We present a theoretical approach to the problem associated with the a
nomalous coercivity observed in granular magnetic solids such as iron
or cobalt embedded in an insulating medium and to amorphous multilayer
thin films. In this paper we show that if the magnetic moments at the
granular surface or multilayer interface are pinned, such enhanced co
ercivity is predictable. The model used assumes a one-dimensional depe
ndence of the magnetization (along the length of the granule or the de
pth of the layer). That dimension is taken to be small to inhibit the
appearance of domain walls parallel to that direction. We consider mat
erials whose energy is dominated by a Zeeman term, an anisotropy term,
a demagnetization term, and an exchange term. The exchange term is de
termined with the use of the Landau semiclassical approximation, and t
hus we do away with the mean-field approximation. The coercivity is de
fined in such a manner as to retain its nonreversible nature. Results
are presented in dimensionless units. When applied to cobalt and iron,
they give values in accordance with experimental data.