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The specific heat jump of superconducting La1-xTbxAl2 related to crystal electric field splitting of the Tb3+ levels
Solid State Communications,
Vol. 13, pp, 1641—1643, 1973.
Pergamon Press.
Printed in Great Britain
THE SPECIFIC HEAT JUMP OF SUPERCONDUCTING ~ Al2 RELATED TO CRYSTAL ELECTRIC FIELD SPLITTING OF THE Th~LEVELS* H. Happel and H.E. Hoenig Physikalisches Institut der Universitat, Frankfurt am Main, Germany (Received 30 July 1973 by B. Muhlschlegel)
Measurements of the specific heat jump &(T~)were performed on superconducting La1 ~Th~A1,compounds in order to investigate the pairbreaking effect of Tb ~ ions in the LaAJ2 host. The results deviate from the Abrikosov— Gorkov theory for superconductors with magnetic 3~in LaAl impurities. Taking into account the crystal field level structure of Tb 2 the results can be qualitatively understood within the model of Fulde, Keller and Peschel. According to calculations published by Müller.Hartmann and Zittartz an influence of the Kondo effect can be ruled out. -
INTRODUCTION
In this letter we present experimental results on
MEASUREMENTS of the specific heat jump at the transition temperature proved to be an important tool to distinguish between different pair-breaking mechanisms of magnetic impurities in superconductors.’ 4 According thejump Abrikosov—Gorkov-theory the specifictoheat &(T~)decreases more (AG) rapidly
the specific heat jump &(T~)for the system La1 -x Tb~Al2 (x ~ 0.008), which again are close to the BCS solution. The results can be understood in an extended temperature range ~ using TC/TCOthe ~ data I within the CEF model of Fulde et a!.0.4 5—8 on the spectroscopic state of the Tb3~-ionsin the LaAI 2 host as given in reference (9).
.~
than the superconducting transition temperature 7~ thus deviating markedly from the BCS law of corresponding states where ~c(T~) is proportional to 7~. While for the system La1_~Gd~A12 the AG-dependence is well confirmed,’ smaller values for &(T~)than predicted by AG have been found for the compound 2 La1 For_~Ce~Al2 the systemand La attributed to the Kondo effect. 3 _~Pr~Tl, however, ~c(7~) is larger than given by the AG theory, approaching the BCS solution down to Tc/T~o~ 07.~This can be explained qualitatively by including the interaction between the conduction electrons and the crystal electric field (CEF) split levels of the impurities. For TC/TCO <0.7 impurity interactions probably become important in this system because of the high concentration (x> Ui).
EXPERIMENTAL DETAILS The samples were prepared in three steps. First La1_~Tb~ were arc-melting amounts ofalloys La and Tb made (both by obtained from appropriate Metals Research, nominal purity 99.9%) together in a high purity, titanium gettered, argon atmosphere. Each button was remelted 6—8 times to ensure homogenity. Then the calculated weight of 99.999% Al was added and the reaction to form the corresponding Laj_xlbx Al2 compound was performed by arc-melting, too. Further homogenization of the brittle samples was established by levitation melting. Ellipsoids of typically 3g obtained by this procedure. X-ray-diffraction andwere electron-microprobe analysis showed that the samples were in a single phase and of the right corn-
*
A project of the Sonderforschungsbereich 65 “Festkorperspektroskopie” financed by special funds of the Deutsche Forschungsgerneinschaft.
position.
l64~
1642
SPECIFIC HEAT JUMP OF SUPERCONDUCTING Lai.~Tb~A12
Some of the samples were wrapped in Ta foil, sealed in quartz tubes under a vacuum better than lO~Torr and annealed at 800°Cfor three days. This procedure has been found to sharpen the 1’2 superconThis effect ducting transition of La1_~(Gd, C e)~M2 was also observed by us for La, ~ In the case of Th additions, however, we found a smearing of the transition and a shift to higher temperatures in cornparison to unannealed samples. The transition ternperature of unannealed samples were in good agree ment with the Ta-values given in reference 10, whereas annealing of an e.g. 0.5 at % Tb doped sample resulted in a shift of 0.5K. Remelting the annealed samples resulted in a sharp transition and a lower T~.We believe that there is some clustering of the Tb-impurities at the grain boundaries during annealing. Thus ~ measurements were done on unannealed samples which were prepared in an identical way. The specific heat measurements between 1.3K and 4.2K were carried out using12a heat pulse method Temperatures were and a cryostat described earlier. determined with an Allen—Bradley carbon resistor, 200 57, 1/8 W, which was calibrated against the He4vapour pressure in each run, using a three point formula for interpolation.
