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Spin correlations and entanglement in partially magnetised ensembles of fermions

We show that the singlet fraction $p_s$ and total magnetisation (or polarisation) $m$ can bound the minimum concurrence in an ensemble of spins. We identify $p_s > (1-m^2)/2$ as a sufficient and tight condition for bipartite entanglement. Our proof makes no assumptions about the state of the system or symmetry of the particles, and can therefore be used as a witness for spin entanglement between fermions. We discuss the implications for recent experiments in which spin correlations were observed, and the prospect to study entanglement dynamics in the demagnetisation of a cold Fermi gas.