Specific heat of the (La , Gd) Al2 system in the superconducting and normal state

Solid State Communications,

Vol. 12, pp. 757—762, 1973.

Pergamon Press.

Printed in Great Britain

SPECIFIC HEAT OF THE (La, Gd) Al2 SYSTEM IN THE SUPERCONDUCTING AND NORMAL STATE* C.A. Luengot and M.B. Maple Institute for Pure and Applied Physical Sciences, University of California, San Diego, La Jolla, California 92037, U.S.A. (Received 4 January 1973 by H. Suhi)

Specific heat measurements between 0.5 and 4.2°K are reported for the system (La, Gd) Al2 in both the superconducting and normal state. The observeclTpecific heat jump at the superconducting transition temperature T~is in excellent agreement with the Abrikosov—Gor’kov (AG) theory. This is in accordance with the previously reported close correspondence of the T~,vs. Gd concentration curve with the AG theory. Two very interesting features occur in the normal state specific heat. First, the Gd impurities cause a surprisingly strong enhancement of the electronic specific heat coefficient. Second, there is a large magnetic field dependent Schottky-like anomaly at low temperatures. This anomaly persists even in the superconducting state.

INTRODUCTION

There is independent evidence for the validity of

DETAILED measurements of the superconducting transition temperature T~as a function of impurity concentration n have been reported for the (La, Gd) Al2 system.’ The T~ vs. nthe curve was found to ~ in excellent agreement with behavior predicted by the Abrikosov—Gor’kov (hereafter AG) theory2 to Gd concentrations very near the critical concentration (flcr = 0.59 at.% Gd substitution for La) at which

both assumptions for the (La,Gd) Al2 system. First, assumption (1) is supported by magnetic susceptibility measurements on (La, Gd) Al2 alloys normal 3 These measurements show thatinthethecurve of state. magnetic ordering temperatures 0 vs. Gd concentration3 falls off rapidly with decreasingn, and does not intersect the T~vs. n curve at an appreciable temperature compared to T~ 0,the T~of the LaAl2 matrix. For example, an alloy of concentration n = l.41n~.has a Curie—Weiss temperature 0,, of 0.07°K corresponding

superconductivity should be completely suppressed. The AG theory is based upon two assumptions: (1) the impurities are randomly distributed in the matrix and their spins S uncorrelated with one another, and (2) a calculation orderdescribes in the exchange interaction parameterto second adequately the impurity spin exchange scattering of conduction electrons which is responsible for the depression of

5

~,.

*

Research supported by the U.S. Air Force Office of

to a reduced temperature op/rca

0.02.

Second, support of assumption (2) comes from 4’5

recent EPR yield and NMR measurements. Both EPR and NMR° a magnitude I 5 I 0.1eV, while the EPRg-shift4’5’7 implies that S has a positive sign. The magnitude of 5 deduced from EPR and NMR measurements is very close to the value derived with the AG theory from the T~vs. n curve according to the relation2 —.

I

SI

=

LkBTC 0I4inCT.W(EF)S(S + 1)1

1/2

(1)

Scientific Research, Grant no. AF—AFOSR—7 1—2073. where ‘y is Euler’s constant and N(EF) is the conduction electron density of states at the Fermi level (for one spin direction). This suggests that when is positive,

t John Simon Guggenheim Fellow 1971—1972. On leave from Centro Atómico Bariloche, Argentina.

5

757

758

SPECIFIC HEAT OF THE (La,Gd) Al2 SYSTEM

Vol. 12, No. 8

LO

__________________________________

72 66 60

Gd A 12

\\\\ \\

\\

54 C-,

~0.5

N

\ .+,

\

21l°/oGd. 10

E36

0

.

,...

.

0

0

________________

05

24 IS 2 6 0

. .~.

.

—

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— — — — —

- - — — — —

-

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.-

LO 24 30 18

—.. -~ ..:~---~ 0.416°/oGd ~

...--

t.—•-.~

— —

.—~

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— — — — — —

— —

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FIG, 2. Reduced specific heat jump L~C/L~C0 vs. reduced transition temperature TCITC0 for (La, Gd) Al2. The dashed line represents the BCS law of corresponding states, while the continuous line is the AG result as 8 calculated by Skalskietal. within a certain Ce impurity concentration range have

— —

two T,’s)9”°and

— — — —

.0

2.0

T(’K)

0

Tc/Tc0

——

3.0

FIG. 1. Specific heat of (La, Gd) Al2 alloys in the normal and superconductiifg states (the (3T~lattice term has been removed). Solid circles represent data taken with H = 0; while solid squares indicate data taken with H = 1700 G for the 0.211 at.% Gd sample, and H = 270 G for the 0.4 16 at.% Gd sample. For comparison, the dashed lines represent the normal state specific heat of the LaA12 matrix. The LaA12 result is from reference 11. it is sufficient to calculate conduction electron-impurity spin exchange scattering to second order in

5.

