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Recent progress in the field of magnetic Compton scattering is reviewed and new momentum-space information about electronic states in magnetic materials is emphasized. Theoretical derivation of the magnetic Compton scattering cross section is made within the framework of the nonrelativistic Hamiltonian of electrons in the electromagnetic field. Discussion on the orbital-spin contribution to the magnetic Compton scattering is also included as a Compton limit. The feasibility of the magnetic Compton scattering experiment using circularly polarized hard synchrotron radiation is demonstrated by many recent experimental results.

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