Influence of spin-orbit coupling on magneto-optical Kerr effect of a magnetic insulator

By using atomic energy-level transition model for local electrons, microscopic quantum expressions of the magneto-optical Kerr rotation (MOKR) are derived, taking into account both spin exchange splitting and spin-orbit coupling interaction. Valiation of the MOKR with the coupling constants of atomic ground state or excited states is investigated for the four-level transition case. Results show that MOKR is not proportional to the spin-orbit coupling splitting energy. It is advantageous to the enhancement of MOKR when the spin-orbit coupling constant of the atomic ground-states is positive or that of the excited states is negative.