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Magnetoresistance of the heavy fermion superconductor UPt3 near Tc
Journal
of Magnetism
and Magnetic
MAGNETORESISTANCE K. KADOWAKI,
Materials
54-57
OF THE HEAVY
A. UMEZAWA
3x5
(1986) 385-386
FERMION
SUPERCONDUCTOR
UPt,
NEAR
T, *
and S.B. WOODS
Depcrr~menr of Ph,‘.w.s, Umcer.Ci_y of Alhrrru, Edmonton. Albertu, Cunudu, T6G ?JI
UPt, have Electrical resistivity. magnetoresistance, and the upper critical field H,, o f the heavy fermion superconductor been investigated with measurements down to 100 mK and in magnetic fields up to 30 kOe. These properties are discussed in terms of the-spin fluctuations in UPt ?.
Since the discovery of the superconductivity of UPt, [l]. it has occupied a unique position among the heavy fermion compounds in the appearance of both the superconductivity and spin fluctuations in its properties. The evidence for the spin fluctuations has been revealed by the T’ dependence of the electrical resistivity [2] and a T7 In T term in the specific heat [l] which appears in addition to the large coefficient, y. of the term linear in T which is evidence for the extremely heavy effective mass of the electrons (= 2OOm.). Owing to the pair breaking effect of spin fluctuations speculation has arisen on whether or not the superconducting mechanism of UPt, is a triplet pairing. Although it is clear that spin fluctuations are not favorable for singlet pairing. the experimental evidence at present does not clearly support a non-singlet pairing mechanism. In this paper, our attention is focussed on the effect of a magnetic field on the conduction mechanism of UPt, in both the normal and superconducting state. Polycrystalline UPt, specimens were made in an arc furnace by melting together carefully weighed quantities of depleted uranium and platinum metal. The purity of the original uranium was 99.9% and the platinum was 99.998%. After melting, the ingot was annealed for 50 h at 980°C in a high vacuum. X-ray analysis of a small piece of the ingot identified the structure to be hexagonal MgCd? type (DO 19). No extra lines were detected. Electrical resistivity and magnetoresistance were measured by a conventional dc four probe method with nanovolt sensitivity from “He temperature to room temperature. Below 1 K. a SQUID null-detection method was used in a ‘H~,J’~H~ dilution refrigerator. Magnetic fields up to 30 kOe were supplied by a superconducting magnet. Three pieces of UPt, of rectangular shape were spark cut from different places in the ingot for resistivity measurements. These specimens had nearly identical characteristics: the resistance ratio, r = R(300 K)/R(Tc++)= 80-85 with 7c = 0.475 K and AT, = 42 mK. The temperature dependence of the resistivity was found to be
* Supported
In part by NSERC
0304~8853/86/$03.50
of Canada.
with p,, = 2.2 p&m. n = 1.96 and a large coefficient A = 2.02 pL?cmK-’ ” at low temperatures. Above = 4 K the resistivity gradually departs from the above relation and shows saturation behavior. A maximum in the derivative of the resistivity occurs at = 7 K and ~(300 K) = 236 p&m. As pointed out by Stewart et al. [l], the superconducting temperature 7; is a strong function of p,,. This behavior has been seen here also; an earlier specimen with r = 30 shows dramatically smaller 7; = 0.28 K and no superconductivity was found in unannealed specimens with Y < 20. Proper annealing improves pr, significantly but it is still unclear what mechamsm controls po. Stress is more probable rather than static impurities. It is this very sensitive p,, dependence of the superconducting transition temperature that arouses speculation that the pairing may not occur via the usual s-state mechanism but by p-state or a higher pairing state, possibly with the assistance of spin fluctuations. However. p,, appears to affect only the superconducting transition temperature without changing the spin fluctuations. The large coefficient A in the T” term in the resistivity is one of the characteristics of the spin fluctuating system and it is insensitive to po. It should be noted that the value A = ZpLOcrnK--” is extraordinarily large, more than an order of magnitude above that of other spin fluctuating systems (A = 0.18 pL8cmK-’ for UAIz [3], A = 0.013 pQcmK ’ for MnSi [4]). This may be a reflection of the extremely high density of states at the Fermi level as well as a strong correlation effect between electrons in a hybridized f band. The longitudinal magnetoresistance of UPt, is shown in fig. 1. The magnetoresistance is always positive below 4.2 K and can be expressed by &(
H)/p(O)
= aH”.
