  The Landau-Lifshitz-Gilbert (LLG) equation, used to model magneto-dynamics in
ferromagnets, tacitly assumes that the angular momentum associated with spin
precession can relax 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 inertia effects. The consensus, however, seems to
be that such effects would be unimportant in slow magneto-dynamics that take
place over time scales much longer that the relaxation time of the angular
momentum, 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 spin
inertia even in slow magneto-dynamics. 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 field strength is close to the threshold value
for 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 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 holds
sway. Spin inertia increases the error probability, which makes the switching
more error-prone. This has vital technological significance because it relates
to the reliability of magnetic logic and memory.