Since the basic assumptions of the AG theory appear to be justified for the (La, Gd) Al2 system over the entire impurity concentration range of interest, it seemed important to test the theory with respect to the behaviour of the specific heat. In particular, the AG theory predicts that the reduced specific heat jump (AC/AC0) vs. reduced transition temperature (r~IT~0) deviates markedly from the 8BCS law of corresponding states in a universal manner. The experiments were further motivated by recent experimental work on the related (La, Ce) Al 2 system. In this system, the T~vs. n curve is re-entrant (samples

~C/~C

as 0 a function of T~/T~0is depressed stron~ycompared to both the BCS law of corresponding states and the AG theory.” 12 These effects occur because the conduction electron-impurity spin exchange coupling for this system is antiferromagnetic is negative) and conduction electron scattering,

(5

which in this case must be calculated to higher order than 52, becomes temperature dependent. It was thought that (La, Gd) Al2 would provide a wellcharacterized ‘normal’ system with which the results for the superconducting-Kondo system (La, Ce) Al2 could be contrasted. EXPERIMENTAL DETAILS The samples were prepared in two steps. First, LaGd alloys were made by arc-melting appropriate amounts of La (Johnson—Matthey, nominal purity 99.99%) and Gd (Research Chemicals, nominal purity 99.9%) together in an argon atmosphere. The calculated weight of 99.999% pure Al was added to each LaGd alloy to form the corresponding (La,Gd) Al2 compound. fabrication the alloys were remelted many times During to achieve a homogeneous distribution of impurities. The arc-melted ingots, each weighing 6 g, where then wrapped successively in foils of Ta, Zr, and Ta, and annealed for 16 hr at 800°C in a helium atmosphere. The critical temperatures, measured

Vol. 12, No.8

SPECIFIC HEAT OF THE (La, Gd) Al2 SYSTEM

I

759

I

(L~,Gd)Al2

02I1°/oGd .h:I700GAUSS H: 270 GAUSS 0416°/osdJ.H:1700 GAUSS

30 ‘ 0.416°/aGd

1.00

-

•

-~.

S

— ——

_

—

AGT

“.,

‘C ‘C

‘C ‘C

CC

‘3

0.10

S

0.2Il°/~Gd

.. ‘C ‘C

..

~

\-..

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0

LoAI2 ,...~. 0

‘C

-

5

~

____________________________________________________ 2(K2~

5

10

15

20

T

‘C ‘C

-

-

tL~,~M 2

“C ‘C

BCS

0.05

.•.

.~20 .~-.

.—.~.

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L.H:3400GALJSS

.

,~

C’

0.50

25

-

FIG. 4. ç/Tvs. i’~in the normal state in various external magnetic fields (the 13T3 lattice contribution has been removed). For comparison, the behavior of the LaAl2 matrix is indicated by the dashed line Ti,, AC, are observed to fall off more rapidly with increasing Gd concentration than T~.l’his is illustrated in Fig. 2 where the reduced specific heat jump AC/AC0

I

I

2

3

4

T1/T

is plotted vs. the reduced transition temperature TcITc0 (AC0 and are AC and T~respectively of

FIG. 3. Semi-logarithmic C,/7NTc vs. TCIT plot for two (La, Gd) Al2 alloys. The continuous line represents BCS bihavior, while the dashed lines indicate AG behavior,

the LaAI2 matrix). The excellent agreement of these data with the AG theory seen in Fig. 2 is consistent 1 with the theory. Values of AC, T~, with the previously reported close correspondence of the n curve width AT~for LaAl and Tc thevs.transition 2 and the two

calorimetrically, were 1somewhat than those from a.c.lower inductance measuredetermined previously ments on much smaller, unannealed samples. mis reveals the influence of the annealing procedure 0 similar to that found for (La, Ce) Al2 alloys.’ The specific heats were measured from 0.5 to 4.2°Kin a He3 calorimeter to be described elsewhere. Temperatures were determined with a Cryocal 250~l germanium resistance thermometer calibrated in a manner previously reported.t’ Magnetic fields up to 3.4 kG were applied with a superconducting solenoid.

