Magnetoelectric and second-harmonic spectra in antiferromagneticCr2O3

We present a microscopic model to understand the magnetoelectric and second-harmonic spectra of ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$ and the interference effect between the magnetic $({\ensuremath{\chi}}^{m})$ and electric $({\ensuremath{\chi}}^{e})$ second-order optical polarizations. The spin-orbit interaction and the crystalline fields of correct symmetry around the ${\mathrm{Cr}}^{3+}$ ion, i.e., the axial and twisted crystalline field of ${C}_{3}$ symmetry, are treated as perturbation on the trigonal states of the ${d}^{3}$ system of ${\mathrm{Cr}}^{3+}$. By these treatments we attempt to describe the observed phenomena associated with the transitions between ${}^{4}{A}_{2g}$ and ${}^{4}{T}_{2g}$ states in ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$. It is possible to reproduce the observed spectra of the polarization rotation and ellipticity, and the second-harmonic generation spectra described by the nonlinear susceptibilities ${\ensuremath{\chi}}^{m}$ and ${\ensuremath{\chi}}^{e}$. The estimated theoretical magnitudes of these quantities are in reasonable agreement with the observed magnitudes.