Primary and Secondary Nucleation of the Transition between the $\mathit{A}$ and $\mathit{B}$ Phases of Superfluid ${}^3\mathrm{He}$

We have studied nucleation in superfluid ${}^3\mathrm{He}$ across the $A-B$ phase transition driven by a magnetic field, in a controllable environment at very low temperatures. Both $B\to A$ and $A\to B$ secondary nucleation appear to be governed by the survival of pockets of the new phase trapped at surfaces. We find that, at fields near $B_{\mathrm{AB}}$, primary $A\to B$ nucleation cannot be triggered by ionizing or neutron irradiation even at very high intensities. In our cell primary $A\to B$ nucleation can only be triggered externally by mild mechanical shock.