  The trapping of excitons in a semiconductor quantum well due to a circular
symmetric nonhomogeneous magnetic field is studied. The effect of the spin
state of the exciton on its trapping energy is analyzed, and the importance of
the interaction of the orbital and spin Zeeman effect as compared to the
diamagnetic term in the exciton Hamiltonian is emphasized. Magnetic field
profiles are considered, which can experimentally be created through the
deposition of ferromagnetic disks on top of a semiconductor heterostructure.
This setup gives rise to a magnetic dipole type of profile in the $xy$ plane of
the exciton motion. We find that the spin direction of the exciton influences
its localization by changing the confinement region in the effective potential.
The exciton confinement increases with magnetic field intensity, and this is
more pronounced when the exciton g-factor is different from zero. The numerical
calculations are performed for GaAs/Al$_{x}$Ga$_{1-x}$As quantum wells and we
show that it open up a new realistic path for experiments designed to probe
exciton trapping in semiconductors.
