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

The magnetic properties of Ho-doped langasites (La:Ho)3⁢G⁡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⁡a5⁢Si⁢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.