Structural and magnetic properties of the iron-containing langasite family A 3 MFe 3 X 2 O 14 (A = Ba, Sr; M = Sb, Nb, Ta; X = Si, Ge) observed by Mössbauer spectroscopy

The occurrence of the long-range magnetic order of high-spin Fe${}^{3+}$ ions is found in iron-containing langasite family crystals ${A}_{3}M$Fe${}_{3}$${X}_{2}$O${}_{14}$ ($A$ = Ba, Sr; $M$ = Sb, Nb, Ta; $X$ = Si, Ge) at $T$ \ensuremath{\le} 40 K. The Neel temperature (${T}_{\mathrm{N}}$) values (27.1--37.1 K) depend on the composition and significantly increase with the strengthening covalence of Fe-O bonds in the 3$f$ tetrahedra. Splitting of iron positions into two magnetic sublattices is established in Ba${}_{3}$TaFe${}_{3}$Si${}_{2}$O${}_{14}$ and Ba${}_{3}$NbFe${}_{3}$Si${}_{2}$O${}_{14}$ crystals at $T$ ${T}_{\mathrm{N}}$. Iron magnetic moments in two sublattices are directed at different angles to the local crystal axes with a mean value \ensuremath{\approx}45\ifmmode^\circ\else\textdegree\fi{}. At the temperatures between 4.2 and 20 K, the iron spins in two sublattices rotate in opposite directions. It can be related to magnetic chirality in the helicoidal magnetic structure. The appearance of nonequivalent Fe${}^{3+}$ sites is associated with the structural phase transition $P$321 \ensuremath{\rightarrow} $P$3 (or $P$321 \ensuremath{\rightarrow} $C$2) induced by the magnetic transition. The presence of the polar threefold axis at this transition provides the conditions for the occurrence of the ferroelectric state. Such crystals can be considered as magnetically induced multiferroics.