- Email: [email protected]
Superconducting lower critical fields in UPt3
PhysicaB 165&166 (1990)345-346 North-Holland
SuperconductingLower Critical Fields in lJPt3??
Zuyu Zhao*, F. Behroozi+, J.B. Ketterson*, Yongmin Guan*, Bimal K. Sarmat and D.G. Hinkse *Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208 USA +Department of Physics, University of Wisconsin-Parkside,Kenosha, WI 53141 USA tDepartment of Physics, University of Wisconsin-Milwaukee,Milwaukee, WI 53201 USA *Material Science Division, Argonne National Laboratory, Argonne, IL 60439 USA
DC magnetization curves of a single crystal of UPts (T, = 542 mK) are obtained with the external field parallel and perpendicular to the hexagonal c-axis, The magnetization curves are analyzed to yield the lower critical field H,, as a function of temperature and orientation. For both the c-axis and basal plane orientations, H,, shows an apparent kink in slope about 150 mK below T,. This behavior appears to confirm the recently proposed model for the superconducting states in upt, in which a two dimensional order parameter leads to the formation of two distinct superconductingphases.
Several cerium and uranium compounds such as CeCuzSi,, UBe,,, and UPt, exhibit very large electronic specific heats (two to three orders of magnitude larger than copper). Strong on site repulsion causes the f electrons to behave essentially as uncorrelated moments at high temperature. However the combined effect of falling temperature and hybridization results in the formation of a highly correlated state at low temperatures, a Fermi liquid, with a Fermi surface well re-presented by the local density band model(l); this Fermi liquid has a characteristic temperature of order 10K. Further, several of these so called heavy fermion systems become superconducting at about T = IK. There is considerable speculation on the nature of superconductivityin these systems(2). It has been suggested that the nearly magnetic character of these systems may lead to pairing via magnetic excitations. Much recent activity has focused on the superconducting behavior of the heavy fermion system UPt, due to its many intriguing properties. Recent heat capacity data(3) show the signature of two phase boundaries near T, which converge to a critical point at a field H = 0.5 T and a temperature T = 0.4 K. Neutron scattering(4)and ultrasonic attenuation(5)data also indicate several unusual features which may be attributed to the interaction of the magnetic and superconducting order parameters, further adding to the evidence for the unconventional nature of superconductivity in UPt,. Recently Hess, Tokuyasu, and Sauls (HTS) proposed(6) a model for the superconducting states of UPt, in which a two dimensional order
parameter gives rise to two superconducting phases of different symmetry which exist in adjacent temperature domains. Hence this model accounts for the existence of two jumps in the specific heat. Further, the model predicts an abrupt change in the slope of the upper critical field phase line when the field is in the basal plane, signaling the transition between the two superconducting phases at a finite field. The lower critical field phase line is also expected to display a kink for all field orientation at a temperature very close to the zero-field transition. With an rf resonance technique which only probes the surface (either the skin or London depths) of the sample, Shivaram et al. recently reported a kink in H,r with the field in the basal plane; however the ratio of the slopes is much larger than that predicted by the theory. No kink was confirmed with the field along the caxis. Here we present new lower critical field data which support the predictions of the HTS model for all field orientations. Our data consist of low field magnetization curves of a single crystal spherical sample of UPt,. The sample was produced by spark cutting techniques from a high quality single crystal ingot. The UPt, sphere, (4.03 + O.Ol)mm in diameter, was etched chemically to remove any surface damage and annealed before use. We emphasize that in order to obtain the lower critical fields reliably, it is essential to uerform the maenetization measurements on a single crystal ellipsodal sample with a well known demagnetizing factor. A spherical sample
*Work supported by the Low Temperature Physics Branch of the National Science Foundation under grant DMR89-07396.
