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Specific heat of superconducting Th, Sc and Th, Y alloys with Ce impurities
Solid State Communications, Vol. 17, pp. 158 1—1583, 1975.
Pergamon Press.
Printed in Great Britain
SPECIFIC HEAT OF SUPERCONDUCTING Th, Sc AND Th, Y ALLOYS WITH Ce IMPURITIES* J.G. Sereni Centro Atómico Banloche (CNEA), Instituto de Fisica Balseiro (UNC), Bariloche, Rio Negro, Argentina J.G. Huber Department of Physics, Tufts University, Medford, MA 02155, U.S.A. and C.A. Luengo and M.B. Maple Institute for Pure and Applied Physical Sciences, University of California, San Diego, La Jolla, CA 92037, U.S.A. (Received 18 July 1975 byA.Pinczuk)
Measurements of the specific heat jump L~Cat the superconducting critical temperature T~,on (Th, Sc)Ce and (Th, Y)Ce Ce impurity, solid solution alloy systems indicate that the former systems obey the BCS law of conesponding states (LCS) characteristic of superconductors with non-magnetic impurities while the latter systems present deviations from the LCS linear relation between reduced parameters which are attributed to the development of localized moments at the Ce ions as the Y concentration increases.
A RECENT calorimetric study of the demagnetization with increasing Th concentration of Ce impurities in superconducting La, Th hosts”2 has shown that a theory for Kondo superconductors due to Muller— Hartmann and Zittartz (MHZ)3’4 is able to give a remarkably good description of the data for La rich systems with the assumption of reasonably low Kondo temperatures TK. Proceeedmg to Th rich systems, it was inferred that the Ce ions demagnetize smoothly since the data converged continuously to the BCS law of corresponding states (LCS) characteristic of nonmagnetic systems. The MHZ theory was unable to describe this behavior, even with unphysically large TK’S. ____________
*
Research supported in part by the Organization of American States Multinational Project on Physics, the Consejo Nacional de Investigaciones Cientificas y T~cnicas(subsidio No. 6450/74), the U.S. Air Force Office of Scientific Research under AFOSR Grant No. AF-AFOSR-71 -2073 and the U.S. Energy Research and Development Administration under contract No. ERDA E(04-3).34 PA227.
The substitution of Y for Th in (Th, Y)Ce systems has been reported5 to modify the superconductmg-normal phase boundary, T~vs n where n is the Ce impurity concentration, by increasing the initial depression, indicative that magnetization of the Ce ions may occur at high Y concentrations. Indeed, YCe is a nonsuperconducting Kondo system with TK 40 K.6 In contrast, partially replacing the host Th by Sc concentrations up to 35 at.% (a/o) decreases the initial depression5 from the ThCe value, suggestive of further demagnetization of the Ce ions. Measurements of ~C at T~were therefore undertaken on (Th,Y)Ce and (Th, Sc)Ce systems to seek additional experimental information regarding the demagnetization of the Ce ions in the nonmagnetic limit (large host Th concentrations). The samples were f.c.c. solid solution arc melted buttons weighing about 3 g, prepared as described previously.5 The specific heat measurements at
1581
1582
Th, Sc AND Th, Y ALLOYS WITh Ce IMPURITIES I
I
I
•ITh~ICe
‘S
Vol. 17, No. 12
•T8
‘S
65Sc35
•
•T880’Y20
‘S
T.
-
\ ‘S
-
—
-
I—
I “S ‘S ‘S ‘S
C-, 0
~O.5
“
-
.0
+
0
‘S\ ‘S ‘S
AG
_______________
\BCS ‘S
-
‘S’
0
FIG. 1. Reduced specific heat jump ~C/i~C0 vsreduced critical temperature TCITCO for the systems: (Tho~65Sc035)Ce,1.46 and 2.10 a/o Ce; (Tho8oYo2~)Ce,0.70 and 1.70 a/o Ce and (Th065Y035)Ce, 0.30 and 0.70 a/o Ce.
•
~
T I
I
II
1.~
T
1
0.6
6IAC/ac,)
I
07
0.8
2.0
FIG. 3. Initial slope [d(L~C/L~Co)/d(T~/T~0)] TC=TCO vs reduced initial depression ~.(T~/T~0)/n.The (~~~)Ce data are from references I and 2. specific heat jump ~C/~tCo is plotted against reduced critical temperature T~/T~0(~Co and ~ are ~Cand T~of the host) for the systems (Th065Sco35)Ce, (~fl~65Y035~~e and (Tho.seYo ~)Ce. To best emphasize any deviations from the BCS LCS, the initial slopes [d(~C/t~Co)/d(T~/T~0)] TC=TC0 in Fig. 1 as
system, like ThCe, has the BCS LCS initial slope of 1.0; whereas clear departures are observed for the others. These departures are sizable and for both the (Th,Y)Ce and the (~j~)Cesystems, the initial slopes approach the BCS value monotonically.
