Magnetoelectric phenomena in Fe langasites

Abstract

Experimental and theoretical studies of the magnetoelectric properties of a series of Fe langasite multiferroics (${\mathrm{Ba}}_{3}{\mathrm{NbFe}}_{3}{\mathrm{Si}}_{2}{\mathrm{O}}_{14}, {\mathrm{Ba}}_{3}{\mathrm{TaFe}}_{3}{\mathrm{Si}}_{2}{\mathrm{O}}_{14}$, and ${\mathrm{Sr}}_{3}{\mathrm{TaFe}}_{3}{\mathrm{Si}}_{2}{\mathrm{O}}_{14}$) with planar triangular spiral magnetic structure and double chiral magnetic order have been carried out. Magnetic field induced electric polarization is observed to emerge in the basal $a{b}^{*}$ plane of the trigonal crystal, depending on both the magnitude (up to 60 T) and orientation of the magnetic field. Remarkably, the induced polarization is very sensitive to the projection of the field onto the $c$ axis, with a sharp increase in polarization found for small deviations of the field from the basal plane and the sign of polarization determined by the direction of the field deviation. At high magnetic fields, the electric polarization behavior changes qualitatively and strongly depends on the magnetic field orientation. A detailed group theoretical analysis of the magnetic and magnetoelectric properties of Fe langasites is presented, and a relationship between the polarization and magnetic order parameters in an external magnetic field is established. We show that, in a magnetic field, the spiral magnetic structure is rotated and canted with respect to the original structure under zero field. The competition between these two processes, rotation and canting, strongly depends on the magnetic field orientation, and determines the polarization behavior. We propose a simplified description of the Fe langasites' triangular spiral magnetic structure at low temperatures and with saturated moments, characterized by the spiral plane orientation and the field-induced magnetization only. We establish that, at weak fields, the appearance of polarization occurs mainly due to the reorientation of the magnetic spiral (analogous to a spin-flop transition) and could be explained by the inverse Dzyaloshinskii-Moriya interaction. At high fields (above 8 T), the polarization change occurs via canting of the magnetic spiral, owing to Fe-Fe exchange and single-ion contributions.