Adiabatic dynamics of local spin moments in itinerant magnets

Using the adiabatic approximation, we derive the equations of motion for local spin moments which are valid for itinerant as well as tight-binding spins. Material parameters in the equations of motion can be obtained using standard density functional methods, because they depend only on the energy and Berry phase of the constrained ground state of frozen spin configurations. For the calculation of spin waves in a collinear magnet, ii. is sufficient to know the quadratic forms of total energy and spin component along the symmetry axis as functions of the spin deviations from the ground state configuration.