Vortices in polar and $\beta$ phases of ${}^3$He

Recently new topological phase of superfluid ${}^3$He has been discovered – the $\beta$ phase, which is obtained by strong polarization of the nematic polar phase. We consider half-quantum vortices, which are formed in rotating cryostat, and discuss the evolution of the vortex lattice in the process of the transition from the polar phase to the $\beta$-phase via the spin-polarized polar phase.