  A coupled atomistic spin and lattice dynamics approach is developed which
merges the dynamics of these two degrees of freedom into a single set of
coupled equations of motion. The underlying microscopic model comprises local
exchange interactions between the electron spin and magnetic moment and the
local couplings between the electronic charge and lattice displacements. An
effective action for the spin and lattice variables is constructed in which the
interactions among the spin and lattice components are determined by the
underlying electronic structure. In this way, expressions are obtained for the
electronically mediated couplings between the spin and lattice degrees of
freedom, besides the well known inter-atomic force constants and spin-spin
interactions. These former susceptibilities provide an atomistic ab initio
description for the coupled spin and lattice dynamics. It is important to
notice that this theory is strictly bilinear in the spin and lattice variables
and provides a minimal model for the coupled dynamics of these subsystems and
that the two subsystems are treated on the same footing. Questions concerning
time-reversal and inversion symmetry are rigorously addressed and it is shown
how these aspects are absorbed in the tensor structure of the interaction
fields. By means of these results regarding the spin-lattice coupling, simple
explanations of ionic dimerization in double anti-ferromagnetic materials, as
well as, charge density waves induced by a non-uniform spin structure are
given. In the final parts, a set of coupled equations of motion for the
combined spin and lattice dynamics are constructed, which subsequently can be
reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations
for spin dynamics and damped driven mechanical oscillator for the ...
