Density functional perturbation theory for lattice dynamics with fully relativistic ultrasoft pseudopotentials: Application to fcc-Pt and fcc-Au

I present density functional perturbation theory for lattice dynamics with the fully relativistic ultrasoft pseudopotentials (PPs) introduced recently for dealing with spin-orbit effects and use it to calculate the phonon dispersions of fcc-Pt and fcc-Au. The results are compared with the dispersions obtained by scalar relativistic PPs and by inelastic neutron scattering. It is found that, on the phonon spectrum of fcc-Au, spin-orbit effects are small, essentially within the numerical accuracy. In fcc-Pt, these effects, although still small, improve the agreement between theory and experiment close to the Kohn anomaly of the $T_1$ branch along the $\Sigma$ line.

Figure 1

Calculated LDA phonon dispersions at $T=0\mathrm{K}$ for fcc-Au obtained with FR US-PPs (solid lines), compared with dispersions obtained with SR US-PPs (dashed lines) and inelastic neutron scattering data at $T=295\mathrm{K}$ from Ref. 47 (solid diamonds). Dot dashed lines are obtained with FR-PPs at $a_0=7.67\mathrm{a.u.}$, the estimated theoretical lattice constant at $T=295\mathrm{K}$.

Figure 2

Calculated LDA phonon dispersions at $T=0\mathrm{K}$ for fcc-Pt obtained with FR US-PPs (solid lines), compared with dispersions obtained with SR US-PPs (dashed lines) and inelastic neutron scattering data at $T=90\mathrm{K}$ from Ref. 31 (solid diamonds).

Figure 3

Calculated LDA phonon dispersions for fcc-Pt in the $\Sigma$ direction [$\mathbf{k}=(\zeta ,\zeta ,0)$ in units $2\pi ∕a_0$]. Solid (dashed) lines show results obtained with FR (SR) US-PPs by interpolating on the $8\times 8\times 8$ $\mathbf{q}$-point grid. Empty circles (squares) are the results of a DFPT evaluation of the phonon frequencies with FR (SR) PPs, while inelastic neutron scattering data from Ref. 31 are shown by solid diamonds.