Science Publishers 0921~4526/90/$9X50 @ 1990- Elsevier
B.V. (North-Holland)
2. Zhao, F. Behroozi, J.B.Ketterson, Y. Guan, B.K. Sarma,D.G. Hinks
346
is perhaps the most convenient with a demagnetizing factor of l/3 for all crystallographic orientations. A top loading Oxford dilution refrigerator with a 12T magnet was used for the dc susceptibility measurements. The dc technique uses two balanced opposing coils, one of which contains the sample. When the external field is ramped, the net emf from the coils is proportional to the dc susceptibilityof the sample(8). Direct integrationof this signal gives the magnetization. Since the demagnetization factor of our spherical sample is accurately known, the Meissner slope can be used to calibrate the magnetization scale precisely. Typically the low field magnetization data were taken by warming the sample above T, in zero field to drive off any trapped flux, then cooling to a fixed temperature. The field was then ramped at about 1 G/s to obtain the low field magnetization data. The lower critical field of the sphere, referred to as (&l)sphere, was taken as the field at which the initial slope of the magnetization curve just began to deviate from the Meissner value; then Hc1 - 3/2(H,l)sphere (1) Figure 1 shows the lower critical fields as a function of temperature for the field parallel to the c-axis, while Figure 2 shows the data for the field parallel to the a and b-axes. In all cases a kink near 0.4 K is apparent. The straight lines for the combined a- and baxes data were fitted by the following procedure. The data were partitioned into low and intermediate field groups and separately fitted to straight lines. The total r.m.s. error was then minimized as a function of the partitioning point. The fitting gives T,', Tc(+) and Tee-)
respectively as 395.0 IRK, 541 mK and 517 mK. Points lying in the &shed region of the lines were not included in the fit. The slope ratios of the %, vs. T curve above and below Tc* for the external field in.the basal plane is esti-
--I
150 -
+---ik-‘A’
‘k
’
400
“‘FFL i 500
60”
TEMPERATURE (mK) FIGURE 2 The lower critical fields vs. temperature for riIC. The squares+(circles)are the experimental data taken with H 11 to the a-(b-) axis. The straight lines are a linear least squares fit (see text). mated to be 1.19 and is in good agreement with the HTS model. The c-axis data appears to exhibit some curvature; however for comparison with the existing theory (which predicts straight Line behavior) the same two-straight line procedure was also adopted for the c-axis data. The intersectionoccurs at T,* - 395.5 mK. Also the ratio of the slope of the two fitted lines (Fig. 1) is estimated to be 1.36. Although the existence of the kink at TE* is in general agreement with the HTS theory, the details need further exploration. REFERENCES (1)
(2) (3)
0
t
/-
0
TEMPERATURE (mK) FIGURE 1 Fe lower critical fields vs. temperaturewith H 11c-axis. The filled circles and the straight lines are respectively the experimental data and the results of a linear least squares fit (see text).
(4) (5) (6) (7) (8)
T. Oguchi and A.J. Freeman, J. Mag. and Mag. Mater. 2, 174 (1985). M.R. Norman, R.C. Albers, A.M. Boring and N.E. Christensen, Solid State Commun. a, 245 (1988). 2. Fisk, D.W. Hess, et al. Science 239, 33 (1988). K. Hasselbach, L. Taillefer, and J. Flouquet, Phys. Rev. Lett. 63, 93 (1989). R.A. Fisher, S. Kim, et al. Phys. Rev. Lett. 62, 1411 (1989). G. Aeppli, D. Bishop, et al. Phys. Rev. Lett. fi, 676 (1989). A. Schenstrom, M-F. Xu, et al. Phys. Rev. Lett. 62 332 (1989). D.W. Hess, T.A. Tokuyasu and J.A. Sauls, J. Phys. Condens. Matter 1, 8135 (1989). B.S. Shivaram, J.J. Gannon, Jr. and D.G. Hinks, Phys. Rev. Lett. 63. 1723 (1989). F. Behroozi, Am. J. Phys. 2. 28 (1983).
SuperconductingLower Critical Fields in lJPt3??
Zuyu Zhao*, F. Behroozi+, J.B. Ketterson*, Yongmin Guan*, Bimal K. Sarmat and D.G. Hinkse *Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208 USA +Department of Physics, University of Wisconsin-Parkside,Kenosha, WI 53141 USA tDepartment of Physics, University of Wisconsin-Milwaukee,Milwaukee, WI 53201 USA *Material Science Division, Argonne National Laboratory, Argonne, IL 60439 USA
DC magnetization curves of a single crystal of UPts (T, = 542 mK) are obtained with the external field parallel and perpendicular to the hexagonal c-axis, The magnetization curves are analyzed to yield the lower critical field H,, as a function of temperature and orientation. For both the c-axis and basal plane orientations, H,, shows an apparent kink in slope about 150 mK below T,. This behavior appears to confirm the recently proposed model for the superconducting states in upt, in which a two dimensional order parameter leads to the formation of two distinct superconductingphases.
Several cerium and uranium compounds such as CeCuzSi,, UBe,,, and UPt, exhibit very large electronic specific heats (two to three orders of magnitude larger than copper). Strong on site repulsion causes the f electrons to behave essentially as uncorrelated moments at high temperature. However the combined effect of falling temperature and hybridization results in the formation of a highly correlated state at low temperatures, a Fermi liquid, with a Fermi surface well re-presented by the local density band model(l); this Fermi liquid has a characteristic temperature of order 10K. Further, several of these so called heavy fermion systems become superconducting at about T = IK. There is considerable speculation on the nature of superconductivityin these systems(2). It has been suggested that the nearly magnetic character of these systems may lead to pairing via magnetic excitations. Much recent activity has focused on the superconducting behavior of the heavy fermion system UPt, due to its many intriguing properties. Recent heat capacity data(3) show the signature of two phase boundaries near T, which converge to a critical point at a field H = 0.5 T and a temperature T = 0.4 K. Neutron scattering(4)and ultrasonic attenuation(5)data also indicate several unusual features which may be attributed to the interaction of the magnetic and superconducting order parameters, further adding to the evidence for the unconventional nature of superconductivity in UPt,. Recently Hess, Tokuyasu, and Sauls (HTS) proposed(6) a model for the superconducting states of UPt, in which a two dimensional order
parameter gives rise to two superconducting phases of different symmetry which exist in adjacent temperature domains. Hence this model accounts for the existence of two jumps in the specific heat. Further, the model predicts an abrupt change in the slope of the upper critical field phase line when the field is in the basal plane, signaling the transition between the two superconducting phases at a finite field. The lower critical field phase line is also expected to display a kink for all field orientation at a temperature very close to the zero-field transition. With an rf resonance technique which only probes the surface (either the skin or London depths) of the sample, Shivaram et al. recently reported a kink in H,r with the field in the basal plane; however the ratio of the slopes is much larger than that predicted by the theory. No kink was confirmed with the field along the caxis. Here we present new lower critical field data which support the predictions of the HTS model for all field orientations. Our data consist of low field magnetization curves of a single crystal spherical sample of UPt,. The sample was produced by spark cutting techniques from a high quality single crystal ingot. The UPt, sphere, (4.03 + O.Ol)mm in diameter, was etched chemically to remove any surface damage and annealed before use. We emphasize that in order to obtain the lower critical fields reliably, it is essential to uerform the maenetization measurements on a single crystal ellipsodal sample with a well known demagnetizing factor. A spherical sample
*Work supported by the Low Temperature Physics Branch of the National Science Foundation under grant DMR89-07396.
