Microscopic analysis of the stability of half-quantum vortices in $p_x + ip_y$ superfluids in an annular geometry.*

We present a microscopic analysis of the thermodynamic stability of a half-quantum vortex (HQV) in $p_x + i p_y$ variant of equal-spin-pairing state which, under suitable conditions, is believed to be realized in $\rm Sr_2RuO_4$ and $^3$He-A. Our approach is based on a description of the HQV in terms of a BCS-like wave function with a spin-dependent boost. Stability criterion is found by comparing energies of half- and full-quantum vortices with appropriate account taken of Fermi liquid corrections. While we confirm earlier phenomenological findings by Suk Bum Chung et al.~(2007) for the stability of the HQV in the annular geometry, we also predict a novel feature that the HQV, if exists, should be accompanied by a non-zero spin polarization of the system.