  The relation between energy and density (known as the nuclear equation of
state) plays a major role in a variety of nuclear and astrophysical systems.
Spin and isospin asymmetries can have a dramatic impact on the equation of
state and possibly alter its stability conditions. An example is the possible
manifestation of ferromagnetic instabilities, which would indicate the
existence, at a certain density, of a spin-polarized state with lower energy
than the unpolarized one. This issue is being discussed extensively in the
literature and the conclusions are presently very model dependent. We will
report and discuss our recent progress in the study of spin-polarized neutron
matter. The approach we take is microscopic and relativistic. The calculated
neutron matter properties are derived from realistic nucleon-nucleon
interactions. This makes it possible to understand the nature of the EOS
properties in terms of specific features of the nuclear force model.
