Resolving the local distortions of Ising-like moments in magnetoelectric Ho-doped langasite

Abstract

The magnetic properties of Ho-doped langasites (La:Ho)3₃G⁢a₅⁢Si⁢O₁₄ are dominated by the Ising-like magnetic moments of the H⁢o³⁺ ions. In their saturated regime, the induced magnetic state breaks both time and space inversion symmetries, leading to a linear magnetoelectric effect. However, due to distortions induced by a shared Ga/Si occupancy of the 2⁢𝑑 sites, resolving the microscopic nature of the magnetic configuration remains a difficult task. Here, we combine polarized neutron diffraction and angular-dependent magnetization experiments to determine the local distortions of the H⁢o³⁺ magnetic moments in doped langasites (L⁢a₁₋ₓ⁢H⁢oₓ)₃⁢G⁢a5₅Si⁢O₁₄ with 𝑥≈0.015 and 0.045. We propose a model for a field-induced magnetic configuration with arbitrary orientations of the local Ising axis of H⁢o³⁺ in distorted positions. The operations of broken local 𝐶₂ symmetry and rotations around the trigonal 𝐶₃ axis connect different sites, restoring the global 𝑃⁢321 symmetry of the crystal and simplifying the description of the magnetic properties. The superposition of two distorted H⁢o³⁺ positions connected by 𝐶₂ symmetry determines the local magnetic susceptibility tensor, which no longer appears Ising-like at low fields.