  The weak ferromagnetism present in insulating La_{2}CuO_4 at low doping leads
to a spin flop transition, and to transverse (interplane) hopping of holes in a
strong external magnetic field. This results in a dimensional crossover 2D
$\to$ 3D for the in-plane transport, which in turn leads to an increase of the
hole's localization length and increased conduction. We demonstrate
theoretically that as a consequence of this mechanism, a frequency-dependent
jump of the in-plane ac hopping conductivity occurs at the spin flop
transition. We predict the value and the frequency dependence of the jump.
Experimental studies of this effect would provide important confirmation of the
emerging understanding of lightly doped insulating La_{2-x}Sr_xCuO_4.
