A close look at antiferromagnetic phase boundary in multidimensional phase diagram of electron-doped copper oxide

In copper-oxide superconductors, spin fluctuations play a predominant role in electron pairing with electron dopants yet composite orders veil the nature of superconductivity for hole-doped family. However, in electron-doped ones the ending point of AFM is still in controversy for different probes or its sensitivity to oxygen content. Here, by carefully tuning the oxygen content, a systematic study of Hall signal and magnetoresistivity up to 58 Tesla on optimally doped La$_{2-x}$Ce$_{x}$CuO$_{4\pm \delta }$ (x $=$ 0.10) thin films identifies two characteristic temperatures at 62.5 K (error is 7.5 K) and 25 K (error is 5 K). The former is quite robust whereas the latter becomes flexible with increasing magnetic field, thereby linked to two- and three-dimensional AFM, evident from the multidimensional phase diagram as a function of oxygen as well as Ce dopants. Consequently, the observation of extended AFM phase in contrast to $\mu $SR probe corroborates an elevated critical doping in field, providing an unambiguous picture to understand the interactions between AFM and superconductivity.