Ab Initio calculations of the lattice dynamics and the ferroelectric instability of the BiFeO$_3$ multiferroic

The pressure dependences of the vibration frequencies of the bismuth ferrite crystal lattice in the ferroelectric and paraelectric rhombohedral phases have been calculated from first principles in terms of the LSDA + U approximation. It has been found that there is a linear relationship between the magnetic moments of iron cations and the band gaps calculated using the same parameters of the correlation interaction. An analysis of the pressure dependences of the frequencies of the transverse optical phonons indicates their high stability in both the paraelectric and ferroelectric phases, which is not typical for classical displacive-type ferroelectrics.