Density functional perturbation theory for lattice dynamics with fully relativistic ultrasoft pseudopotentials: The magnetic case

We extend density functional perturbation theory for lattice dynamics with fully relativistic ultrasoft pseudopotentials to magnetic materials. Our approach is based on the application of the time-reversal operator to the Sternheimer linear system and to its self-consistent solutions. Moreover, we discuss how to include in the formalism the symmetry operations of the magnetic point group which require the time-reversal operator. We validate our implementation by comparison with the frozen phonon method in fcc Ni and in a monatomic ferromagnetic Pt wire.

Figure 1

Computed FR LDA (dashed lines) and PBE (solid lines) phonon dispersions of ferromagnetic fcc Ni, compared to inelastic neutron scattering data (solid diamonds). Phonon modes are classified using symmetry, but only the operations that do not require $\mathcal{T}$ are used.

Figure 2

Computed FR LDA phonon dispersions of ferromagnetic Pt nanowire. Left panel: Magnetization parallel to the wire. Right panel: Magnetization perpendicular to the wire.