Tc:Tc
dcT~/T~,~
—
S
— —
.0
well as those for several (Th, La)Ce systems studied 2 are graphed vs Th concentration by Luengo et al.” in Fig. 2. Within experimental error, the (Th, Sc)Ce
• (
zof
BCS
n
0.5
9)Ce • ~T~~lCe
•-f--~
______
‘S
0
i
—
C-)
A more significant systematic in the variation of ics
1.0
09
Th
09
I 08
07
FIG. 2. Initial slope [d(~C/z~Co)/d(T~/T~0)]T~= T~0 vs Th composition. The (Th, La)Ce data are from references 1 and 2. temperatures between 0.5 and 4 utilizing K were made a 3 semiadiabatic calorimeter7 a heatinpulse He technique. The Ge resistor temperature scale was calibrated against He4 vapor pressure and a CMN magnetic thermometer above and below 1.5 K respectively, For each sample the measurements were restricted to the vicinity of its T~.L~Cwas determined by extrapolation of both the superconducting and the normal state data to the midpoint of the transition. The primcipal results are displayed in Fig. 1 where reduced
[d(z~C/~C0)/d(T~/T~0)] illustrated in Fig. where this initial slope isTc=Tc plottedisagainst that of the 3 reduced phase boundary, ~(T~/T~)/n, for the (Th, Sc)Ce, and (Th, La)Cethese systems studied here(Th, and Y)Ce, elsewhere.1~~m data it can be inferred that if the BCS LCS is taken as the critenon for defmmg these superconducting host-Ce impurity systems to be nonmagnetic, there is a critical value ~(T~/T~0)/n 0.4 beyond which out suchthat systems become magnetic. It should be pointed other apparently nonmagnetic systems, like AIMn and ThU, obey the BCS LCS8 but have initial slope values for their reduced superconducting-normal phase boundaries substantially greater than 0.4. The heat capacity measurements reported here provide further documentation of the demagnetization of Ce impurity ions in a number of
Vol. 17, No. 12
Th, Sc AND Th, YALLOYS WITh Ce IMPURITIES
superconducting Th-nch solid solution alloy hosts. These data along with some reported by Luengo et al.1’2 follow a general pattern which appears to suggest that once a critical value of about 0.4 is exceeded for the initial depression of the reduced phase boundary, deviations from the BCS LCS set in. For all of the systems depicted in Figs. 2 and 3 the detailed shape of the phase boundary can be fitted to T~less than 0.1 T~, 0by the modified exponential 7’, = T~0exp [— An/(15 — Dn)J where Aform and D This functional forare adjustable parameters. T~vs n was derived by Kaiser9 in a theory predicated upon the assumptions that the host be a BCS superconductor and the impurity be nonmagnetic. Kaiser’s
1583
theory, moreover, predicts the BCS LCS to hold for the alloys of the host-impurity system; thus, this seems a reasonable criterion for defming a nonmagnetic system, and the deviations from the BCS LCS found for systems with sufficient host Y and La content can be taken as indicative of the onset of magnetic behavior. As yet, no 4,10~1 which attempts to describe the variety of magnetic behaviors of impurities in metals is compatible with our data. The incompatibility the theoretical ability of describing appears a smoothinapproach to the inBCS LCS as the impurity ions demagnetize with increasing Th concentrations.
REFERENCES 1. 2.
LUENGO C.A., HUBER J.G., MAPLE M.B. & ROTH M., Phys. Rev. Lett. 32,54(1974). LUENGO C.A., HUBER J.G., MAPLE M.B. & ROTH M.,J. Low Temp. Phys. 21,129(1975).
3.
MULLER-HARTMANN E. & ZITIARTZ L, Z. Phys. 234~58(1970).
4.
MULLER-HARTMANN E. & Z1TTARTZ I., Solid State Commun. 11,401(1972).
5.
HUBER J.G. & MAPLE M.B., Proc. 13th mt. Conf. on Low Temp. Phys., Boulder, Colorado; 2,579 Plenum Press, New York (1974); See also HUBER J.G, Phi). Thesis, University of California, San Diego (1971). SUGAWARA T. & YOSHIDA S., J. li,iw Temp. Phys. 4,657(1971). LUENGO C.A., Ph.D. Thesis, University of Cuyo, Argentina (1972). See, for example MAPLE M.B. in Magnetism: A 7)’eatise on Modern Theory and Materials (Edited by SUHL H.) (1. 10. NY (1973). KAISER A.B., I. Phys. C3, 409 (1970). SHIBAH.,I~vg.Theor~Phys.50, 50 (1973). ROSSLER J. & KIWI M.,Phys. Rev. BlO, 95(1974).
