We present a complete theory of neutron reflection from a magnetic mul
tilayer in the presence of an external magnetic field. Several effects
have been taken into account, in particular the non-eigenstate for th
e neutron in each layer and the Larmor precession of the neutron in th
e layers which induce a breakdown of the plane-wave approximation. We
describe also a new spectrometer built at the reactor Orphee in Saclay
in order to perform polarized neutron reflectivity on thin films and
magnetic layers with polarization analysis.