Vortices in rotating superfluidHe3-A

We investigate the properties of rotating ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$ in the absence of a magnetic field. For fast rotating ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$ ($\Omega \gg {\Omega }_{c1\mathrm{}}$) we find a transition from the type-I lattice of nonsingular vortex textures discussed by Fujita et al. to a lattice of singular $2\pi$ vortex textures with polar cores at a rotation speed of $\Omega =\left(\frac{\hslash }{2m_3}\right){\left(3\mathrm{}{L}_D\right)}^{-2\mathrm{}}\simeq 32$ rad/sec for $T\simeq T_c$. A second transition to a lattice of singular vortices occurs at a much higher rotational speed $\Omega \simeq {10}^{-1\mathrm{}}{\Omega }_{c2\mathrm{}}$. We also discuss ion mobility and sound attenuation in these vortex textures.