with n = 1.63 and (Y= 3.44 x 10 m4 kOe_ I.” at 0.55 K n increases slightly with increasing temperature. Nc significant difference has been found between transverse and longitudinal magnetoresistances. The positive magnetoresistance is in contrast with that of other heavy Fermion compounds, which show a negative magnetoresistance, but is more like a normal metal or like other spin fluctuating systems. Positive magnetoresistance
5~3Elsevier Science Publishers B.V.
-
\
10’
1oj
Magnetic Fig. 1. Longitudinal
Field
(KOe)
magnetoresistances
of UPt
OL
1 in magnetic
_J
0
fields up to 30 kOe. should not arise from ferromagnetic spin fluctuations because the external magnetic field always suppresses them. On the other hand. antiferromagnetic spin fluctuations will be enhanced by applying a magnetic field below a critical field at which a sharp peak may occur in the resistivity [5]. The positive magnetoresistance up to 30 kOe presented here and up to I10 kOe obtained by Stewart et al. [6] could be a low field effect preceding a transition under an intense magnetic field possibly of = 200 kOe observed by Franse et al. [7]. However. since there is no long range magnetic order in UPt 1 in zero field, this behavior under high magnetic field must still be regarded as quite anomalous. The superconducting upper critical field H,, is shown in fig. 2. A needle-like specimen was placed in a bundle of fine copper wires suspended from the mixing chamber of the dilution refrigerator and the magnetic field was applied perpendicular to the specimen. The field was slowly swept with a speed of = 10 Oe/s in order not only to prevent eddy current heating but also any temperature change because of the specific heat jump at Hcz.The critical field is defined by the midpoint of the total change of the resistivity. The HLz curve in fig. 2 has a pronounced positive curvature near 7;.. Disregarding this behavior, the slope ~(d H,,/dT),C is estimated to be 43 kOeK_ ‘. This value of the slope is in excellent agreement with the data of Palstra et al. [X] but is significantly different from that of Chen et al. [2]. This difference may be associated with a large anisotropy effect in single crystals or with the higher TCof 0.54 K of their crystal. Another difference must be pointed out. According to Chen et al the critical field slope between
0.2
0.4
Temperature
0.6
( K)
Fig. 2. Tcmprrature dependence of the supercc>nducting upper critical field ffL2. A dc current denslty of 27 A/cm’ U;L\ u\ed.
0.5 and 0.3 K is higher than that of our specimen but it saturates below about 0.3 K for both field directions becoming less anisotropic in Hc2.Although the absolute values of H,, in fig. 2 are lower than those of Chen et al.. the extrapolated value of H,,(O)at T= 0 agree5 fairly well, the result being H,,(O) = 17 kOe. Using the equation for strong coupling superconductivity [9], and assuming that the Ferm’i surface is spherical with a mean Fermi velocity ?, one can obtain a mean Fermi wave vector I
agreement
with
previous
estimates
121.
[II G.R. Stewart, Z. Fisk. J.0. Willis and J.L. Smith. Phys. Rev. Lett. 52 (19X4) 679. PI .I.W’.Chen. S.E. Lamhert, M.B. Maple. Z. Fisk, J.L. Smith. G.R. Stewart and J.O. Willis. Phys. Rev. 830 (19X4) lSX.1 [31 K.H.J. Buschow and H.J. van Daal, AIP Conf. Proc. Yo. 5. Magn. and Magn. Mat. (1971) p. 1464. [41 K. Kadnwaki. K. Okuda and M. Date. J. Phy\. Sot. Japan 51 (1982) 2433. [51 K. Usami. J. Phys. Sot. Japan 45 (1978) 466. I61 G.R. Stewart. Z. Fisk. J.O. Willi? and J.L. Smith. Phy\lca I278 (1984) 448. 171 J.J.M. Franse. P.H. Frings. A. de Vissrr and A. Menov
of Magnetism
and Magnetic
MAGNETORESISTANCE K. KADOWAKI,
Materials
54-57
OF THE HEAVY
A. UMEZAWA
3x5
(1986) 385-386
FERMION
SUPERCONDUCTOR
UPt,
NEAR
T, *
and S.B. WOODS
Depcrr~menr of Ph,‘.w.s, Umcer.Ci_y of Alhrrru, Edmonton. Albertu, Cunudu, T6G ?JI
UPt, have Electrical resistivity. magnetoresistance, and the upper critical field H,, o f the heavy fermion superconductor been investigated with measurements down to 100 mK and in magnetic fields up to 30 kOe. These properties are discussed in terms of the-spin fluctuations in UPt ?.
