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

The magnetic properties of Ho-doped langasites (La:Ho)₃Ga₅SiO₁₄ are dominated by the Ising-like magnetic moments of the Ho³⁺ 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 $2d$ 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 Ho³⁺ magnetic moments in doped langasites (La_1-xHoₓ)₃Ga₅SiO₁₄ 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 Ho³⁺ in distorted positions. The operations of broken local C₂ symmetry and rotations around the trigonal C₃ axis connect different sites, restoring the global $P321$ symmetry of the crystal and simplifying the description of the magnetic properties. The superposition of two distorted Ho³⁺ positions connected by C₂ symmetry determines the local magnetic susceptibility tensor, which no longer appears Ising-like at low fields.