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Specific Heat Study of the Non-centrosymmetric Superconductor LaPt3Si in Magnetic Fields

We have measured the specific heat of poly- and single-crystalline LaPt3Si samples in various magnetic fields. In zero magnetic field, we observed distinct superconducting transitions at Tc ∼ 0.64 K and 0.61 K for the poly- and single crystals, respectively. Temperature T dependences of the specific heat C of both samples around Tc resembled each other and could be well described by an exponential equation for a conventional superconductor at low temperatures. In a magnetic field, a characteristic peak of C/T appeared while the Tc was considerably suppressed. These trends were pronounced for the single crystal. The transition of the polycrystal became broad above 40 Oe and a characteristic tail appeared at temperatures above the peak of C/T. We suggest that the tail is induced by domains that have crystallographic disorders of the non-centrosymmetry and a higher critical magnetic field than that of the bulk. These domains became superconducting at temperatures above the peak of C/T and then formed the tail. Both the poly- and single-crystalline LaPt3Si samples have been found to show characteristics that are in-between those of type-I and type-II superconductors.


Introduction
Non-centrosymmetric superconductors are attracting a great deal of interest [1]. In such systems, the conventional classification of the odd or even pair wave function for the orbital part and the singlet or triplet for the spin part is not valid anymore [2]. Thus, unconventional superconductivity with a nontrivial pair wave function is expected to appear. Two kinds of Fermi surfaces that are due to the antisymmetric spin-orbit interaction have been clearly observed for LaPt 3 Si by the de Haas van Alphen measurements [3]. LaPt 3 Si exhibits superconducting transition at T c ∼ 0.6 K without f-electron magnetism [4]. In order to investigate the characteristics of the non-centrosymmetric superconductor LaPt 3 Si, we measured specific heat in various magnetic fields [5].

Experimental methods
A polycrystalline LaPt 3 Si sample was synthesized by arc melting and a single-crystalline LaPt 3 Si sample was grown by the Bridgman method and/or mineralization. These sample preparations were described in refs. 5 and 6. Specific heat was measured using the adiabatic heat pulse method over the temperature range of 0.1 to 0.8 K and the magnetic field range of 0 to 80 Oe. It was conducted in the heating up process after applying a magnetic field at ∼ 1 K and cooling down to the lowest temperature. The measured sample weighed approximately 20 mg (size: ∼1×1×1 mm 3 ).

Figures 1(a) and (b)
show the T dependences of C/T of the single-crystalline sample in several selected H applied along the a-and c-axes, where T , C, and, H are temperature, specific heat, and, external magnetic field, respectively. In H = 0 Oe , C/T exhibited a sharp jump at T c = 0.61 K. T c is defined as the temperature at which the entropy is dominantly released from the sample. The value of ΔC/γ n T c was 1.1 (BCS value = 1.43). C(T ) below 0.55 K is well described by a single-exponential equation as C = A exp(-Δ/T ) + γ s T , where γ s = 0.5 mJ/(K 2 ·mol), A = 67 mJ/(K·mol), and Δ = 1.0 K. 2Δ/k B T c is 3.2 (BCS value = 3.53). C at H = 0 Oe looks like that of the s-wave superconductor with an isotropic superconducting gap. T c decreased with increasing H and superconductivity was almost completely suppressed above approximately 60 Oe. We should note here that a characteristic sharp peak appeared at just below the superconducting transition temperature in the magnetic fields. At first glance, the transition looked like that of a type-I superconductor in the magnetic field. This result may lead us to recall that the superconducting transition of the single-crystalline sample in the magnetic field is of the first order. However, residual γ s increases with increasing H. Therefore, the sample has normal areas where superconductivity is broken by external magnetic fields in spite of in a superconducting phase. In order to further our understanding, we calculated the entropy S of the single-crystalline sample with the heat capacity data. T dependences of S are shown in Figs. 1(c) and (d). S decreased rapidly below T c , especially H = 20 ∼ 50 Oe. The rapid decreases correspond to the sharp peaks of C/T . However, it should be noted that S decreased smoothly below T c . No discontinuity of S was observed around T c . These results may imply that the transition is not of the first order, but of the second order indicating that the crystal is a type-II superconductor.  Fig. 2(b). The behavior of S is similar to that of the single crystal. However, S decreased more smoothly below T c than that of the single crystal, even H = 20 ∼ 50 Oe. T dependence of C/T in zero magnetic field is quite similar to that of the single crystal, as shown in Fig. 3(a). The similarity of the T dependence of C/T between the  single crystal and the polycrystal was preserved in the low magnetic fields. However, for H = 40 Oe, the large peak immediately below T c was suppressed for the polycrystal and an additional broad tail appeared above the temperature where the jump appeared, as shown in Fig. 3(b). The onset of the superconducting transition (T c,onset ) is 0.1 K higher than T c of 0.42 K. This broadening of transition for the polycrystal cannot be explained by the small anisotropy of T c observed for the single crystal. The broadening became remarkably large with increasing H.
We note that the above-mentioned broad tail for the polycrystal above T c appeared only in a magnetic field that was larger than approximately 40 Oe. No such tail was observed in zero or a smaller magnetic field. It is natural to consider that the polycrystal includes some local domains where the suppression of the T c by H is relatively small. This interpretation may be represented in terms of the critical magnetic field H c , so that the local domains have larger H c than that in the bulk of the sample. We have pointed out in our previous work that the polycrystal includes a considerable amount of crystal disorders, particularly disorders of the 'non-centrosymmetry' [6,5]. Such disorders should considerably decrease the coherence length of the Cooper pair and increase H c in the local domains. We consider that the above-mentioned broad tail is due to this reason; that is, the broad tail appeared because there was a considerable amount of local domains having crystallographic disorders. As noted above, S of the polycrystal decreased below T c more slowly than that of the single crystal. We consider that this behavior is caused by the local domains. We should also note that the T c of the polycrystal is almost the same in zero magnetic field as that of the single crystal. Therefore, the crystal disorders change directly not the T c but the H c in the local domains.
We show the T dependences of the superconducting critical magnetic field H c (T ) (H-T phase diagram) of poly-and single-crystalline (a-and c-axes) LaPt 3 Si in Fig. 4. The transition temperature T c for each H is defined as the midpoint temperature between the onset and the peak of C/T . For the polycrystal, T c,onset is also plotted in the fig. 4(b).  Oe with decreasing T . Similar H-T phase diagram was obtained from the electrical resistivity measurements, too. These properties, particularly the behavior of T c,onset , are consistent with the idea that the local domains have higher critical magnetic fields than that of the bulk.

Conclusions
We have measured the specific heat of poly-and single-crystalline LaPt 3 Si samples in several magnetic fields in order to investigate the characteristics of non-centrosymmetric superconductors. For H = 0 Oe, both the polycrystal and single crystal showed almost the same T dependence of C/T , which could be well described in terms of a conventional superconductor.
In the presence of a magnetic field, however, T c was considerably suppressed and a sharp peak of C/T appeared for the poly-and single-crystal. The superconducting transition of the polycrystal had a broad tail above H = 40 Oe. It is concluded that the origin of this broad tail is the domains that have crystallographic disorders of the non-centrosymmetry, in which suppression of T c is relatively small. H c (T ) for the single crystal for H//a and H//c and the polycrystal monotonically increased with decreasing T , and was well fitted by the conventional formula. H c (0) for the single crystal exhibited a small anisotropy. Both the poly-and single-crystals show characteristics that are in-between those of type-I and type-II superconductors, although we consider that the superconducting transitions lead to the second-order phase transitions due to the disorders of the non-centrosymmetry.