Ferromagnetic tunneling junctions at low voltages: elastic versus inelastic scattering at $T=0K$

In this paper we analyze different contributions to the magnetoresistance of magnetic tunneling junctions at low voltages. A substantial fraction of the resistance drop with voltage can be ascribed to variations of the density of states and the barrier transmission with the bias. However, we found that the anomaly observed at zero bias and the magnetoresistance behavior at very small voltages, point to the contribution of inelastic magnon-assisted tunneling. The latter is described by a transfer parameter $T^J$, which is one or two orders of magnitude smaller than $T^d$, the direct transmission for elastic currents. Our theory is in excellent agreement with experimental data, yielding estimated values of $T^J$ which are of the order of $T^d$ / $T^J$ ~ 40.