  Motivated by a need to understand spin-momentum transport in CPP (current
perpendicular to the plane) structures, a quantum field theoretical treatment
of spin-spin interactions in ferromagnets is presented. The sd interaction of
the conduction electrons and the magnetic medium is treated non-perturbatively
from first principles in real space. The localized magnetic moments also
interact with each other through a Heisenberg exchange potential. To take into
account correlation effects, a second quantized formulation is used. The
semi-classical limit is taken by using a coherent-state path-integral technique
which also allows us to go beyond a linear-response approach. We derive a set
of coupled equations of motion for the nonuniform magnetization, the spin
current and the two-point correlation functions of the magnetization. The rate
of change of the magnetization is shown to obey a generalized Landau-Lifshitz
equation that takes into account interaction with the conduction electrons.
Within the relaxation time approximation it is shown that the polarization of
the conduction electrons obeys a diffusion equation. The diffusion tensor,
which has off-diagonal terms due to the sd exchange interaction, is now
explicitly dependent on the magnetization of the medium. We also show that the
magnetization fluctuations satisfy a diffusion-type equation. The derived
equations are used in two illustrative examples.
