Relationship Between the Magnetoelectric Effect and Local Magnetic and Electric Moments in Paramagnetic Terbium Langasite

Abstract

Magnetic field-induced anisotropic electric polarization has been detected in langasite single crystals doped with magnetic rare-earth Tb ions (5%). This polarization strongly depends on the field magnitude and orientation. A sharp change in the polarization sign has been observed upon magnetic field rotation in the basal plane, which correlates with the reversal of the anisotropic (Ising) magnetic moments of Tb³⁺ ions along local two-fold axes. A microscopic approach has been proposed suggesting the superposition of local polarizations of single-ion origin in three nonequivalent sites of Tb ions. This has allowed us to identify the relationship between macroscopic and local polarizations and to establish that the latter is almost orthogonal to the Ising axis of Tb ions in the corresponding site, linearly depends on the magnetic field (upon Tb moment saturation), and changes sign upon the reversal of Tb moments. The parameters of the magnetoelectric interaction have been determined, which have made it possible to estimate the local electric dipole moment of ~0.1 D per Tb ion in a field of 5 T.