The conditions for occurrence of the magnetoelectric, magnetoelastic, and piezomagnetic effects in crystals of the langasite family with a triangular magnetic lattice are considered on the basis of the phenomenological model. It is shown that the iron-containing langasites with a triangular magnetic lattice may have piezoelectric properties above the Nèel temperature $T_{\mathrm{N}}$, but they are not ferroelectrics. Occurrence of either ferroelectric or both ferroelectric and piezoelectric states is possible below $T_{\mathrm{N}}$, and these crystals can be considered as multiferroics with a helicoid of magnetic moments oriented along the $c$ axis. The observation of electric polarization $p_z$ in these crystals at $T<T_N$ is possible at sufficiently large values of piezocoefficients $e_{zyz}$ (class 2) or $e_{zxx}$ (class 3) and as a result of mechanical deformations occurring due to magnetostriction. Moreover, because of magnetoelastic interactions (appearing due to lowering symmetry $P$321 → $P$3 below $T_{\mathrm{N}}$), the electric polarization and the axis of the magnetic helicoid can both be parallel to the $z$ axis even in the absence of the Dzyaloshinskii-Moriya (DM) effect. Possible ferroelastic and ferroelectric transitions are considered at $T<T_{\mathrm{N}}$. The occurrence of the magnetic helicoid with its axis in the $ab$ plane is also discussed. It may appear due to the spin-orbit interaction (DM effect). In this case, electric polarization must appear also in the $ab$ plane.

• Received 23 February 2012

DOI:https://doi.org/10.1103/PhysRevB.86.064414