Spin waves with source-free time-dependent spin density functional theory

Time-dependent spin density functional theory (TD-SDFT) allows the theoretical description of spin and magnetization dynamics in electronic systems from first quantum mechanical principles. TD-SDFT accounts for electronic interaction effects via exchange-correlation scalar potentials and magnetic fields, which have to be suitably approximated in practice. We consider here an approach that was recently proposed for the ground state by Sharma et al. [J. Chem. Theor. Comput. 14, 1247 (2018)], which enforces the so-called "source-free" condition by eliminating monopole contributions contained within a given approximate exchange-correlation magnetic field. This procedure was shown to give good results for the structure of magnetic materials. We analyze the source-free construction in the linear-response regime, considering spin waves in paramagnetic and ferromagnetic electron gases in three and two dimensions. We observe a violation of Larmor's theorem in the paramagnetic case and a wrong long-wavelength behavior of ferromagnetic magnons. The practical implications of these violations are discussed.