Resolving the local distortions of Ising-like moments in magnetoelectric Ho-doped langasite
Résumé
Themagnetic properties of Ho-doped langasites (La : Ho)$_3$Ga$_5$SiO$_{14}$ are dominated by the Ising-like magnetic moments of the Ho$^{3+}$ 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 Ho$^{3+}$ magnetic moments in doped langasites (La$_{1−x}$Ho$_x$)$_3$Ga$_5$SiO$_{14}$ 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 Ho$^{3+}$ in distorted positions. The operations of broken local C$_2$ symmetry and rotations around the trigonal C$_3$ 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 Ho$^{3+}$ positions connected by C$_2$ symmetry determines the local magnetic susceptibility tensor, which no longer appears Ising-like at low fields.
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