Brillouin scattering studies in $Fe_{3}O_{4}$ across the Verwey transition

Brillouin scattering studies have been carried out on high quality single crystals of $Fe_{3}O_{4}$ with [100] and [110] faces in the temperature range of 300-30 K. The room temperature spectrum shows a surface Rayleigh wave (SRW) mode at 8 GHz and a longitudinal acoustic (LA) mode at 60 GHz. The SRW mode frequency shows a minimum at the Verwey transition temperature $T_{V}$ of 123 K. The softening of the SRW mode frequency from about 250 K to $T_{V}$ can be quantitatively understood as a result of a decrease in the shear elastic constant $C_{44}$, arising from the coupling of shear strain to charge fluctuations. On the other hand,the LA mode frequency does not show any significant change around $T_{V}$,but shows a large change in its intensity. The latter shows a maximum at around 120 K in the cooling run and at 165 K in the heating run,exhibiting a large hysteresis of 45 K. This significant change in intensity may be related to the presence of stress-induced ordering of $Fe^{3+}$ and $Fe^{2+}$ at the octahedral sites, as well as to stress-induced domain wall motion