Nonlinear Optical Spectroscopy of the Two-Order-Parameter CompoundYMnO3

We have observed two types of optical second harmonic spectra of ${\mathrm{Mn}}^{3+}$ ions in hexagonal ${\mathrm{YMnO}}_3,$ one of which is caused by the noncentrosymmetric ferroelectric ordering of charges, whereas the other is due to the centrosymmetric antiferromagnetic ordering of spins. Partial overlapping between the electronic transitions gives rise to a new kind of nonlinear optical polarization $\mathbf{P}\left(2\omega \right)={\mathbf{P}}^{\mathrm{FE}}\left(2\omega \right)+{\mathbf{P}}^{\mathrm{AFM}}\left(2\omega \right),$ which depends on two order parameters. The magnitude and phase of $\mathbf{P}\left(2\omega \right)$ can be changed by varying the ratio between the two contributions, as demonstrated by changing the contrast between $180°$ antiferromagnetic domains, which are indistinguishable in linear optics.