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Anomalous Tc-behavior of LaSn3 under pressure
Solid State Communications, Vol. 16, pp. 409—412, 1975.
Pergamon Press.
Printed in Great Britain
ANOMALOUS TcBEHAVIOR OF LaSn3 UNDER PRESSURE t and C.W. Chu* S. Huang Department of Physics, Cleveland State University, Cleveland, Ohio 44115, U.S.A. and F.Y. Fradint Argonne National Laboratory, Argonne, illinois 60439, U.S.A. and L.B. Welsh~ Department of Physics, Northwestern University, Evanston, Illinois 60201, U.S.A. (Received 9 October 1974 by A.G. Chynoweth)
The superconducting transition temperature Tc of LaSn 3 has been measured up to 22 kbar and was observed to increase through a maximum under hydrostatic compression. The anomalous Tc-behavior is attributed to a pressure induced Fermi surface topology change. 1 have shown that the superconductHAVINGA eta!. ing transition temperature Tc, the magnetic suscepti. biity x and the thermo-electric power of a number of the pseudo-binary AR 3.type compounds with Cu3Au. structure vary oscillatorily with the valence.electron concentration z. Tc peaks near z = 2.95, 3.3 and 3.7. The In, constituent elements areThe La, results Y, Th and for A, and Sn, 11 and Pb for B. wereCaexplained in terms of a similar variation of the electron density
the change of z. However, the lattice parameter of these compounds fails to exhibit any anomaly that is common in many alloy systems undergoing Fermi surface topology changes. In addition, similar oscillatory variations of Tc and x were also observed in the transition metal alloy superconductors thatneed follow the 2 without the to invoke empirical rule topology. Hence further aMatthias change of Fermi surface study on the AB 3.compounds is essential.
of states N(EF) and the electron—phonon interaction V of these compounds with z. The peculiar features of N(EF) and V were attributed to the change of Fermi surface topology or the Brillouin.zone effect due to
LaSn3 has a z 3.75, which is very close to one of the Tc-maxima. If the model of Havinga eta!. is correct the LaSn3 Fermi surface would be very close to the Brillouin zone boundary and the application of hydrostatic pressure would induce a Fermi surface topology change. An anomalous pressure behavior of T1~is expected when the Fermi surface topology changes 3 Re4 and AuGa~. under for the cases ofthe Tl,Tc of LaSn In this pressure, study, weashave measured 3 up
____________
*
Research supported by National Science Foundation Grant No. GH-40866 and Research Corporation.
4
Work performed under the auspices of the U.S. Atomic Energy Commission.
:1
Supported by Air Force Office of Scientific Research Grant No. 71-2012 and by NSF through the Northwestern University Material Research Center.
to 22 kbar. The results are consistent with the sug. gestion by Havinga et al. 409
410
ANOMALOUS Tc-BEHAVIOR OF LaSn3 UNDER PRESSURE
IC
Vol. 16, No.4
0.08
~ !08
\\ \
Nonlinear La Sn3
0.04 Total
Pressure
~°04
000~ 5890
5930
5970
6010
1(K)
The superconducting transitions at different pressures. The number represents the sequential order of the ex erimental runs
I
0
5
I
I
10 P (k bar)
15
20
FIG. 1.
