In this paper we establish a model explaining the experimentally obser
ved anomalous enhanced coercivity of granular magnetic solids and thin
films or multilayers that have pinned surface magnetic moments. We al
so predict a normalized critical length for the material, above which
the magnetic reversal mechanism is coercive and below which it occurs
by a switching mode which is non-energy dissipative. The model used as
sumes a dependence of the magnetization along the small dimension of t
he granule or the depth of the layer. The contribution of the exchange
term is obtained using the Landau semi-classical, formalism, and thus
we do away with the mean field approximation. The coercivity is defin
ed in such a manner as to retain its nonreversible nature. Results are
presented in dimensionless units. When applied to cobalt and iron, th
ey show coercivities larger than the theoretical maximum obtainable wi
thout pinning in accord with experimental data.