (C5 CN)IT3s a function of temperature. The uncertainties of the results are given by the bars.temperature By the procedure 7 avertical transition Te~ = 1described .15 K previously and a specific heat jump ~ = (0.19 ±0.04) mJ/g at. K are determined from Fig. 2. As the transition —

temperature T~1,determined from susceptibility, coincides with the transition temperature from the specific heat measurement, we conclude that the Ce distribution in the sample is highly homogeneous. This is confirmed by the sharpness of the transition, showing a width ~T~of only 0.11 K (~ T~1being the interval temperatures in which ~AC isdefinedby reduced from 90% to of 10% of its maximum value). 3~isfound to change its sign twice. This indicates the existence of a second phase transition being present

~/ric1(r, x, 7’)H~(x,7’). (4) Whereas x~depends only weakly on the resistance ratio for r SO,” unfortunately its dependence on =

substitution temperature is unknown. It is assumed 2 that for (La, and Ce)A1 2 alloys Kj (x,rough 7), similar to K2 (x, T),’ varies at best by 50%. In a very approximation, ~c 1may be regarded to be independent ofx and T. Hence, the simple relation H~(x,7)

—

H~2(x, 7)

(5) 14(0,0) H~2 (0, 0) is valid, 142(0, 0) being about I K Oe for r ~ 5011 and 14(0,0) as determined from 7 being 360the Oe.specific heat jump AC0 of pure LaA12 For critical Ce substitutions the experimental H~ 8’5 2(7)curves they exhibit maxima at about l’oin=temperature 0.7 K. Furthermore, look quite symmetric —

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TEMPERATURE SUPERCONDUCTIVITY AS A BULK EFFECT

Vol. 14, No. 10

corresponding to this maximum position. Assuming equation (5) to be valid, H~can, therefore, be approxi-

Within this model one can calculate the maximum value of the thermodynamic critical field H~(T0)=

mated fairly well by a parabolic dependence on tempera. ture. The simple model implies ‘corresponding states’ with respect to T0:

(9 ±l)Oe, using the experimental results for T~1and ~C1. By substituting this result into equation (5) one obtains H~2(To)= (25 ±3) Oe. This value agrees

=

—

—

,

h5TI < To.

(6)

1’ T~,+&T T T,6T l’his is realized from the H~(7’)curve, using the thermodynamical relation (MKSA system) =

Po ~

[11~(d2H~IdT2)+ (d11~IdT)2]

(7)

(~uo = I .256 10-6 Vsec/Am, =

reasonably well with H~2(To) 30 Oe, as derived for 5 (Lao ~Ce0 ooM)Al2 from mutual inductance measurements. We find that the specific heat measurements confirm fairly well the results for physical quantities which have been dete~minedbefore by other methods. In particular, they give evidence for ‘intermediate temperature superconductivity’ being a bulk effect.

1.357 105m3/g at.)

Acknowledgements We gratefully acknowledge stimulating discussions with Professor G. von —

The resulting ~C/Tvs 7’ curve is parabolic too as shown in Fig. 2. The deviations from the experimental data are probably due to the actual variation of ,~ with x and 7’ —

Minnigerode, Dr. G. Riblet, K. Winzer Professor J. Zittartz. ThanksDr. should also beand given to Dr. W. Felsch who performed the susceptibility measurement at low temperatures. This work was supported by the Deutsche Forschungsgemeinschaft.

REFERENCES I.

MULLER.HARTMANN E. and ZITTARTZ J.,Phys. Rev. Lert. 26, 428 (1971).

2.

RIBLET G. and WINZER K., Solid State Commun. 9, 1663 (1971).

3.

5.

MAPLE M.B., FERTIG W.A., MOTA A.C., DELONG L.E., WOHLLEBEN D. and FITZGERALD R., Solid State Commun. 11,829(1972). MINNIGERODE G.V., ARMBRUSTER H., RIBLET G., STEGLICH F. and WINZER K., Proc. 13th mt. Conf on Low Temperature Physics, Boulder, Colorado (1972) (forthcoming). WINZERK.,Z. Phys. 265, 139 (1973).

6.

MOESER J.H., STEGLICH F. and MINN1GERODE G.V.,J. Low Temp. Phys. 15, Nos. 1,2 (1974).

7.

ARMBRUSTER H., LöHNEYSEN H.V., RIBLET G. and STEGLICH F., So/id State Commun. 14,55(1974).

8.

RJBLET G. and WINZER K., Solid State Commun. 11, 175 (1972).

9.

STEGLICH F., to be published.

4.

10.

LUENGO C.A., MAPLE M.B. and FERTIG W.A., Solid State Commun. 11, 1445 (1972).

11.

PEPPERL G., UMLAUF E., MEYER A. and KELLER J., Solid State Commun. 14, 161(1974).

12.

MAKI K.,J. Low Temp. Phys. 6,505 (1972).

Die spezifische Wãrme einer homogenisierten Probe aus (L.a 0 ~6Ce0 0~)Al2 wurde zwischen 0.35 und 1 .5 K im supraleitenden und im normalleitenden Zustand gemessen. Es wurde eine zweifache Vorzeichenanderung der Differenz der spezifischen Warmen ~C = C.~ CN beobachtet. Damit wird die Existenz eines ‘Supraleiters mit zwei t)bergangstemperaturen’ durch einen echten Volumeneffekt nahegelegt. Zwischen den Folgerungen aus den Messungen der spezifischen Warme und neuen Ergebmssen von Winzer zum oberen kritischen Magnetfeld wird befriedigende Ubereinstimmung festgestellt. —