The LaSn3 sample was prepared by arc melting (3—4 times) stoichiometric quantities of lanthanum (99.9 per cent Research Chemical Division of Nuclear Corporation of America) and tin (99.999 per cent Vulcan Materials Co.). Weight loss after melting amounted to 0.36 per cent. The ingot was homogenized for five days at 800°Cin quartz under vacuum and water quenched. Powders for X-ray determination of the lattice parameters were obtained by crushing in an argon glove box. The powders were annealed for two hours at 400°C prior to X-ray examination, The lattice parameter isa0 = 4.773(2) A. Two small samples of 100 and 75 mg respectively cut from two ends of the LaSn3 ingot were investigated. Both samples have the same Tc (5.98 K) with a transition width of 15 mK at atmospheric pressure, reflecting the high homogeneity of the ingot. Our slightly lower T~in comparison that observed 1 may bewith associated with thepreviously possible higher 6.4 K)level in our starting elements. A self-clamp impurity technique was employed to provide the hydrostatic environment in a 1 1 fluid mixture of n-pentane and isoamyl alcohol. The pressure was generated inside and locked by the clamp at room temperature. A superconducting Pb-manometer6 situated next to the sample —
—
‘~‘
(‘—j
was used to determine the pressure at low temperature. The transition to the superconducting state was detected by a standard a.c. inductance technique operating at 10 Hz. Temperature was measured by a Ge-thermometer. The relative accuracy of the mometer is estimated to be within ±0.002 K. ther-
FIG. 2. The pressure dependence of the Tc-shift and its breakdown to the linear and nonlmear contnbutions. The pressure dependences of the two samples investigated are identical and hence only results of one sample are shown. The superconducting transitions of LaSn3 at different pressures are shown in Fig. 1. The number represents the sequential order of the experimental runs. The results are summarized in Fig. 2 where the Tc-shift, I~T0is plotted as a function of pressure. The circular (or triangular) symbol denotes the mid-point of the transition during the pressurizing (or depressurizing) cycle. The vertical bar stands for the width of the transition determined by the extrapolation of the linear portion of the transition curve to the fully normal and fully superconducting states. The horizontal bar indicates the uncertainty in pressure. In strong contrast to the linear pressure effect of the great majority of 7 Tcon ofT~ LaSn superconductors, 3 is observed to increase initially,with pass pressure. a maximum, and finally decreasewithin linearly No pressure hysteresis our experimental error was detected, indicating that any possible strain or dislocation introduced during pressurization should be negligibly small. The Fermi surface topology,change occurs when the Fermi level EF crosses a critical energy E 0 in the energy spectrum E(k). Ec is defined as the energy at a critical point where VE(k) = 0. The change gives rise to an additional rapidly varying contribution ~N(EF) to the density of states N(EF) at EF. 6N(EF) T usually is proportional to ± (EFof change Ec)~orof±Fermi (E0 EF) depending on the specific kind surface topology.8 Makarov and Baryakhtar9 examined —
—
Vol. 16, No.4
ANOMALOUS Ta-BEHAVIOR OF LaSn3 UNDER PRESSURE
the effect of ~N(EF) on the superconducting properties using the BCS formalism. They found that Tc varies drastically over an energy range kOD about 0D is Ec antemperature. extremum ofFor aTC/aEF at Ec, where the with Debye the four possible kinds of topology changes, the following changes of Tc were predicted: Tc will have a jump over the energy range (Ec — kOD) EF (Ec + kOD), when the Fermi surface transforms from a closed to an open surface or when a cavity in the Fermi surface is formed, while Tc will have a drop over the same energy range when the Fermi surface transforms from an open to a closed surface or when a cavity is destroyed. At E = Ec, the jump of Tc is associated with a maximum of aTcIaEF, and the drop of T~is associated with a minimum of aTC/aEF. In a similar way, Higgins and Kaehn1°later showed that aTCIaEF cc aN(EF)/aEF or (EF — Ec)~ near the critical point but is smeared out by imperfection scattering. The shift of Tc under pressure is mainly caused by changes in EF [or N(EF)] and V (the electron—phonon interaction), i.e. dT dP
aT dE —~
—f +
aEF dP
411
butions. The slope of the linear part is equal to that of the total L~Tcin the high pressure region. The nonlinear which starts at. zero pressure rapidlycontribution and saturates at pressures 15 kbar. Thisrises is similar to the predicted Tc change associated with a Fermi surface topology change corresponding to a transformation from a closed to an open surface or to the creation of a cavity.9 The uncertainty in the exact shape of the nonlinear contribution of L~Tcand the lack of information about the band structure of the compound prevent us from further identifying the specific kind of Fermi surface topology change induced by pressure. The slope of this nonlinear portion shows a maximum at a pressure <8 kbar. This suggests that a critical pressure of < 8 kbar is sufficient to move EF crosses Ec and thus to induce a change in the Fermi surface topology. The linear part of L~Tcrepresents the pressure effect on T~had the Fermi surface topology not changed under pressure. In conclusion, we have observed a non-linear
aT d V
pressure effect on Tc of LaSn
__c aV ~
3 - This is attributed to a pressure induced Fermi surface topology change consistent with the alloying study of AB3-compound
—,
Since the second term and dEF/dP vary only slowly with pressure, any rapid variation in aTC/aEF will appear as a drastic variation in dTcfdP. In Fig. 2, we have separated the total Tc-shift
by Havinga eta!. The effect of the Fermi surface change on the lattice parameter be too small 4 The present resultsmay demonstrate the to be need detected. for detailed band calculations” and de Haas— van Alphen studies of LaSn 3.
under pressure into its linear and nonlinear contri-
REFERENCES 1.
