  Standard approaches to magneto-mechanical interactions in thermal magnetic
crystalline solids involve Landau functionals in which the lattice anisotropy
and the resulting magnetization easy axes are taken explicitly into account. In
glassy systems one needs to develop a theory in which the amorphous structure
precludes the existence of an easy axis, and in which the constituent particles
are free to respond to their local amorphous surroundings and the resulting
forces. We present a theory of all the mixed responses of an amorphous solids
to mechanical strains and magnetic fields. Atomistic models are proposed in
which we test the predictions of magnetostriction for both bulk and nano-film
amorphous samples. The application to nano-films with emergent self-affine free
interfaces requires a careful definition of the film 'width' and its change due
to the magnetostriction effect.
