Second-harmonic-generation spectra of the hexagonal manganites RMnO3

Non-linear susceptibilities for use in describing the second-harmonic gener ation (SHG) recently observed in the hexagonal manganites RMnO3 (R = Sc, Y, Ho, Er, Tm, Yb, Lu) below the Neel temperature TN are derived. Their expli cit 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 antiferro magnetic phase. The calculated SHG spectra are compared with experiments an d it is found that they can be used to explain the observed features and sp ectra satisfactorily.