Vol. 13, No. 10 Tb Al •
‘°
\~—4 \ .tl
\
~
-
._‘~
\~,
,...
x. 0
:~
..~\
.-~
‘i” 20
-_________________________________ rs 20 25 10 .15 T.mp.ratur.
K
FIG I. Specific heat cIT at the phase transition versus temperature of La 1 -x Th~Al2samples with different Tb concentrations. The solid lines are drawn merely for clearness. -
1.0
L~ La
4 C0
~
TbX A 12
/ /
05
4
/
4/
RESULTS AND DISCUSSION Results of the specific heat measurements for pure LaAl, and four La 1 _~Th~Al, samples are shown in Fig. I. For LaAI2 we fmd a transition temperature of 3.22 ±0.03K and an electronic heat isconstant The ratiospecific ~Ac(T~)/7T~ found ~ of 10.3 mJ mol’ 2 to be 1.50 in of good with Substitution La agreement by magnetic Tb other atomsauthors.’ decreases T~,the transition temperatures of the samples agree with the Ta-values given in reference 10.
2.
-
r
Figure 2 shows the reduced specific heat jump &(T~)/&o(T~o) versus the reduced transition ternperature TdT~owhere the subscript o refers to undoped samples. The solid line is the AG result as calculated by Skalski et ~ the experimental points deviate clearly from this curve. However, it should be noted that in the AG-theory no influence of higher levels is considered. This was first done by Fulde, Hirst, and Luther5 and in following papers;6—8 In particular Fulde and Keller have calculated the jump in the specific heat at the phase transition taking into account
0
I
05
1.0
T
0/ ~
FIG. 2. Reduced specific heat jump I~.c(Tc)/&o(Tco) versus reduced transition temperature T~/T~ for Lai...~Th~A1 1 which corres2. The continuous solid i~the AG result as by level Skalski et a!. 6~ine ponds tocalculated a degenerate system = 0. In the dashed line, CEF splitting of the Tb impurities is taken into account, the excitation energy to the first excited level is equal to T~.The arrow marks a lower limit of &/&° for the sample with the lowest T~. a given sequence of crystal field split energy levels of the impurities.8 In order to determine the spectroscopic state of Th3~in the LaAl 2 host we measured the Schottky specific heat and the magnetic susceptibility of L.a098
Vol. 13, No. 10
SPECIFIC HEAT JUMP OF SUPERCONDUCTING La1 -xTbxAl2
9 and Th0~Al, indata the temperature L5 to 10K fitted these to the / = 6 range level scheme given by Lea, Leask, and Wolf.14 With a level sequence accordihg to x = — 0.2 (this parameter is defmed in reference 14) and an energy separation of 3—4K between the magnetic ground state and the F 3 nonmagnetic doublett as first excited state we obtamed a reasonable fit of the experimental data. Based on this level scheme, A.c(T~)was computed by Keller solving equation 19 of reference 8. The result is presented by the dashed line in Fig. 2 for a splitting 6/Tao = 1 where 6 is the ground state isolation energy. The systematic deviation of this theoretical result from the AG solution explains at least qualitatively the experimental data.
r’~
The results of Fig. 2 are also interesting with respect to calculations of MilhJer—Hartmann and Zittartz on the influence of the Kondo-effect on the specific heat the superconducting phasec~’of 15 jump These at authors calculated the slope transition.
1643
the curve in Fig. 2 in the limit T,jT~ 1 as function of the Kondo temperature Tx in the interval 1 O~< TKITC.~O< l0~with the impurity spin S as parameter. In most cases c* is larger than the slope of the AG curve. In particular for Tb, which has a spinS = 3, the -*
calculated slope c~exceeds the value derived from experiment by at least 40%. Thus, one can exclude any significant influence of the Kondo effect in the Lai.~ Th~Al,system. In summary, we have shown that the specific heat jump at the superconducting transition temperature in the La1 -x Th~,,Al2 system is strongly influenced by crystal electric field effects. The experimental results are in qualitative agreement with theory down to the lowest temperature where measurements have been performed, that is T~/T~ ~ 0.4. Acknowledgements We thank Prof. Dr. J. Keller for stimulating this work and performing the numerical calculations. —
REFERENCES 1.
LUENGO C.A. and MAPLE M.B.,Solid State Commun. 12, 757 (1973).
2.
