Isotope Effect and Phonon Softening in Superconducting Borocarbides and Boronitrides

The isotope effect in the recently disvovered class o superconductors LuNi₂B₂C and La₃Ni₂B₂N₃ is investigated in the context of electron-squezed phonon interaction renormalizing the Ni-d electron-electron correlations. Squeezed phonon mode originates from the anharmonic character of the tetragonal Ni-B structure and is polarized in the vortical direction to the Ni layers. The isotope effect arises as a result of the zero point motion of the Ni-Ni d-electron hopping amplitude dominantly due to this vertical phonon mode. Within this model the isotope exponent is calculated to be α_B ≤ 0.20 as compared to the recently found experimental value α^exp_B=0.27∓0.10. Finally, the phonon frequency softening predicted by our model eletron-phonon interaction is discussed within the context of recent experiments on the relevant boron A_1g softening.