There is compelling evidence that sleep contributes to the long-term consolidation of new memories. This function of sleep has been linked to slow (<1 Hz) potential oscillations, which predominantly arise from the prefrontal neocortex and characterize slow wave sleep. However, oscillations in brain potentials are commonly considered to be mere epiphenomena that reflect synchronized activity arising from neuronal networks, which links the membrane and synaptic processes of these neurons in time. Whether brain potentials and their extracellular equivalent have any physiological meaning per se is unclear, but can easily be investigated by inducing the extracellular oscillating potential fields of interest. Here we show that inducing slow oscillation-like potential fields by transcranial application of oscillating potentials (0.75 Hz) during early nocturnal non-rapid-eye-movement sleep, that is, a period of emerging slow wave sleep, enhances the retention of hippocampus-dependent declarative memories in healthy humans. The slowly oscillating potential stimulation induced an immediate increase in slow wave sleep, endogenous cortical slow oscillations and slow spindle activity in the frontal cortex. Brain stimulation with oscillations at 5 Hz--another frequency band that normally predominates during rapid-eye-movement sleep--decreased slow oscillations and left declarative memory unchanged. Our findings indicate that endogenous slow potential oscillations have a causal role in the sleep-associated consolidation of memory, and that this role is enhanced by field effects in cortical extracellular space.