Phonon dispersion anomalies and superconductivity in metal substituted MgB2

Abstract

We have calculated the extent of the E2g phonon anomaly for Mg1−xMxB2 where M=Sc, Ti, Cd and Ba for 0<x<1 using ab initio DFT models with the LDA and GGA functionals. Using superlattice models along the c axis to represent metal substitution in MgB2, we show that phonon dispersion (PD) plots vary significantly with x, in particular, the nature and extent of the phonon anomaly around the origin, G, of the reciprocal lattice. Measurement of this phonon anomaly along the G-K and G-M directions provides an estimate of the thermal energy, Tδ, of the anomaly, which approximates experimentally determined Tc within standard error for Sc and Ti substitution. We demonstrate that substitutions of Cd and Ba in MgB2 show a higher calculated Tδ than MgB2 by more than 20K. Syntheses of these Cd and Ba compositions are not extant and may not be possible given the limited solubility of metals in MgB2. Nevertheless, ab initio DFT models of phonon behaviour in AlB2–type structures provide an effective tool for prediction of physical properties and for design of new materials.