Dielectric, magnetic, magneto-optical and nonlinear optical properties of ferroelectric ferromagnetic semiconductor BiMnO$_{3}$ from first-principles calculations

BiMnO$_{3}$ is a biferroic (ferroelectric and ferromagnetic) semiconductor, and hence a member of the family of multiferroic materials. In order to gain a full understanding of its interesting properties such as biferroic behavior, we have calculated from first-principles the electronic structure, exchange coupling, linear and non-linear optical susceptibilities as well as magneto-optical Kerr rotation of BiMnO$_{3}$. The calculations are based on density functional theory with generalized gradient approximation plus on-site Coulomb correlation (GGA+U). The all-electron full potential linearized augmented plane wave (FLAPW), frozen core full potential projector augmented wave (PAW), and also all-electron tight-binding linear muffin-tin orbital methods (TB-LMTO) are used. In this contribution, we will present and analyze the obtained exchange coupling parameters, magneto-optical Kerr rotation spectra, dielectric constants and second-harmonic generation coefficients.