Resonant A₁ phonon and four-magnon Raman scattering in hexagonal HoMnO₃ thin film

We present the results of resonant Raman scattering of the A₁ phonon at 680 cm^-1 and of the four-magnon at 760 cm^-1 in hexagonal HoMnO₃ thin film. We find that the A₁ phonon at 680 cm^-1 shows a strong resonance effect near the on-site Mn d-d transition at ∼1.7eV. Our Raman results show that the four-magnon scattering can be selectively excited with red lasers of 647 nm (1.92eV) and 671 nm (1.85 eV), but are not detectable with green lasers of 532 nm (2.33 eV), indicating that the four-magnon scattering in hexagonal HoMnO₃ has an extremely strong resonance effect also near the on-site Mn d-d transition at ∼1.7 eV. Furthermore, through the analyses of our study of the resonant four-magnon Raman scattering and earlier studies of the resonant twomagnon Raman scattering, we propose a simple general model for all resonant magnon scattering. Our simple general model predicts a simple method for the investigation of the spin-flipping/spin-wave in magnetic materials, which would have significant impacts on the applications of spintronic devices.