  We study squeezing of the spin uncertainties by quantum non-demolition (QND)
measurement in non-polarized spin ensembles. Unlike the case of polarized
ensembles, the QND measurements can be performed with negligible back-action,
which allows, in principle, perfect spin squeezing as quantified by [G. Toth et
al., Phys. Rev. Lett. 99, 250405 (2007)]. The generated spin states approach
many-body singlet states, and contain a macroscopic number of entangled
particles, even when individual spin is large. We introduce the Gaussian
treatment of unpolarized spin states and use it to estimate the achievable spin
squeezing for realistic experimental parameters. Our proposal might have
applications for magnetometry with a high spatial resolution or quantum
memories storing information in decoherence free subspaces.