6. 7. 8. 9. 10. 11.
Pergamon Press.
Printed in Great Britain
SPECIFIC HEAT OF SUPERCONDUCTING Th, Sc AND Th, Y ALLOYS WITH Ce IMPURITIES* J.G. Sereni Centro Atómico Banloche (CNEA), Instituto de Fisica Balseiro (UNC), Bariloche, Rio Negro, Argentina J.G. Huber Department of Physics, Tufts University, Medford, MA 02155, U.S.A. and C.A. Luengo and M.B. Maple Institute for Pure and Applied Physical Sciences, University of California, San Diego, La Jolla, CA 92037, U.S.A. (Received 18 July 1975 byA.Pinczuk)
Measurements of the specific heat jump L~Cat the superconducting critical temperature T~,on (Th, Sc)Ce and (Th, Y)Ce Ce impurity, solid solution alloy systems indicate that the former systems obey the BCS law of conesponding states (LCS) characteristic of superconductors with non-magnetic impurities while the latter systems present deviations from the LCS linear relation between reduced parameters which are attributed to the development of localized moments at the Ce ions as the Y concentration increases.
A RECENT calorimetric study of the demagnetization with increasing Th concentration of Ce impurities in superconducting La, Th hosts”2 has shown that a theory for Kondo superconductors due to Muller— Hartmann and Zittartz (MHZ)3’4 is able to give a remarkably good description of the data for La rich systems with the assumption of reasonably low Kondo temperatures TK. Proceeedmg to Th rich systems, it was inferred that the Ce ions demagnetize smoothly since the data converged continuously to the BCS law of corresponding states (LCS) characteristic of nonmagnetic systems. The MHZ theory was unable to describe this behavior, even with unphysically large TK’S. ____________
*
Research supported in part by the Organization of American States Multinational Project on Physics, the Consejo Nacional de Investigaciones Cientificas y T~cnicas(subsidio No. 6450/74), the U.S. Air Force Office of Scientific Research under AFOSR Grant No. AF-AFOSR-71 -2073 and the U.S. Energy Research and Development Administration under contract No. ERDA E(04-3).34 PA227.
The substitution of Y for Th in (Th, Y)Ce systems has been reported5 to modify the superconductmg-normal phase boundary, T~vs n where n is the Ce impurity concentration, by increasing the initial depression, indicative that magnetization of the Ce ions may occur at high Y concentrations. Indeed, YCe is a nonsuperconducting Kondo system with TK 40 K.6 In contrast, partially replacing the host Th by Sc concentrations up to 35 at.% (a/o) decreases the initial depression5 from the ThCe value, suggestive of further demagnetization of the Ce ions. Measurements of ~C at T~were therefore undertaken on (Th,Y)Ce and (Th, Sc)Ce systems to seek additional experimental information regarding the demagnetization of the Ce ions in the nonmagnetic limit (large host Th concentrations). The samples were f.c.c. solid solution arc melted buttons weighing about 3 g, prepared as described previously.5 The specific heat measurements at
1581
1582
Th, Sc AND Th, Y ALLOYS WITh Ce IMPURITIES I
I
I
•ITh~ICe
‘S
Vol. 17, No. 12
•T8
‘S
65Sc35
•
•T880’Y20
‘S
T.
-
\ ‘S
-
—
-
I—
I “S ‘S ‘S ‘S
C-, 0
~O.5
“
-
.0
+
0
‘S\ ‘S ‘S
AG
_______________
\BCS ‘S
-
‘S’
0
FIG. 1. Reduced specific heat jump ~C/i~C0 vsreduced critical temperature TCITCO for the systems: (Tho~65Sc035)Ce,1.46 and 2.10 a/o Ce; (Tho8oYo2~)Ce,0.70 and 1.70 a/o Ce and (Th065Y035)Ce, 0.30 and 0.70 a/o Ce.
•
~
T I
I
II
1.~
T
1
0.6
6IAC/ac,)
I
07
0.8
2.0
FIG. 3. Initial slope [d(L~C/L~Co)/d(T~/T~0)] TC=TCO vs reduced initial depression ~.(T~/T~0)/n.The (~~~)Ce data are from references I and 2. specific heat jump ~C/~tCo is plotted against reduced critical temperature T~/T~0(~Co and ~ are ~Cand T~of the host) for the systems (Th065Sco35)Ce, (~fl~65Y035~~e and (Tho.seYo ~)Ce. To best emphasize any deviations from the BCS LCS, the initial slopes [d(~C/t~Co)/d(T~/T~0)] TC=TC0 in Fig. 1 as
system, like ThCe, has the BCS LCS initial slope of 1.0; whereas clear departures are observed for the others. These departures are sizable and for both the (Th,Y)Ce and the (~j~)Cesystems, the initial slopes approach the BCS value monotonically.
