  We investigate the magnetization processes of a standard Ginzburg-Landau
model for chiral p-wave superconducting states in an applied magnetic field. We
find that the phase diagram is dominated by triangular lattices of doubly
quantized vortices. Only in close vicinity to the upper critical field, the
lattice starts to dissociate into a structure of single-quanta vortices. The
degeneracy between states with opposite chirality is broken in a nonzero field.
If the magnetization starts with an energetically unfavorable chirality, the
process of chirality-inversion induced by the external magnetic field results
in the formation of a sequence of metastable states with characteristic
magnetic signatures that can be probed by standard experimental techniques.
