Negative Hopping Magnetoresistance and Dimensional Crossover in Lightly   Doped Cuprate Superconductors
  We show that, due to the weak ferromagnetism of La$_{2-x}$Sr$_x$CuO$_4$, an external magnetic field leads to a dimensional crossover 2D $\to$ 3D for the in-plane transport. The crossover results in an increase of the hole's localization length and hence in a dramatic negative magnetoresistance in the variable range hopping regime. This mechanism quantitatively explains puzzling experimental data on the negative magnetoresistance in the N\'eel phase of La$_{2-x}$Sr$_x$CuO$_4$. 
Valeri N. Kotov, Oleg P. Sushkov, M. B. Silva Neto, L. Benfatto, A. H.   Castro Neto