Multiple Half-Quantum Vortices in Rotating Superfluid $^3$He

Half-quantum votices and ordinary vortices in a rotating thin film superfluid $^3$He under a strong magnetic field are considered. It is shown that $2n+1$ half-quantum vortices interpolates between $n$ singular vortices and $n+1$ singular vortices as the angular velocity is changed. The phase diagram of the vortex configurations in the angular velocity-magnetic field space is obtained for a paramagnon parameter $\delta=0.05$.