Spin non-collinear real-time time-dependent density-functional theory and implementation in the modern GPU-accelerated <scp>INQ</scp> code

Time-dependent density functional theory (TDDFT) describes the time evolution of quantum mechanical many-electron systems under the influence of external time-dependent electric and magnetic fields. INQ is especially designed to efficiently solve the real-time TDDFT equations on graphics processing units, which aims to overcome the computational limitation of time and size scales of non-equilibrium quantum dynamics. In this work, we present an implementation of non-collinear TDDFT for the INQ code to simulate spin dynamics in real time. We discuss the implementation of non-collinear magnetic effects, exchange correlation magnetic fields, spin–orbit coupling, and the interaction between the electronic system and external magnetic fields, with plane-wave basis and pseudopotential approximations. We consider several prototypical examples of spin dynamics in magnetic clusters and solids after light excitation.