  A theory for the magnetization of ferromagnetic films is formulated within
the framework of many-body Green's funtion theory which considers all
components of the magnetization. The model Hamiltonian includes a Heisenberg
term, an external field, a second- and fourth-order uniaxial single-ion
anisotropy, and the magnetic dipole-dipole coupling. The single-ion anisotropy
terms can be treated exactly by introducing higher-order Green's functions and
subsequently taking advantage of relations between products of spin operators
which leads to an automatic closure of the hierarchy of the equations of motion
for the Green's functions with respect to the anisotropy terms. This is an
improvement on the method of our previous work, which treated the corresponding
terms only approximately by decoupling them at the level of the lowest-order
Green's functions. RPA-like approximations are used to decouple the exchange
terms in both the low-order and higher-order Green's functions. As a first
numerical example we apply the theory to a monolayer for spin S=1 in order to
demonstrate the superiority of the present treatment of the anisotropy terms
over the previous approximate decouplings.
