Magnetic moment of inertia within the torque-torque correlation model

An essential property of magnetic devices is the relaxation rate in magnetic switching which strongly depends on the energy dissipation. This is described by the Landau-Lifshitz-Gilbert equation and the well known damping parameter, which has been shown to be reproduced from quantum mechanical calculations. Recently the importance of inertia phenomena have been discussed for magnetisation dynamics. This magnetic counterpart to the well-known inertia of Newtonian mechanics, represents a research field that so far has received only limited attention. We present and elaborate here on a theoretical model for calculating the magnetic moment of inertia based on the torque-torque correlation model. Particularly, the method has been applied to bulk itinerant magnets and we show that numerical values are comparable with recent experimental measurements. The theoretical analysis shows that even though the moment of inertia and damping are produced by the spin-orbit coupling, and the expression for them have common features, they are caused by very different electronic structure mechanisms. We propose ways to utilise this in order to tune the inertia experimentally, and to find materials with significant inertia dynamics.