Science Publishers 0921~4526/90/$9X50 @ 1990- Elsevier
B.V. (North-Holland)
2. Zhao, F. Behroozi, J.B.Ketterson, Y. Guan, B.K. Sarma,D.G. Hinks
346
is perhaps the most convenient with a demagnetizing factor of l/3 for all crystallographic orientations. A top loading Oxford dilution refrigerator with a 12T magnet was used for the dc susceptibility measurements. The dc technique uses two balanced opposing coils, one of which contains the sample. When the external field is ramped, the net emf from the coils is proportional to the dc susceptibilityof the sample(8). Direct integrationof this signal gives the magnetization. Since the demagnetization factor of our spherical sample is accurately known, the Meissner slope can be used to calibrate the magnetization scale precisely. Typically the low field magnetization data were taken by warming the sample above T, in zero field to drive off any trapped flux, then cooling to a fixed temperature. The field was then ramped at about 1 G/s to obtain the low field magnetization data. The lower critical field of the sphere, referred to as (&l)sphere, was taken as the field at which the initial slope of the magnetization curve just began to deviate from the Meissner value; then Hc1 - 3/2(H,l)sphere (1) Figure 1 shows the lower critical fields as a function of temperature for the field parallel to the c-axis, while Figure 2 shows the data for the field parallel to the a and b-axes. In all cases a kink near 0.4 K is apparent. The straight lines for the combined a- and baxes data were fitted by the following procedure. The data were partitioned into low and intermediate field groups and separately fitted to straight lines. The total r.m.s. error was then minimized as a function of the partitioning point. The fitting gives T,', Tc(+) and Tee-)
respectively as 395.0 IRK, 541 mK and 517 mK. Points lying in the &shed region of the lines were not included in the fit. The slope ratios of the %, vs. T curve above and below Tc* for the external field in.the basal plane is esti-
--I
150 -
+---ik-‘A’
‘k
’
400
“‘FFL i 500
60”
TEMPERATURE (mK) FIGURE 2 The lower critical fields vs. temperature for riIC. The squares+(circles)are the experimental data taken with H 11 to the a-(b-) axis. The straight lines are a linear least squares fit (see text). mated to be 1.19 and is in good agreement with the HTS model. The c-axis data appears to exhibit some curvature; however for comparison with the existing theory (which predicts straight Line behavior) the same two-straight line procedure was also adopted for the c-axis data. The intersectionoccurs at T,* - 395.5 mK. Also the ratio of the slope of the two fitted lines (Fig. 1) is estimated to be 1.36. Although the existence of the kink at TE* is in general agreement with the HTS theory, the details need further exploration. REFERENCES (1)
(2) (3)
0
t
/-
0
TEMPERATURE (mK) FIGURE 1 Fe lower critical fields vs. temperaturewith H 11c-axis. The filled circles and the straight lines are respectively the experimental data and the results of a linear least squares fit (see text).
(4) (5) (6) (7) (8)
T. Oguchi and A.J. Freeman, J. Mag. and Mag. Mater. 2, 174 (1985). M.R. Norman, R.C. Albers, A.M. Boring and N.E. Christensen, Solid State Commun. a, 245 (1988). 2. Fisk, D.W. Hess, et al. Science 239, 33 (1988). K. Hasselbach, L. Taillefer, and J. Flouquet, Phys. Rev. Lett. 63, 93 (1989). R.A. Fisher, S. Kim, et al. Phys. Rev. Lett. 62, 1411 (1989). G. Aeppli, D. Bishop, et al. Phys. Rev. Lett. fi, 676 (1989). A. Schenstrom, M-F. Xu, et al. Phys. Rev. Lett. 62 332 (1989). D.W. Hess, T.A. Tokuyasu and J.A. Sauls, J. Phys. Condens. Matter 1, 8135 (1989). B.S. Shivaram, J.J. Gannon, Jr. and D.G. Hinks, Phys. Rev. Lett. 63. 1723 (1989). F. Behroozi, Am. J. Phys. 2. 28 (1983).