  Today, further downscaling of mobile electronic devices poses serious
problems, such as energy consumption and local heat dissipation. In this
context, spin wave majority gates made of very thin ferromagnetic films may
offer a viable alternative. However, similar downscaling of magnetic thin films
eventually enforces the latter to operate as quasi-two dimensional magnets, the
magnetic properties of which are not yet fully understood, especially those
related to anisotropies and external magnetic fields in arbitrary directions.
To this end, we have investigated the behaviour of an easy-plane and easy-axis
anisotropic ferromagnet -- both in two and three dimensions -- subjected to a
uniform magnetic field, applied along an arbitrary direction. In this paper, a
spin-1/2 Heisenberg Hamiltonian with anisotropic exchange interactions is
solved using double-time temperature-dependent Green's functions and the
Tyablikov decoupling approximation. We determine various magnetic properties
such as the Curie temperature and the magnetization as a function of
temperature and the applied magnetic field, discussing the impact of the
system's dimensionality and the type of anisotropy. The magnetic reorientation
transition taking place in anisotropic Heisenberg ferromagnets is studied in
detail. Importantly, spontaneous magnetization is found to be absent for
easy-plane two-dimensional spin systems with short range interactions.
