Equation of state and structural phase transitions in iron-based Ba$_3$TaFe$_3$Si$_2$O$_{14}$ langasite at high hydrostatic pressures

Synchrotron X-ray diffraction studies of the structural characteristics of Ba$_3$TaFe$_3$Si$_2$O$_{14}$ langasite are performed at high hydrostatic pressures (up to $60$ GPa) created in a diamond anvil cell. At pressures up to $20$ GPa, the Mössbauer absorption spectra for $^{57}$Fe nuclei and the Raman spectra are recorded. Two structural phase transitions at $P\approx5.5$ and $20$ GPa are observed. The first transition corresponds to the displacements of light oxygen atoms and to an increase in the local symmetry of $3f$ oxygen tetrahedra surrounding iron ions. The second one is accompanied by a pronounced change in the lattice parameter $c$, and the unit cell volume undergoes a stepwise drop as large as $8.6\,\%$. An appreciable decrease in the parameter $c$ at the structural transition should result in a significant increase in the exchange coupling constants between iron ions in neighboring $ab$ planes underlying the giant increase in the Nйel temperature in this crystal at pressures exceeding $20$ GPa.