Since the discovery of the superconductivity of UPt, [l]. it has occupied a unique position among the heavy fermion compounds in the appearance of both the superconductivity and spin fluctuations in its properties. The evidence for the spin fluctuations has been revealed by the T’ dependence of the electrical resistivity [2] and a T7 In T term in the specific heat [l] which appears in addition to the large coefficient, y. of the term linear in T which is evidence for the extremely heavy effective mass of the electrons (= 2OOm.). Owing to the pair breaking effect of spin fluctuations speculation has arisen on whether or not the superconducting mechanism of UPt, is a triplet pairing. Although it is clear that spin fluctuations are not favorable for singlet pairing. the experimental evidence at present does not clearly support a non-singlet pairing mechanism. In this paper, our attention is focussed on the effect of a magnetic field on the conduction mechanism of UPt, in both the normal and superconducting state. Polycrystalline UPt, specimens were made in an arc furnace by melting together carefully weighed quantities of depleted uranium and platinum metal. The purity of the original uranium was 99.9% and the platinum was 99.998%. After melting, the ingot was annealed for 50 h at 980°C in a high vacuum. X-ray analysis of a small piece of the ingot identified the structure to be hexagonal MgCd? type (DO 19). No extra lines were detected. Electrical resistivity and magnetoresistance were measured by a conventional dc four probe method with nanovolt sensitivity from “He temperature to room temperature. Below 1 K. a SQUID null-detection method was used in a ‘H~,J’~H~ dilution refrigerator. Magnetic fields up to 30 kOe were supplied by a superconducting magnet. Three pieces of UPt, of rectangular shape were spark cut from different places in the ingot for resistivity measurements. These specimens had nearly identical characteristics: the resistance ratio, r = R(300 K)/R(Tc++)= 80-85 with 7c = 0.475 K and AT, = 42 mK. The temperature dependence of the resistivity was found to be
* Supported
In part by NSERC
0304~8853/86/$03.50
of Canada.
with p,, = 2.2 p&m. n = 1.96 and a large coefficient A = 2.02 pL?cmK-’ ” at low temperatures. Above = 4 K the resistivity gradually departs from the above relation and shows saturation behavior. A maximum in the derivative of the resistivity occurs at = 7 K and ~(300 K) = 236 p&m. As pointed out by Stewart et al. [l], the superconducting temperature 7; is a strong function of p,,. This behavior has been seen here also; an earlier specimen with r = 30 shows dramatically smaller 7; = 0.28 K and no superconductivity was found in unannealed specimens with Y < 20. Proper annealing improves pr, significantly but it is still unclear what mechamsm controls po. Stress is more probable rather than static impurities. It is this very sensitive p,, dependence of the superconducting transition temperature that arouses speculation that the pairing may not occur via the usual s-state mechanism but by p-state or a higher pairing state, possibly with the assistance of spin fluctuations. However. p,, appears to affect only the superconducting transition temperature without changing the spin fluctuations. The large coefficient A in the T” term in the resistivity is one of the characteristics of the spin fluctuating system and it is insensitive to po. It should be noted that the value A = ZpLOcrnK--” is extraordinarily large, more than an order of magnitude above that of other spin fluctuating systems (A = 0.18 pL8cmK-’ for UAIz [3], A = 0.013 pQcmK ’ for MnSi [4]). This may be a reflection of the extremely high density of states at the Fermi level as well as a strong correlation effect between electrons in a hybridized f band. The longitudinal magnetoresistance of UPt, is shown in fig. 1. The magnetoresistance is always positive below 4.2 K and can be expressed by &(
H)/p(O)
= aH”.
