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

The celebrated Landau-Lifshitz-Gilbert (LLG) equation governing magneto-dynamics in ferromagnets tacitly assumes that the angular momentum associated with spin precession relaxes instantaneously when the real or effective magnetic field causing the precession is turned off. This neglect of “spin inertia” is unphysical and would violate energy conservation. Recently, the LLG equation was modified to account for spin inertia and revealed that it gives rise to nutation dynamics lasting for the first few fs to tens of ps at the start of the magnetodynamics in most ferromagnets. Since the nutation is so ephemeral, it was believed that its effect, if any, will be imperceptible in slow magnetodynamics that lasts over ~ns. Here, we show that there is at least one very serious and observable effect of spin inertia even in slow magneto-dynamics and it involves the switching error probability associated with flipping the magnetization of a nanoscale ferromagnet with an external agent, such as a magnetic field. The switching may take ~ns to complete when the magnetic field strength is close to the threshold value for switching 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 it results in success or failure, is influenced by what happens in the first few ps of the switching action when nutational dynamics due to spin inertia is dominant. This is reminiscent of chaos theory where final outcomes are very sensitive to initial conditions. Spin inertia increases the switching error probability, which makes the switching more error-prone. This has important technological ramifications for magnetic logic and memory which have little tolerance for switching errors.