Interference of second harmonics due to electric and magnetic dipoles in antiferromagneticCr2O3

The second-harmonic (SH) spectra arising from magnetic- and electric-dipole contributions and the interference of these two channels are analyzed for antiferromagnetic ${\mathrm{Cr}}_2{\mathrm{O}}_3.$ A microscopic model which comprises boundary conditions and local-field corrections for electromagnetic waves is introduced for the nonlinear nonreciprocal optical responses. Effects of cross relaxation between the different ${\mathrm{Cr}}^{3+}$ $3d$ levels are also taken into account. Among these dissipative processes, the local-field correction for the magnetic field seems to be the most important. The origin of this correction is found to come from the presence of a coupling of orbital angular momenta of two magnetic ${\mathrm{Cr}}^{3+}$ ions which makes possible the excitation transfer between them. Only through the inclusion of this effect are the phases of the magnetic and electric susceptibilities appreciably different from each other, leading thus to the interference effect of the two channels in agreement with experimental observations.