Anomalous In-plane Magnetoresistance of Electron-doped Cuprate La$_{\mathrm{2-}}_{x}$Ce$_{x}$CuO$_{\mathrm{4-}}_{\delta }$

We report the systematic in-plane magnetoresistance (MR) measurements on electron-doped cuprate La$_{\mathrm{2-}}_{x}$Ce$_{x}$CuO$_{\mathrm{4-}}_{\delta }$ thin films as a function of doping and oxygen contents in the magnetic field up to 14 T. A crossover from negative magnetoresistance ($n$-MR) to positive magnetoresistance ($p$-MR) occurs between $x=$ 0.07 and 0.08, corresponding to the boundary of long-range antiferromagnetic order determined by $\mu $SR [Saadaoui, H.\textit{ et al.} \textit{Nature Commun.} \textbf{6}, 6041 (2015)]. With increasing the doping level, the $p$-MR effect becomes weaker and is hardly discernable at $x=$ 0.15, in accordance with the boundary of two-dimensional antiferromagnetic order [K. Jin, \textit{et al}. \textit{Phys. Rev. B.} 80, 012501 (2009), \textit{Nature }476,73(2011)]. At $x=$ 0.15, the as-grown samples show $n$-MR, whereas the optimally annealed ones display $p$-MR, similar to that in NCCO [J. Wu \textit{et al}. \textit{Phys. Rev. Lett.} 73, 1291(1994)] and PCCO [J. Higgins \textit{et al}. \textit{Phys. Rev. B.} 73,104510(2006)]. We also find linear MR at $x=$ 0.06 and $x=$ 0.1, and the plausible origins will be discussed.