LUENGO C.A., MAPLE M.B. and FERTIG W.A., Solid State Commun. 11, 1445 (1972).
3. 4.
BUCHER E., MAITAJ.P. and COOPER A.S.,Phys. Rev. B6, 2709 (1972). ABRJKOSOV A.A. and GORKOV L.P.,Sovier Phys., JETP 12, 1243 (1961).
5.
FULDE P., HIRST L.L. and LUTHER A.,Z. Phys 230, 155 (1970).
6.
FULDE P. and PESCHEL I.,Adv. Pkys. 21, 1(1972).
7.
KELLER J. and FULDE P.,J. Low Temp. Phys. 4, 289 (1971).
8. 9.
KELLER J. and FULDE P., J. Low Temp. Phi’s. 12,63 (1973). HAPPEL H., HOLZER P., IJMLAUF E. and HOENIG H.E., to be published.
10. 11.
MAPLE M.B.,Solid State Commun. 8, 1915 (1970). HOENIG H.E. and BARTH N, J. Low Temp. Phys. 4, 355 (1969).
12.
HUNGSBERG R.E. and GSCHNEIDNER Jr. K.A.,J. Phys. Chem. Solids 33,401(1972).
13. 14.
SKALSKI S., BETBEDER-MATIBET 0. and WEISS PR.,Phys. Rev. 136, A 1500 (1964). LEA K.R., LEASK M.J.M. and WOLF W.P.,J. Phys. C’hem. Solids 23, 1381 (1962).
15.
MULLER-HARTMANN E. and ZITTARTZ J.,Solid State Commun. 11,401 (1972). Es wurden Messungen des Sprungs in der spezifischen Warme &(T~)an supraleitenden La 1_jb~Al2 Verbindungen ausgefUhrt, urn den Paarbrechungseffekt von Tb~-Ionenirn LaAl2-Wirt zu untersuchen. Die Ergebnisse weichen von der Abrikosov—Gorkov—Theorie ab. Beriscksichtigt 3~im LaAI man die Kristallfeldniveaus von Tb 2, kOnnen die Ergebnisse mit dem Modell von Fulde. Keller und Peschel qualitativ erklart werden. Auf Grund von Rechnungen. die Muller-Hartmann und Zittartz verOffentlichien. kann em Einflufi des Kondo Effekts ausgeschlossen werden.
Vol. 13, pp, 1641—1643, 1973.
Pergamon Press.
Printed in Great Britain
THE SPECIFIC HEAT JUMP OF SUPERCONDUCTING ~ Al2 RELATED TO CRYSTAL ELECTRIC FIELD SPLITTING OF THE Th~LEVELS* H. Happel and H.E. Hoenig Physikalisches Institut der Universitat, Frankfurt am Main, Germany (Received 30 July 1973 by B. Muhlschlegel)
Measurements of the specific heat jump &(T~)were performed on superconducting La1 ~Th~A1,compounds in order to investigate the pairbreaking effect of Tb ~ ions in the LaAJ2 host. The results deviate from the Abrikosov— Gorkov theory for superconductors with magnetic 3~in LaAl impurities. Taking into account the crystal field level structure of Tb 2 the results can be qualitatively understood within the model of Fulde, Keller and Peschel. According to calculations published by Müller.Hartmann and Zittartz an influence of the Kondo effect can be ruled out. -
INTRODUCTION
In this letter we present experimental results on
MEASUREMENTS of the specific heat jump at the transition temperature proved to be an important tool to distinguish between different pair-breaking mechanisms of magnetic impurities in superconductors.’ 4 According thejump Abrikosov—Gorkov-theory the specifictoheat &(T~)decreases more (AG) rapidly
the specific heat jump &(T~)for the system La1 -x Tb~Al2 (x ~ 0.008), which again are close to the BCS solution. The results can be understood in an extended temperature range ~ using TC/TCOthe ~ data I within the CEF model of Fulde et a!.0.4 5—8 on the spectroscopic state of the Tb3~-ionsin the LaAI 2 host as given in reference (9).
.~
than the superconducting transition temperature 7~ thus deviating markedly from the BCS law of corresponding states where ~c(T~) is proportional to 7~. While for the system La1_~Gd~A12 the AG-dependence is well confirmed,’ smaller values for &(T~)than predicted by AG have been found for the compound 2 La1 For_~Ce~Al2 the systemand La attributed to the Kondo effect. 3 _~Pr~Tl, however, ~c(7~) is larger than given by the AG theory, approaching the BCS solution down to Tc/T~o~ 07.~This can be explained qualitatively by including the interaction between the conduction electrons and the crystal electric field (CEF) split levels of the impurities. For TC/TCO <0.7 impurity interactions probably become important in this system because of the high concentration (x> Ui).
