  This is an analytical study of pinning and spontaneous vortex phase is a
system consisting of a superconducting thin film pierced by a long
ferromagnetic columnar defect of finite radius $R$. The magnetic fields,
screening currents, energy and pinning forces for this system are calculated.
The interaction between the magnetic field of vortices and the magnetization
outside the plane of the film and its close proximity enhances vortex pinning
significantly. Spontaneous vortex phase appears when the magnetization of the
columnar defect is increased above a critical value. Transitions between phases
characterized by different number of flux quanta are also studied. These
results are generalized to the case when the superconductor is pierced by an
array of columnar defects.
