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${}_4$.