  We study theories of gravity with non-minimal coupling between polarized
media with pole-dipole and quadrupole moments and an arbitrary function of the
space-time curvature scalar $R$ and the squares of the Ricci and Riemann
curvature tensors. We obtain the general form of the equation of motion and
show that an induced quadrupole moment emerges as a result of the curvature
tensor dependence of the function coupled to the matter. We derive the explicit
forms of the equations of motion in the particular cases of coupling to a
function of the curvature scalar alone, coupling to an arbitrary function of
the square of the Riemann curvature tensor, and coupling to an arbitrary
function of the Gauss-Bonnet invariant. We show that in these cases the extra
force resulting from the non-minimal coupling can be expressed in terms of the
induced moments.
