The inverted hysteresis loop is claimed to be possible, in an exchange
-coupled bilayer, when a magnetically soft material is affected by the
demagnetizing field of the hard material. These demagnetizing fields
are caused by the charge on the surfaces, neglected in all the theorie
s that assume a strictly one-dimensional structure, in an infinite mat
erial. For these one-dimensional models, an analytic solution is prese
nted, which reduces the computation from a numerical integration of a
set of differential equations to the solution of an algebraic, transce
ndental equation (which contains elliptic functions) for fitting only
the boundary conditions. It may then be feasible to introduce at least
an approximation for the demagnetizing effect of the surfaces in a fi
nite sample.