  We present a method to detect bipartite entanglement based on
number-phase-like uncertainty relations in split spin ensembles. First, we
derive an uncertainty relation that plays the role of a number-phase
uncertainty for spin systems. It is important that the relation is given with
well-defined and easily measurable quantities, and that it does not need
assuming infinite dimensional systems. Based on this uncertainty relation, we
show how to detect bipartite entanglement in an unpolarized Dicke state of many
spin-1/2 particles. The particles are split into two subensembles, then
collective angular momentum measurements are carried out locally on the two
parts. First, we present a bipartite Einstein-Podolsky-Rosen (EPR) steering
criterion. Then, we present an entanglement condition that can detect bipartite
entanglement in such systems. We demonstrate the utility of the criteria by
applying them to a recent experiment given in K. Lange et al. [Science 360, 416
(2018)] realizing a Dicke state in a Bose-Einstein condensate of cold atoms, in
which the two subensembles were spatially separated from each other. Our
methods also work well if split spin-squeezed states are considered. We show in
a comprehensive way how to handle experimental imperfections, such as the
nonzero particle number variance including the partition noise, and the fact
that, while ideally BECs occupy a single spatial mode, in practice the
population of other spatial modes cannot be fully suppressed.
