  We investigate sensing of magnetic fields using quantum spin chains at finite
temperature and exploit quantum phase crossovers to improve metrological bounds
on the estimation of the chain parameters. In particular, we analyze the $ XX $
spin chain and show that the magnetic sensitivity of this system is dictated by
its adiabatic magnetic susceptibility, which scales extensively (linearly) in
the number of spins $ N $. Next, we introduce an iterative feedforward protocol
that actively exploits features of quantum phase crossovers to enable
super-extensive scaling of the magnetic sensitivity. Moreover, we provide
experimentally realistic observables to saturate the quantum metrological
bounds. Finally, we also address magnetic sensing in the Heisenberg $ XY $ spin
chain.