HAVINGA E.E., Phys. Lett. 28A, 350 (1968); HAVINGA E.E., DAMSMA H. and VANMAAREN M.H., J. Phys. Chem Solids 31, 2653 (1970); TOXEN A.M., GAMBINO R.J. and WELSH L.B., Phys. Rev. B8, 90 (1973).
2.
MATTHIAS B.T.,Phys. Rev. 97, 74(1955).
3.
4.
BRANDT N.B., GINZBURG N.I., IGNAT’EVA T.A., LAZAREVAB.G., LAZAREVA L.S. and MAKAROV V.Z., Zk Eksperim. I Teor. Fiz. 49, 85 (1965) [English Transl.: Soviet Phya-JETP 21 1151 (1965)] and references therein. CHU C.W., SMITH T.F. and GARDNER W.E.,Phys. Rev. Lett. 20, 198 (1968); Phys. Rev. Bi, 214 (1970).
5.
SHIRBER J.E., Phys. Rev. Lett. 28, 1127 (1972).
6. 7.
SMITH T.F., CHU C.W. and MAPLE M.B., Cryogenics 9, 53 (1969). BRANDT N.B. and GINZBURG N.J., Usp. Fiz. Nauk 98, 95 (1969). [Englishtransi.: Soviet Phys. Uspekhi 12, 344 (1969)] and references therein. ZIMAN J.M., Principles of the Theory ofSolids p. 48, Cambridge University Press, New York (1964).
8.
412
ANOMALOUS Tc-BEHAVIOR OF LaSn3 UNDER PRESSURE
9.
MAKAROV V.1. and BARYAKHTAR V.G., Zh. Eksperim. i. Teor. Fiz. 48, 1717 (1965) [English transi.: SovietPhys.-JETP21, 1151 (1965)].
Vol. 16, No.4
10.
HIGGINS R.J. and KAEHN H.D.,Phys. Rev. 182,649 (1969).
11.
GROBMAN W.D., J. Chem. Phys. Solids 33 1307 (1972); GRAY D.M. and MEISEL L.V., Phys. Rev. B5, 1299 (1972); GRAY D.M. and MEISEL L.V., Phys. Rev. B5, 1308 (1972).
Pergamon Press.
Printed in Great Britain
ANOMALOUS TcBEHAVIOR OF LaSn3 UNDER PRESSURE t and C.W. Chu* S. Huang Department of Physics, Cleveland State University, Cleveland, Ohio 44115, U.S.A. and F.Y. Fradint Argonne National Laboratory, Argonne, illinois 60439, U.S.A. and L.B. Welsh~ Department of Physics, Northwestern University, Evanston, Illinois 60201, U.S.A. (Received 9 October 1974 by A.G. Chynoweth)
The superconducting transition temperature Tc of LaSn 3 has been measured up to 22 kbar and was observed to increase through a maximum under hydrostatic compression. The anomalous Tc-behavior is attributed to a pressure induced Fermi surface topology change. 1 have shown that the superconductHAVINGA eta!. ing transition temperature Tc, the magnetic suscepti. biity x and the thermo-electric power of a number of the pseudo-binary AR 3.type compounds with Cu3Au. structure vary oscillatorily with the valence.electron concentration z. Tc peaks near z = 2.95, 3.3 and 3.7. The In, constituent elements areThe La, results Y, Th and for A, and Sn, 11 and Pb for B. wereCaexplained in terms of a similar variation of the electron density
the change of z. However, the lattice parameter of these compounds fails to exhibit any anomaly that is common in many alloy systems undergoing Fermi surface topology changes. In addition, similar oscillatory variations of Tc and x were also observed in the transition metal alloy superconductors thatneed follow the 2 without the to invoke empirical rule topology. Hence further aMatthias change of Fermi surface study on the AB 3.compounds is essential.
of states N(EF) and the electron—phonon interaction V of these compounds with z. The peculiar features of N(EF) and V were attributed to the change of Fermi surface topology or the Brillouin.zone effect due to
LaSn3 has a z 3.75, which is very close to one of the Tc-maxima. If the model of Havinga eta!. is correct the LaSn3 Fermi surface would be very close to the Brillouin zone boundary and the application of hydrostatic pressure would induce a Fermi surface topology change. An anomalous pressure behavior of T1~is expected when the Fermi surface topology changes 3 Re4 and AuGa~. under for the cases ofthe Tl,Tc of LaSn In this pressure, study, weashave measured 3 up
____________
*
Research supported by National Science Foundation Grant No. GH-40866 and Research Corporation.
