Magnetic and magnetoelectric excitations of BiFeO3

We have determined a model which describes the magnetic and magnetoelectric excitations of multiferroic BiFeO$_3$. Using the full magnetic dispersion relations which are obtained by neutron inelastic scattering measurements [1], parameters for the Heisenberg model with 1st and 2nd neighbor exchange couplings as well as Dzyaloshinskii-Moriya interaction and the single ion anisotropy are estimated. The model also shows excellent agreements with the observed peaks in THz [2] and Raman [3] spectroscopies, which leads to successful assignments of the excitation modes to these peaks. We also discuss that the mode observed at 21.5 cm$^{-1}$ is an electromagnon excitation which should be both magnetic and electric active. This can be verified by the non-reciprocal directional dichroism measurements. {\it REFERENCES: } [1] Matsuda et al., PRL {\bf 109}, 067205 (2012). [2] Talbayev et al., PRB 83, 094403 (2011). [3] Rovillain et al., PRB 79, 180411 (2009).