  The formation of topological defects in continuous phase transitions is
driven by the Kibble-Zurek mechanism. Here we study the formation of single-
and half-quantum vortices during transition to the polar phase of $^3$He in the
presence of a symmetry-breaking bias provided by the applied magnetic field. We
find that vortex formation is suppressed exponentially when the length scale
associated with the bias field becomes smaller than the Kibble-Zurek length. We
thus demontrate an experimentally feasible shortcut to adiabaticity -- an
important aspect for further understanding of phase transitions as well as for
engineering applications such as quantum computers or simulators.
