Phase transitions and second-harmonics of ferroelectric and antiferromagnetic RMnO3

At every phase transition of ferroelectric (FEL) and antiferromagnetic (AFM) RMnO3(R = Y, Ho, Er), one of mirror symmetries is frozen. Some tensor components contributing to second-harmonic generation (SHG) are derived to be linearly proportional to these order-parameters. As a result, we can determine the sign of these order-parameters and consequently the domain structures by observing the interference effects of SHG signals. A clamping of the AFM Bloch wall is found at the FEL domain boundary and is understood microscopically in terms of mirror symmetry freezing.