Suppressing the Kibble-Zurek mechanism by a symmetry-violating bias

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.