with n = 1.63 and (Y= 3.44 x 10 m4 kOe_ I.” at 0.55 K n increases slightly with increasing temperature. Nc significant difference has been found between transverse and longitudinal magnetoresistances. The positive magnetoresistance is in contrast with that of other heavy Fermion compounds, which show a negative magnetoresistance, but is more like a normal metal or like other spin fluctuating systems. Positive magnetoresistance
5~3Elsevier Science Publishers B.V.
-
\
10’
1oj
Magnetic Fig. 1. Longitudinal
Field
(KOe)
magnetoresistances
of UPt
OL
1 in magnetic
_J
0
fields up to 30 kOe. should not arise from ferromagnetic spin fluctuations because the external magnetic field always suppresses them. On the other hand. antiferromagnetic spin fluctuations will be enhanced by applying a magnetic field below a critical field at which a sharp peak may occur in the resistivity [5]. The positive magnetoresistance up to 30 kOe presented here and up to I10 kOe obtained by Stewart et al. [6] could be a low field effect preceding a transition under an intense magnetic field possibly of = 200 kOe observed by Franse et al. [7]. However. since there is no long range magnetic order in UPt 1 in zero field, this behavior under high magnetic field must still be regarded as quite anomalous. The superconducting upper critical field H,, is shown in fig. 2. A needle-like specimen was placed in a bundle of fine copper wires suspended from the mixing chamber of the dilution refrigerator and the magnetic field was applied perpendicular to the specimen. The field was slowly swept with a speed of = 10 Oe/s in order not only to prevent eddy current heating but also any temperature change because of the specific heat jump at Hcz.The critical field is defined by the midpoint of the total change of the resistivity. The HLz curve in fig. 2 has a pronounced positive curvature near 7;.. Disregarding this behavior, the slope ~(d H,,/dT),C is estimated to be 43 kOeK_ ‘. This value of the slope is in excellent agreement with the data of Palstra et al. [X] but is significantly different from that of Chen et al. [2]. This difference may be associated with a large anisotropy effect in single crystals or with the higher TCof 0.54 K of their crystal. Another difference must be pointed out. According to Chen et al the critical field slope between
0.2
0.4
Temperature
0.6
( K)
Fig. 2. Tcmprrature dependence of the supercc>nducting upper critical field ffL2. A dc current denslty of 27 A/cm’ U;L\ u\ed.
0.5 and 0.3 K is higher than that of our specimen but it saturates below about 0.3 K for both field directions becoming less anisotropic in Hc2.Although the absolute values of H,, in fig. 2 are lower than those of Chen et al.. the extrapolated value of H,,(O)at T= 0 agree5 fairly well, the result being H,,(O) = 17 kOe. Using the equation for strong coupling superconductivity [9], and assuming that the Ferm’i surface is spherical with a mean Fermi velocity ?, one can obtain a mean Fermi wave vector I
agreement
with
previous
estimates
121.
[II G.R. Stewart, Z. Fisk. J.0. Willis and J.L. Smith. Phys. Rev. Lett. 52 (19X4) 679. PI .I.W’.Chen. S.E. Lamhert, M.B. Maple. Z. Fisk, J.L. Smith. G.R. Stewart and J.O. Willis. Phys. Rev. 830 (19X4) lSX.1 [31 K.H.J. Buschow and H.J. van Daal, AIP Conf. Proc. Yo. 5. Magn. and Magn. Mat. (1971) p. 1464. [41 K. Kadnwaki. K. Okuda and M. Date. J. Phy\. Sot. Japan 51 (1982) 2433. [51 K. Usami. J. Phys. Sot. Japan 45 (1978) 466. I61 G.R. Stewart. Z. Fisk. J.O. Willi? and J.L. Smith. Phy\lca I278 (1984) 448. 171 J.J.M. Franse. P.H. Frings. A. de Vissrr and A. Menov