  Magnetized ferromagnetic disks or wires support strong inhomogeneous fields
in their borders. Such magnetic fields create an effective potential, due to
Zeeman and diamagnetic contributions, that can localize charge carriers. For
the case of two-dimensional transition metal dichalcogenides, this potential
can valley-localize excitons due to the Zeeman term, which breaks the valley
symmetry. We show that the diamagnetic term is negligible when compared to the
Zeeman term for monolayers of transition metal dichalcogenides. The latter is
responsible for trapping excitons near the magnetized structure border with
valley-dependent characteristics, in which, for one of the valleys, the exciton
is confined inside the disk, while for the other, it is outside. This spatial
valley separation of exciton can be probed by circularly polarized light, and
moreover, we show that the inhomogeneous magnetic field magnitude, the
dielectric environment, and the magnetized structure parameters can tailor the
spatial separation of the exciton wavefunctions.
