Superconductivity in ZrB 12 and LuB 12 with Various Boron Isotopes

In BCS-type superconductors Zr N B12 (T C≈6 K) and Lu N B12 (T C≈0.42 K) heat capacity C(T) and magnetization measurements have been carried out on high quality single crystals with various boron isotopes (with N=10, 11, and with natural composition of 10B and 11B). Parameters of the superconducting and normal states have been deduced from this study, allowing comparison between these two dodecaborides. It was shown that ZrB12 is a type-II superconductor in which the Ginzburg–Landau parameter varies in the range κ=0.8–1.12. A detailed analysis of specific heat in the normal state of R10B12, R11B12 and RnatB12 (where R=Zr, Lu) has revealed three Einstein type vibration modes of Zr4+-ions in ZrB12 with characteristic energies θ E1(Zr N B12)≈200 K and θ E2,3(Zr N B12)≈450 K, whereas only one quasi-local mode of Lu3+-ions in LuB12 with θ E1(Lu N B12)≈160–170 K was detected. This difference of vibration spectra has been found to be the main reason for the dramatic change of T C for ZrB12 and LuB12. Using strong coupling approximation, moreover, the Coulomb pseudopotential μ ∗, electron–phonon interaction constant λ ∗ and logarithmic average frequency ω ln were determined.