The influence of crystal field split impurities (Tb) on the superconducting properties of LaAl2

Solid State Communications,

Vol. 14, pp.l6l—l65, 1974.

Pergamon Press.

Printed in Great Britain

ThE INFLUENCE OF CRYSTAL FIELD SPUT IMPURITIES (Tb) ON THE SUPERCONDUCTING PROPERTIES OF LaA1 2* G. Pepperl, E. Umlauf Zentralinstitut fur Tieftemperaturforschung der Bayerischen Akademie der Wissenschaften, 8046 Garching, Germany A. Meyer Forschungslaboratorium der Siemens AG, 8000 Munchen, Germany and J. Keller Fachbereich Physik der Universitat Regensburg, 8400 Regensburg, Germany (Received 24 September 1973 by B. Muhlschlegel)

The superconducting transition temperatures of the system Lap. ~Tb~A12 have been measured. By making use of the theory of Keller and Fulde the energy state and the first excited state of 3~is splitting found tobetween be 5 ±I the K. ground Furthermore, we have determined the upper Th critical field 1-4 2(T) of these alloys and compared the results with those found for Lai_~Gd~A12. In this way the influence of the crystal field splitting of Tb on the critical fIeld data is clearly demonstrated.

IN THE presence of a crystalline electric field the (21 + 1)-fold degenerate ground-state of a rare earth impurity angular momentum J splits upfield in a sequence with of crystal field levels. Such crystal split impurities break up the Cooper-pairs even if the crystals field levels are non-magnetic, as in the case for non-Kramers ions. In this case pairbreaking is due to inelastic scattering of conduction electrons on the crystal field levels.”2 The depression of the superconducting transition temperature T~for fmite

from the data of T~versus the impurity concentration. Crystal field effects should show up in the temper5 ature dependence ofso thedrastic upper as critical field, too,assumed but the effect is not was originally in the paper of Fulde and Hoenig.6 The influence of crystal field split impurities on T~has been investigated in several alloy systems7~ but without a quantitative comparison with theory. Measurements of the upper critical field 1i of 7 do not show the effects as 2expected (La1_~Pr~)3 In A recent work9 reports measurefrom the theory. ments of 1:42 on La 1_~Tm~Sn3 which should demonstrate crystal field effect. However, it is not clear to us in how far mean free path effects would change the interpretation of these results.

impurity has been by Keller andconcentrations Fulde3 who found thatcalculated drastic deviations from Abrikosov—Gorkov (AG)-theory4 may appear if the found state of the impurity is non-magnetic. Furthermore, it is possible to determine the splitting energy between ground state and first excited state *

Research supported by the Deutschen Forschungs-

In this paper we present measurements of 7~,(x)

gememschaft.

and 142(T, x) for the alloy system Lai_~Tb~A12. The 161

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CRYSTAL FIELD SPLIT IMPURITIES (Tb)

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results are compared with those for Lai-~Gd~A12 which should notS-state show and, crystal field effects since field 3~has a pure therefore, no crystal Gd splitting occurs to first order perturbation theory. Due to the work of Cooper1°the level scheme of Tb in LaAl 2 should consist of a non-magnetic ground state I’3 and a magnetic first excited state I’5 with 5 K level separation. From a measurement of the thermopower anomaly a ground state splitting of 7 ±1 K has been found.” The alloys were prepared from 3N rare earth and SN aluminium in a high frequency inductance furnace on a water cooled copper bottom under high purity argon atmosphere. The samples were shaped to cylinders with typically 3 mm diameter and 12 mm length. The upper critical fields were taken from magnetization curves, and from the extrapolation of 142(1) the transition temperatures were determined. These measurements gave unambiguous results only if the samples were annealed at 800°Cfor 16 hr in high vacuum. The transition temperature T~of Lai_~Tb~A12 as a function of the impurity concentration x is shown in Fig. 1. For comparison there is also plotted the AG-curve with the same initial slope. Whereas Gdalloys are found to follow the AG-curve2 in thecorresmeapondence with earlier results of sured transition temperatures of Maple’ the Tb-alloys deviate drastically from this curve. This can be explained by the crystal field theory. The temperature dependence of the pairbreaking by the crystal field split impurities is determined (a) by inelastic scattering processes leading to a pairbreaking mechanism, which becomes less effective with decreasing temperature (b) by elastic scattering processes from thermal excited magnetic crystal field levels, whose occupation probability decreases with decreasing temperature. We have calculated the transition temperature as a function of impurity 13 concentration for the Lea, 0.8; Leask, X = 0;— 0.4;— 0.6;— Wolf (LLW)-paraineters and the sign of W such that the ground state is nonmagnetic. These calculations turned out to be relatively insensitive to the special type of the lowest crystal field level, as long as it is non-magnetic, but it depends sensitively on the splitting energy ~ between ground state and first excited state. In the case of a magnetic ground state the theory cannot be fitted to our data

LU 0•

\

.4

1-x

Tb N x 2

\N N

~..

