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The Landau-Lifshitz-Gilbert (LLG) equation, used to model magneto-dynamics inferromagnets, tacitly assumes that the angular momentum associated with spinprecession can relax instantaneously when the real or effective magnetic fieldcausing the precession is turned off. This neglect of "spin inertia" isunphysical and would violate energy conservation. Recently, the LLG equationwas modified to account for inertia effects. The consensus, however, seems tobe that such effects would be unimportant in slow magneto-dynamics that takeplace over time scales much longer that the relaxation time of the angularmomentum, which is typically few fs to perhaps ~100 ps in ferromagnets. Here,we show that there is at least one very serious and observable effect of spininertia even in slow magneto-dynamics. It involves the switching errorprobability associated with flipping the magnetization of a nanoscaleferromagnet with an external agent, such as a magnetic field. The switching maytake ~ns to complete when the field strength is close to the threshold valuefor switching, which is much longer than the angular momentum relaxation time,and yet the effect of spin inertia is felt in the switching error probability.This is because the ultimate fate of a switching trajectory, i.e. whether itresults in success or failure, is influenced by what happens in the first fewps of the switching action when nutational dynamics due to spin inertia holdssway. Spin inertia increases the error probability, which makes the switchingmore error-prone. This has vital technological significance because it relatesto the reliability of magnetic logic and memory.

An observable effect of spin inertia in slow magneto-dynamics: Increase of the switching error rates in nanoscale ferromagnets