Spin Non-Collinear Real-Time Time-Dependent Density-Functional Theory and Implementation in the Modern GPU-Accelerated INQ Code

Time-dependent density functional theory (TDDFT) is a theory that describes the time evolution of quantum mechanical many-electron systems under the influence of external time-dependent electric and magnetic fields. INQ is a specially designed software to efficiently solve the real-time TDDFT equations on graphics processing units (GPUs), which aim to overcome the computational limitation of time and size scales of non-equilibrium quantum dynamics. In this work we will present an implementation of non-collinear TDDFT for the INQ code to simulate spin dynamics in real time and discuss the implementation of non-collinear magnetic effects into the code. We will discuss the implementation of exchange-correlation magnetic fields, spin-orbit coupling, and the interaction between the electronic system and external magnetic fields. We will then consider several prototypical examples of spin dynamics in magnetic clusters and solids after light excitation. Potential applications range from the study of real-time dynamics of magnons to ultrafast spin dynamics under linear and circularly polarized laser excitation, as well as spectroscopic signatures such as magnetic circular dichroism and pump-probe Kerr rotation.