2

N ~

2

0

006

.012 X

FIG. 1. Reduced superconducting transition temperature TCITCO as a function of the impurity concentration xlated for La1_~Tb~A12. The theoretical curves aredifferent calcufor the LLW-parameterX = 0.6 and values for the energy separation between the ground state and the first excited state: 5/Tao = 0; 1; 2. T~o= 3.24 K is the transition temperature of pure I~,aM2. —

points. In Fig. 1 the theoretical values, calculated with the LLW-par~meterx = 0.6 and the splitting energies ~ = 0; 1 L.~o and 2T~,are plotted. Comparing these calculations with the experimental data, we find a ground state splitting 5 = 5 ±I K. The upper critical field f42 is changed by two effects if LaAl 2 is doped with Tb and Gd impurities: —

(1) The elctron means free path decreases and, therefore, 1:42(T) is enhanced by a constant factor. (2) Due to the paribreaking effect 142 decreases and its temperature dependence may be changed according to the temperature dependence of the paiibreaking mechanism. In order to separate the two effects, we have determined the mean-free path effects by measuring 142 of LaAI2 with different non-magnetic lattice defect concentrations. For this purpose LaAI2 has been annealed successively in high vacuum and hence the residual of p the resistivity slope aHCp was changed. At different values 2IarITTCwas determined. From this we get the function ftp) which described the meanfree-path dependence of142 for LaAl2, according to the defmition: =

(8142(T’ a)”) I(’aH~2T~ Po)) \ ~T 1/ \ ~)T /

(1)

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CRYSTAL FIELD SPLIT IMPURITIES (Tb)

163

I

f

I

1

_____________________________

La 1-x Gd x AL 2 _-~

1 2:

x~0 ~.001 3: r.002 4: ~.003 5’ 00!.

~ 0

1

p

2

1I

IpS?crr~

‘

FIG. 2. Normalized initial slope of the upper critical field 142 of LaAI2 as a function of the residual resistance.

.1.

.2 6 ~7cm is the residual resistivity of the Po = 0.3after sample icr 16 hours annealing, H~ 2(T,Po) denotes the critical field of this sample. ftp) is plotted in Fig. 2. It departs essentially from thc dirty limit, 4 Itaccording should to which a linear dependence is expected.’ be mentioned that a similar non-linear function has been found in La if1i,~2(l.4 K)measured is plottedresidual versus the 5 With the residual resistivityresistivity.’ of each sample and ftp) from Fig. 2 we have calculated

0 0

.2

.4

T /1

FIG. 3. The upper critical field 1-I~

cc

2(T,x, Pa) of La1_~Gd~M2 function of the mean-free-paths reduced temperatures (data correctedasfor the different of the samples) theory. AG-curve; Double pairbreaking ___________________________________________ —. —. —-—.

14 2(T,

X,

Po)

=

ftpj~142(T,x, p)

(2)

La

Tb 1-x

In Figs. 3 and 4H~2(T,x, Po) for Lai-~Gd~A12 and La1_~Tb~ Al2 are plotted. Let us first discuss Fig. 3. First of all the 1:42(7) data of LaA12 depart from the AG-curve. If the AG-curve is fitted to the experimental values in the neighbourhood of T~then

behaviour to at low the bandstructure temperatures is also similar 142 and is tothe larger Laanisotropy and than mayexpected. be ofascribed theof Fermi This 6 To compare the pairbreaking effect the surface.’ Gd impurities with theory we look at the differences between the doped and the undoped samples. The double pairbreaking theory of Fulde and Maki’7 predicts in the case of randomly distributed impurities that the difference should be a constant, independent of temperature.

2

—

x~O .0015 008

.6 .2 0 0

.2

.L

i / i~ Cd

FIG. 4. The upper critical field 14 2(T, x, temperature p0)of LaI_XTbXM2 as function of the reduced (data corrected for the different mean-free-paths of the samples) AG-curve; Double pairbreaking theory. —-—.

Figure 3 shows, however, that the difference between doped and undoped samples is not a constant (a temperature independent difference is indicated by the broken lines) but increases with decreasing temperature. This effect is the more pronounced the higher the Gd concentration is. It has been found before on other alloys and is ascribed to magnetic ordering ordering of the GdGd spins. A spontaneous ferromagnetic has not been found in samoles with higher Gd concentrations than ours.12 Therefore, spontaneous ferrom. ..ic orc’ering is not believed to be present in our

AL x

—.

—.

samples. But the external field orders the spins and produces thereby an exchange field which is depending on the temperature and the applied field. The pairbreaking due to this field 17exchange in the case of has shortbeen spincalculated orbit by Fulde and Maki mean free path l~ ~ and in dirty limit li.,. ~ A quantitative evaluation of our data is not possible since we do not know the different scattering times which are needed to make a computation, in particular ~.

