Lattice-dynamical properties of black phosphorus under pressure studied by inelastic neutron scattering

Acoustic-phonon dispersion relations of black phosphorus in its orthorhombic $A11\mathrm{}$ phase have been measured along three principal directions mainly at 1 bar and 15.4 kbar. An anomalous softening has been observed on the LA[100] branch whose vibrational patterns (eigenvectors) have been analyzed based on a force-constant-model fit by Kaneta et al. It is suggested that this softening is caused through electron-phonon interactions associated with a large change in bonding angles. The ${\mathrm{TA}}_y\mathrm{}\left[001\right]\mathrm{}$ mode at the zone boundary, which can be assigned to the atomic displacements relevant to the $A11\mathrm{}$-to-$A7\mathrm{}$ (rhombohedral) structural transition at 45 kbar, does not soften, but at least the hardening shows a tendency to saturate at pressure higher than 15.4 kbar.