(La, alloys aregood collected in Table 1. We note here Gd) that Al2 comparably agreement of AC/AC 0 vs. T~/T~0 (deduced from critical field measurements) with the AG theory has been previously observed for the T!~Gd system.’3

RESULTS AND DISCUSSION The specific heat C, vs. temperature T of LaM 11 2 and two (La, Gd) Al 2 alloys in both the superconducting 3 term, corand normal to states is shown in Fig. 1.°D A of 13T376 ±3°K, responding a Debye temperature has been subtracted from the data in order to eliminate the lattice contribution. The specific heat jumps at

The AG theory also predicts that the zero ternperature energy gap ~ decreases with increasing paramagnetic impurity concentration faster than T~ and falls to zero in the concentration range 0.9 ‘NCr < n
760

SPECIFIC HEAT OF THE (La, Gd) Al2 SYSTEM

Vol. 12, No. 8

Table 1 fl

2

7N

at.%Gd

mJ/mole°K

0 0.211 0.416

9.55 ±0.05 10.75 ±0.07 11.90±0.07

-

=

376

mJ/mole °K2 l/at.%Gd A7/fl

°K T~

°K .AT~

3.305 2.40 1.39

—

5.76 ±0.5 5.67±0.3

mJ/mole°K

0.030 0.075 0.120

43.2 ±0.05 27.4 ±1.0 10.35±0.45

±3°K.

for the two (La, Gd) Al 2 alloys are compared in Fig. 8 3(dashed with BCS behavior (solid line) andappropriate AG behavior lines) corresponding to the value

6

.

(uGd)A1

,

2-0416°/ood

of ~/~cr for each alloy. The data clearly deviate from the BCS result in the direction expected for a decreased energy gap, but they also bend away from the AG dependence at lower temperatures. This appears to be due to contributions in the superconducting state, visible in C3/Tvs. 1~plots as low temperature upturns, which arise from interactions between Gd spins. Measurements on more alloys to lower temperatures are required in order to characterize and eliminate the contribution to C8 due to Gd spin—spin interactions before a quantitative comparison with the AG theory in terms of the energy gap can be made. As the specific heat contribution due to interactions does not exhibit a peak above 0.5°K, the specific heat jump is probably not affected by Gd spin interactions because T~,is clearly much larger than any possible sharp ordering temperature at the concentrations in question. It should be noted, however, that even in zero field the low temperature upturn in the 0.416 at.%Gd alloy already accounts for about 25% of the total heat capacity at T~,(1.39°K). 2 for Presented in Fig. the two (La, Gd) Al 4 are plots of ~/Tvs. T 2 samples in the normal state3and, for comparison, the LaAl2 matrix (again, These the ~rdata phonon contribution has been removed). exhibit large enhancements of the normal state electronic specific heat coefficient 7N and a low temperature upturn. From the data for the 0.416 at,% Gd sample, it can be seen that the low temperature upturn is strongly dependent on the applied magnetic field. To find the form of this anomaly above the low ternperature limit of 0.5°K,a 7NT term has been subtracted from the specific heat of the1N0.416 at.%determined Gd alloy from has been where the average value of

-

.

‘

270 GAUSS

‘H

,

-

.

H~ 700 GAUSS H~3400 GAUSS

.

~

2

‘“.

I

,

‘

,

‘ ‘~ ~‘~‘‘C.:.’

0

L0,C~I2

O~5

10152025

30 3’5 40

T (‘K

FIG. 5. Excess heat capacity c5C of the 0.4 16 at.% Gd alloy due to exchange scattering in the normal state for various external magnetic q1lds. ÔC (in i/mole Ce°K) ~ri~i ~ is also shown for corn-

the data between 3 and 4.2°K.The resultant excess specific heat ~C(per mole Gd)is plotted vs.ln Tin Fig. 5. Also shown in Fig. 5, for comparison, is the behavior previously reported for the (La, Ce) Al, system” 0.5 (dashed W is linearin in of T the between and line) 2.5°where K. A suprising feature

(!~~ data is that in the lowest G) in used Gd)A12 to quench superconductivity, 6C field is also(270 linear In T between 0.5 and 3°K.However, the excess specific heat of the (I..a, Gd) Al 2 system is very dependent upon magnetic field, in contrast to the (La, Ce) Al, system for which it does not show any field dependence below 1.7 kG. In the highest field (3.4 kG), a maximum in ‘SC vs. Tappears in our experimental range at a ternperature TM 0.65°K. By extrapolating ‘SC linearly from 0.5°Kto T = 0, the entropy cS associated with the anomaly estimated be which S = 0.77kB 1n8, afor value somewhatisless than JiBto1n8 is expected Gd ‘~

