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Submitted on 1 Jan 1980
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LOW TEMPERATURE THERMAL PROPERTIES OF
AMORPHOUS SUPERCONDUCTING ZrCu
H.V. Löhneysen, M. Platte, W. Sander, H. Schink, G.V. Minnigerode, K.
Samwer
To cite this version:
LOW TEMPERATURE THERMAL PROPERTIES OF AMORPHOUS SUPERCONDUCTING ZrCu
H.v. ~Ehneysen, M. Platte, W. Sander, H.J. Schink, G.V. ~inni~erode* and K. Samwer
*
P h y s i k a Z i s c h e s I n s t i t u t d e r RWTH, D-5100 Aachen, R.F.A.
*
P h y s i k a Z i s c h e s I n s t i t u t d e r U n i v e r s i t i i t , 0-3400 G i i t t i n g e n , R.F.A.1
.
IntroductionThe present interest in supercon- ducting amorphous metals stems
-
besides other reasons including possible technical- applications-
from two major points:(1) the investigation of superconductinq properties yields information about the electron-phonon interaction in these noncrystalline materials, and (2) well below the superconductinp transition temperatufe Tc, the condensation of electronic quasiparticles permits access to "intrinsic" phonon properties which' in + a normal metal are likely to be masked by
electronic effects. In particular the question if amorphous metals contain
(additional) low energy excitations
-
besides electrons and phonons-
has received considerable interest. These excitations are present in a wide variety of insulating glasses [I] as evidenced by their influence on the specific heat C and-
via phonon scattering-
the thermal conductivity k. Measurements of k [2,3] and C [3] in amorphous superconductors provided first evidence that low eneray excitations (often labeled two level tunneling systems) are also ?resent in these materials. In this paper we present measurements of the thermal conductivityand specific heat of Zrl-xCux metallic glasses which corroborate the above
observations and in addition vield infor- mation on the electron-phonon couwlinq
in amorphous trans it ion metals.
2. Results and discussion
The ZrxCul-x samples were obtained in the form of thin (=I5 wm) ribbons'by nuenchinp from the melt with the spinning wheel technique. They were checked to be amorphous by X-ray analysis. The very sharp transition to superconductivity (measured resistively) indicates good sample homogenity. The transition width ATc from 10 % to 90 % of the normal state
resistivity value po is smaller thah 20 mK for all samples.
The thermal conductivity k of ZrCu was measured between 0.5 K and 20 K in the standard stationary state technique. Fig. 1 shows k vs. T on a log-log scale for
two samnles (x = 0.50 and x = 0.65) which have superconducting transition tempera- tures of 0.8 K and 1.7 K, respectively, as determined by the electrical
resistivity. The thermal conductivity of
a 6oCU0. 40 samwle was qualitatively similar and is therefore not shown. The main features of the thermal conductivit~7
JOURNAL DE PHYSIQUE
Fiq. 1 Thermal conductivity k as a function of temperature for Z ~ I - ~ C U , on a log-log plot. Super- conducting transition temperatures as determined resistively are indicated by arrows.
inferred from Fig.1 are: (1) In the normal state both alloys show a monotonous
increase of k with temperature, however at Tc, k increases with decreasinz tempe- rature. For Zr0~50C~0~50 this increase is only relative to the normal state values of k. (2) Well below Tc, i.e. below 1 K for Zr0.65C~0.35, k varies approximately
1.8
as T
.
The increase of k when the sample becomes superconducting can be understood easily: In a normal metal heat is carried by electrons and phonons, k = ke + kPh. In addition, electrons act as scattering centers for phonons (the same holds vice versa for phonons, but this is masked by the large "defect" scattering of electrons in amorphous alloys). Hence ke decreases and kph increases when a metal turns
sunerconductinp. Therefore, the overall increase of k in ZrCu indicates that
phonon heat conduction is dominant near Tc. From the Wiedemann-Franz law ke = (L/po)T with L = 2.45. Wi2/IZ2 we estimate that ke contributes only 25 % to k at Tc due to the high resistivity
(pas
200 ~ Q c m for both samples). In addition the initial rise of k in the superconductin? state indicates that phonon-electron scattering is important near T as previously foundC
in other amorphous superconductors [2-41. Well below Tc both electron heat transport and phonon-electron scattering become neglegible, i-e., the thermal con- ductivity' is equal to kph as limited by some other scattering mechanism. The temperature Cependence
,
k-
TI ' and the magnitude, k s 8 ' 1o - ~
W/cmK at 1 K, suggest that low energy excitations which strongly scatter phonons are nresent also in amorphous ZrCu and thus corroborate findinqs on other amorphous superconduc- tors 12-41. Furthermore, the phonon thermal conductivity below 1 K is rather similar to that of Si02 glass where k-~'.' and k = 2.4-
W/cmK at1 K 111.
