4H-SiC metal-oxide-semiconductor field-effect transistors have a substantially lower effective channel mobility than silicon-based counterparts. Nitric oxide annealing has been primarily utilized to provide an order of magnitude improvement in the effective channel mobility. Barium interface layers provide an additional doubling of the mobility over nitric oxide anneals. However, barium-based 4H-SiC transistors show more susceptibility to oxide leakage. We have investigated the atomic scale mechanisms of oxide leakage in barium-based devices with electrically detected magnetic resonance. We observe the presence of E' centers within the oxides of modestly stressed devices. Our measurements directly demonstrate that these E' centers are important and very likely the dominating cause of these leakage currents. In conventional silicon-based devices, E' centers are known to be important defects in reliability issues such as bias temperature instabilities and stress-induced leakage currents.