Parameter estimation with Dzyaloshinskii-Moriya interaction under external magnetic fields

We study the effects of external magnetic fields on the precision of parameter estimation with thermal entanglement of two spins in XX model, in the presence of Dzyaloshinskii-Moriya (DM) interaction. Although DM interaction excites but external magnetic fields usually decrease quantum mechanical properties of spin systems such as entanglement, we show by calculating the quantum Fisher information that not only DM interaction D but also homogeneous magnetic field B can increase the precision of parameter estimation, overwhelming the destructive effects of thermalization. We also show that inhomogeneous magnetic field b increases (decreases) the precision of parameter estimation if it is less (greater) than D