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We investigate the magnetization processes of a standard Ginzburg-Landaumodel for chiral p-wave superconducting states in an applied magnetic field. Wefind that the phase diagram is dominated by triangular lattices of doublyquantized vortices. Only in close vicinity to the upper critical field, thelattice starts to dissociate into a structure of single-quanta vortices. Thedegeneracy between states with opposite chirality is broken in a nonzero field.If the magnetization starts with an energetically unfavorable chirality, theprocess of chirality-inversion induced by the external magnetic field resultsin the formation of a sequence of metastable states with characteristicmagnetic signatures that can be probed by standard experimental techniques.

Lattices of double-quanta vortices and chirality inversion in $p_x+ip_y$ superconductors