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$$propto$$V$) and the lowest-order nonlinear ($I$$propto$$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 Julliere 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.
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