Theory of the zero-bias anomaly in magnetic tunnel junctions: Inelastic tunneling via impurities

Using the closed-time path-integral approach, we nonperturbatively study inelastic tunneling of electrons via magnetic impurities in the barrier accompanied by phonon emission in a magnetic tunnel junction. The spectrum density of phonon emission is found to show a power-law infrared singularity ∼ω−(1−g) with g the dimensionless electron-phonon coupling. As a consequence, the tunneling conductance G(V) increases with bias voltage ∣V∣ as G(V)−G(0)∼∣V∣2g, exhibiting a discontinuity in slope at V=0 for g⩽0.5. This theory can reproduce both cusplike and noncusplike features of the zero-bias anomaly of tunneling resistance and magnetoresistance widely observed in experiments.