Orbital nature of spin magnetic moment

In view of the application of spintronics, it is important to understand the physical observable of the spin, i.e. its magnetic moment. We show by constructing a wave-packet in the upper bands of the Dirac equation that the spin magnetic moment (Bohr magneton) is a direct result of the self-rotation in the wave-packet. In this sense, an non-relativistic electron is really a rotating charged object, confirming the original speculation on the physical nature of the electron spin. In a Bloch band of a crystal, a wave-packet can acquire additional self-rotating orbital angular momentum, giving rise to a change of the spin magnetic moment and causing a modification of the g-factor from 2.