  We report an extended family of spin textures in coexisting modes of
zero-dimensional polariton condensates spatially confined in tunable open
microcavity structures. The coupling between photon spin and angular momentum,
which is enhanced in the open cavity structures, leads to new eigenstates of
the polariton condensates carrying quantised spin vortices. Depending on the
strength and anisotropy of the cavity confinement potential and the strength of
the spin-orbit coupling, which can be tuned via the excitonic/photonic
fractions, the condensate emissions exhibit either spin-vortex-like patterns or
linear polarization, in good agreement with theoretical modelling.
