Negative correlation between the linear and the nonlinear conductance in magnetic tunnel junctions

The current-voltage ($IV$) characteristics beyond the linear response regime of magnetic tunnel junction (MTJ) is systematically investigated. We find a clear negative correlation between the two coefficients to characterize the linear ($I\ensuremath{\propto}\phantom{\rule{0.16em}{0ex}}V$) and the lowest-order nonlinear ($I\ensuremath{\propto}\phantom{\rule{0.16em}{0ex}}{V}^{3}$) currents, which holds regardless of the temperature and the thickness of the tunnel barrier. This observation cannot simply be explained by the standard tunneling model such as the Brinkman model, suggesting a mechanism intrinsic to MTJ. We propose a phenomenological model based on the Jullire model that attributes the observed negative correlation to the spin-flip tunneling assisted by a magnon. These results suggest a fundamental law between the linear and the nonlinear response of MTJ.