Tc:Tc
dcT~/T~,~
—
S
— —
.0
well as those for several (Th, La)Ce systems studied 2 are graphed vs Th concentration by Luengo et al.” in Fig. 2. Within experimental error, the (Th, Sc)Ce
• (
zof
BCS
n
0.5
9)Ce • ~T~~lCe
•-f--~
______
‘S
0
i
—
C-)
A more significant systematic in the variation of ics
1.0
09
Th
09
I 08
07
FIG. 2. Initial slope [d(~C/z~Co)/d(T~/T~0)]T~= T~0 vs Th composition. The (Th, La)Ce data are from references 1 and 2. temperatures between 0.5 and 4 utilizing K were made a 3 semiadiabatic calorimeter7 a heatinpulse He technique. The Ge resistor temperature scale was calibrated against He4 vapor pressure and a CMN magnetic thermometer above and below 1.5 K respectively, For each sample the measurements were restricted to the vicinity of its T~.L~Cwas determined by extrapolation of both the superconducting and the normal state data to the midpoint of the transition. The primcipal results are displayed in Fig. 1 where reduced
[d(z~C/~C0)/d(T~/T~0)] illustrated in Fig. where this initial slope isTc=Tc plottedisagainst that of the 3 reduced phase boundary, ~(T~/T~)/n, for the (Th, Sc)Ce, and (Th, La)Cethese systems studied here(Th, and Y)Ce, elsewhere.1~~m data it can be inferred that if the BCS LCS is taken as the critenon for defmmg these superconducting host-Ce impurity systems to be nonmagnetic, there is a critical value ~(T~/T~0)/n 0.4 beyond which out suchthat systems become magnetic. It should be pointed other apparently nonmagnetic systems, like AIMn and ThU, obey the BCS LCS8 but have initial slope values for their reduced superconducting-normal phase boundaries substantially greater than 0.4. The heat capacity measurements reported here provide further documentation of the demagnetization of Ce impurity ions in a number of
Vol. 17, No. 12
Th, Sc AND Th, YALLOYS WITh Ce IMPURITIES
superconducting Th-nch solid solution alloy hosts. These data along with some reported by Luengo et al.1’2 follow a general pattern which appears to suggest that once a critical value of about 0.4 is exceeded for the initial depression of the reduced phase boundary, deviations from the BCS LCS set in. For all of the systems depicted in Figs. 2 and 3 the detailed shape of the phase boundary can be fitted to T~less than 0.1 T~, 0by the modified exponential 7’, = T~0exp [— An/(15 — Dn)J where Aform and D This functional forare adjustable parameters. T~vs n was derived by Kaiser9 in a theory predicated upon the assumptions that the host be a BCS superconductor and the impurity be nonmagnetic. Kaiser’s
1583
theory, moreover, predicts the BCS LCS to hold for the alloys of the host-impurity system; thus, this seems a reasonable criterion for defming a nonmagnetic system, and the deviations from the BCS LCS found for systems with sufficient host Y and La content can be taken as indicative of the onset of magnetic behavior. As yet, no 4,10~1 which attempts to describe the variety of magnetic behaviors of impurities in metals is compatible with our data. The incompatibility the theoretical ability of describing appears a smoothinapproach to the inBCS LCS as the impurity ions demagnetize with increasing Th concentrations.
REFERENCES 1. 2.
LUENGO C.A., HUBER J.G., MAPLE M.B. & ROTH M., Phys. Rev. Lett. 32,54(1974). LUENGO C.A., HUBER J.G., MAPLE M.B. & ROTH M.,J. Low Temp. Phys. 21,129(1975).
3.
MULLER-HARTMANN E. & ZITIARTZ L, Z. Phys. 234~58(1970).
4.
MULLER-HARTMANN E. & Z1TTARTZ I., Solid State Commun. 11,401(1972).
5.
HUBER J.G. & MAPLE M.B., Proc. 13th mt. Conf. on Low Temp. Phys., Boulder, Colorado; 2,579 Plenum Press, New York (1974); See also HUBER J.G, Phi). Thesis, University of California, San Diego (1971). SUGAWARA T. & YOSHIDA S., J. li,iw Temp. Phys. 4,657(1971). LUENGO C.A., Ph.D. Thesis, University of Cuyo, Argentina (1972). See, for example MAPLE M.B. in Magnetism: A 7)’eatise on Modern Theory and Materials (Edited by SUHL H.) (1. 10. NY (1973). KAISER A.B., I. Phys. C3, 409 (1970). SHIBAH.,I~vg.Theor~Phys.50, 50 (1973). ROSSLER J. & KIWI M.,Phys. Rev. BlO, 95(1974).
6. 7. 8. 9. 10. 11.