Specific heat and magnetization of aZrB12single crystal: Characterization of a type-II/1 superconductor

Abstract

We measured the specific heat, the magnetization, and the magnetoresistance of a single crystal of ZrB 12 , which is superconducting below T c Х 6 K. The specific heat in zero field shows a BCS-type superconducting transition. The normal-to superconducting-state transition changes from first order ͑with a latent heat͒ to second order ͑without latent heat͒ with increasing magnetic field, indicating that the pure compound is a low-, type-II/1 superconductor in the classification of Auer and Ullmaier ͓Phys. Rev. B 7, 136 ͑1973͔͒. This behavior is confirmed by magnetization measurements. The H-T phase diagram based on specific-heat and magnetization data yields H c2 ͑0͒ = 550 G for the bulk upper critical field, whereas the critical field defined by vanishing resistance is a surface critical field H c3 ͑0͒ϳ1000 G.

Two-gap superconductivity inZrB12: Temperature dependence of critical magnetic fields in single crystals

“…Clearly, ZrB 2 (T R =700 K) and ZrB 12 have very different ρ(T) dependence due to different T R . At the same time, the phonon Debye temperature, T D , for ZrB 12 calculated from C(T) on rather large sample (4.7×4.8×2.9 mm) prepared by one of us (VAG) (without metallographic study) [19,23], is three times higher. Furthermore T D increases from 800 to 1200 K as temperature rises from T c up to room temperature.…”

“…The measurements were performed in the liquid helium variable temperature cryostat in the temperature range between 1.3 K and 350 K. Magnetic measurements of ρ(T,H) and λ(T,H) were carried out using a superconducting coil in applied fields of up to 6 T down to 1.3 K. Additional dc and ac ρ(H) measurements were performed in the National High Magnetic Field Laboratory in Tallahassee, Florida (NHMFL) at the temperatures down to 0.35 K. The dc magnetic field was applied in the direction of the current flow. The critical temperature of the ZrB 12 samples, measured by RF susceptibility and ρ(T) was found to be T c0 =6.0 K. 12 single crystal cross section in (100) plane from the same parts of ingot as in [19,23]. The needle like long grains are ZrB 2 phase, while the small black lines correspond to etching pits from small angle boundaries.…”

“…Tsindlekht et al [22] came to a similar conclusion from tunneling and magnetic characterization of ZrB 12 single crystals at the temperatures also very close to T c (4.5 K -6 K). Lortz et al [19] and Wang et al [23], reported C(T), ρ(T), magnetic susceptibility, and thermal expansion measurements of ZrB 12 samples prepared by one of us (VAG) and concluded that it is a single gap marginal BCS superconductor which undergoes transition from type-I superconductor near T c to type II superconductor below 4.6 K with 2∆(0)/k B T c =3.7, the value that is lower than that obtained from PCS [21] and STM data [22]. Large difference in H c2 characteristics reported in the above-mentioned papers was discussed in terms of surface superconductivity.…”

Type-I superconductivity in KBi2single crystals

“…The extracted electronic specific heat jump at T c (∆C es /γT c = 6.06) is much larger than the weakly coupled BCS value 1.43, indicating the strongly coupled superconductivity in KBi 2 . 24 The thermodynamic critical field H c (T ) can be obtained by integrating the differences of specific heats and the specific heats divided by temperature between the zero-field superconducting (s) and normal (n) states (H = 207 Oe) (free energy analysis), 8,25 …”

Superconductivity in LuxZr1-xB12 Dodecaborides with Cage-Glass Crystal Structure

“…Among them, in the family of dodecaborides, ZrB 12 is a BCS (Bardeen-Cooper-Schriffer) superconductor with the highest T c ≈ 6 K [2,3]. However, in case of LuB 12 the superconducting transition temperature reduces dramatically (T c ≈ 0.4 K for LuB 12 [4][5][6]), and the origin of the large T c difference for these two compounds with similar conduction bands and crystalline structures is not yet clarified.…”