Second-harmonic-generation spectra of the hexagonal manganites RMnO3

Non-linear susceptibilities for use in describing the second-harmonic generation (SHG) recently observed in the hexagonal manganites RMnO3 (R = Sc, Y, Ho, Er, Tm, Yb, Lu) below the Neel temperature TN are derived. Their explicit expressions show that they should give rise to quite different spectra according to whether the magnetic ordering is P6 ' (3)cm ' or P6 ' (3)c 'm. The excited states around 2.45 eV are treated as excitons in the antiferromagnetic phase. The calculated SHG spectra are compared with experiments and it is found that they can be used to explain the observed features and spectra satisfactorily.