Theory of the elastic and inelastic scattering of light by magnetic crystals. II. Second‐order processes

The second quantization of the magneto‐optical interactions in ferromagnetic crystals is extended to second‐order processes. From the electric and magnetic dipole transitions induced by an incident radiation, the evolution of the electromagnetic field is analysed in the cases of bi‐gyrotropic and quadratic magneto‐optical materials. The physical and analytical relations between the elastic (linear magnetic birefringence) and inelastic (two‐magnon Raman effects) scatterings are derived from the second‐order magneto‐optical Hamiltonians. It is shown that the two‐magnon Raman susceptibility is proportional to the second power of the specific linear magnetic birefringence. In isotropic media the second‐order magneto‐optical interactions may be separated in an isotropic (or scalar) part and in an anisotropic (or tensorial) part. From the corresponding Hamiltonians the polarization rules are deduced for the second‐order inelastic scatterings. In ferrites and orthoferrites the first‐ and second‐order magneto‐optical constants may have equivalent values. As supported by experiments the influence of the quadratic magneto‐optical interactions on the first‐order inelastic scattering is shown from the magneto‐optical polarization and Hamiltonians. The one‐magnon Stokes component may be higher than the anti‐Stokes component when the polarization of the incident photons is parallel to the dc magnetization. The opposite result is obtained with light polarized perpendicular to the dc magnetization. The one‐magnon Raman Hamiltonians and susceptibilities modified by the quadratic effects are derived from the optical polarization and compared with experimental data.