Spin dynamics in the density functional: problems and perspectives

We discuss general dynamics in the charge-current-magnetization density functional theory.
Starting from dynamics of one electron wave function we analyze transformation to coupled dynamics of charge, magnetization and current one electron densities. Further we concentrate on a coupled dynamics of total spin and spin current densities. From a methodical point of view we show a connection with the phenomenological Landau-Lifshitz dynamics, effective interactions of Heisenberg model and discuss major assumptions and key adiabatic approximations behind it. Practical expressions for the interatomic interactions parameters of this coupled dynamics are shown also in a standard long wave approximation. Realistic applications of such ab-initio coupled dynamics have been performed for spin excitations and exchange interactions in 3d ferromagnetic metals where “spin current enhancement” of spin waves appears as a perturbation. Several opposite examples of strongly coupled and non adiabatic spin dynamics have been found in 122 family of iron pnictides.