Sum rules for electron energy loss near edge spectra

We derive four sum-rule expressions for spectra measured in electron energy loss near edge structure experiments. These sum rules permit the determination of spin and orbital magnetic moments, spin-orbit interaction, and number of states, analogously to the sum rules of x-ray magnetic circular dichroism. The derivation of the sum rules is based on dynamical electron diffraction theory and the properties of the mixed dynamic form factor. The accuracy of the sum rules is tested by a complete evaluation of the thickness-dependent electron energy loss spectra for iron, cobalt, and nickel crystals. We find that the sum rules reproduce both spin and orbital moments with very good accuracy. Our results provide a foundation for the use of the energy loss magnetic chiral dichroism technique as a quantitative probe of element-specific magnetic properties.