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CRYSTAL FIELD SPLIT IMPURITIES (Th)

we do not know if our samples satisfy the conditions L.~~ ~ and li,. ~ ~ of the Fulde—Maki theory.

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At low impurity concentrations the field- and temperature-dependence of the polarization effect causes the deviations from double pairbreaking theory. With increasing impurity concentration the polarization

Qualitatively one can describe the experimental 142-curves by three pairbreaking mechanisms:

effect is more and more compensated by the temperature dependence of the pairbreaking mechanism of the crystal field split impurities. It should be mentioned that the corrections of the 142-curves due to the different residual resistances of the different samples are small and the characteristic result is evident too in the experimental data without the mean-free-path correction.

(a) the external field acting on the electron orbital motion (b) the randomly oriented impurities which break, the Cooper-pairs according to the AG-theory (c) the temperature- and field-dependent exchangefield acting on the electron spins which is caused by the polarization of the impurities.

The comparison between La1_~Gd~Al2and La1_~Tb~Al2 thows the influence of crystal field split impurities on superconductivity. In the transition temperature versus impurity concentration curve of La1_~Tb~Ali there are drastic deviations from the AG-curve but there is a good agreement with the crystal field theory. In the upper critical field curves of La~_~Tb~A12 the crystal field effect is visible, too.

In the Tb alloys (Fig. 4) we find at low impurity concentrations an analogous behaviour to the Gd alloys, the difference in 142 between doped and undoped samples increases with decreasing temperature. But with increasing Tb concentration the deviation from the double pairbreaking theory goes to zero at x = 0.008 and later the deviation goes to the opposite direction (at x = 0.012). Again there are three pairbreaking mechanisms acting:

The pairbreaking mechanism of Tb impurities becomes less effective when temperature decreases. Unfortunately this effect cannot be separated quantitatively from the plarization effect which goes in the opposite direction.

(a) the external field (b) the crystal field split impurities according to references 1—3, 5 (c) an exchange field produced by the polarization of the impurities which is greatly reduced, when cornpared with Gd, due to the level splitting,

Acknowledgements We would like to acknowledge fruitful discussions with P. Fulde. —

REFERENCES 1.

FULDE P., HIRST L.L. and LUTHERA.,Z. Phys. 230, 155 (1970).

2.

For a review of the effects of crystalline electric fields on magnetically doped superconducting and normal metals, see FULDE P. and PESCHEL I.,Adv. Plays. 21, 1(1972).

3. 4.

KELLERJ. and FULDE P.,J. Low Temp. Phys. 4,289(1971). ABRIKOSOV A.A. and GORKOV K.P, Soviet Phys. JETP 12, 1243 (1961).

5.

KELLERJ. and FULDE P.,J. Low Temp. Phys. 12,63(1973).

6. 7.

FULDE P. and HOENIG H.E., Solid State Commun. 341 (1970). BUCHER E., ANDRES K., MALTA J.P. and HULL G.W., Helv. Phys. Acta 41,723(1968).

8.

HEINIGER F., BUCHER E., MAlTA J.P., LONGINOTTI L.D., COOPER AS. and DESCOUTS P., to be published. Some data are cited in reference 2.

9.

GUERTIN R.P., CROW J.W., SWEEDLER A.R. and FONER S., Solid State Commun. 13, 25 (1973).

,

10. 11.

COOPER J.R., Solid State Commun. 9, 1429 (1971). UMLAUF E., PEPPERL G. and MEYER A., Plays. Rev. Lett. 30, 1173 (1973).

12.

MAPLE M.B.,Phys. Lett. 26A, 513 (1968).

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CRYSTAL FIELD SPLIT IMPURITIES (Tb)

13.

LEAK.R., LEASKM.J. and WOLF W.P.,J. Plays. Chem. Solids 23, 138 (1962).

14.

GOODMAN B.B.,IBM J. Res. Dev. 6,63 (1962); EILENBERGER G.,Phys. Rev. 153, 584 (1967).

15.

CHAIKIN P.M. and MIHALISIN T.W.,Phys. Rev. B6, 839 (1972).

16.

HOHENBERG P.C. and WERTI-IAMER N.R., Plays. Rev. 153, 493 (1971).

17.

FULDE P. and MAKI K., Plays. Rev. 141, 275 (1966).

Am System La1_~Tb~Al2 wurde die supraleitende Ubergangstemperatur gemessen. Mit Hilfe der Theorie von Keller und Fulde wurde die Aufspaltungsenergie zwischen Grundzustand und erstem angeregten Zustand zu (5 ± 1) K bestimmt. Au~erdembahen wir das obere kritische Feld dieser Legierungen gemessen und die Ergebnisse mit den am System 3’~-Ionenauf das obere Feld La1_~Gd~Al2 erhaltenen verglichen. Auf diese Weise wirdkritische der Einflu~ aufgezeigt. der Kristallfeldaufspaltung der Tb

165