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

## TL;DR

This paper extends density functional perturbation theory to magnetic materials using fully relativistic ultrasoft pseudopotentials, incorporating time-reversal symmetry and magnetic point group operations for accurate lattice dynamics calculations.

## Contribution

It introduces a novel formalism for including magnetic effects and symmetry operations in relativistic lattice dynamics calculations within density functional perturbation theory.

## Key findings

- Validated approach against frozen phonon method in ferromagnetic Ni and Pt wire.
- Demonstrated accurate treatment of magnetic symmetry in lattice dynamics.
- Extended DFT perturbation theory to fully relativistic magnetic systems.

## Abstract

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.