Hall resistivity correlations in disordered electron-doped Nd$_{2-x}$Ce$_x$CuO$_{4+\delta}$ films

The resistivity tensor correlations $\rho_{xy}$($B$)$\sim$ $[\rho_{xx}(B)]^\beta$ for the mixed state magnetic field dependencies of the resistivity tensor of electron-doped Nd$_{2-x}$Ce$_x$CuO$_{4+\delta}$/SrTiO$_3$ single crystal films near the antiferromagnetic (AF) - superconducting (SC) phase transition and with varying degree of disorder ($\delta$) were studied. The decrease of $\beta$ from 1.2$\pm$0.2 at $x$ = 0.14 to 0.6$\pm$0.1 at $x$ = 0.15 points out on the evidence of the change from the anisotropic $s$ - wave to the $d$ - wave pairing symmetry in the external magnetic field at the transition from underdoped to optimally doped region. Peculiarities of the power law dependence of the vortex motion in the mixed state can be connected with some features of the nonstoichiometric disorder in layered electron-doped superconductors.