  In metrological tasks, employing entanglement can quantitatively improve the
precision of parameter estimation. 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. \textbf{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 metrology, 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 demonstrated that one can find decoherence-free subspaces and
subsequently achieve the Heisenberg precision scaling for an approximated
dynamics induced by spatially correlated environments.

Quantum Physics