  Spin squeezing is a form of entanglement that reshapes the quantum projection
noise to improve measurement precision. Here, we provide numerical and analytic
evidence for the following conjecture: any Hamiltonian exhibiting finite
temperature, easy-plane ferromagnetism can be used to generate scalable spin
squeezing, thereby enabling quantum-enhanced sensing. Our conjecture is guided
by a connection between the quantum Fisher information of pure states and the
spontaneous breaking of a continuous symmetry. We demonstrate that
spin-squeezing exhibits a phase diagram with a sharp transition between
scalable squeezing and non-squeezing. This transition coincides with the
equilibrium phase boundary for XY order at a finite temperature. In the
scalable squeezing phase, we predict a sensitivity scaling that lies in between
the standard quantum limit and the scaling achieved in all-to-all coupled
one-axis twisting models. A corollary of our conjecture is that short-ranged
versions of two-axis twisting cannot yield scalable metrological gain. Our
results provide insights into the landscape of Hamiltonians that can be used to
generate metrologically useful quantum states.
