We show that, due to the weak ferromagnetism of La_(2-x)Sr_xCuO_4, an external magnetic field leads to a dimensional crossover from two to three dimensions 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 Neel phase of La_(2_x)Sr_xCuO_4.
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