Phenomenological model of multiferroic properties in langasite-type crystals with a triangular magnetic lattice

Abstract

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 N\`eel 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 \ensuremath{\rightarrow} $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.