Assuming that the phonon thermal conductivity as limited by intrinsic scattering only, kP:, obeys the law kP1
-
T'.~ at least up to 1.7 K ( as in Si02 [ I ] ) , one obtains a rough estimate of the phonon thermal resistivity as limited by scattering from normal electrons wEh:wPh
e = (kPh)-I-
(kph)-'1,
Zr0.50 C U ~alloy. Note that this . ~ ~ analysis makes use of the fact that the thermal conductivities of both samples in the normal state (T > 1.7 K) agree better than 5 % accidentally ( the geometry factor is generally known only within
+
25 % because of the inhomogenious shape of the samples). In addition it relies on the assumption that kfh and l?zh are not much affected when changing the Zr concen- tration from x = 0.50 to x = 0.65. As a result of this analysis, we obtainWEh = DT-I. This temperature dependence is
in agreement with the theory for metals with extremely short electron mean free path [51. However, the magnitude D = 1.4
-
10'cm~~/?? as determined experimentally is almost five times larqer than calculated from the free electron model [41 which puts into question the validity of this model for amorphous transition metals.
The specific heat C of ZrCu was measured between 2 K and 6 K in a Ee 4 cryostat and between 0.1 K and 2.5 K in a dilution refrigerator. In both cases, C was determined with the standard heat pulse technique. Fig. 2 shows the "high-tempera- ture" (T > Tc) snecific heat of Zro 65%.35
plotted as C/T vs. T ~ . For the normal state values the intercept with the C/T
axis yields y = 3 - 9 mJ/mole K' while the slope gives P = 0.18 mJ/mole K ~ , i .e., a Debye temperature of 220 K. The values of -j and €3 are in reasonable agreement
with those obtained by Mizoguchi et al.
[61 on an amorphous Zr0.43C~0.57 alloy.
Fig. 2 Specific heat C divided by temperature T vs. T~ for Zr0+65C~0.35 in the normal state.
The specific heat of ZrCu alloys at low temperatures is shown in Fig. 3. As the specific heat varies over several orders of magnitude, the data are presented on a log-log plot. The jump of the specific heat at Tc is close to the BCS value of
1.43 yTc. This indicates that amorphous ZrCu alloys are weak-coupling supercon- ductors and supports findings on other amorphous transition metals [ 7 ] .
The rapid decrease of the specific heat below Tc is of course due to the condensation of electronic quasiparticles into the BCS groundstate. Eowever below 0.3 K we note a positive deviation which approaches an appro xi mat el^ linear depen- dence on temperature near 0.1 K. A similar behavior was also found for a Zr
0.60~~0.40 alloy. Note that due to the rather high Debye temperature the lattice contribution to C is onlv 15 % at 0.3 K and quickly vanishes to lower temperatures. We suggest that the additional low temperature linear contribution C = aT in ZrCu is due to
JOURNAL DE PHYSIQUE
Fig. 3 Specific heat C as a function of temperature T for Zr0-65CU0.35 On a log-log plot.
existence was already inferred above from our thermal conductivity results. The co- 2 efficient of this term is a=62 ~J/mole K
,
or about 2 % of the electronic y value in the normal state.A linear term of the same order of magnitude has previously been found in amorphous superconducting ZrPd [ 3
I
and very recently in amorphous superconducting Bi films [81. From our value of a, for Zr0.65C~0.35 without heat treatment we2 2 estimate a density of states D = 3aln kg
= 0.026 (e~#atom)-'. This value is in rather good agreement with a recent calcu-
order to test this model further, measure- ments on annealed samples are in progress.
In conclusion we summarize our main results: The low temperature specific heat and thermal conductivity of amorphous superconducting ZrCu alloys give evidence for the existence of low energy excitations in this material. The phonon-electron scattering observed in k is much larger than expected form the free electron model, and finally, the jump of the specific heat at Tc indicates that this material is a weak coupling su?>erconductor.
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