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An essential property of magnetic devices is the relaxation rate in magneticswitching which strongly depends on the energy dissipation and magnetic inertiaof the magnetization dynamics. Both parameters are commonly taken as aphenomenological entities. However very recently, a large effort has beendedicated to obtain Gilbert damping from first principles. In contrast, thereis no ab initio study that so far has reproduced measured data of magneticinertia in magnetic materials. In this letter, we present and elaborate on atheoretical model for calculating the magnetic moment of inertia based on thetorque-torque correlation model. Particularly, the method has been applied tobulk bcc Fe, fcc Co and fcc Ni in the framework of the tight-bindingapproximation and the numerical values are comparable with recent experimentalmeasurements. The theoretical results elucidate the physical origin of themoment of inertia based on the electronic structure. Even though the moment ofinertia and damping are produced by the spin-orbit coupling, our analysis showsthat they are caused by undergo different electronic structure mechanisms.

Magnetic moment of inertia within the breathing model