Raman scattering studies of spin-waves in hexagonal BaFe₁₂O ₁₉

We present the results of polarized Raman spectroscopy of hexagonal BaFe₁₂O₁₉ single crystal. The spectra, recorded from 200 to 800 cm^-1 and 1100 to 1700 cm^-1 in the 20-250 K temperature range, are analyzed on the basis of both crystal vibrations and spin-waves. In the low wavenumber range, the Γ-point phonons are observed. In the high wavenumber range, phonon mixings are observed; more interestingly, four modes of spin-waves are identified in hexagonal BaFe₁₂O ₁₉. Both have not been studied previously. Our analyses of the spin-waves provide an optical method for quantitatively estimating the spin exchange interactions in hexagonal BaFe₁₂O₁₉. The four strong exchange integrals are found to have the values of J_ce = 1.31 meV, J_ae = 1.36 meV, J_cd = 1.46 meV, and J_bd = 1.71 meV. Our results also indicate that at ~200 and ~80 K, there would be additional spin-ordering transitions in hexagonal BaFe₁₂O ₁₉.