  We report on the non-linear in-plane electrical transport in coherently grown
[La0.7Sr0.3MnO3/SrTiO3] multilayers with ultrathin (< 3 nm) single layers.
Current-induced switching of the conductance, with low conductance at larger
currents, is demonstrated. The conductance switching is modified under a
magnetic field, resulting in an extremely large magnetoresistance of negative,
or in a special case even positive, sign. Our results suggest a percolative
nature of transport where a large local current density gives rise to a
spin-polarizing and a thermal effect of current.
