Second harmonic generation in a polar ferrimagnet GaFeO3
Abstract
We have studied second harmonic generation (SHG) in a polar ferrimagnet GaFeO3, employing a FeO6 cluster model in which the Fe atom is slightly shifted from the center of the octahedron. The electric-dipole transition could take place between the 3d states through the effective hybridization of the 4p states with the 3d states, due to the breaking of the space-inversion symmetry. In the third-order perturbation with Hint = -(j.A)/c, we calculate the probability per unit time, Iη aa, for the process that two photons are absorbed with polarization parallel to the a axis and one photon is emitted with polarization parallel to the η (=a,b,c) axis. The calculated SHG intensities consist of several peaks as a function of two-photon energy in agreement with the experiments. It is found that the corresponding amplitude Saaa at each Fe site changes its sign while Sbaa remains the same with the reversal of the direction of the local magnetic moment. This implies that Iaaa would disappear while Ibaa would survive in the paramagnetic phase in accordance with the experiment.