EXPERIMENTAL DETAILS The samples were prepared in three steps. First La1_~Tb~ were arc-melting amounts ofalloys La and Tb made (both by obtained from appropriate Metals Research, nominal purity 99.9%) together in a high purity, titanium gettered, argon atmosphere. Each button was remelted 6—8 times to ensure homogenity. Then the calculated weight of 99.999% Al was added and the reaction to form the corresponding Laj_xlbx Al2 compound was performed by arc-melting, too. Further homogenization of the brittle samples was established by levitation melting. Ellipsoids of typically 3g obtained by this procedure. X-ray-diffraction andwere electron-microprobe analysis showed that the samples were in a single phase and of the right corn-
*
A project of the Sonderforschungsbereich 65 “Festkorperspektroskopie” financed by special funds of the Deutsche Forschungsgerneinschaft.
position.
l64~
1642
SPECIFIC HEAT JUMP OF SUPERCONDUCTING Lai.~Tb~A12
Some of the samples were wrapped in Ta foil, sealed in quartz tubes under a vacuum better than lO~Torr and annealed at 800°Cfor three days. This procedure has been found to sharpen the 1’2 superconThis effect ducting transition of La1_~(Gd, C e)~M2 was also observed by us for La, ~ In the case of Th additions, however, we found a smearing of the transition and a shift to higher temperatures in cornparison to unannealed samples. The transition ternperature of unannealed samples were in good agree ment with the Ta-values given in reference 10, whereas annealing of an e.g. 0.5 at % Tb doped sample resulted in a shift of 0.5K. Remelting the annealed samples resulted in a sharp transition and a lower T~.We believe that there is some clustering of the Tb-impurities at the grain boundaries during annealing. Thus ~ measurements were done on unannealed samples which were prepared in an identical way. The specific heat measurements between 1.3K and 4.2K were carried out using12a heat pulse method Temperatures were and a cryostat described earlier. determined with an Allen—Bradley carbon resistor, 200 57, 1/8 W, which was calibrated against the He4vapour pressure in each run, using a three point formula for interpolation.
Vol. 13, No. 10 Tb Al •
‘°
\~—4 \ .tl
\
~
-
._‘~
\~,
,...
x. 0
:~
..~\
.-~
‘i” 20
-_________________________________ rs 20 25 10 .15 T.mp.ratur.
K
FIG I. Specific heat cIT at the phase transition versus temperature of La 1 -x Th~Al2samples with different Tb concentrations. The solid lines are drawn merely for clearness. -
1.0
L~ La
4 C0
~
TbX A 12
/ /
05
4
/
4/
RESULTS AND DISCUSSION Results of the specific heat measurements for pure LaAl, and four La 1 _~Th~Al, samples are shown in Fig. I. For LaAI2 we fmd a transition temperature of 3.22 ±0.03K and an electronic heat isconstant The ratiospecific ~Ac(T~)/7T~ found ~ of 10.3 mJ mol’ 2 to be 1.50 in of good with Substitution La agreement by magnetic Tb other atomsauthors.’ decreases T~,the transition temperatures of the samples agree with the Ta-values given in reference 10.
2.
-
r
Figure 2 shows the reduced specific heat jump &(T~)/&o(T~o) versus the reduced transition ternperature TdT~owhere the subscript o refers to undoped samples. The solid line is the AG result as calculated by Skalski et ~ the experimental points deviate clearly from this curve. However, it should be noted that in the AG-theory no influence of higher levels is considered. This was first done by Fulde, Hirst, and Luther5 and in following papers;6—8 In particular Fulde and Keller have calculated the jump in the specific heat at the phase transition taking into account
0
I
05
1.0
T
0/ ~
FIG. 2. Reduced specific heat jump I~.c(Tc)/&o(Tco) versus reduced transition temperature T~/T~ for Lai...~Th~A1 1 which corres2. The continuous solid i~the AG result as by level Skalski et a!. 6~ine ponds tocalculated a degenerate system = 0. In the dashed line, CEF splitting of the Tb impurities is taken into account, the excitation energy to the first excited level is equal to T~.The arrow marks a lower limit of &/&° for the sample with the lowest T~. a given sequence of crystal field split energy levels of the impurities.8 In order to determine the spectroscopic state of Th3~in the LaAl 2 host we measured the Schottky specific heat and the magnetic susceptibility of L.a098
Vol. 13, No. 10
SPECIFIC HEAT JUMP OF SUPERCONDUCTING La1 -xTbxAl2
9 and Th0~Al, indata the temperature L5 to 10K fitted these to the / = 6 range level scheme given by Lea, Leask, and Wolf.14 With a level sequence accordihg to x = — 0.2 (this parameter is defmed in reference 14) and an energy separation of 3—4K between the magnetic ground state and the F 3 nonmagnetic doublett as first excited state we obtamed a reasonable fit of the experimental data. Based on this level scheme, A.c(T~)was computed by Keller solving equation 19 of reference 8. The result is presented by the dashed line in Fig. 2 for a splitting 6/Tao = 1 where 6 is the ground state isolation energy. The systematic deviation of this theoretical result from the AG solution explains at least qualitatively the experimental data.
