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 $\left({\chi }^m\right)$ and electric $\left({\chi }^e\right)$ 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 ${\chi }^m$ and ${\chi }^e$. The estimated theoretical magnitudes of these quantities are in reasonable agreement with the observed magnitudes.