Maki Parameter and Upper Critical Field of the Heavy-Fermion Superconductor UBe₁₃

Abstract

We have performed low-temperature specific-heat measurements in magnetic fields for a single crystal UBe 13 . It has been observed that our sample exhibits a superconducting transition at an intermediate temperature (T c ∼ 0.81 K) between previously reported values for two variant samples called H type and L type. The specific heat C(T ) of our sample shows a T 3 behavior below ∼ 0.7 T c , which is similar to the behavior of the H-type sample, suggesting the existence of point nodes in the superconducting gap function. We have obtained the upper-critical-field curves H c2 for the [001], [110], and [111] crystal axes, which show no anisotropy at least down to the lowest measured temperature of 0.5 K. We have also derived the Maki parameter κ 2 , and it has been revealed that the κ 2 steeply decreases isotropically upon cooling just below T c . Paramagnetic effects and the symmetry of Cooper pairing of UBe 13 are discussed. KEYWORDS: Unconventional Superconductor, Heavy Fermion, Paramagnetic EffectThe heavy-fermion compound UBe 13 has attracted much attention since the discovery of unconventional superconductivity 27 years ago. 1) UBe 13 has a cubic structure with the space group O h 6 (Fm−3c), and exhibits a superconducting (SC) transition at around 0.85 K with a large specific-heat jump ∆C. Despite prolonged scientific efforts to unravel the superconductivity of this material, many open questions remain, in particular concerning the symmetry of Cooper pairing and the unusual SC phase diagram. 2, 3)As for the SC gap structure, which is related to the parity of Cooper pairing, the temperature dependence of low-T specific heat C(T ) 4) and magnetic field penetration depth λ(T ) 5) suggest the presence of point nodes, whereas nuclear magnetic resonance (NMR) spin-relaxation rate 1/T 1 6) and ultrasonic attenuation α(T ) 7) suggest a line node. A p-wave AndersonBrinkman-Morel (ABM) state, which is identified as the A phase in superfluid 3 He,8) has been proposed for the SC of UBe 13 from the T 3 -like behavior observed in the low-T specific heat.4) An early NMR study also suggests the occurrence of the ABM state, because the Knight shift does not decrease below T c . 9) However, recent muon spin-rotation (µSR) measurements performed in field, H || [001], have revealed that the muon Knight shift shows a clear decrease below T c . 10)Furthermore, a recent NMR study by Tou et al. has suggested that the Knight shift decreases below T * ( ∼ 0.7 K < T c ) for [001], whereas increases below T * for [111]. 11) Therefore, no consensus has been achieved regarding the behavior of Knight shift below T c as well as the SC-gap structure. Namely, it is still debated whether the Cooper-pairing state of UBe 13 is triplet or singlet.In order to obtain further information about the parity of Cooper pairing, it is important to investigate the presence (or absence) of paramagnetic effects. The value of H c2 estimated experimentally by extrapolation to T = 0 for UBe 13 is about 80-130 kOe, which is much larger than the Pauli limit * E-mai...

Temperature-Dependent Ginzburg–Landau Parameter

“…Similar observations have been done recently 11 in heavy fermionic compound UBe 13 . This case demands further investigation because it seems that this material having extremely high upper critical field 12 and T 3 behavior of specific heat at low temperatures 13 belongs to triplet superconductors with point nodes in the quasiparticle spectrum.…”

Observation of an Unusual Magnetic Anomaly in the Superconducting Mixed State of Heavy-Fermion CompoundUBe13by Precise dc Magnetization Measurements

“…1) [24], suggesting that the used single crystal is of high quality, because the flux-pinning centers are impurities or lattice defects in general. We also checked the large and sharp specific-heat jump at the SC transition for the same sample [25]. We then consider that the observed magnetic anomaly is an intrinsic phenomenon for a good-quality sample, which is related to the SC nature of UBe 13 .…”

“…If the FM correlation in UBe 13 is reinforced only in its SC sate by some undefined reason, the FM instability might be deeply involved to the USC in UBe 13 . The presence of such a FM correlation between f electrons in UBe 13 is more natural than that of an AF correlation to form a parallel-spin Cooper pairing, which is suggested from the CðTÞ results [11,25,29]. It is intriguing to investigate the FM fluctuation in UBe 13 by another experiment, focusing on the weak magnetism below H Ã Mag .…”

DC Magnetization Study on Heavy-Electron Superconductor UBe13

“…Figure 2 Mag from the present magnetization measurements for H || 001 and H || 110 , are plotted. The results of our previous specific-heat measurements for the same single crystal, for H || 001 , 110 , and 111 , are also plotted [17]. One can see several interesting features of this phase diagram.…”

“…The results of H Mag c2 , and H * Mag for H || 001 , and H || 110 , obtained from magnetization measurements, are plotted. In addition, the uppercritical field, obtained from our previous specific-heat measurements, are also plotted[17]. Here, H top c2 was defined by the peak top of superconducting transition, whereas H c2 was defined by considering the entropy conservation at the superconducting transition.…”