r’~
The results of Fig. 2 are also interesting with respect to calculations of MilhJer—Hartmann and Zittartz on the influence of the Kondo-effect on the specific heat the superconducting phasec~’of 15 jump These at authors calculated the slope transition.
1643
the curve in Fig. 2 in the limit T,jT~ 1 as function of the Kondo temperature Tx in the interval 1 O~< TKITC.~O< l0~with the impurity spin S as parameter. In most cases c* is larger than the slope of the AG curve. In particular for Tb, which has a spinS = 3, the -*
calculated slope c~exceeds the value derived from experiment by at least 40%. Thus, one can exclude any significant influence of the Kondo effect in the Lai.~ Th~Al,system. In summary, we have shown that the specific heat jump at the superconducting transition temperature in the La1 -x Th~,,Al2 system is strongly influenced by crystal electric field effects. The experimental results are in qualitative agreement with theory down to the lowest temperature where measurements have been performed, that is T~/T~ ~ 0.4. Acknowledgements We thank Prof. Dr. J. Keller for stimulating this work and performing the numerical calculations. —
REFERENCES 1.
LUENGO C.A. and MAPLE M.B.,Solid State Commun. 12, 757 (1973).
2.
LUENGO C.A., MAPLE M.B. and FERTIG W.A., Solid State Commun. 11, 1445 (1972).
3. 4.
BUCHER E., MAITAJ.P. and COOPER A.S.,Phys. Rev. B6, 2709 (1972). ABRJKOSOV A.A. and GORKOV L.P.,Sovier Phys., JETP 12, 1243 (1961).
5.
FULDE P., HIRST L.L. and LUTHER A.,Z. Phys 230, 155 (1970).
6.
FULDE P. and PESCHEL I.,Adv. Pkys. 21, 1(1972).
7.
KELLER J. and FULDE P.,J. Low Temp. Phys. 4, 289 (1971).
8. 9.
KELLER J. and FULDE P., J. Low Temp. Phi’s. 12,63 (1973). HAPPEL H., HOLZER P., IJMLAUF E. and HOENIG H.E., to be published.
10. 11.
MAPLE M.B.,Solid State Commun. 8, 1915 (1970). HOENIG H.E. and BARTH N, J. Low Temp. Phys. 4, 355 (1969).
12.
HUNGSBERG R.E. and GSCHNEIDNER Jr. K.A.,J. Phys. Chem. Solids 33,401(1972).
13. 14.
SKALSKI S., BETBEDER-MATIBET 0. and WEISS PR.,Phys. Rev. 136, A 1500 (1964). LEA K.R., LEASK M.J.M. and WOLF W.P.,J. Phys. C’hem. Solids 23, 1381 (1962).
15.
MULLER-HARTMANN E. and ZITTARTZ J.,Solid State Commun. 11,401 (1972). Es wurden Messungen des Sprungs in der spezifischen Warme &(T~)an supraleitenden La 1_jb~Al2 Verbindungen ausgefUhrt, urn den Paarbrechungseffekt von Tb~-Ionenirn LaAl2-Wirt zu untersuchen. Die Ergebnisse weichen von der Abrikosov—Gorkov—Theorie ab. Beriscksichtigt 3~im LaAI man die Kristallfeldniveaus von Tb 2, kOnnen die Ergebnisse mit dem Modell von Fulde. Keller und Peschel qualitativ erklart werden. Auf Grund von Rechnungen. die Muller-Hartmann und Zittartz verOffentlichien. kann em Einflufi des Kondo Effekts ausgeschlossen werden.