Anomalous sound velocity in multiferroic BiFeO3

The sound velocity in multiferroic BiFeO3 (BFO) is studied with using Green's function technology on the basis of the magnetoelectric coupling, the spin-phonon interaction and the anharmonic phonon-phonon interaction. The Heisenberg-like model is employed to describe the magnetic subsystem, and the transverse Ising model is used to explain the ferroelectric subsystem. The reduced velocity is obtained in the limit of zero wave vectors. It is shown that the reduced velocity of sound in BiFeO3 exhibits a kink at the magnetic phase transition temperature TN. This anomaly in reduced velocity can be explained as an influence of vanishing magnetic ordering above TN and the ferroelectric subsystem can not be influenced by the magnetic subsystem above TN due to TN≪TC in the BFO. It is shown that the influence of the RM is only below TN in the phase where ferroelectric and magnetic properties exist together, whereas the RE influences the properties of the reduced velocity in the whole temperature region (T