  The theoretical formulation of x-ray resonant magnetic scattering from rough
surfaces and interfaces is given for specular reflectivity. A general
expression is derived for both structurally and magnetically rough interfaces
in the distorted-wave Born approximation (DWBA) as the framework of the theory.
For this purpose, we have defined a ``structural'' and a ``magnetic'' interface
to represent the actual interfaces. A generalization of the well-known
Nevot-Croce formula for specular reflectivity is obtained for the case of a
single rough magnetic interface using the self-consistent method. Finally, the
results are generalized to the case of multiple interfaces, as in the case of
thin films or multilayers. Theoretical calculations for each of the cases are
illustrated with numerical examples and compared with experimental results of
magnetic reflectivity from a Gd/Fe multilayer.
