Anisotropic low-temperature in-plane magnetoresistance in electron doped Nd$_{2-x}$Ce$_x$CuO$_{4+\delta}$

Nominally electron doped antiferromagnetic tetragonal nonsuperconducting Nd$_{2-x}$Ce$_x$CuO$_{4+\delta}$ ($x= 0.12$) has been shown to manifest strong angular dependence of the in-plane magnetoresistance on the orientation of the external magnetic field within the $ab$ plane in many aspects similar to that observed in hole doped YBa$_{2}$Cu$_3$O$_{7-\delta}\,$ and La$_{2-x}$Sr$_{x}$CuO$_{4}$. Specific fourfold angular magnetoresistance anisotropy amounting to several percents was observed in oxygen annealed films at low temperatures and in external magnetic field up to 5.5 T. Strong temperature dependence and fourfold symmetry observed in our sample points to a specific role of rare-earth (Nd) ions in magnetoresistance anisotropy. At low temperature $T=1.4\,$K we observed the unusual transformation of magnetoresistance response with increasing the external magnetic field which seems to be a manifestation of a combined effect of a crossover between first and second order spin-flop transitions and a field-dependent rare-earth contribution to quasiparticle magnetotransport.