In metrological tasks, employing entanglement can quantitatively improve the precision of parameter estima- tion. However, susceptibility of the entanglement to decoherence fades this capability in the realistic metrology and limits ultimate quantum improvement. One of the most destructive decoherence-type noise is uncorrelated Markovian noise which commutes with the parameter-encoding Hamiltonian and is modelled as a semigroup dynamics, for which the quantum improvement is constrained to a constant factor. It has been shown [Phys. Rev. Lett. 109, 233601 (2012)] that when the noisy time evolution is governed by a local and non-semigroup dynamics (e.g., induced by an uncorrelated non-Markovian dephasing), emerging the Zeno regime at short times can result in the Zeno scaling in the precision. Here, by considering the impact of the correlated noise in metrol- ogy, we show that spatially correlated environments which lead to a nonlocal and non-semigroup dynamics can improve the precision of a noisy frequency measurement beyond the Zeno scaling. In particular, it is demon- strated that one can find decoherence-free subspaces and subsequently achieve the Heisenberg precision scaling for an approximated dynamics induced by spatially correlated environments.
