  Spin dynamics is usually described as massless or, more precisely, as free of
inertia. Recent experiments, however, found direct evidence for inertial spin
dynamics. In turn, it is necessary to rethink the basics of spin dynamics.
Focusing on a macrospin in an environment (bath), we show that the spin-to-bath
coupling gives rise to spin inertia. This bath-induced spin inertia appears
universally from all the high-frequency bath modes. We expect our results to
provide new insights into recent experiments on spin inertia. Moreover, they
indicate that any channel for spin dissipation should also be accompanied by a
term accounting for bath-induced spin inertia. As an illustrative example, we
consider phonon-bath-induced spin inertia in a YIG/GGG stack.
