Inertial effects in ultrafast spin dynamics

The dynamics of magnetic moments consists of a precession around the magnetic field direction and a relaxation towards the field to minimize the energy. While the magnetic moment and the angular momentum are conventionally assumed to be parallel to each other, at ultrafast time scales their directions become separated due to inertial effects. The inertial dynamics gives rise to additional high-frequency modes in the excitation spectrum of magnetic materials. Here, we review the recent theoretical and experimental advances in this emerging topic and discuss the open challenges and opportunities in the detection and the potential applications of inertial spin dynamics. •Magnetic moment and angular momentum are not parallel due to inertial effects.•The inertial dynamics gives rise to high-frequency modes in magnetic materials.•We review the recent theoretical and experimental advances in inertial spin dynamics.