4
Work performed under the auspices of the U.S. Atomic Energy Commission.
:1
Supported by Air Force Office of Scientific Research Grant No. 71-2012 and by NSF through the Northwestern University Material Research Center.
to 22 kbar. The results are consistent with the sug. gestion by Havinga et al. 409
410
ANOMALOUS Tc-BEHAVIOR OF LaSn3 UNDER PRESSURE
IC
Vol. 16, No.4
0.08
~ !08
\\ \
Nonlinear La Sn3
0.04 Total
Pressure
~°04
000~ 5890
5930
5970
6010
1(K)
The superconducting transitions at different pressures. The number represents the sequential order of the ex erimental runs
I
0
5
I
I
10 P (k bar)
15
20
FIG. 1.
The LaSn3 sample was prepared by arc melting (3—4 times) stoichiometric quantities of lanthanum (99.9 per cent Research Chemical Division of Nuclear Corporation of America) and tin (99.999 per cent Vulcan Materials Co.). Weight loss after melting amounted to 0.36 per cent. The ingot was homogenized for five days at 800°Cin quartz under vacuum and water quenched. Powders for X-ray determination of the lattice parameters were obtained by crushing in an argon glove box. The powders were annealed for two hours at 400°C prior to X-ray examination, The lattice parameter isa0 = 4.773(2) A. Two small samples of 100 and 75 mg respectively cut from two ends of the LaSn3 ingot were investigated. Both samples have the same Tc (5.98 K) with a transition width of 15 mK at atmospheric pressure, reflecting the high homogeneity of the ingot. Our slightly lower T~in comparison that observed 1 may bewith associated with thepreviously possible higher 6.4 K)level in our starting elements. A self-clamp impurity technique was employed to provide the hydrostatic environment in a 1 1 fluid mixture of n-pentane and isoamyl alcohol. The pressure was generated inside and locked by the clamp at room temperature. A superconducting Pb-manometer6 situated next to the sample —
—
‘~‘
(‘—j
was used to determine the pressure at low temperature. The transition to the superconducting state was detected by a standard a.c. inductance technique operating at 10 Hz. Temperature was measured by a Ge-thermometer. The relative accuracy of the mometer is estimated to be within ±0.002 K. ther-
FIG. 2. The pressure dependence of the Tc-shift and its breakdown to the linear and nonlmear contnbutions. The pressure dependences of the two samples investigated are identical and hence only results of one sample are shown. The superconducting transitions of LaSn3 at different pressures are shown in Fig. 1. The number represents the sequential order of the experimental runs. The results are summarized in Fig. 2 where the Tc-shift, I~T0is plotted as a function of pressure. The circular (or triangular) symbol denotes the mid-point of the transition during the pressurizing (or depressurizing) cycle. The vertical bar stands for the width of the transition determined by the extrapolation of the linear portion of the transition curve to the fully normal and fully superconducting states. The horizontal bar indicates the uncertainty in pressure. In strong contrast to the linear pressure effect of the great majority of 7 Tcon ofT~ LaSn superconductors, 3 is observed to increase initially,with pass pressure. a maximum, and finally decreasewithin linearly No pressure hysteresis our experimental error was detected, indicating that any possible strain or dislocation introduced during pressurization should be negligibly small. The Fermi surface topology,change occurs when the Fermi level EF crosses a critical energy E 0 in the energy spectrum E(k). Ec is defined as the energy at a critical point where VE(k) = 0. The change gives rise to an additional rapidly varying contribution ~N(EF) to the density of states N(EF) at EF. 6N(EF) T usually is proportional to ± (EFof change Ec)~orof±Fermi (E0 EF) depending on the specific kind surface topology.8 Makarov and Baryakhtar9 examined —
—
Vol. 16, No.4
ANOMALOUS Ta-BEHAVIOR OF LaSn3 UNDER PRESSURE
