Electron/phonon coupling in group-IV transition-metal and rare-earth nitrides

Abstract

Transport electron/phonon coupling parameters and Eliashberg spectral functions αtr2F(ℏω) are determined for group-IV transition-metal (TM) nitrides TiN, ZrN, and HfN, and the rare-earth (RE) nitride CeN using an inversion procedure based upon temperature-dependent (4 < T < 300 K) resistivity measurements of high-crystalline-quality stoichiometric epitaxial films grown on MgO(001) by magnetically-unbalanced reactive magnetron sputtering. Transport electron/phonon coupling parameters λtr vary from 1.11 for ZrN to 0.82 for HfN, 0.73 for TiN, and 0.44 for CeN. The small variation in λtr among the TM nitrides and the weak coupling in CeN are consistent with measured superconducting transition temperatures 10.4 (ZrN), 9.18 (HfN), 5.35 (TiN), and <4 K for CeN. The Eliashberg spectral function describes the strength and energy spectrum of electron/phonon coupling in conventional superconductors. Spectral peaks in α2F(ℏω), corresponding to regions in energy-space for which electrons couple to acoustic ℏωac and optical ℏωop phonon modes, are centered at ℏωac = 33 and ℏωop = 57 meV for TiN, 25 and 60 meV for ZrN, 18 and 64 meV for HfN, and 21 and 39 meV for CeN. The acoustic modes soften with increasing cation mass; optical mode energies remain approximately constant for the TM nitrides, but are significantly lower for the RE nitride due to a lower interatomic force constant. Optical/acoustic peak-intensity ratios are 1.15 ± 0.1 for all four nitrides, indicating similar electron/phonon coupling strengths αtr(ℏω) for both modes.