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SPECIFIC HEAT OF THE (La, Gd) Al2 SYSTEM

spins with S = 7/2. Although resembling Schottky anomalies, the curves definitely cannot be fitted by free-ion Schottky curves calculated for S = 7/2. Again, an extension of the measurements to lower temperatures, higher fields, and higher Gd concentrations promises to be very revealing, Finally, the enhancement of the ~T term induced by the Gd impurities is surprisingly large; A7NIfl = 0.57 J/mole Gd°K’.The normal state parameters 7N and A’yN/n where A’yN 77.J 7N 0’ ~Il~ being the electronic specific heat coefficient of the LaAl, matrix, are given in Table 1. A similar enhancement of 7N with A7N/n = 0.37 J/mole Ce°K’ was recently reported in the related (La, Ce) Al2 system.” It would seem that the apparent enhancement of 7J.J is due to the

761

exchange coupling of conduction electron and impurity spins, although the coupling is of different sign in the two systems (i.e. ~ >0 for (~, Gd) Al2, while ~ <0 for7N (La, Ce)inAl2). comparably enhancehave, fact,As been observed large previously ments in the of systems LaGd and ~Gd over temperature ranges extending from 2°Kto 8°Kand 35°K,respectively,’4 large specific heat contributions, linear in T, seem to be a general feature of dilute alloy systems with ionic solutes such as Gd and trivalent Ce. We remark that

—

this apparent enhancement of ~“Nis not the linearly T dependent behavior predicted by the molecular field approximation for T < TM ~ since our measurements were made at temperatures T TM. ~‘

Acknowledgements We thank D.K. Wohileben for useful comments concerning this manuscript. —

REFERENCES 1.

MAPLE MB.,Phys. Left. 26A, 513 (1968).

2.

ABRIKOSOV A.A. and GOR’KOV L.P.,Zh. ~ksp. i Teor. Fiz. 39, 1781 (1960); Soviet Phys. JETP 12, 1243 (1961).

3. 4.

MAPLE M.B., Ph. D. thesis, University of California, San Diego (1969), unpublished. DAVIDOV D., CHELKOWSKI A., RETTORI C., ORBACH R. and MAPLE M.B.,Phys. Rev. (forthcoming).

5.

KOOPMANN G., ENGEL U., BABERSCHKE K. and HUFNER S., Solid State Commun. 11, 1197 (1972).

6.

MCHENRY M.R., SILBERNAGEL B.G. and WERNICK J.H.,Phys. Rev. B5, 2958 (1972).

7.

COLES B.R., GRIFFITHS D., LOWIN R.J. and TAYLOR R.H.,J. Phys. C3, L121 (1970).

8.

SKALSKI S., BETBEDER-MATIBET 0. and WEISS P.R.,Phys. Rev. 136, Al 500 (1964).

9.

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

10. 11.

MAPLE M.B., FERTIG W.A., MOTA A.C., DELONG L.E., WOHLLEBEN D. and FITZGERALD R., Solid State Commun. 11, 829 (1972). LUENGO C.A., MAPLE M.B. and FERTIG W.A, Solid State Commun. 11, 1445 (1972).

12.

V. MINNIGERODE G., ARMBRUSTER H., RIBLET G., STEGLICH F. and WINZER K., to appear in Proc. 13th mt. Conf on Low Temperature Physics, Boulder, Colorado (1972).

13. 14.

DECKER W.R. and FINNEMORE D.K.,Phys. Rev. 172,430(1968). BONNEROT J., CAROL! B. and COQBLIN B.,Ann. Acaa’~Sci. Fennicae ÀY!, 120 (1966),

15.

MARSHALL W.,Phys. Rev. 118, 1519 (1960).

762

SPECIFIC HEAT OF THE (La, Gd) Al, SYSTEM Es wird berichtet über Messungen der spezifischen Warme am System (LaGd) Al, zwischen 0.5 und 4.2°K,im normalleitenden und im supraleitenden Zustand. Der sprung der spezifischen Wãrme an der supraleitenden Ubergangstemperatur 7’,. ist in ausgeseichneter Uberinstimmung mit der Abrikosov—Gorkov Theorie, und im Einklang mit der frtther gefundenen engen Korrespondenz der Abhangigkeit von T,~,von der Gd konzentration mit der AG theorie. Es wurden zwei sehr interssante Eigenschaften der spezifischen Wärme im Normalzustand beobachtet: Erstens verursachen die Gd Verunreinigungen eine Uberraschend starke Erhohung des Koeffizienten der elektronischen spezifischen Warne und zweitens existiert eine grosse Schottky-ahnliche Anomalie bei tiefen Temperaturen, die vom magnetischen Feld Abhángt. ,

Vol. 12, No. 8