the effect of ~N(EF) on the superconducting properties using the BCS formalism. They found that Tc varies drastically over an energy range kOD about 0D is Ec antemperature. extremum ofFor aTC/aEF at Ec, where the with Debye the four possible kinds of topology changes, the following changes of Tc were predicted: Tc will have a jump over the energy range (Ec — kOD) EF (Ec + kOD), when the Fermi surface transforms from a closed to an open surface or when a cavity in the Fermi surface is formed, while Tc will have a drop over the same energy range when the Fermi surface transforms from an open to a closed surface or when a cavity is destroyed. At E = Ec, the jump of Tc is associated with a maximum of aTcIaEF, and the drop of T~is associated with a minimum of aTC/aEF. In a similar way, Higgins and Kaehn1°later showed that aTCIaEF cc aN(EF)/aEF or (EF — Ec)~ near the critical point but is smeared out by imperfection scattering. The shift of Tc under pressure is mainly caused by changes in EF [or N(EF)] and V (the electron—phonon interaction), i.e. dT dP
aT dE —~
—f +
aEF dP
411
butions. The slope of the linear part is equal to that of the total L~Tcin the high pressure region. The nonlinear which starts at. zero pressure rapidlycontribution and saturates at pressures 15 kbar. Thisrises is similar to the predicted Tc change associated with a Fermi surface topology change corresponding to a transformation from a closed to an open surface or to the creation of a cavity.9 The uncertainty in the exact shape of the nonlinear contribution of L~Tcand the lack of information about the band structure of the compound prevent us from further identifying the specific kind of Fermi surface topology change induced by pressure. The slope of this nonlinear portion shows a maximum at a pressure <8 kbar. This suggests that a critical pressure of < 8 kbar is sufficient to move EF crosses Ec and thus to induce a change in the Fermi surface topology. The linear part of L~Tcrepresents the pressure effect on T~had the Fermi surface topology not changed under pressure. In conclusion, we have observed a non-linear
aT d V
pressure effect on Tc of LaSn
__c aV ~
3 - This is attributed to a pressure induced Fermi surface topology change consistent with the alloying study of AB3-compound
—,
Since the second term and dEF/dP vary only slowly with pressure, any rapid variation in aTC/aEF will appear as a drastic variation in dTcfdP. In Fig. 2, we have separated the total Tc-shift
by Havinga eta!. The effect of the Fermi surface change on the lattice parameter be too small 4 The present resultsmay demonstrate the to be need detected. for detailed band calculations” and de Haas— van Alphen studies of LaSn 3.
under pressure into its linear and nonlinear contri-
REFERENCES 1.
HAVINGA E.E., Phys. Lett. 28A, 350 (1968); HAVINGA E.E., DAMSMA H. and VANMAAREN M.H., J. Phys. Chem Solids 31, 2653 (1970); TOXEN A.M., GAMBINO R.J. and WELSH L.B., Phys. Rev. B8, 90 (1973).
2.
MATTHIAS B.T.,Phys. Rev. 97, 74(1955).
3.
4.
BRANDT N.B., GINZBURG N.I., IGNAT’EVA T.A., LAZAREVAB.G., LAZAREVA L.S. and MAKAROV V.Z., Zk Eksperim. I Teor. Fiz. 49, 85 (1965) [English Transl.: Soviet Phya-JETP 21 1151 (1965)] and references therein. CHU C.W., SMITH T.F. and GARDNER W.E.,Phys. Rev. Lett. 20, 198 (1968); Phys. Rev. Bi, 214 (1970).
5.
SHIRBER J.E., Phys. Rev. Lett. 28, 1127 (1972).
6. 7.
SMITH T.F., CHU C.W. and MAPLE M.B., Cryogenics 9, 53 (1969). BRANDT N.B. and GINZBURG N.J., Usp. Fiz. Nauk 98, 95 (1969). [Englishtransi.: Soviet Phys. Uspekhi 12, 344 (1969)] and references therein. ZIMAN J.M., Principles of the Theory ofSolids p. 48, Cambridge University Press, New York (1964).
8.
412
ANOMALOUS Tc-BEHAVIOR OF LaSn3 UNDER PRESSURE
9.
MAKAROV V.1. and BARYAKHTAR V.G., Zh. Eksperim. i. Teor. Fiz. 48, 1717 (1965) [English transi.: SovietPhys.-JETP21, 1151 (1965)].
Vol. 16, No.4
10.
HIGGINS R.J. and KAEHN H.D.,Phys. Rev. 182,649 (1969).
11.
GROBMAN W.D., J. Chem. Phys. Solids 33 1307 (1972); GRAY D.M. and MEISEL L.V., Phys. Rev. B5, 1299 (1972); GRAY D.M. and MEISEL L.V., Phys. Rev. B5, 1308 (1972).