Bias-voltage dependence of the magneto-resistance in ballistic vacuum tunneling: Theory and application to planar Co(0001) junctions

Motivated by first-principles results for jellium and by surface-barrier shapes that are typically used in electron spectroscopies, the bias voltage in ballistic vacuum tunneling is treated in a heuristic manner. The presented approach leads in particular to a parameterization of the tunnel-barrier shape, while retaining a first-principles description of the electrodes. The proposed tunnel barriers are applied to Co(0001) planar tunnel junctions. Besides discussing main aspects of the present scheme, we focus in particular on the absence of the zero-bias anomaly in vacuum tunneling.